Quantum Physics Research Papers

Path Integrals in Quantum Physics (English Version)

2017, arXiv:1209.1315v4

These lectures are intended for graduate students who want to acquire a working knowledge of path integral methods in a wide variety of fields in physics. In general the presentation is elementary and path integrals are developed in the... more

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The Self-Awareness Course for Teens

by Daniel M Keeran MSW

How well do you know yourself? You can learn to make healthy choices intentionally rather than to unconsciously repeat unhealthy patterns. This course is highly recommended for mental strengthening.

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Physics Formulary

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For the metric outside a rotating, charged spherical mass the Newman metric applies:

».10 The Fabry-Perot interferometer The width of the peaks at half height is given by y = 4/ VF. The finesse F is defined as F = 4nVF. The maximum resolution is then given by Af min = c/2ndF.

When this is expanded it becomes: Interaction of electromagnetic waves in plasma’s results in scattering and absorption of energy. For electro- magnetic waves with complex wave number k = w(n + i«)/c in one dimension one finds: BR. = Fyre *’2/€ cosh y(t — nx /e)). The refractive index 7 is civen bv: Number of populating processes of level » = Number of depopulating processes of level p , To find the population densities of the lower levels in the stationary case one has to start with a macroscopic equilibrium:

12.3.3 Phonons and is 0 on the edge of a Brillouin Zone. Here, there is a standing wave. The quantum mechanical excitation of a crystal vibration with an energy hw is called a phonon. Phonons can be viewed as quasi-particles: with collisions, they behave as particles with momentum ik’. Their total momentum is 0. When they collide, their momentum need not be conserved: for a normal process holds: Ky, + Ko = Kz, for an umklapp process holds: kK, + Ky = K3 + G. Because phonons have no spin they behave like bosons.

The following graph shows the magnetization versus fieldstrength for different types of magnetism: The quantum mechanical origin of diamagnetism is the Larmorprecession of the spin of the electron. Starting with a circular electron orbit in an atom with two electrons, there is a Coulomb force F’, and a magnetic force on each electron. If the magnetic part of the force is not strong enough to significantly deform the orbit holds: 12.4 Magnetic field in the solid state

The band structures and the transitions between them of direct and indirect semiconductors are shown it the figures below. Here it is assumed that the momentum of the absorbed photon can be neglected. For al indirect semiconductor a transition from the valence- to the conduction band is also possible if the energy o the absorbed photon is smaller than the band gap: then, also a phonon is absorbed. This difference can also be observed in the absorption spectra:

So indirect semiconductors, like Si and Ge, cannot emit any light and are therefore not usable to fabricate lasers. When light is absorbed holds: ky = —ke, En(kn) = —Ee(ke), th = te and m, = —mié if the conduction band and the valence band have the same structure. Instead of the normal electron mass one has to use the effective mass within a lattice. It is defined by:

There are type I and type II superconductors. Because the Meissner effect implies that a superconductor is a perfect diamagnet holds in the superconducting state: H = j1oM. This holds for a type I superconductor, for a type II superconductor this only holds to a certain value H .1, for higher values of H the superconductoris in a vortex state to a value H.2, which can be 100 times H.,. If H becomes larger than H.2 the superconductor becomes a normal conductor. This is shown in the figures below. The transition to a superconducting state is a second order thermodynamic state transition. This means that there is a twist in the 7 — S diagram and a discontinuity in the C, — T diagram.

The expressions for S‘”) contain time-ordered products of normal products. This can be written as a sum of normal products. The appearing operators describe the minimal changes necessary to change the initial state into the final state. The effects of the virtual particles are described by the (anti)commutator functions. Some time-ordened products are: The term 4A¥ (a — y) is called the contraction of @(x) and ®(y), and is the expectation value of the time- ordered product in the vacuum state. Wick’s theorem gives an expression for the time-ordened product of an arbitrary number of field operators. The graphical representation of these processes are called Feynman diagrams. In the zx-representation each diagram describes a number of processes. The contraction functions can also be written as:

Further, for stars of the solar type, the composing plasma can be described as an ideal gas The structure of a star is described by the following equations: 16.4 Composition and evolution of stars

one can derive the following Hamilton equations with the new Hamiltonian Kk: Starting with the coordinate transformation:

where h is the perpendicular distance from the point the light ray hits the mirror to the optical axis. Spherical aberration can be reduced by not using spherical mirrors. A parabolical mirror has no spherical aberration for light rays parallel with the optical axis and is therefore often used for telescopes. The used signs are: 6.2.3 Principal planes The nodal points N of a lens are defined by the figure on the right. If the lens is surrounded by the same medium on both sides, the nodal points are the same as the principal points H. The plane | the optical axis through the principal points is called the principal plane. If the lens is described by a matrix m ,, than for the distances h, and hz to the boundary of the lens holds: For images of mirrors holds:

The quantities of state and their differentials are: 5 State functions and Maxwell relations

The eigenvalue equations for an atom or ion with with one electron are: 10.12.3 Spin-orbit interaction 10.12.2 Eigenvalue equations The total momentum is given by _ LE + M. The total magnetic dipole moment of an electron is then M = M, + Mg = —(e/2m.)(L + gsS) where gs = 2.0023 is the gyromagnetic ratio of the electron. Further holds: J? = L? + S* + BE - es [? + $7 +2L,8,+ 1,8 + L_S\. Hl has quantum numbers j with possible values j = 1 + 4, with 2j + 1 possible z-components (m € {—j,.., 0,.. ,j}). If the interaction energy between S$ and L is small it can be stated that: E = E,, + Es, = En +aS- L. It can then be derived that: |E,|Z202

Here B is the baryon number and L the lepton number. It is found that there are three different lepton numbers, one fore, 4. and r, which are separately conserved. T is the isospin, with 7’; the projection of the isospin on the third axis, C the charmness, S the strangeness and B* the bottomness. The anti particles have quantum numbers with the opposite sign except for the total isospin T. The composition of (anti)quarks of the hadrons is given in the following table, together with their mass in MeV in their ground state: An overview of particles and antiparticles is given in the following table:

Each quark can exist in two spin states. So mesons are bosons with spin 0 or 1 in their ground state, while baryons are fermions with spin 4 or 3. There exist excited states with higher internal L. Neutrino’s have a helicity of — 4 while antineutrino’s have only + 3 as possible value.

so [Y, T;] = 0. The group U(1))-@SU(2)+ is taken as symmetry group for the electroweak interaction because the generators of this group commute. The multiplets are classified as follows:

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Redalyc.APRENDIZAJE BASADO EN PROYECTOS COLABORATIVOS. Una experiencia en educacion superior

by Magdaly Gordillo

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Shamanism in Europe? Three ritual healers: The Basque salutariyua, the French marcou and the Italian maramao.

by Roslyn Frank

Preface Throughout all of Europe we find examples of folk-belief assigning special qualities to the seventh-born son or daughter of a family. At times these attributes were positive, at times negative. However, they always had a magical... more

Preface
Throughout all of Europe we find examples of folk-belief assigning special qualities to the seventh-born son or daughter of a family. At times these attributes were positive, at times negative. However, they always had a magical aura about them (Bloch [1924] 1983). For the most part, these beliefs have been written off as superstitious residue from times past and as a result little attention has been paid to documenting the concrete social practices associated with them. An exception to this tendency is the work of Marc Bloch, who in 1924, called attention to the supernatural powers attributed to the seventh son and at times, to the seventh daughter, born after an uninterrupted series of the same sex, remarking that seventh-born children were credited with a “particular supernatural power” (Bloch [1924] 1983: 293, 296). Writing in 1924, Bloch observed that “La croyance sous cette forme a été et est sans doute encore très largement répandue dans l’Europe occidentale et centrale: on l’a signalée en Allemagne, en Biscaye, en Catalogne, dans presque toute la France, dans les Pays-Bas, en Angleterre, en Escosse, en Irlande […]” (Bloch [1924] 1983: 294-295).

Specifically, Bloch noted that from at least the 16th century onwards, children born into a seventh position in their family supposedly had the power to heal by touch. Such extraordinary people, often deemed sorcerers, even devils, were also referred to by a variety of expressions such as mahr (German) or murawa (Polish) and consequently they had the ambivalent privilege of tapping into powers that were inaccessible to normal humans. Specifically, they were viewed as having healing and divinatory powers, which could entail shape-shifting (Vaz da Silva 2003). That is, those individuals were endowed with the ability to take the form of an animal. From the point of view of modern Western thought this belief causes the dividing line between humans and animals to become blurred. Nonetheless, that blurring or fusion of two natures would be in accordance with the cosmology of native peoples in other parts of the world, especially contemporary hunter-gatherers, where such animistic beliefs also prevail (Bird-David 1999; Brightman 2002; Ingold 2000; Willerslev 2007).

It is quite clear that the qualities assigned to the seventh-son or daughter harken back to an earlier animistic mindset, notions of nonhuman personhood and social practices that in turn connect back to shamanic modes of healing. At the same time, as noted in the earlier chapters of this study, the fused nature of the Bear Son, the half-human, half-bear being known as Hamalau “Fourteen” in Basque, reflects a similar blurring of the Western human-animal divide and related cultural conceptualizations.

And as Bertolotti has demonstrated in his detailed and extraordinarily well researched study Carnevale di Massa 1950 (1992), European versions of the Bear Son folktales, e.g., Giovanni l’Orso, may well reproduce much earlier beliefs, more in consonance with the cosmovision of hunter-gatherers who inhabited these zones in times past. More concretely, the fact that the figure of Hamalau is grounded in the belief that humans descended from bears allows us to consider the significance and symbolism of this character’s own genesis: he is born of a human female, but his father is a bear. In this sense, he is a double-natured intermediary occupying the ontological ground between humans and bears.

Fig. 2. Scene of the “Death before Resurrection” of s’Urtzu as performed by the Mamutzones of Samugheo. Source: Fois (2002a).

Fig. 1. A typical Mamuthone. Source: http://www.tropiland.it/sardegna/Mamuthones.jpg. identify the etymology of the root mamu-. As he pointed out, written documentation on the Mamutzones and s’Urtzu (the bear) will not take us further back than the 19th century where they are first mentioned. However, there is abundant toponymic evidence for this root across Sardinia, and especially in the central part of it, a zone considered to be somewhat more conservative in terms of the retention of older cultural elements. Therefore, while written documentation on this phenomenon has a relatively shallow time depth, the toponymic evidence suggests a different picture: a far deeper time depth, although not one that can be dated with any precision. Stated differently, one avenue that might provide further insights into the origins of the Mamutzones and s’Urtzu would be to trace the etymology of the root mamu-.

Graziano laid out his theory to me in a short essay called “Liason entre Basque et Sarde pour un possible racine *mamu /*momu /*mumu” (Fois, 2002b). In it he compared a series of terms in Basque and Sardu which appeared to be cognate with each other, that is, theit phonological shape and semantic meaning coincide closely. I found what he wrote quite intriguing, although until I read his article I had heard nothing about the Sardinian Mamutzones and their bear.

Fig. 3. Momotxorros of Alsasua, Nafarroa. Source: Tiberio (1993: 58). Photo by Luis Otermin.

Fig. 4. Joaldunak bells. Source: http://www.dantzan.com/albisteak/joaldunak-eta-abar.

Fig. 5. Joaldunak of Ituren, Nafarroa. Source: http://www. ituren.es/es/. Photo by Ernesto Lopez Espelta.

Fig. 6. One of the J oaldunak of Ituren. Source: Tiberio (1993: 38). Photo by Luis Otermin. 2¢, a date known across Europe both as Candlemas and as Bear Day.*

Fig. 7. Joaldunak of Zubieta. Source: Tiberio (1993: 35). Photo by Luis Otermin.

Fig. 8. Procession of Joaldunak. Source: http://www.pnte.cfnavarra.es/kzeta/ituren_erreport.htm

Fig. 9. Joaldunak in Ituren, Nafarroa. Source: http://www. ituren.es/es/. Photo by Emesto Lopez Espelta. I would note that the Basque Bear or Hartza who is accompanied by these performers

Fig. 12. Hartza of Ituren, Nafarroa. Source: http://www. ituren.es/es/. Photo by Ernesto Lopez Espelta. Fig. 11. Hartza in Ituren, Nafarroa with its Keeper. Source: http://www. pnte.cfnavarra.es/kzeta/ituren_erreport.htm.

Fig. 14. Another “horned” Hartza from Ituren with its Keeper. Source: Tiberio (1993: 14). Photo by Luis Otermin. Fig. 13. Hartza in Arizkun, Nafarroa, chasing bystanders. Source: Tiberio (1993: 71). Photo by Luis Otermin.

Pyrenees at Sainte-Engrace [Santa Garazi], in the province of Soule [Zuberoa] in Euskal Herria [Basque Country].) (Peillen, 1986: 171)°

Fig. 17. Bear leader and musicians. Source: engraving from Olatis Magnus, Historia de gentibus septentrialibus. Rome 1555. Reproduced in Michel and Clébert (1968: 329)

Fig. 19. Winter Bear Carnival Sites in Cantabria, Spain. Source: Molina Gonzalez & Vélez Pérez (1986: 134) Fig. 18. Sites of Candlemas Bear Day celebrations in the Pyrenées. Source: Gastou (1987: 20).

Fig. 20. Scene of the “death before resurrection” of s’Urtzu. Source: Fois (2002). In summary, it was believed that the earthly bear’s report served to inform the Celestial Bear of the details of the behavior of its human offspring. A positive report card guaranteed the health and well being of the Celestial Bear’s human descendants. If the ceremonies were properly performed, in the spring the bones of the earthly bear would take on flesh anew in the form of bear cubs, while the souls of all the other beings would be released by the bear in the spring when it awoke from hibermation, thus guaranteeing an abundant food supply for all (Chiclo, 1981; Elgstrom & Manker, 1984; Fabre, 1968; Lebeuf, 1987; Tiberio, 1993). In this way, by closing the “good-luck visit” with a social critique, the latter served to reinforce the traditional norms and values of the community in question.

Similarly, the recognized genetic and cultural isolation of Sardinia, as reflected in the genetic structure of its population, it status as a genetic “outlier” (Sanna, 2006: 173-184) as well as certain distinct characteristics of its language, could be an indication that the Mamutzones and their bear might form part of this more archaic belief system.*? Indeed, there are remarkable similarities holding between the genetic makeup of Sardinians and Basques which set them apart from other European populations, that is, in the sense that they appear to have retained elements of the older European genetic substrate which was once common to much Europe and which dates back to at least to the Mesolithic if not the Upper Palaeolithic:

Recent work in the field of molecular genetics dealing with the genetic makeup of populations of European descent, particularly the frequencies of certain Y -chromosomes (which are transmitted through the male line) and mitochondrial DNA or mtDNA (which is transmitted through the female line), has suggested that at the end of the Last Glacial Maximum, there was an expansion of populations out of the Pyrenean-Cantabrian refugium. Over time these groups moved north and east to repopulate territory that had been depopulated during previous glaciations. For example, in 1998, Torroni et al. (1998: 1148) proposed the following patterns of repopulation based on the distribution of haplogroup V.*° As can be appreciated in the figure reproduced below (fig. 23), the limits proposed for the Pyrenean-Cantabrian refugium overlap closely with boundaries of the geographical extent of the Basque-speaking zone (as shown in fig. 22). Similarities between the populations of the Euskal Herria and Sardinia are also identified in the case of classic genetic markers of ABO blood types, i.e., the prevalence of high O blood type (Bauduer et al., 2005; Bernard & Ruffié, 1976; Cavalli-Sforza, 1988; Piazza et al. 1988; Piazza & Cavalli-Sforza, 2006). In summary, today three populations demonstrate particularly high frequencies of the Y-chromosome and mtDNA haplogroups which are associated with the western refugium zone: Basques, Sardinians and Saami.

[...] the word does not forget where it has been and can never wholly free itself from the dominion of the contexts of which it has been part. E-mail: roz-frank@ uiowa.edu Roslyn M. Frank University of Iowa ‘-—mail: roz-frank®@ 110wa2.ed

Figure 3. “Que viene el Coco”. An etching by Francisco de Goya.°” equivalent of the asustanifos (Caro Baroja 1986: 320).°°

Figure 4. “El ogro mas famoso y temido, 'El Coco”’. Source: www.fundacion-cajarioja.es."

Figure 1. Names of the gift-bringers on St. Martin’s Day (November 11). Adapted from Erich and Beitl (1955: 509). For example, today in many parts of Europe on the saint’s day in question, November 11", an actor appears in the guise of the bishop St. Martin. But, more importantly, when the individual dressed as a bishop does appear, he continues, as before, to be accompanied on his rounds by a bear-like creature, his pagan double. In short, these ursine administrants, in recent times merely ordinary human actors, perform their duties authorized by a kind of Christian dispensation that permits them to continue to preside, quite discreetly, over the festivities (Miles [1912] 1976: 208). In tum the bishop in question takes over the role and attributes of the bear trainer through this process of symbolic hybridization. Thus, the meaning of the bishop’s companion, the masked figure representing the bear, is transparently obvious once one understands the mechanisms of hybridization involved in the renaming processes themselves.® In short, any attempt to discover the identity of the furry, often frightening, masked figures associated with St. Martin’s day must take these facts into account (Figure 1).

Figure 2. Names of the gift-bringers on St. Nikolaus’s Day (December 6). Adapted from Erich and Beitl (1955: 564). who dressed up as this bishop made their house calls on the sixth of December (Figure 2) century to the time of the Protestant Reformation in the sixteenth century, the individuals

Figure 3. Dag, Sinterklaasje (Hello, Sinterklaas). Source: Vriens (1983). Illustration by Dagmar Stam.

Figure 4. St. Nikolaus Eve. Source: W eber—Kellermann (1978: 27).

Figure 5. Painting by Franz Xaver von Paumgartten: Christmas Eve and St. Nicholas with the Krampus. Vienna 1820. (Museen der Stadt Wien). Reproduced in Weber-Kellermann (1978: 26).

Figure 6. Krampus. Austrian postcard from circa 1900.

Figure 7. Krampus Group. Salzburg, December 2002. Source: http://www.krampusverein- anras.com/home.htm.

Figure 8. Nikolaus und Krampus. Pettneu am Arlberg, December 2003. © Karl C. Berger.”

Figure 9. A very large Krampus. December 2002. Source: ttp://www.luehrmann.at/BildderW oche/2002/02-12-04-krampus. jr

Figure 10. Waidhofen Station: Krampus performers preparing to catch a special steam locomotive that will take them to Y bbsitz, Austria. December 2, 2006. Source: http://www.ybbstalbahn.at/nostalgie alt. htm.

Fig. 12. St. Nicholas and his Servant - St. Nikolaas en zijn knecht by J. Schenkman]. Amsterdam: J. V lieger, [ca.1885]. Source: http://www.kb.nl/uitgelicht/kinderboeken/sinterklaas/sinterklaas-ill html.

Figure 13. Christkind and Hans Trapp in Elsace 1850. Reproduced in Weber-K ellermann (1978: 35).

Figure. 15. Franz Regi Goz. Knecht Ruprecht 1784. Reproduced in Weber—K ellermann (1978: 32). The menacing nature of the eighteenth and nineteenth century portrayals of the Pelznickel and Knecht Ruprecht provides us with a way to gauge, albeit indirectly, the kind of the discourse employed by adults at that point in time, as they explained to their offspring the dangers of misbehaving: failure to obey could result in a frightening punishment; the child might be stuffed into the sack (or basket) of this night visitor and carried off to meet a horrible fate (Figure 15). dangers of misbehaving: failure to obey could result in a frightening punishment; the child

Figure 16. St. Nikolaus with his companions in Berchtesgaden, Bavaria 1958. Photo Wolf Luking. Reproduced in Weber-K ellermann (1978: 33). Schimmelreiter enters first, followed by Christpuppe who makes the children repeat some verse of Scripture or a hymn; if they know it well, he rewards them with gingerbreads from his wallet; if not, he beats them with a bundle filled with ashes. Then both he and the Schimmelreiter dance and pass on. Only then are the Feien allowed to enter; they jump about and frighten the children (Miles [1912] 1976: 230-231) (Figures 16, 17, 18). Indeed, the ritual of smearing ashes on the faces of those encountered, as well as the fact that ashes form an integral part of the make-up of the performers themselves, are recurrent features of the performances. As such, the use of ashes may have been a fundamental component of the “good-luck” healing ceremonies themselves. There are many examples of the old European belief in the “good luck” conferred by ashes, blackening one’s face with them and black creatures in general (Alford 1930: 277 ff; Barandiaran 1973, II: 375; Creighton 1950: 20-21; Frank 2005b)

Figure 17. St. Nikolaus with his companions in Bavaria 1958. Photo Wolf Luking. Reproduced in Weber—Kellermann (1978: 29).

Figure 18. Oscar Graf (1861-1902). Perchtenlaufen Festival in Salzburg 1892. Reproduced in Weber- Kellermann (1978: 21).

characters were absent.** Today the performers’ appearance is manipulated so as to make them appear extremely bulky, larger than life, similarto En Peirot of Catalunya, a characte! we will examine in more detail shortly. In order to achieve this effect, the actors stuff their costumes with straw, while the costumes themselves are made out of gunny sacks. As a result, the expression azaku-zaharrak ([Ihauteriak] 1992) has undergone further phonological erosion and semantic reanalysis, being reduced, at least by some writers, to zaku-zaharrak, and interpreted, erroneously, as meaning “sacos viejos” (“old sacks”) as if the first element corresponded to the old gunny sacks used to make the costumes. the first element corresponded to the old gunny sacks used to make the costumes. In summary, in the case of the compound hamalau-zaingo we find three intertwined meanings that, in turn, reveal three distinct yet interlocking aspects or characteristics that are closely associated with the entity in question. First, the phonologically eroded variants of hamalauzanko and hamalauzaku appear to be reflexes of the name of the official who was in charge of watching over the community and insuring that its norms and rules of conduct were observed; second, we note that it is the name assigned to the fantastic being invoked to make children behave; and finally, it shows up in the name of a bizarre bear- like masked performer, the hamalauzaku. Stitching these clues together we discover a cleat pattern, one that illuminates yet another dimension of the Hamalau cultural complex: that in all likelihood the individual who was in charge of watching over the community was also the individual who dressed in a particular fashion, not like the other members of the community, and was also expected to take an active part in public rituals, if not preside

Por los valles altos pirenaicos de la region leridana se habia acudido asimismo al oso, y en Andorra, asu hembra, la osa, mucho mas temible aun que éste. La representacion del oso danzarin habia sido muy frecuente en Carnaval; y, cual En Peirot 0 el Marraco, los nifos lo miraban con pavor, no como un fiero animal, sino en su condicion de traganifios traviesos. [In the high Pyrenean valleys of the region of Lérida, they have also resorted to the bear, and in Andorra, to the female bear, which is even more fearsome than the former. The representation of a dancing bear is very common during Carnival; and, like En Peirot or the Marraco, children looked at it with terror, not because it was as a wild animal, but rather because of its condition as a devourer of disobedient children.] (Amades 1957: 269-270)

Figure 23. “Los osos.” Solsona-Solsonés. Source: Amades (1957). In the traditional festivals of the town of Solsona four “bears” took part performers whose presence terrified of the children of Solsona, Vall del Hort anc Ribera Salada, meanwhile their parents would repeatedly speak to their offsprinc about the “bears” to in order to make them obey (Amades 1957: 270). Based on the only photo I have found of them, today they look like harmless Disney-like characters indeed, looking more like mice than bears. However, in times past there was a dearth o: images other than those found in one’s own everyday environment, no television, nc magazines, no Internet. So any unfamiliar creature, especially a strange unnatural maskec one, would have given any child goose-bumps. Also, we do not know how these fou “bears” dressed centuries ago (Fig. 23). In the passages cited above Amades mentions another performer known as En Peirot. According to Amades, the characteristics of this “ogre” appear to replicate those of the Sardinian Marragau, although its name, En Peirot, bears no resemblance to any of the phonological variants of Hamalau we have discussed so far. It is noteworthy that geographically speaking this performer also inhabits the region of Lérida where in a certain sense it must have competed (or co-habited) with performers dressed as “bears”. Amades describes the participation of this actor as follows:

Figure 24. The Marraco of Lérida. Source: Amades (1957) ————_———O———— SO “The first Marraco, made of cardboard, fell apart and was substituted by another ncredibly bigger one. While the new version was also mounted on wheels, it no longer vas capable of swallowing up the little ones as its predecessor did. In short, the “child- ating” Marraco that previously had inhabited every child’s imagination, albeit with an imorphous shape, was now given a concrete plastic representation and, consequently, leftly converted into an innocuous object of entertainment (Figure 24). deftly converted into an innocuous object of entertainment (Figure 24).

While there is a great deal of confusion concerning what is fact and what is fiction witl espect to the point in time in which the kings of France and England began practicing thi ype of ritual healing, there is little doubt that by 1272 there were those among the populact vho thought that both the kings of France and England were curing the so-called king’ lisease by their touch, and, moreover, that the disease was called royal because kings curec t. The logic was circular: kings cured scrofula because it was the royal disease and scrofuli vas called the royal disease because kings cured it (Barlow, 1980: 13). Moreover, as wi hall see, by the close of the Middle Ages the cult of a particular saint had come to b nvolved in granting the gift of the “royal touch” to the sovereigns of France, the sam aint, it should be noted, that was linked to the curative powers attributed to the popula ealers called marcous. , i : i : , of i i, Sh oO ie Oe i i: es , er er i

Fig. 3. Resurrecting the bear in Bigorre, Haute Pyrénées. Source: Lajoux (1996: 90). souffler au cul de l’ours mort et le ramener a la vie” (Lajoux, 1996: 91). At this juncture we can begin to explore in more detail the way that the scene of Death and Resurrection is performed in other venues and more importantly why an instrument such as a chalumeau, bellows or syringe might play a major role in the events represented visually in this particular scene. In Bagneres de Bigorre, Hautes-Pyrenées, France, ¢ slightly different version of this scene of the play is encountered, as witnessed and photographed by Jean-Dominique Lajoux in 1975. His description of this aspect of “la sortie de l’ours en Bigorre” is as follows: “Une troupe de masques va de maison en maison, présenter un ours savant conduit par un oursaire. Lors de la représentation, |’ours est tué par méprise. Le médecin de la troupe ne saura ramener |’animal a la vie, mais |’ oursaire réussira dans cette entreprise en utilisant son grand baton comme un chalumeau pou! souffler au cul de l’ours mort et le ramener a la vie” (Lajoux, 1996: 91).

Fig. 5. Cap. Babeo and Cucuba An etching by Jacques Callot. Source: http://sged.bm- lyon. fr/Edip.B ML/Publilmg/images/EST A /00/00/09/57/GED 00000000.JPG. ac elimamiaalemaas cammmmeaiaiaaae * lia nascent: 1 aici taainmmamaiaaa S|. uaa "eal carmen aad aan aia ame aa ilar aaiadie* Danial In another etching of what appears to be the same scene, the figure of Maramao shows up as Captain Babeo while Captain Cardoni becomes Cucurucu. Whether there is a relationship between the name Babeo and the entity known as Babau is unclear. Assuming Captain Babeo is the counterpart of Maramao, the latter is no longer portrayed holding a syringe in his hand. However, in the background we see the iconic charivaric figure of l’asino with it backwards-seated rider, being pursued by another character with a set of bellows in his hands, as if the rather phallic looking instrument Captain Babeo / Maramao holds in his hand, is being commented upon visually by the action seen in the background frame of the etching.'*? However it is interpreted, the scene leaves little doubt that Captain Cardoni / Cucurucu is the “victim”. In summary, whatever symbolism was once associated with this scene, whatever its relationship to Good-Luck Visit performances and to the itinerant troupes of performers and popular street theater antedating the Commedia dell’Arte, the scene’s structure parallels in many respects elements found in the scene of the Death and Resurrection of the Bear, and these structural parallels are even more suggestive if the other ethnographic and linguistic data discussed in this study are kept in mind.

Table 1. Three theories concerning the development of Proto-Indo-European (A linei, 2001: 16)

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Unification Accomplished: Einstein's dream realized in the Single Field Theory

by James (Jim) E Beichler

Since Einstein died in 1955, very few theoretical scientists have tried to complete his work because the pendulum of history has swung toward favoring field theories based on the quantum for the expected unification of physics. Nearly... more

If Einstein, Schrodinger and their colleagues had not been so intent on relating the non-symmetric tensor to EM and thus unify GR and EM, they could have ptedicted DM and DE as secondary gravitational effects five decades before they were first observed After working on the five-dimensional theory with Bergmann and Bargmann [11], Einstein returned to his 1925 efforts [12] based on a non-symmetric model in 1945 [13]. He continued supporting this mode until his death in 1955. Schrodinger was instead interested in the earlier ideas of Eddington concerning the affine connection and parallel transport which had been used in the Einstein-Cartan anti-symmetric model of 1929 [14], so he adopted the anti-symmetric approach in 1944 [15]. In 1947 [16] and again in his 1951 book Space-Time Structure [17], Schrodinger demonstrated how and acknowledged that his anti-symmetric tensor could be mathematically reduced to an equivalent form that combined the metri and non-symmetric tensors with a constant A. He even suggested that the constant could be Einstein’s old cosmological constant or perhaps it represented the nuclear force or a new gravitational effect [18] but Einstein rejected the notion completely since he was happy with and only thought he needed the metric and non-symmetric tensors to unify gravity and electromagnetism. anti-symmetric tensor could be mathematically reduced to an equivalent form that combined the metric

So, it would seem from Heisenberg uncertainty principle’s expression of uncertainty that bringing space and time back together (from their unnatural mathematical separation) suppresses the quantum effect as exemplified by the disappearance of Planck’s constant, rendering the event physically real for consideration by classical physics. In other words, suppressing Plank’s constant by combining the different quantum expressions for space and time results in a reality described by Newtonian physics and general relativity. This implies that Planck’s constant is at least proportional to a binding constant for space and time at individual quantum points. as exemplified by the disappearance of Planck’s constant, rendering the event physically real for

The difficulty in understanding how a point can be discrete (disconnected and indeterministic) quantum upon reduction while it is just another point in a continuous line (O-D point-element), space or manifold is the real problem for physics and unification. As suggested above, the solution to this problem lies in the fact that the collection of all discrete quantum points that are possible does not represent the relative space of extension, but rather a point-absolute or quantum absolute space of possibilities that reduces to the Riemannian extension or metric-space of relativity when the collapse of the wave function produces a relative reality. So, technically the uncertainty is in the discrete point itself and thus a defining characteristic of the is the real problem for physics and unification. As suggested above, the solution to this problem lies in

All the quantum theory, including the standard model of particles can now be merged with the five- dimensionally extended unified field theory and the n=1 ‘sheet’ can be used to represent the results | or inwardly contain, the superstrings, branes, quantum loops, supergravity and quantum gravity themselves. This ‘quantized curvature’ would also define the real material particles, all of which have half-spin due to the ‘twist’ to the fourth dimension at the single pole: Protons represent the maximur amount of quantized curvature at locations where quantum fluctuations in the rapidly expanding surface blew out to end cosmic inflation, at least until the blowout locations (new protons) were cap} by neutrinos; An electron would be the maximum amount of quantized curvature that could occur before blowout where the surface tension of the ‘sheet’ stopped the blowout, giving the electron an opposite electric charge; And free neutrinos which represent the minimum amount of measurable quantized curvature in the ‘sheet’. All the quantum theory, including the standard model of particles can now be merged with the five- or inwardly contain, the superstrings, branes, quantum loops, supergravity and quantum gravity

For electromagnetism, the anti-symmetric Faraday tensor emerges, and for gravity the anti-symmetric Schrédinger-Einstein-Cartan tensor emerges, completely describing these two manifestations of the single field as extrinsically curved space-time within a ‘sheet’ within the context of classical theories that are already well known, tested and adequately expressed in normal physics.

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Lucretius I: An Ontology of Motion (Edinburgh University Press, 2018)

by Thomas Nail

The most original and shocking interpretation of Lucretius in the last 40 years. Thomas Nail argues convincingly and systematically that Lucretius was not an atomist, but a thinker of kinetic flux. In doing so, he completely overthrows... more

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Ashok Das - Lectures of Quantum Field Theory

by Akshay SB

2008

Ashok Das - Lectures of Quantum Field Theory (2008, World Scientific Publishing Company)

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A Journey into Quantization in Astrophysics: A collection of scientific papers

by Florentin Smarandache

ABSTRACT

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Is Nature Continuous or Discrete? How the Atomist Error was Born

by Thomas Nail

Interpreting Lucretius as an atomist was one of the biggest interpretive errors in the history of philosophy and science.

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Research and treatment approaches to depression

by Ma-Li Wong

2001, Nature Reviews Neuroscience

Depression costs the US economy, directly and indi- rectly, over 43 billion dollars per year", and it is aleading cause of disability worldwide". Suicide, which is usually a consequence of depression, is the eighth leading cause of death in the United States. The rate of suicide is even more alarming when it is examined asa function of age. Suicide is the sixth leading cause of death in the 5- 14 age group, the third leading cause of death in the 15-24 age group, and the fourth leading cause of death in the Several lines of evidence indicate an important con- tribution of depression to medical morbidity. Depressed patients have an increased risk of premature death when compared with control subjects!*”. Epidemiological studies point to heart disease as one possible explana- tion for the decreased life expectancy, as depression is an independent risk factor for cardiovascular disease. It

A mild but chronic and disabling manifestation of depression that had been previously conceptualized asa personality disorder (depressive personality disorder) is now Classified in the DSM-IV as a distinct mood disor- der— dysthymia. The work of Akiskal was instrumen- From a historical perspective, there have been large swings in the classification pendulum, ranging from

Figure 1 | A conceptual approach to depression. Available evidence consistently indicates that neurobiological substrates underlying depression phenotypes are the outcome ofa combination of genetic and environmental factors.

Figure 2 | Differential displays comparing RNAs from saline (S}-, imipramine (I)- or fluoxetine (F)-treated rats. Total RNA was extracted from hypothalami of animals treated with the different drugs for two months. Autoradiograms of amplified a-[*°S }dATP -labelled PCR (polymerase chain reaction) products after electrophoresis in 6% polyacrylamide gels are shown for two different primer combinations that identified one upregulated (arrowhead) and one downregulate: arrow) fragment in the groups treated with antidepressants.

Table 1 | Lifetime and annual rates and onset age for major depression, ages 18-64 years* *Figures standardized to US age and sex distribution. *Data from former Federal Republic of Germany (West Germany) based on ages 26 to 64 years. (SE, standard error) (Adapted with permission from REF 9 © (1996) American Medical Association.)

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The Electron is a Charged Photon with the de Broglie Wavelength

by Richard Gauthier

A charged photon and its light-speed helical trajectory form a surprising new solution to the relativistic electron’s energy-momentum equation. This charged photon model is a new model for the electron, and quantitatively resembles the... more

Figure 1. Energy and momentum relationships in the charged photon model of the electron. Since the charged photon’s total momentum circulates along the helix, the value of the transverse momentum Prrans =e can be associated with an _ internally

Figure 2. The de Broglie wavelength generated from the charged photon model of electron. right with velocity v and the charged photon travels along its helical path with velocity c. velocity v,,.,=c /v as the electron travels to the phase 16. Conclusions The de Broglie equation for the electron forms the basis of quantum mechanics, described by the Schrédinger equation for the electron in non-relativistic quantum mechanics and by the Dirac equation in relativistic quantum mechanics. The charged-photon approach may lead to a somewhat more fundamental and unified description of the quantum world than is provided by the current standard model of physics and

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Problem Book Quantum Field Theory

by Oscar Javier

The quantities A;(p) and A_(p) are energy projection operators. 4.4. Using the solution of Problem 4.2 show that 4.5. Show that AZ. = Az, and A, A_ = 0. How do these projectors act on the basic spinors u,(p) and v,;(p)? Derive these results with and without using explicit expressions for spinors.

Fig. 6.1. The integration contours C’ and C4 in terms of integrals over three momentum, k. The integration contours are given in Fig. 6.1. A(z) is also called the principal-part propagator.

Also, check the results using the formula [6]:

Fig. 2.1. Graphical solution of the dispersion relation (2.25) for V < 2m

3.19 By applying the Baker—Hausdorff formula If we now multiply equations (3.4) and (3.6) by I, and take trace of the re- sulting expressions, we get cy = 0. So, each of the coefficients in the expansion (3.4) is equal to zero except the unit matrix coefficient.

where N is the normalization factor. It is easy to see that the spinors u,(p) and v,(p) are not eigenspinors of the operator © -n, unless vectors n and p are parallel. 4.8 The transformation operator from the rest frame to the frame moving along the z-axis with velocity v, is S(A(vez)) = e- 34030" By using the relation wo3 = —p = — arctan(v), we obtain For arbitrary boost, o3p should be replaced by o-p. The operator S(A) is not unitary one. Since the Lorentz group is noncompact, it does not have finite dimensional irreducible unitary representations.

By substituting (4.30) and (4.27) in the formula (4.28), we obtain: Thus, in the Dirac representation of y—matrices, 754 is given by

4.30 In this case the coefficients c,(p) and d*(p) in expansion (4.51) are 4.31 The equation for spin 1/2 particle in the electromagnetic field has the where the coefficients c,(p) and d*(p) are given in (4.53).

where p = Vf? — m?. The terms proportional to the coefficient a, b and d in (4.59) are the initial win, reflected w, and transmitted wave v;. Since the Dirac equation is the first order equation, the continuity condition is satisfied for the wave function only. The condition w7(0) = wrr(0) gives

4.32 The solution of the Dirac equation is 3. If E+m < V, the momentum gq is real, which implies that the wave function in region z > 0 becomes oscillating. This is caused by the fact that there are two parts of electron spectrum separated by a gap, whose width is equal to 2m. The expressions for the coefficients of reflection and transmission are the same as in the second case. But in this case, the coefficient of reflection is greater then 1, while T < 0. The described effect is known as the Klein paradox. The explanation of this paradox is given in Problem 2.9.

Further, we will distinguish two classes of solutions: odd and even. If B = F and C' = D, the third and the fourth equations give the following dispersion relation: ee i: rr rn or a

Fig. 4.1. Graphical solution of Equation (4.72) for even states (V < 2m) In the case of odd solutions, the dispersion relation

Fig. 4.2. Graphical solution of Equation (4.73) for odd states (V < 2m)

Then, the new Hamiltonian is given by Under proper orthochronous Lorentz transformations, V,, is transformed in the following way:

Momentum is inverted under parity. Time reversal transforms the wav function into 4.42 We directly obtain: and using C~!y#C = —(y#)", one gets the requested result.

From the well known identity [x, f(p)] =iVf(p) we get two auxiliary results: 4.47 First prove that: 4.45 The transformed Hamiltonian is

Fig. 6.2. The integration contour for the advanced boundary conditions Fig. 6.1. The integration contour for the retarded boundary conditions By evading poles as in Fig. 6.2 we get the so-called advanced Green function

Fig. 6.4. The integration contour for the Dyson Green function Fig. 6.3. The integration contour which defined the Feynman propagator

We can conclude that positive (negative) energy solutions propagate forward (backward) in spacetime. This is what we need in the relativistic quantum physics in contrast to the classical theory (for example in classical electrody- namics), where all physically relevant information is contained in the retarded Green function. Dyson Green function is obtained by evading poles as in Fig. 6.4. This Green function can be evaluated in a way similar to the previous three cases. It is recommended to do this calculation as an exercise.

6.5 Let us take 9 < 0. The integral over the contour in Fig. 6.5 vanishes since there are no poles within the contour of integration. So, we get Fig. 6.5. The integration contour that defined the principal-part propagator

For the case t < 0 one also obtains the expression (6.24); this is left as an exercise. Now, we shall consider separately two cases: t > 0 and t < 0. In the first one, t > 0 the second term in the integrand of (6.20) is zero. The first part of the integrand has bad behavior for large k. We regularize it by making substitution t > t — ie, where « — 0* . In this way we ensure convergence of this integral. Then from (6.20) it follows that 6.10 We shall start from (6.5) and use spherical coordinates. Integration over angles @ and ¢ leads to

where we used the equal-time anticommutation relations (8.C,D). The integration over y leads to First we suppose that all indices are the spatial: yp =71,v = j, p = k. Then,

In the last expression we used that y and y are Grassmann variables. The other identities can be proved in the same way. For the second one the following identity is useful: cg0"02 = GT. From here the requested result follows. Using the identities from the Problems 3.6(b),(d),(e) and (i) we obtain

The transformation rules under time reversal and charge conjugation in the previous problem were found using the general properties of matrices JT’ and C. Here, we use explicit expressions for them. Starting from the anticommutation relation among y—matrices and introducing derivatives with respect to new coordinates t/ = —t, x’ = x instead of the old ones gives

From the last line we can read off that helicity is X = +1. Polarization of these photons is circular. 9.6 The four-momentum of the photon for observer S’ is

Using the facts that ys anticommutes with y“ matrices and that (ys)? = 1, the last expression becomes By applying expression for the projection operator into positive-energy solu- tions (Problem 4.4) we have

The coefficient 5 in the first term (10.13) can be obtained in the following way: contraction $(x,) with ¢(y,) can be done in three ways, as well as the contraction $(x2) with (yz). Two contractions (yi) with ¢(y2) can be done in two ways. The obtained result has to be multiplied by 2! which comes from the interchange yi-vertices with yo-vertices, because, for instance, we could contract (21) with o(y2) instead of é(y1). Thus, the overall coefficient is which can be represented by the following diagram:

Delta function which appears in the transition amplitude (10.26) indicates on the energy conservation law, which is satisfied because potential A‘ does not depend on time. As three-space is inhomogeneous (the potentia depends on x), the three-momentum is not conserved. The average valuc of the squared transition amplitude is obtained from (10.26)

The squared amplitude is The squared amplitude per unit time as viewed from the center—of—mass frame is:

where E, = Ey = E| = ES = E are the energies of the initial and final particles. All four fermions carry the momenta of the identical intensity |p]. In the high energy limit from (10.37) one obtains

By using the definition of number e, the integral (11.8) becomes

By using (11.9) and the previous expression we have 11.4 By applying the Feynman parametrization (11.G), the integral becomes

By introducing the Feynman parametrization (11.G) and integrating over the momentum k we get: As we know from the complex analysis the logarithm function, w = Inz has a branch cut along the positive z—axis which starts at the branch point z =0. This branch cut is necessary if we want that branches of logarithm function to be single valued and holomorphic functions. Let us find the branch point for function It is the smallest value of p? for which the argument of logarithm function vanishes:

Combining the terms in the previous formula we get By doing partial integration we have

where pi,2 are the momenta of the decay products. Also we take that x particle is in the rest. The decay rate is The integral in the previous formula can be simplified by introducing the new variable t = 27 — 1. The result is (see [9])

By using the Feynman parametrization formula (11.G) the last expression becomes Fig. 11.1. The one-loop contribution to the self-energy of ¢@ field

The self-energy of the 7 particle is determined by the diagrams given in Fig. 11.3. The full line depict the a field, while the dashed line depict o. The first diagram is one of the terms in the second order of the nerturbation

Note that only the last diagram depends on the momentum p. The renormal- ized mass is determined by m7, = ¥7(0) . It is easy to see that The symmetry factor of this diagram is 6, since one 7 field can be contracted to m field from mzo-vertex in two ways, while go contraction in the vertex ooo can be done in 3 ways. Other diagrams are: Fig. 11.3. The one-loop correction to the 7 propagator

Fig. 11.4. Superficially divergent diagrams in the Yukawa theory Superficially divergent amplitudes are shown in Fig. 11.4. The first diagram is the vacuum one and it can be ignored; the second and fifth are equal to zero. The bare Lagrangian density is

The full one-loop correction to the fermionic propagator is Fig. 11.6. The one-loop correction to fermionic propagator

Fig. 11.5. Feynman rules in renormalized Yukawa theory

where we use the Feynman parametrization formula (11.G). Introducing a new variable | = k + px we further have The first diagram is

The quantities with index 0 are called bare. The Feynman rules are given in Figure 11.8. Superficially divergent amplitudes are:

and it does not depend on momentum. Summing all diagrams we get

Fig. 11.11. Vertex correction in ¢? theory The second diagram is

From the last formula we find that the divergent part of iI” is given by

where D is generator of dilatation, and K” are four generators for SCT . Conformal group has 15 parameters. The commutation relations of the algebra can be evaluated from multiplication rules of the group. Let (A, a, p,c) denote group element. If we start from

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A REPORT ON COMPLETION OF STUDENT industrial work experience scheme

by John Jay

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Quantization in Astrophysics, Brownian Motion, and Supersymmetry

by Marco Pereira and

2007

The present book discusses, among other things, various quantization phenomena found in Astrophysics and some related issues including Brownian Motion. With recent discoveries of exoplanets in our galaxy and beyond, this Astrophysics... more

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Solutions physics by resnick halliday krane, 5th ed. vol 3 e 4

by Rute Melo

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The Landscape of Theoretical Physics: A Global View; From Point Particles to the Brane World and Beyond, in Search of a Unifying Principle

by Matej Pavsic

Kluwer Academic Publishers, 2001

This a book is for those who would like to learn something about special and general relativity beyond the usual textbooks, about quantum field theory, the elegant Fock-Schwinger-Stueckelberg proper time formalism, the elegant description... more

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Shamanic Vision Quest, pps. 309 - 337, in NeuroQuantology Special Issue 2016

by Kathryn LaFevers Evans, Three Eagles and

This special edition by guest editors, Cheryl L. Fracasso, Kaleb R. Smith, and Stanley Krippner, presents 22 articles that cover a vast array of interdisciplinary and multicultural views on health, healing, and consciousness. The reader... more

Cheryl L. Fracasso, Ph.D. is currently a psychotherapist in private practice with a specialty in spiritual psychotherapy, career counseling, and stress management, while pursuing post-graduate clinical psychology licensure at Saybrook University. She serves as faculty at University of Phoenix, and is an editorial /advisory board member with NeuroQuantology, and advisory board member with the American Center for the Integration of Spiritually Transformative Experiences (ACISTE). She is currently conducting an international study on near-death experiences (NDEs) with co-researchers Harris Friedman and Joshua Wyner on electromagnetic and physiological aftereffects of these experiences. In addition, she has served as Principal Investigator for three studies on NDEs that have explored clinicians’ tap RR eRALeantelAamoreres,

Figure 1. Areas of the visual brain necessarily conscious enough to respond to commands. Our understanding of these cases must be addressed by the model of consciousness states that is developed, and reconciled with the hierarchy of conscious, preconscious, and subliminal processing that is well understood (Dehaene et al., 2006). states that is developed, and reconciled with the

Figure 2. A hierarchical model of autonomous agents

Figure 3. The checker shadow illusion by Edward H. Adelson (A and B have identical shades), and the rabbit and duck illusion from the 23 October 1892 issue of Fliegende Blatter.

Figure 1. Combined BACARQ Scores 2013-2015

NeuroQuantology | June 2016 | Volume 14 | Issue 2 | Page 193-212 | doi: 10.14704/nq.2016.14.2.93 Bova et al., Healing tradition in Calabria, Italy Informants Pasquale and wife Giuseppina invited us into their home to talk about Calabrese traditional medicine.

Remedies are known primarily by the women of Calabria. Giuseppina (mid left) and daughter Rosa (mid right) have imparted their traditional healing knowledge to treat family members, Saverio (left) and Pasquale (right). Bova holds the family dog in the middle. knowledge of folk remedies, and seem to be willing to use both traditional and Western modalities. NeuroQuantology | June 2016 | Volume 14 | Issue 2 | Page 193-212 | doi: 10.14704/nq.2016.14.2.9 Bova et al., Healing tradition in Calabria, Italy

Galante (right) interviews an informant on traditional medicine while exploring ancient ruins.

Not all informants were willing to speak with us about traditional medicine especially when it involved treating malocchio. Locals were often reluctant to address such issues in the open, even though they may be commonly and deeply believed. Suspicion of witchcraft or giving evil eye can carry the price of social stigmatization or even ostracism. Of course, with respect to malocchio and witchcraft, there are social risks and costs. As with many societies, people are often reluctant to address such issues in the open, even though they may be commonly and deeply believed. Suspicion of witchcraft or giving evil eye can carry the price of social stigmatization or even ostracism. Given increasingly modern and “rational” attitudes toward these matters, dabbling in these arts may subject one to epithets like crazy, superstitious, or backward. Nevertheless, belief in malocchio and witchcraft are still a powerful undercurrent, even in the cities. Some will turn to the latter to solve various social and health related problems, but most tend to keep a respectful distance.

The statues remain in the Church of San Nicola di Bari all year, except when they are transported to the Sanctuary of Saints Cosma and Damian for the duration of the feast.During the closing ceremony they are returned to San Nicola di Bari. While attending a service at the church, several people placed ex voto offerings at the base of the statues, and children were positioned at their feet, or touched them, presumably for blessings. Galante holds an ex voto.

Romani primarily convened near the sanctuary of the saints. Since most were already assembled closer to the destination point, they preceded the assembled procession. One of our photographs clearly shows a group of Roma at the very head of the procession, followed by a line of police that separated them from the other members of the procession (priests, a choral group, non-Romani community members, and visitors joining the procession). Procession of celebrants with statues of Saints Cosma and Damian through the town of Riace. Romani are in the front of the procession separated by police from those following the traditional Roman Catholic celebration.

Rom holding paranze, or capo bastoni indicating his clan leadership. All appear captivated by nonstop traditional music.

Fratel Cosimo greets a young visitor at his prayer congregation. nearly 50,000 people attended a special Mass in May 2003. During the winter months, services at the shrine begin at 3:00PM, and during the summer at 4:30PM. The average service lasts about four hours and involves singing, praying, recitation of the rosary, testimonies, and concludes with a sermon and prayer from Cosimo.

with a couple from Switzerland, "Hans" and "Bertha," who frequently visited Madonna dello Scoglio. Hans expressed his enthusiasm for worshipping at the shrine because in his daily life as a corporate executive, he could not discuss his spiritual feelings and beliefs with his colleagues. For him, coming to the shine was like "breaking out of the cage of mundane everyday life." Moreover, his wife professed that she was a "tried and true Protestant," yet, for her, Fratel Cosimo's message transcended the division between denominations despite a Catholic bias. As a result, she now prefers to simply refer to herself as "a Christian." Pilgrims worship at I] scoglio, the rock where the Virgin Mary purportedly appeared to Fratel Cosimo.

This type of relationship is suggestive of Cosimo's public role as a charismatic leader. Charles Lindholm (1992) has described charisma simply as "a certain quality of an individual personality by virtue of which he or she is considered extraordinary and treated as endowed with special power or at least specifically exceptional powers or qualities" (p. 289). The notion of charisma also embodies a sense of intensified emotion and excitement; the extreme case evidenced in the euphoric episodes we witnessed. Cosimo did not engage in any ecstatic or overtly manipulative behavior that we noticed; however, he was certainly viewed by congregants as a truly exemplary person, blessed with divine powers. Pilgrims waiting at Madonna dello Scoglio for Fratel Cosimo to lead a prayer service and to provide private healings for the lucky few picked through a lottery.

The prayer service begins for pilgrims and participants. Next to the crowd on the right is a room filled with crutches, eye glasses and other assistive devices from those who were purportedly healed from their maladies and disabilities.

Such mandalas are most commonly created in two-dimensional painted form, but may also be constructed in elaborate three- dimensional designs, such as the twelve-foot in diameter, multi-tiered Kalachakra mandala of gold that is found in the Potola Palace in Lhasa, Tibet (Bryant, 1992). The Kalachakra system, which according to the 14 Dalai Lama “was one of the last and most complex tantric systems to be brought from to Tibet from India” (Bryant, 1992, p. xi), serves as the basis for the Kalachakra initiation that includes the creation of a strikingly colorful, complex, and intricate sand mandala. This elaborate twelve-day ritual was first conferred by the 14 Dalai Lama in a cornfield outside of Madison, Wisconsin in 1981 and has since been repeated throughout the world on numerous’ occasions, which makes_ the Kalachakra mandala--with its direct association to the mythic Kingdom of Shambala--perhaps the most representative symbol of tantric practice found in the world today.

The aim... is to effect a reversal of the relationship between ego-consciousness and the unconscious, and to represent the unconscious as the generator of the empirical personality. This reversal suggest that in the opinion of the “other side,’ our unconscious existence is the real one and our conscious world a kind of illusion, an apparent _ reality constructed for a specific purpose, like a dream that seems a reality as long as we are in it. Itis clear that this state of affairs resembles very closely the Oriental conception of Maya (p. 324).

Figure 1. The ancient Aztec god, Xochipilli, or “Prince of Flowers,” shown in the throes of entheogenic ecstasy (image courtesy of Wasson, 1980). Notice the blossoming mushroom mandala carved into the base of the stone statue. The “flower” symbol in Nahuatl texts is utilized in an entirely spiritual sense, in that the sacred teonancatle ceremony, so depicted, caused ‘the soul to bloom.’ The distinct incurved margins of these mushroom carvings are a taxonomically correct representation of the Psilocybe caerulescens, or ‘landslide mushroom’ (Stamets, 1996). the violent and devastating persecution by the conquering Spanish on the sacred heritage of the Aztecs and other Mesoamerican cultures, the ancient teonandcatl ceremony continued in secret, surviving only by remaining hidden to outsiders. Successfully kept secret for hundreds of years, the ceremonial sacrament was featured on the front cover of Life magazine on May 13, 1957. And, all at once, the secret was out - very out.

Figure 2. The semantic network is cognitive architecture which organizes declarative knowledge within branched hierarchies, with each concept represented as a “node,” which may be primed in patterns of spreading activation during the associative processes underlying the formation of thought. Psilocybin induces distinct changes to this normal priming process, referred to as “hyperpriming.”

Figure 3. The hyperpriming state of cognition is induced by psilocybin ingestion and can be thought of as the result of a change in attentional processes, like latent inhibition (LI). These changes expand normal semantic activation range outwards from its baseline state, to prime semantic nodes from distant “branches” not typically associated in one’s ordinary state of consciousness. volume of fluid flowing through channels. In this view, the hypersensitive psilocybin state “floods” our semantic network with attention, a broad volume which spreads far outwards across new conceptual branches, priming them into long associative strands. By thinking of spreading activation in terms of attention in this way, an individual’s limited capacity to focus and clearly express those expanded semantic associations may be partially defined by the limits of that individual’s attention span. “Under the influence of the mushroom, one’s power of concentration is far more pronounced than normally. You become deeply absorbed in whatever you may be thinking. There is no external distraction” (Swain, 2004, p. 206).

Figure 4. Mean plasma levels of psilocin, the primary metabolite of psilocybin (graph courtesy of Spitzer, 1996). Blood tests reveal psilocin is formed rapidly after drug intake, reaching peak plasma levels approximately 80 minutes after ingestion (data from Holzmann, 1995). Psilocybin-induced increase in indirect semantic priming, and subsequent decay, overlaid in 4 points.

Figure 1. C.M. Evans, 2012, Snake. 16 x 24 mixed media on wood. a Humans conceive of a cosmology that begins with a big bang and ends with a black hole. They are the observable effects of something greater that encompasses both light energy and dark matter, something we often describe as Unity or the One, and which we embrace with various unifying theories. At the end of Section 2 on depth psychology, I _ posit specific correspondences between shamanic practice and quantum physics, based on one such unified theory formulated by L.A. Glinka (2012) in his book Aethereal Multiverse: A New Unifying Theoretical Approach to Cosmology, Particle Physics, and Quantum Gravity. Natural magic, as defined in Section 3, and depth psychology tell us that humankind experiences the divine through unifying the bipolar coincidence of opposites; and shamans balance the four directions, along with above and below, in the central shaman stone. Again, fix your attention on the image of the ouroboros serpent swallowing its tail; the idea of a black hole whose event horizon swallows multitudes, but whose center is a singularity.

Figure 2.C.M. Evans, 2014. Rabbit I’s 3 x3 each, oil on canvas.

Figure 4. Mississippian Rattlesnake Gorget, ca. 1200-1400, Native American. (Brooklyn Museum, 2016, online)

Figure 6. Photo credit Three Eagles, 2016. 2lfhree Eagles’ medicine wheel rug. Navajo Storm design.

What we are looking for in these few pages, is the nature of the human experience depicted in the ouroboros image. At a medieval and Renaissance conference a few years ago, after my presentation on De magia naturali and The Red Book, an elder scholar came up to me and asked delightedly in a quizzical whisper, “Now have you seen that, where you are going along in the created world, and suddenly, ... ‘poof’... ?” Yes. The experience occurs in dreamtime consciousness—outside of space-time, because at the event horizon of the serpent’s circumference, all of creation is annihilated. One cyclic creation is all that exists before the serpent swallows its tail and becomes again the absolute abyss, dark matter. An unbound Unity, the dark mother: world soul, anima mundi, the great animal. Figure 8. C. M. Evans, 2009, Serpent Queen. 40 x 30 oil on canvas.

Figure 10. Graviton Seed of Life. Figure 12. Big Bang.

Figure 11. Brilliant Darkness of a Hidden Silence.

Figure 9. Primordial Universe. Dark Matter.

Figure 15. Gravitational Waves. Figure 14. Light Waves from Dark Matter.

NeuroQuantology | June 2016 | Volume 14 | Issue 2 | Page 309-337 | doi: 10.14704/nq.2016.14.2.94¢ Evans KL., Shamanic vision quest Figure 13. Gravitational Waves from Dark Matter.

Figure 17. Macrocosm Reflected in Microcosm. As Above So Below.

NeuroQuantology | June 2016 | Volume 14 | Issue 2 | Page 309-337 | doi: 10.14704/nq.2016.14.2.94 Evans KL., Shamanic vision quest Figure 18. Gold Starlight

Figure 19. Graviton Stone in the Center of Earth.

Figure 22. All Worlds Created and Uncreated. Figure 21. Creative Dark Matter.

Figure 24. Her Footstep on Wet Sand. Outside of Time and Space. Figure 23. Waves from the Womb of the Dark Mother.

Figure 25. Draws Primordial Waters Back Within.

NeuroQuantology | June 2016 | Volume 14 | Issue 2 | Page 309-337 | doi: 10.14704/nq.2016.14.2.94 Evans KL., Shamanic vision quest Figure 27. Brilliant Darkness of a Hidden Silence.

Figure 28. Touch the Stone of Dark Lightning.

When we returned home from our family camping trip, I began vision questing in the dreamtime towards a physical medicine wheel rug to plant my feet on, to ground those adornments on earth. I needed to bind above to below. Storm design rug offered itself, and | learned from it what the lightning bolts meant, and how to charge a shaman stone placed at its center with the power of lightning through my body. I began to practice the ritual that storm taught me called medicine wheel of the six directions, and storm spoke this invocation through me: The following year in the High Sierras, as I walked in the dreamtime medicine wheel, up the switchbacks to Third Falls, I was adorned with Great Eagle’s ritual invocation, which I brought back down with me to the mountain’s base. To ground the adornment in time, instead of returning to camp, I took the straight trail up the middle of that glacier-carved valley, and up onto the immense erratic boulder that the glacier had dropped in the center. Thereon I performed the ritual invocations: first the medicine wheel of the six directions, to transcend into the dark mother

Figure 33. Love is the lightning bolt calling ancestors and animal guides. Figure 32. Atand on the Ston e in the navel of the storm...

\leuroQuantology | June 2016 | Volume 14 | Issue 2 | Page 309-337 | doi: 10.14704/nq.2016.14.2.94¢€ Evans KL., Shamanic vision quest

Figure 35. Photo credit Three Eagles, 2016. RATES SRS! TERRES RETESET R RACER ESETEIRS gly, SS STRESSES, SRSA ERTS SSE I RRR Nn SEE In The Red Book, Jung renders this divine child archetype as a flower of life, naming Image 82 “The Divine Child” (Jung et al., 2009, p. 82). This flower of life image, the archetypal divine child, is a fiery red 8-petaled star-like flower, floating in the waters of life that nourish the green earth both rest upon. This entire image of the genesis of creation is embedded in a dark purple field—the dark mother, dark matter. As mentioned in this paper’s Methodology section, image expresses the archetypal idea intuited during shamanic research, which is conducted within consciousness. Image is a clear argument of research results: archetypal ideas are re- created by shamans throughout the ages as the same image. To demonstrate that, I offer another shamanic image of the divine child, the son of the fire flower:

Figure 36. Rendition by Three Eagles, 2016. a a a a al CD in the De magia, and later through the sole image in Quincuplex Psalterium—a flower of life. Both cosmologies depict the genesis of creation out of Unity. Lefévre divides natural philosophy into two divisions: philosophy, the theoretical science; and natural magic, the practical science. This magic works through attractions and repulsions that knit together heavenly and earthly things (Rice, 1976, pp. 19-29). Natural magic was the term used for describing numerical correspondence between positions of heavenly bodies and musical intervals, belonging to a cosmological theory that the whole universe is constructed on musical proportions (Walker, 2000, p. 81). Lefévre’s Book II discerns the process of genesis through the number mysticism of numerical ascension. This practical philosophy exercises the relationship between macrocosm and microcosm, through human embodiment, by virtue of their isomorphism. Practitioners of natural magic utilize Kabbalistic number mysticism such as the 10 sephirot (spheres) or tree of life, and gematria or correspondence between letters and numbers. NeuroQuantology | June 2016 | Volume 14 | Issue 2 | Page 309-337 | doi: 10.14704/nq.2016.14.2.94 Evans KL., Shamanic vision quest

Enliven the medicine wheels that bind earth to sky with a lightning bolt of love, the human nervous system. Figure 37. Photo credit C.M. Evans, 2015. 4. Conclusion: The Shaman’s Creations

Figure 38. Photo credit Three Eagles, 2016. NeuroQuantology | June 2016 | Volume 14 | Issue 2 | Page 309-337 | doi: 10.14704/nq.2016.14.2.94 Evans KL., Shamanic vision quest

Figure 38. C.M. Evans, 2005. The Shaman’ creations. 18 x 11.5 mixed media on paper.

NeuroQuantology | June 2016 | Volume 14 | Issue 2 | Page 338-347 | doi: 10.14704/nq.2016.14.2.94 Marchionni et al., Integrated quantum therapy in an epileptic child Figure 1. Trigger-point for the application of EHF-BRR treatment through yellow radiators: one on the skin projection area of CAEMH and one on the skin projection area of the epileptic focus (in this case, the superior parietal region)

Purusha is unmanifested, formless, passive, beyond attributes, beyond cause and effect, space and time. Purustia is Pure Existence. Prakruti is the creative force of action, the source of form, manifestation. attributes and nature. Mafad is the Cosmic Intelligence or Buddhi. Ahamkar is ego, the sense of “| am.’ Satva is stability, pure aspect, awakening, essence and light. Rajas is dynamic movement. Tamas is static, It is potential energy. inertia. darkness. ignorance and matter,

Ego operates according to three different frames of reference or viewpoints. Sattva is light, and pure intentioned ego. Rajas is the action- oriented ego. Tamas is the inert, darkness filled ego. All three of these exist within every dimension and form of creation. We are accustomed to thinking of ego in connection to personality, yet the same principles exist in all cosmic dimensions, animate and_ inanimate, intellectual and emotional expressions. The braided strands of three cosmic energies gunas operate in a continually changing way. One of the three energies is always dominate, and supported by the other two. This occurs in the microcosm and the macrocosm (Rao, 2002). The moon is an example of continual change of the gunas that takes place in nature and the influence it has on people. When full, the moon’s influence is uplifting sattvic and rajasic. It is generally believed to have a positive energizing effect on plants, animals, and humans. When the moon’s energy is in the dark phase, the energetics are said to be more dense, dull, or tamasic.

In the Christian tradition we find the phrase ‘in the beginning there was light, and the light became word, and the word became knowledge.’ This could be likened to the process of Mahat’s evolution and its first evolutes. The phrase is a statement of sentience dominated by sattva, supported by rajasic intelligent action, and supported by tamasic structural formation of language and words. Sattva and rajas working together have a close affinity with consciousness, the principle of illumination whose pervading reflection enlivens.

Figure 1.The basic operational principle ofa meditative exercise. The individual will gradually exercise his capacity of being "focused in the anchor." At the very moment he/she perceives oneself involved in the stream of thoughts, he/she will immediately return to be "focused in the anchor." But if (despite one’s "intention" to maintain the so-called "logic relaxation”) perceives oneself involved in the stream of thoughts he/she will - again and again - "return to the anchor" (Cardoso et al., 2007).

Table 1. Duality and complementarity in knowledge

Table 2. Duality and complementarity in visual perception

Table 1. Sample Characteristics. In the domain of sexual abuse, over half (51.6%) reported no exposure. Low to moderate levels were reported by 6.5% of the participants. Nearly 13 percent (12.9%) reported experiencing moderate to severe levels of sexual abuse, and 29.1% reported experiencing severe to extreme

Table 3. CTQ Profiles of Interview Participants.

Legend: D = duration of the reflex in seconds. Table 1. Duration of Cerebro-Gastric Aspecific Reflex for the diagnosis of epilepsy

Four vials containing neutral water were labeled such that the word “neutral” was clearly visible. These neutral vials were used for neutral baseline, after each of the emotionally-charged vials were held by the participant, and at the conclusion of the live cell analysis in order to decrease the possibility of any residual effects due to participation in the study.

Table 3. The veterans’ usefulness ratings of the information received are shown. Table 4. The guardians’ overall usefulness ratings are shown.

Veteran’s Questions: publication, all questions or responses are not included. Guardians also submitted questions for each of the 12 horses, but because of the restriction of paper length for publication, this information is not included. The complete data set is available from the principal researcher upon request. As outlined above, seven horses were assigned to veterans, and six veteran interviews were completed. All veterans submitted their questions for their horses. The responses allegedly received by the animal communicator are summarized below. Because of the paper length restriction for

NeuroQuantology | June 2016 | Volume 14 | Issue 2 | Page 404-426 | doi: 10.14704/nq.2016.14.2.95 Erickson et al., A mixed methods study of telepathic interspecies communication

better than other people, some horses like people better. And I like him. I feel good when I’m with him. James and I know what we’re doing together, he doesn’t have a lot of expectations. What we do together is okay with him and it’s okay with me. I like that. He’s not pushing me to do something I don’t want to do or making me do the same old thing over and over and over and over again.

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The Secret Doctrine Volume IV, The Nature of Everything

by Madonna-Megara Holloway

Part I – Spirilla Theory and Cosmology Stephen Hawking once proclaimed that String Theory may be able to unify the various forces although later he became disillusioned thinking that there may be no Theory of Everything. This very... more

Part I – Spirilla Theory and Cosmology
Stephen Hawking once proclaimed that String Theory may be able to unify the various forces although later he became disillusioned thinking that there may be no Theory of Everything. This very condensed book pulls together the various forces into the Spirilla Theory which supersedes String Theory and introduces the Relativity of Consciousness.

The foundation of the Spirilla Theory is based on the writings of H. P. Blavatsky, A. B. Bailey, and A. Besant. By overlaying the works of Einstein, Bohm, de Broglie, Dirac, Bell and other great scientific minds, on top of the foundation, the unification of the various forces and theories starts to appear; each field of study supplying a part of the puzzle but only a holistic view of ALL endeavors will solve the mystery. The book starts by laying the groundwork through the Introduction, a review of Bell’s Theorem and p-adic mathematics; following this, each major section begins with a quote from the foundational works followed by the quotes from scientific papers demonstrating the current known thinking on the various topics; no attempts are made to edit the works (except with a few exceptions for clarity and/or length) of the various authors and references to the scientists’ works are maintained. Each section is pulled together so that a picture can be seen.
This section;
1. Redefines the atom with the addition of a subquark;
2. Defines the Spirilla Theory which unifies Quantum Mechanics and General Relativity, and explains Quantum Entanglement;
3. Defines new particles;
4. Redefines time and space;
5. Defines and solves the mystery of Black Holes and links the cosmic and quantum black hole through the spirillae;
6. Delves into the mystery of the Macroverse;
7. Outlines the steps in the origins of the universe;
8. Adds an equation to Einstein’s original 1905 paper on relativity which sees the speed of light approaching infinity;
9. Gives the foundation for developing space travel; and, as an appendix,
10. Gives detailed information for the development of a new energy source – Quantum Energy.

Part II - Ontology, Epistemology & Manifestations
Part II is divided into three sections:
1. Ontology and the fundamental concepts of reality which discusses:
a. consciousness and delves into the mystery of human consciousness having cosmic origins;
b. reincarnation and gives the various laws affecting rebirth, with a discussion on the principle of mutation and the perfecting of form;
c. the work of form-building, transmutation of form and the building of a human form.
2. Epistemology which covers a great deal of topics however; for the purposes of NOE the subject is restricted to;
a. evolution including a definition of the Law of Evolution, the cyclic ebb and flow and the rhythmic work of creation, the process of substitution, the evolution of man and the genesis of the pithecoid stocks; and
b. death including the processes of death, two main reasons for cremation and the sequence of events at death.
3. Manifestations of the various religions including:
a. why Christians don’t believe in reincarnation;
b. the coming science of invocation and evocation;
c. Quantum Entanglement Over Time (QEoT) or The Law of Cause and Effect, and The Law of Karma with a discussion on The Golden Rule ; and
d. The New World Religion.

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Quantum Field Theory: An Introduction

by Ryan Reece

2007

Notes I took on QFT as a graduate student at Penn, mainly inspired in lectures by Burt Ovrut, but also working through Peskin and Schroeder (1995), as well as David Tong's lecture notes available online. They take a slow pedagogical... more

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Tuning the Mind: Geometries of Consciousness --> Holonomic Brain Theory And The Implicate Order

by Shelli Joye

This paper is about consciousness and how it is structured, and how it may be navigated. Presented here is a psychophysical map, a guide for 21st century psychonauts (those highly inquisitive individuals motivated to explore altered... more

This paper is about consciousness and how it is structured, and how it may be navigated. Presented here is a psychophysical map, a guide for 21st century psychonauts (those highly inquisitive individuals motivated to explore altered states of awareness, states attained through natural ability, or through drugs, prayer, meditation, dreams, religious rituals, or physical exercises). I have been exploring non-ordinary noetic dimensions for almost fifty years now, ever since, as a young physics student between semesters at Rice University (during the “Summer of Love” in 1967), I first experienced the full impact of ranges and dimensions of my mind tuning in to bandwidths far beyond my normal spectrum of awareness, beyond anything I could ever have previously imagined.
My lifelong search for a map of consciousness began around a small campfire on a lovely Pacific Ocean beach just south of Big Sur, California, at around midnight on a clear July night, shortly after ingesting three small yellow tablets of LSD (“Owsley acid”). Having just completed the third year of a double major program in mathematics and electrical engineering, my vision of the universe was deeply influenced by such things as frequency charts, Fourier and Laplace transforms, and electromagnetic theories describing invisible energy waves. Suddenly all of these dry theories became vividly alive for me, overlaid and energized by the direct visual, auditory, and tactile experience of other entities in an enormous sea of energy. Astonished, I found myself floating on the vast depths of oceans of consciousness that I had never realized lay beyond the shores of my own familiar mind, and I realized that we are all immersed in planetary and galactic energy fields swirling in and out of our own limited islands of awareness.
The map presented in this book is derived from direct experience. It is also an extension of several major new concepts that have emerged in recent quantum physics and brain research, primarily the “holonomic mind/brain” theory put forth by the neurosurgeon Karl Pribram and the cosmology of the “Implicate/Explicate orders” proposed by the British quantum physicist David Bohm. Woven together, a synergy emerges as the holoflux hypothesis, revealing a new map of consciousness in an expanding universe. The holoflux hypothesis presented here offers a new paradigm which is shown to be consistent with physics and found surprisingly to be in accord with the writings and verbal traditions of the numerous metaphysical interpretations brought back by millenia of introspective mystics, saints, and shamanic psychonauts.

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Atomic Structure Theory Lectures on Atomic Physics With 21 Figures and 45 Tables

by Yu Mendoza

In Fig. 2.1, we plot the Coulomb wave functions for the n = 1, 2 and 3 states of hydrogen, Z = 1. In this figure, the angular momentum states are labeled using spectroscopic notation: states with 1 = 0,1,2,3,4,--- are given the labels s, p,d, f,g,---, respectively. It should be noted that the radial functions with the lowest value of / for a given n have no nodes for r > 0, corresponding to the fact that n, = 0 for such states. The number of nodes is seen to increase in direct proportion to n for a fixed value of /. The outermost maximum of each wave function is seen to occur at increasing distances from the origin as n increases.

The number of nodes increases with increasing energy. To reduce the num- ber of nodes, we must, therefore, lower the energy. We do this by multiplying E (which is of course negative) by a factor of 1.1. Repeating steps 2 - 4 with FE = —0.110 a.u., leads to the curve shown in the dot-dashed curve in the figure. The number of nodes remains n, = 3, so we repeat the steps again with & = 1.1(—0.110) = —0.121 a.u.. At this energy, the number of nodes nN, = 2 is correct, as shown in the dashed curve in Fig. 2.2; however, the derivative of the wave function is still discontinuous at a,. To achieve a wave function with a continuous derivative, we make further corrections to FE using a perturbative approach. From this equation, we find that

An iterative scheme is set up to solve the Thomas-Fermi differential equa- tion. First, two initial values of X are guessed: X = X, and X = Xp». The Thomas-Fermi equation (2.111) is integrated inward to r = 0 twice: the first time starting at « = X,, using initial conditions ¢(X,) = 0, dd/dx(X,) = —(Z — N)/X,Z, and the second time starting at x = Xp, using initial condi- tions d(Xy) = 0, dd/da(X,) = —(Z — N)/X,Z. We examine the quantities (0) — 1 in the two cases. Let us designate this quantity by f; thus, fu is the value of ¢(0) — 1 for the first case, where initial conditions are imposed at « = X,, and fy, is the value of 4(0) — 1 in the second case. If the product fafy > 0, we choose two new points and repeat the above steps until f, f, < 0. If fa fo < 0, then it follows that the correct value of X is somewhere in the interval between X, and X,. Assuming that we have located such an interval, we continue the iteration by interval halving: choose X = (Xq + X,)/2 and integrate inward, test the sign of ff, and f fp to determine which subinterval contains X and repeat the above averaging procedure. This interval halving is continued until |f| < «, where ¢€ is a tolerance parameter. The value chosen for ¢ determines how well the boundary condition at x = 0 is to be satisfied. In the routine THOMAS, we use the fifth-order Runge-Kutta integration scheme given in [1] to solve the Thomas-Fermi equation. We illustrate the solution obtained for the sodium ion, Z = 11, N = 10 in Fig. 2.4. The value of R obtained on convergence was R = 2.914 a.u.. In the top panel, we show

Fig. 3.2. Solutions to the HF equation for helium, Z = 2. The radial HF wave function P;;(r) is plotted in the solid curve and electron potential vo(1s,1r) is plotted in the dashed curve.

where the sums extend over all one-electron orbital quantum numbers in the set {a,b,--- ,n}. The terms gabap and gabba are matrix elements of the Coulomb interaction g(ri2) = 1/rig. The term gabap is called the direct ma- trix element of the operator g(r12) and gaboa is called the exchange matrix ele- ment. The lowest-energy eigenstate of Hp for an N-electron atom is a product of the N lowest-energy one-electron orbitals. For two-electron atoms, these are the two 1s orbitals with different spin projections. In atomic model po- tentials, such as those discussed in the previous chapter, the lowest few orbital eigenvalues are ordered in the sequence €15 < €25 < €2p < €35 < €3p. (The or- dering beyond this point depends on the potential to some extent and will be considered later.) Tiles be Due: gee Ts eee es PR Re pe ee ee Napa gees ol] In the above rules, we have introduced the notation:

This method of solving a linear inhomogeneous set of equations is known as the method of variation of parameters. We use the resulting formulas to obtain numerical solutions to (3.92-3.93) at each stage of iteration. Consider the pair of inhomogeneous differential equations

Fig. 3.3. Radial HF wave functions for neon and argon.

Fig. 3.4. Radial HF densities for beryllium, neon, argon and krypton.

These equations are solved at each stage of iteration and the energy adjusted using a variation of parameters scheme similar to that used in the nonrela- tivistic case. We leave it to the reader to write out the detailed formulas for The numerical techniques used to solve the Dirac-Fock equations are similar to those used in the nonrelativistic case. Starting from Coulomb wave functions, a model potential U(r), taken to be the direct part of the HF potential scaled to give the correct asymptotic behavior, is obtained iteratively using the Dirac routine MASTER. The Dirac-Fock equations are rewritten as inhomogeneous equations, in a form suitable for iteration, starting from the model-potential orbitals:

states can be further combined to give eigenstates of J having eigenvalues L-1,L,0+1. Nonrelativistically, the triplet states with different values of J are degenerate. This degeneracy is lifted in relativistic calculations. The observed spectrum of helium consists of singlets and triplets of various angular symmetries S, P,... corresponding to L = 0, 1, .... The triplets are slightly split by relativistic effects. [.S-coupled states with orbital angular momentum L, spin angular momentum S', and total angular momentum J, are designated by the spectroscopic notation ?°+1L;. In Fig. 4.1, we show the approximate ordering of the low-lying singlet and triplet levels of helium in an energy level (or Grotrian) diagram. To form the LS-coupled states, we combine the degenerate states according

Fig. 4.2. Variation with nuclear charge of the energies of 1s2p states in heliumlike ions. At low Z, the states are LS-coupled states; while at high Z, they become jj-coupled states. Solid circles 1P;; Hollow circles 3P9; Hollow squares 3P,; Hollow diamonds °P.

The wave function for the atom is, therefore, factorizable into a product of a plane wave describing the center of mass motion and an N-electron wave function describing the motion relative to the nucleus. The Hamiltonian for the relative motion is The kinetic energy term in the original Hamiltonian can be rewritten: We find, using the four previous equations:

The effect of the finite nuclear mass on the first term H,, is to scale the infinite mass energies by the ratio p/m = M4/(M4 +m). The infinite mass energy levels are commonly measured in units of the Rydberg constant R,., which has the value 1/2 (a.u.) = 109737.31 cm~!. The shift of the energy from the infinite-mass value is referred to as the normal mass shift. The value of the normal mass shift is

Fig. 5.1. Comparison of the nuclear potential |V(r)| and field-shift factor F'(r) cal- culated assuming a uniform distribution (given by solid lines) with values calculated assuming a Fermi distribution (dashed lines).

The spin sums in this equation can be easily carried out leading to a factor of 6s'S0MiMs in the two direct terms and a factor of (—1)$*15ss6,mMs in the two exchange terms. The orbital angular momentum sums are a bit more difficult. From the Wigner-Eckart theorem, it follows that each of the four terms in the sum must be proportional to

7.1.2 Example: Second-Order Energy in Helium

Fig. 7.1. The n = 30 B-splines of order k = 6 used to cover the interval 0 to 40 on an “atomic” grid are shown. Note that the splines sum to 1 at each point.

quantum number increases, the cavity spectrum departs more and more from the real spectrum. This is illustrated in Table 7.1, where we list the eigen- values obtained for | = 0 states in a Coulomb potential with Z = 2. In this example, we use n = 40 splines with k = 7. In Fig. 7.2, we show the B-spline components of the 2s state in a Coulomb potential with Z = 2 obtained using n = 30 splines of order k = 6.

To aid in the angular momentum decomposition, we start with an easily proved graphical identity: where the + sign pertains to the nonrelativistic case, where j; takes on integer values, and the — sign pertains to the relativistic case, where 7; takes on half-integer values. From this identity, it follows that the anti-symmetrized Coulomb matrix element can be written in the nonrelativistic case as: 7.3.2 Angular Momentum Decomposition

Fig. 7.3. The radial charge density p, for the 3s state in sodium is shown togethe1 with 10xdp,, where dp, is the second-order Brueckner correction to py. If we let P,(r) and 6P,(r) be radial functions associated with ¢, and dd, respectively, then the radial probability density is p,(r) = P?(r) and the perturbed radial probability density is dp,(r) = 2P,(r) 6P,(r). We illustrate these radial densities for the 3s state of sodium in Fig. 7.3. One sees from this figure that the Brueckner correction draws the valence wave function ir toward the atomic core, in harmony with the attractive nature of 5().

Fig. 7.4. Lower panel: radial density of neutral Pd (Z=46). The peaks correspond- ing to closed n = 1, 2, --- shells are labeled. Upper panel: radial density of the 5s ground-state orbital of Pd~. The 5s orbital is obtained by solving the quasi-particle equation.

Fig. 7.5. MBPT contributions for He-like ions. 2 to 90. Notice that E@) is roughly constant and that E®) falls off approxi- mately as 1/Z. By contrast, B™) and B®) grow as Z° and Z?, respectively. From the table, it is obvious that contributions from B“ and B®) are almost negligible for neutral He. However, for Z > 5, B“) is larger than |E@)| and for Z > 17, B“ is larger than |E©)|. Indeed, beyond Z = 70, we even find |B? | > |B@|. Thus, while the Breit interaction is a relatively small per- turbation for low Z atoms and ions, it is the dominant correction to the HF energy at high Z.

Substituting into the expression (7.117) for the second-order energy matrix. we find,

The RPA matrix element tR?4 is evaluated by solving (8.8-8.9), then substi- tuting into (8.10). The resulting dipole matrix element is gauge independent. As will be shown below, LZ and V forms of the dipole matrix element are iden- tical in the RPA. For this to be true in relativistic calculations, the virtual- orbital index m in the RPA equations must range over both positive- and negative-energy states. A discussion of the role of negative energy states in transition amplitudes for highly-charged ions can be found in [26], where it is shown that the length-form amplitudes for highly-charged ions are insensitive to negative-energy states. The particle-hole RPA equations can be expressed in terms of reduced

Iterating these equations leads to the first- and second-order matrix elements together with a subset of third-, fourth-, and higher-order corrections. The RPA was originally introduced to treat Coulomb interactions in a degenerat« electron gas by [8] and has subsequently become an important mathematica tool in almost every branch of physics. Substituting the RPA matrix element: tRPA and tRPA into the sums on the right-hand side of (8.7), leads to the random-phase approximation to the matrix element t,,,,

Fig. 8.1. First- and second-order Breit corrections to the ground-state energies of neonlike ions shown along with the second-order correlation energy. The first-order Breit energy B™ grows roughly as Z°, B (2) grows roughly as Z*, and the second- order Coulomb energy E) is nearly constant.

The first four lines give the RPA corrections to one-electron transition am- plitudes. The two final lines give the electron-electron correlation corrections. The index 7 in each of the four final sums runs over both bound and virtual states with restrictions. Thus, in the first sum on the next to last line 7 and a cannot be members of the initial-state complex (v,w), and in the second sum i and y cannot be in the (v, w) complex. Similarly, in the first sum on the last line i and w cannot be in the final-state complex (x,y), and in the final sum i and v cannot be in the (x, y) complex. After coupling final state orbitals (ay) to Jp and initial state orbitals (vw)

From the above, it follows MATHEMATICA program, P = {1, Table[Expand[D[(x*2 - 1)°1, {x, 1}]/(271 1!)], {1, 1, 9}]} // Flatten // TableForm

1.11 Reduced matrix element of a normalized spherical harmonic:

In either coupling scheme, there are a total of 81 magnetic substates.

The extra terms in the second-order energy from Vj are:

The first and sixth terms above cannot contribute. The remaining terms vive, in order,

Table 2.1. Adams-Moulton integration coefficients.

Table 2.2. Weights a; = ci/d and error ex coefficients for trapezoidal rule with endpoint corrections.

Table 2.3. Comparison of n = 3 and n = 4 levels (a.u.) of sodium calculated using parametric potentials with experiment. The second term in each of these potentials approximates the electron-electron interaction. As an exercise, let us determine the values of the parameters a and 6 in (2.92) and (2.93) that best represent the four lowest states (3s, 3p, 4s and 3d) in the sodium atom. For this purpose, we assume that the sodium spectrum can be approximated by that of a single valence electron moving in one of the above parametric potentials. We choose values of the parameters to minimize the sum of the squares of the differences between the observed levels and the corresponding numerical eigenvalues of the radial Schrodinger equation. To solve the radial Schrédinger equation, we use the routine MAS- TER described above. To carry out the minimization, we use the subroutine GOLDEN from the NUMERICAL RECIPES library [40]. This routine uses the golden mean technique to find the minimum of a function of a single variable, taken to be the sum of the squares of the energy differences considered as a function of the parameter in the potential.

Table 2.4. Parameters for the Tietz and Green potentials.

Table 2.5. Energies obtained using the Tietz and Green potentials. Show that the leading term in powers of R of the finite size shift in energy

2.7. The low lying states of the sodium-like ion Al*? (Z = 18) are that gives the best least-squares fit to the 4s, 5s, 6s, 4p, 5p, 3d and 4d levels in potassium. Use the resulting potential to predict the value of the 1s binding energy in potassium. How does your prediction compare with experiment? The data for the energy levels are found in [38]. You should average over the fine-structure of the p and d levels.

Table 3.1. Coefficients of the exchange Slater integrals in the nonrelativistic Hartree-Fock equations: A;,1,. These coefficients are symmetric with respect to any permutation of the three indices.

A comment should be made in connection with the use of the subroutine MASTER. As discussed previously, the routine MASTER itself uses an iterative procedure to determine the radial wave functions. MASTER requires only a few iterations if an accurate estimate of the eigenvalue is provided initially. To produce such an estimate, we use perturbation theory to determine the change in the eigenvalues induced by changing the potential. A small loop is introduced after U(r) is changed at the end of an iteration step to calculate the first-order change in each of the energy eigenvalues. Perturbation theory We add U(r) to the nuclear potential and solve the radial equations once again to obtain a second approximation. This second approximation is used to obtain new values of p(r) and U(r). These values are used to obtain a third approximation. This iteration procedure is continued until the potential is stable to some desired level of accuracy.

Table 3.5. Dirac-Fock eigenvalues (a.u.) for mercury, Z = 80. Etot = —19648.8585 a.u.. For the inner shells, we also list the experimental binding energies (— Bru, ) from Bearden and Burr [4] for comparison.

The degeneracy of LS multiplets is lifted in relativistic calculations, giving to a J-dependent fine-structure of 2°+1Z states. As a specific example, let us consider heliumlike neon (Z = 10). For simplicity, we choose U = 0, and calculate the energies of the two (1s2s) states and the four (1s2p) states. In Table 4.3, we show the lowest-order and first-order energies E© and BO) together with the resulting sum. These energies are all given relative to the one-electron ion. The energies of the °P, and ‘'P, states were obtained by solving the 2 x 2 eigenvalue problem in (4.121). The three ?P; states have slightly different energies in this relativistic calculation; the J-dependent fine structure of the 3P state obvious from the table. In Bic AY we illuiectrate the tranaition fram 7,9 tan 49 eaninlinge aac 7 in- This is precisely the matrix, obtained in a more direct way in Sec. 4.6, that transforms the 77 coupled states structure OF the f state Obvious from the table. In Fig. 4.2, we illustrate the transition from LS to jj coupling as Z in- creases along the helium isoelectronic sequence by presenting the results of a series of calculations of the energies of (1s2p) states for two-electron ions with nuclear charges ranging from Z = 4 to Z = 90. We plot the ratio of the snergy of each of the four substates to the average energy of the states. For low values of Z, near the nonrelativistic limit, the states divide into a singlet state and a triplet state. As Z increases, the triplet state splits apart into J lependent fine-structure components. For large Z, the states come together again to form the two jj states (1s1/22p1/2) and (181/22p3/2).

values are seen to be in only qualitative agreement with experiment. The agreement between theory and experiment can be improved to the level of 5% or better by including corrections from first- and second-order perturba- tion theory. For the heavier alkali atoms, a significant part of the difference between calculation and measurement is due to the use of the nonrelativistic approximation. For example, if we use the relativistic expression (5.31) rather than (5.38) to evaluate a for rubidium, we obtain a = 643.9 MHz instead of the value a = 542.0 MHz given in the table.

Table 6.1. Reduced oscillator strengths for transitions in hydrogen.

Table 7.1. Eigenvalues of the generalized eigenvalue problem for the B-spline ap- proximation of the radial Schrodinger equation with | = 0 in a Coulomb potential with Z = 2. Cavity radius is R = 30 a.u. We use 40 splines with k = 7. which leads to the orthogonality relations

fable 7.3. Contributions to the second-order correlation energy for helium.

One Valence Electron: Relativistic Case The relativistic expression for the second-order valence energy in a one- electron atom in state v is

orbitals modified by the self-energy operator. Other solutions with € < 0 also exist in some cases; the new bound-state solutions being associated with the negative ion. To obtain the solution corresponding to a loosely-bound electron, it is usually sufficient to set « = 0 in the expression for 5) (e). As a specific example, we consider the case of palladium (Pd), 7=46. This atom has closed n = 1, 2, and 3 shells and closed 4s, 4p, and 4d subshells. The Pd negative ion is found experimentally [47] to have a 5s bound state with binding energy, (or affinity) 562.13 meV. The expansion coefficients c; in (7.75) for the 5s eigenstate are given in Table 7.5. The 5s eigenvalue is found to be €5, = —0.01957 a.u., corresponding to an electron affinity of 532.5 meV. The radial density of neutral Pd is shown in the lower panel of Fig. 7.4 and the 5s Brueckner orbital of Pd~ is shown in the upper panel. the core —a,/2r+. There is an obvious difficulty in describing such an atom within the frame- work of MBPT; the bound state does not exist in the HF approximation. In- deed, the force responsible for binding shows up first in second-order MBPT. One approach that can be used in this case is to solve the quasi-particle equa- tion exactly, without recourse to perturbation theory. To this end, we expand the Brueckner orbital ~ as a linear combination of HF basis orbitals @;,

Table 7.6. Contributions to the ground-state energy for He-like ions. Linearizing this expression in powers of b,;47, we may write this in the form

7.5.1 Relativistic CI Calculations In table Table 7.8, we show the results of a sequence of CI calculation: of the helium ground-state energy, including configurations with successively larger values of the orbital angular momentum. The major contributions are from (msns) configurations, and contributions from higher-partial waves are seen to converge rapidly. The final extrapolated value of the CI energy differs from the experimental energy by 1 part in 10°; the difference being due tc omitted reduced-mass, relativistic, and quantum-electrodynamic corrections. where, as in the nonrelativistic case, nx is a symmetry factor defined by

Table 7.10. 77 designations of even- and odd-parity states in the model space o magnesium and magnesiumlike ions. As shown earlier, the total angular momentum J must be even in the identical particle case, k = 1. The parity of ®,;(JM) is P = (—1)'*+". The magnesium model states ®,;(JM) are a restricted set of configuration state functions formed from n = 3 orbitals. Designations of the configuration state functions in the 77 coupling scheme for the model space of magnesium are listed in Table 7.10. Note that the dimension d of the model space ranges from seven

Table 8.2. Second-order reduced matrix elements and sums of first- and second- der reduced matrix elements for F1 transitions in lithium and sodium in length ind velocity forms. The RPA values given in the last column are identical in length und velocity form.

Table 8.9. Isotope shifts 6v?*:?3 (MHz) for 3s and 3p states of Na. 8.5 CI Calculations for Two-Electron Atoms

8.6 Second-Order Matrix Elements in Divalent Atoms and 25 states In helum. Several comments should be made concerning these transitions. Firstly, the relativistic CI calculations automatically account for the splitting of the 23P level into fine-structure components J = 0, 1, 2. Secondly, the theoretical wavelengths predicted by the relativistic CI calculations are in precise agree- ment with observed energies; the largest difference in Table 8.10 is 0.02%. By contrast the differences between theoretical and experimental wavelengths in the nonrelativistic CI calculations range from 2% to 25%. Since oscillator strengths are proportional to the square of the respective transition energies, we find substantial differences between nonrelativistic independent-particle predictions and relativistic CI predictions. Thirdly, since the dipole transi- tion operator is spin independent, E1 transitions between singlet and triplet states (intercombination transitions) are forbidden nonrelativistically. Such transitions, however, have nonvanishing rates in the relativistic theory. The 23P, - 1'Sg transition is the only possible El transition from the triplet state. The 2°Po - 1'So transition is strictly forbidden by angular momentum con- servation, while the 2°P, - 11S, transition is an allowed M2 transition with transition rate A = 0.3271(s~'). A complete study of 2-1 and 2-2 transitions in heliumlike ions is presented in [26].

Table 8.11. Second-order transition energies w (a.u.), reduced electric-dipole matrix elements D, line strengths S, and transition rates A (1/ns) are listed for singlet- singlet transitions in P IV. Lifetimes 7 (ns) of the initial states obtained from second- order calculations are also listed.

Energies for Na from NIST transformed to a.u.. 2.10 The only term in the Dirac Hamiltonian that does not commute with Lor S isa: p. Writing Li = €:;.x;pp, one finds that:

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"'Mysticism' in quantum mechanics: the forgotten controversy"

by Juan Miguel Marin

This paper argues that a European controversy over a 'mystical' hypothesis, one assigning the mind a role to play at the material level of reality, shaped much of the debate over the interpretation of the quantum equations. It traces back... more

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MANAGING AND EVALUATING THE IMPACTS OF LARGE RESEARCH PROGRAMMES

by Trevor Wren BSc MA MPhil PhD MBA

2009

This research was funded by, and implemented within, a UK national research organisation, while the author was the KE and Impact Evaluation Manager responsible for assessing impact on a £15m UK government-funded research programme. This... more

This research was funded by, and implemented within, a UK national research organisation, while the author was the KE and Impact Evaluation Manager responsible for assessing impact on a £15m UK government-funded research programme.

This work was also submitted as the authors MBA dissertation which was accepted and awarded in 2009.

ABSTRACT: A methodology and methods ‘toolbox’ is proposed for conducting impact research and assessment from within research programmes. The emphasis is upon how to clarify and assess the wider impacts from the early stages onwards.

The approach explicitly acknowledges, and attempts to address, the known issues and challenges of impact assessment while drawing upon the resources and opportunities available to research managers and researchers within such programmes.

The study has two triangulating foundations. Firstly, it examines the academic literature to help identify and design the pilot methodology and methods. Secondly it trials these in a real programme to both test and improve them.

The study was conducted over one year within one leading UK research organisation, where two research programmes (and around 60 research projects of £15m total value) were being assessed for their impacts. The study draws upon actual impact management experience and reflection, prospective (ex ante) and retrospective (ex post) assessments, participatory contributions from leading researchers undergoing assessment, and consultation with external users. The findings of this study outline the pilot and its first iteration. Recommendations are made for improvement to the methodology and methods.

A subsequent follow-on bid to UK government incorporating the impacts identified from implementing this methodology, successfully led to a further £15m of government funding.

It is expected the pilot methodology and methods will be applicable to other organisations, conducting and funding such research programmes, required to research and assess the wider research impacts.

Although primary focus of implemetation trials was upon research in physical sciences, technology, high-tech engineering, computing/IT, and environment, the wider literature study, the methodology design and justification, the methods proposed and used, and the resulting general recommendations and lessons are expected to apply more broadly to many other research areas, where the impact is to be found more widely in the society, economy, government or public sector or within organizations, policies, professions or the public.

Interest in this work is expected from research programme managers, impact managers and assessors, management consultants advising in this area, and government funding managers, all seeking to embed a developing approach to understand, capture, and enhance wider impact.

earlier and later stages, linking idea generation to the marketplace:

TABLE 3.1: Grounding methodology and methods in literature best practice

Table 3.2: Three proposed methods within the methodology

TABLE 3.3: Analysis summary for each proposed method

2D analysis matrix with possible assessment ‘grades’ is exemplified in the table below.

TABLE 8.1: Complimentary aspects of the different methods

TABLE 10.1: Method improvements suggested after trial

data matrix analysis, gives the table below gives some case examples. information needed, and enable easier communication of the programme as a whole.

impact research and assessment may differ by impact mechanism (to be developed).

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Measurement of the inclusive jet cross section in pp¯ interactions at s=1.96TeV using a cone-based jet algorithm

by Levi Guimarães

2006, Physical Review D

We present a measurement of the inclusive jet cross section in ppbar interactions at sqrt{s}=1.96 TeV using 385 pb^{-1} of data collected with the CDF II detector at the Fermilab Tevatron. The results are obtained using an improved... more

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Thermodynamics and Statistical Mechanics An Integrated Approach - Robert J. Hardy, Christian Binek.pdf

by Sulistiyawati Dewi Kiniasih

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Sarfatti Stargate March282014

by Jack Sarfatti

generating a universally quasi-static repulsive non-propagating confined gravity field. generating a universally quasi-static repulsive non-propagating confined gravity The weak field Newtonian gravity limit gives an approximate Poisson equation

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Boyd Nonlinear Optics Third Edition

by Itzel Reyna

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Handbook of Whiteheadian Process Thought

by Michel Weber

"Michel Weber and Will Desmond, (eds.), Handbook of Whiteheadian Process Thought, Frankfurt / Lancaster, ontos verlag, Process Thought X1 & X2, 2008. (695 p. + 726 p. ; ISBN 978-3-938793-92-3 ; 398 €) Gathering 115 entries written by 101... more

"Michel Weber and Will Desmond, (eds.), Handbook of Whiteheadian Process Thought, Frankfurt / Lancaster, ontos verlag, Process Thought X1 & X2, 2008. (695 p. + 726 p. ; ISBN 978-3-938793-92-3 ; 398 €)
Gathering 115 entries written by 101 internationally renowned experts in their fields, the Handbook of Whiteheadian Process Thought aims at interpreting Whitehead secundum Whitehead, at canvassing the current state of knowledge in Whiteheadian scholarship and at identifying promising directions for future investigations through (internal) cross-elucidation and (external) interdisciplinary and crossdisciplinary development.
Table of Contents
Introduction
I. Aesthetics
II. Anthropology
III. Ecology
IV. Economy
V. Education
VI. Ethics
VII. Gender Studies
VIII. History
IX. Language
X. Mathematics and Logic
XI. Metaphysics
XII. Psychology and the Philosophy of Mind
XIII. Public Policy
XIV. Science
XV. Sociology of Science
XVI. Theology and Religion
XVII. Theory of Knowledge
XVIII. Urbanism & Architecture
XIX. Biographical entries
XX. Critical Apparatus

Authors : A Sister of St-John, Adam Scarfe , Albert C. Lewis, Alessandro Sardi, Alix Parmentier, Andrew Dawson, Annamaria Miranda, Arran Gare, Barbara Muraca, Berit Brogaard, Beth Lord, Brian G. Henning, Bruce Duncan MacQueen, Bruce G. Epperly, Carol F. Johnston, Carol P. Christ, Claude de Jonckheere, Claus Michael Ringel, Clifford Cobb, Craig Eisendrath, Daniel A. Dombrowski, David G. Butt, David Ray Griffin, Dominic J. Balestra, Donald Wayne Viney, Donna Bowman, Douglas R. Anderson, Elias L. Khalil, Elie During, Frédéric Fruteau de Laclos, Franck Robert, Gao Shan, Gary A. Cook, George Allan, Giangiacomo Gerla , Gottfried Heinemann, Graham Bird, Granville C. Henry, jr., Gudmund Smith, Guillaume Durand, Howard Woodhouse, Ivor Grattan-Guinness, Jaime Nubiola, James Connelly, James Williams, Jean-Pascal Alcantara, Johanna Seibt, John B. Cobb, Jr., John H. Buchanan, John Quiring , John W. Lango, Jonathan Delafield-Butt, Jorge Luis Nobo, Joseph A. Bracken, S.J., Joseph E. Earley, Sr., Joseph Grange, Juan Vicente Mayoral de Lucas, Judith Jones, Julie A. Nelson, Kipton Jensen, Leemon McHenry, Les Muray, Lieven Decock, Liliana Albertazzi, Luca Gaeta, Luca Vanzago, Manuel Bächtold, Marc Maesschalck, Maria Pachalska , Mark Modak-Truran, Mark R. Dibben, Mary Elizabeth Moore, Max Velmans, Michael Epperson, Michael Fortescue, Michel Weber, Murray Code, Mustafa Ruezgar, Norman Sieroka, Patrick J. Coppock, Paul Custodio Bube, Peter Hare, Peter Simons, Pierfrancesco Basile, Les Muray, Randall E. Auxier, Richard Feist, Robert Castiglione, Robert J.Valenza, Ronny Desmet , Ross L. Stein, Rudolf Windeln, Stephen T. Franklin, Sylviane R. Schwer, T. L. S. Sprigge, Thomas A. F. Kelly, Thomas E. Hosinski, C.S.C., Timothy E. Eastman, Vincent Shen, Volker Peckhaus, William Jay Garland, William T. Myers"

Frankfurt | Paris | Lancaster | New Brunswick

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The Meaning of the Wave Function: In Search of the Ontology of Quantum Mechanics

by Shan Gao

2017

The meaning of the wave function has been a hot topic of debate since the early days of quantum mechanics. Recent years have witnessed a growing interest in this long-standing question. Is the wave function ontic, directly representing a... more

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PhD Dissertation: Cosmophenomenology: The Alterity and Harmony of Consciousness as Quantum Energy

by Dr. Wanyoung E. Kim (PhD, MSc, MA)

2019

ABSTRACT Published 2019 with Atropos Press and Edited in 2021 The upload is a sample, and the full dissertation can be purchased from Barnes and Noble, Amazon, or other vendors online. Golden Lab Bookstore in Queens, New York carries... more

ABSTRACT
Published 2019 with Atropos Press and Edited in 2021
The upload is a sample, and the full dissertation can be purchased from Barnes and Noble, Amazon, or other vendors online. Golden Lab Bookstore in Queens, New York carries this book.

Cosmophenomenology, a term coined by Danish religious philosopher K.E. Løgstrup, is used to describe an approach that extends the traditional phenomenology of Edmund Husserl to include an interrelation between human beings and reality as a whole (nature or Greek Physis) from the standpoint of the universe, rather than simply human-to-human inter-relation. As such, it extends beyond anthropocentric and speciesist views of consciousness. My thesis hinges upon the primordial form of consciousness as quantum energy which has a continuation of existence after a person’s bodily or physical death. The First Thermodynamic Law states that energy neither goes out of being nor comes into being. Consciousness is not dependent on the existence of matter, space, or time, although it interacts with these variables. As a fundamental force, dark energy would retain its form regardless of space or time. I compare the continuation of consciousness after death in the Orch-OR theory of Sir Roger Penrose and Stuart Hameroff with that of the monadology in Leibniz. Both theories concern the inscribing of consciousness as quantum information into small structures called microtubules/monads, which allows this information to pass on into different realms after death. In an infinitely expanding universe not confined by space or time, there would potentially be an infinity of such multiple universes and their included dimensions. I have preceded the discussion of these theories with an explanation of quantum mechanics and the interaction between the dark energy of consciousness and matter in the universe.
My thesis is primarily about metaphysics: the ontology of consciousness. I theorize that consciousness, otherwise known as the soul, is an uncategorized form of quantum energy and life force that is polymorphous, expressible as biophotons as well as waves. The wave is the form consciousness takes up as dark energy or Brahman, while biophotons are atman, the form consciousness takes on in neurons.
Dark energy is surmised by physicists to be Einstein’s cosmological constant because it shapes the relativity of spacetime, dictating the behavior of atoms and light photons and also existing in a void. The mistake of materialists is to equate the 4% of the universe that dark energy literally moves about, to the force itself which constitutes over 70% of the universe. Dark energy and ordinary matter are highly different in constitution, but curiously interact psycho-kinetically. Dark energy is responsible for the very expansion of space between galaxies and smaller objects like brain neurons. In place of classical physics which cannot be used to study quantum energy, I use the approach of cosmophenomenology (cosmological physics and phenomenology) to study the ontology of consciousness.

multiverse theory in the theory of Quantum Immortality, in Chapter Ten.

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The Einstein unified field theory completed: A direct challenge to the basic assumptions, theories and direction of modern and post-modern physics (1st Edition)

by James (Jim) E Beichler

2015

The golden ring to which most physicists aspire is a unified field theory that incorporates all of modern and classical physics. Some scientists and others call this a TOE or ‘theory of everything’, but it is no more than false hubris to... more

The golden ring to which most physicists aspire is a unified field theory that incorporates all of modern and classical physics. Some scientists and others call this a TOE or ‘theory of everything’, but it is no more than false hubris to believe that humans could possibly know and explain everything about the universe at this time. Einstein chased this goal for the last three decades of his life, basing his theoretical research on his general theory of relativity. Meanwhile, the vast majority of scientists supporting the other major accomplishment of the Second Scientific Revolution were investing all of their time and efforts to advancing the quantum theory and their quest has been extremely successful. They originally had no interest in a unified field theory. After Einstein died in 1955, his efforts were all but abandoned because of his philosophical stance against the prevalent Copenhagen Interpretation of quantum theory even though he had been one of quantum theory’s founders. During the 1970s the tables started to turn and quantum theorists became interested in unifying physics, although not from the foundational principles of relativity theory. They claimed that quantum theory was more fundamental than relativity so they began the same quest from a totally different direction despite their claims to be continuing Einstein’s quest. Throughout the development of the ensuing standard quantum model, superstring theory and many other theoretical schemes, quantum theorists have remained resolute in their conviction that the quantum and relativity are mutually incompatible so the quantum must completely do away with and replace relativity once and for all. However, the quantum theory and relativity are not actually incompatible and, in fact, say the some of the same things about the nature of physical reality. When the similarities are fully defined and studied and the basic assumptions behind each of the theories are altered to reflect the similarities instead of the incompatibilities, only then can the point of their compatibility be determined and act as a unifying principle resulting in a completed unified field theory of the type that Einstein once sought. The development of this physical model of reality is not without irony. Not only is the quantum theory incomplete as Einstein argued in EPR, but Einstein’s general relativity is also seriously incomplete and true unification cannot be rendered complete at any level of reality until all the theoretical models being unified are themselves complete.

But the particle cannot be physically reduced to a point, so the measurement taken as the vice closes on tl particle would be the smallest measurable ‘unit of change’ associated with any given experiment. True uncertainty would go to zero when that outer extended boundary of the particle or the ‘unit of change’ is reached. The radius of that boundary would be proportional to h/4z since we would have a situation whe the surface area of the sphere around the origin point of the axes is 4ar*. This would yield the relationship 4nr’ = kh where k is an as yet unspecified constant of proportionality that would differ for each and every experimental situation. Of course, the quantity of h/4z is already, if not coincidentally, expressed in the uncertainty equations. At that point, the outer boundary of the particle or object being measured would b equal to the smallest possible measure by which the particle or object size could be determined real rather than a true quantum which would appear as a dimensionless point at the axis of a space-time diagram representing the quantum or measuring event. On the other hand, as Ax—0 in this case the corresponding uncertainy Ap—infinity by mathematical Reruns J Reins Peet YOR een, eet ey 8 The quantity Ax—0 actually means that the measuring device being used (a high-energy collision experiment) closes in on the outer material limits of the extended object being measured, rather like a vice clamping down tight on a hard round ball (2e. a proton), rather than implying that the particle itself (the target) occupies or is reduced to a point. If the object beng measured could be reduced to a point, then tha point would represent the center of a space-time axis or diagram and no mote, but in reality the particle is extended aorund the pnojnt.

The incomplete nature of the non-Riemannian fix

Reactions of EM and Gravitation to the duality of space ¢ cal = In reality, this duality in the fundamental concept of space and time is or should be reflected in all yhysical theories of nature that involve differentials in space and/or time. The metric represents an -xtended line between two centers of mass or gravity, while the non-symmetric (skew- or anti-symmettic) ortion represents the center of rotation of motion (Clifford’s twist or the later concept of torsion based o1 lis twist) at a point in space. So point and extension differ in the fundamental concept of a rotation. In fact here are two and only two real points or locations in space that naturally emerge in all of physical reality, he centers of mass (gravity) and rotation.

If the velocity ‘v’ goes to zero and the mass ‘m7’ is just falling due toward ‘M’ due to gravity, then the Heaviside term goes to zero and does not contribute at all to gravity. Within a more modern context the equation can be rewritten as

Assume each intersection is a dimensionless point in 3-D space and there is no space between points. At each dimensionless point in 4-D space-time a perpendicular line called an A-line extends into the 5th- D and closes back into the point in 4-D space-time. Each A-line or loop is equal and constant length. Since all of the loops are are of equal size in the 5th-D and parallel to each other, they form a cylinder (A-cylindricity) of sorts in the higher dimension. The 5th-D of space-time is not itself closed with respect to 4-D space-time, but each individual point is closed in the higher dimension with respect to 4-TD snace-time. length and each A-line exited three-dimensional space and returned to that some point in three-dimensional space to form a closed loop.

Furthermore, if the non- or anti-symmettic tensor represents a secondary and unsuspected effect of gravity due to the dualistic nature of space itself, how can electromagnetism and gravity be unified into a single theory? Actually this structure simplifies the unification because gravity-gravnetism is now symmetric with electricity-magnetism. So despite the fact that everything points to a higher fourth dimension of space as well as the (point/extension) duality of space, no one has either attempted or even suspected combining the two methods to unify physics. Yet by recognizing the promise and validity of the hyperspatial model, some scientists have seen it instead as a way t to unify gravity and the quantum. i. re 7 T od as < wt rT>- 1 5 171 . 1 a a ~ Ge In reality, the gravnetic (gravitational) vector potential and the magnetic vector potential A are not intrinsic to the curvature at discrete points in space (in the non-Riemannian-like and tangent space-like fashion), but rather imply that curvature must be extrinsic in a higher dimensional embedding manifold ot space-like structure, thus implying the necessity of a five-dimensional embedding manifold.

The Evolution of Classical Unified Field Theories a a eS “oe Wilson nat Flint sbylously noticed éhe value of the ‘five- dimensional model for incorporating the quantum into relativity very early on in the development of the quantum theory. Wilson even stated that doing so was the only way forward for physics. Yet this strategy for advancing physics has been downplay by almost all other scientists over the past century. How could this have been? Quite simply, this group c English scientists did not accept the Copenhagen Interpretation of the quantum and quantum mechanics. So their work implied that the quantum and relativity could be easily unified if the Copenhagen Interpretation, which puts up synthetic barriers between the quantum and relativity (discrete versus continuity and determinism versus indeterminism) that cannot be easily overcome as well as discourages attempts to do so. So if the Copenhagen Interpretation is disregarded, the unification of the quantum and relativity should not be that difficult although it should be made within a five-dimensional framework of space-time.

These lines would normally remain parallel in the fourth direction and equidistant apart no matter how far they are extended, which is a direct violation of the very concept of the non-Euclidean geometries that were developed to take into account the possibilities presented by the failed parallel postulate and which does nothing to verify the possible physical reality of the three-dimensional space. by-point) was analyzed, but continuity was not ‘proven’ between any individual points in the three- dimensional extension emanating from a line extending in the fourth direction or between individual discrete points and other such points in the three-dimensional extensions. A first step was made though by Einstein’s proving that the physics in every parallel three-dimensional space displaced along the line in the fourth direction of space would be the same, which is also important. It is only necessary now to prove tha discrete points can be used to construct the continuity of three-dimensional space. © Wee gloss ee oes wee 2 lowe = 2 eee mes Bee esol ve eee wee ela ws lee cm BK Tee eee gee chee Poxeeeet: hie ees ll

Each point is equidistant from its contiguous neighbor point

and related theories. This problem is ubiquitous such that all of physics and mathematics suffers from this same problem in one form or another, but it is especially crucial for the standard model of the quantum, which is basically a non-geometrical theory that defaults to a Euclidean flat pseudo-geometrical structure for space-time.

* 4 . The halo forms around the galaxy to maintain three-dimensional integrity of the whole and continuity with the rest of the universe. But only local variations from the spherical universe are allowed, thus we ‘observe’ galaxies as part of our three-dimensional surface with the added ‘halos’. cy So in essence, or perhaps ‘quintessence’, when the matter in the galactic rim extends into the fourth dimension it is gaining DE in the form of inertial momentum (my) without the corresponding gain in mass from the universe as a whole as represented by the global curvature. DE, or the gravitational vector potential, exists everywhere in empty space, but when it is bound or restricted inside a particle it becomes or rather ‘is’ active inertia. However, when the DE is constrained or bound into a material particle by spatial cutvature (under quantum conditions) it becomes ot ‘is’ passive inertia. Within one context, DE supplies the extra speed to the stars and systems in the galactic rim, but within another it is extra inertia because it is constrained within the body of the galaxy (local curvature relative to global curvature) by the matter in the

The halo is like a shadow or mirror image of the galactic core due to the centrifugal force (equal and opposite) of the gravity of the rest of the universe represented by This dependence is exactly what is observed as shown in the graph below. It should be quite clear from this equation that the contribution of the global curvature to the total force in the form of the kinetic energy (applied dark energy) increases as a function of the radius and the slowing of gravitationally derived speed from the central body or local curvature (gravitational field). As each star or star system is added to the galaxy and orbits the galactic core, it has a component of gravitationally derived velocity as well as an extra component that corresponds to the four-dimensionality of the galactic plane. This dependence is exactly what is observed as shown in the graph below. The curves representing the scalar and vector potential contributions to energy add to give the speed curve for the Andromeda galaxy, as shown. The kinetic energy gained from the vector potential graphs as a straight line running from the zero point (galactic center) to the edge of the galactic rim, supplying exactly the kinetic energy needed to explain the constant speeds of stars and star systems around the galactic core. Nearer the galactic core, the vector potential correction to speed is masked or dominated by the stronger

Given the calculated value of the halo curvature, the amount of curvature at the center of the galaxy could then be found by simple triangulation.

No anti-particles (oppositely directed bumps and hills) are created while the creation of protons and electrons slows expansion enough to end the inflationary period

oat causing a wake at its forefront. The wake would contribute increased the inertia of the particle (the nertial points absorbed by the particle would raise the overall internal that constitutes the particle higher und steeper in the fourth dimension) as each point in the wake (external space) is overrun by the advancing yarticle/boat. This would be similar to Higgs’ analogy for describing how a Higgs boson is transferred to a sarticle from the Higgs field to increase the mass of the particle while the particle moves point-by-point through space.

The quantum nature of the universe is reflected in the first equation as a fundamental property of the space-time continuum, but exactly how to apply the quantum concept to the single field and space-time curvature still needs some explanation. Klein had the right idea when he tried to quantize Kaluza’s five- dimensional extension of general relativity. If you quantize the extension along the fifth direction of space-

ime (or the fourth direction of space), then the lower four dimensions of space-time (or three dimensions of space) will also be quantized. However, since Klein was working with the Kaluza model, which was vast »ver-restricted in its application of a higher embedding geometry, Klein’s model was subsequently over- estricted. The fact that what happens along the extra dimension of space also affects the lower three limensions of space is also implied in the Einstein-Bergmann model of Kaluza’s work, although they did 1ot apply this to the quantum as did Klein. Instead, Einstein added a footnote that he and Rosen had ittempted to explain particles, unsuccessfully, on the basis of the Einstein-Rosen Bridge. If instead, we go back to the Heaviside equation or its modern equivalent, quantization becomes a very ~~ “ am The implications of this simple quantization are quite profound. First of all, the dark matter halo round galaxies, represented by the second term in the equation, can now be viewed as a wave interactio: superposition of outgoing quantized gravity waves from the core mass due to the changes in velocity of 1 orbiting masses interacting with the incoming gravity wave (represented by I in “/sec”’ units). In this cas he quantity TP could be likened to David Bohm’s concept of the quantum potential field which is a yackeround field consisting of all possible quantum waves. Secondly, this equation indicates that the stat sravity view of F = mg cannot be quantized in any normal way within the three-dimensional space wher 10rmal gravity acts. This implies that gravity can only be quantized within the higher embedding dimenst “rom a purely static point-of-view, normal gravity is purely structural in our world while the quantum mmediately invokes an interaction which is wholly dynamical and non-structural except in the fact that i changes structure through the interaction.

Each loop is not connected to the other loops outside of the normal three-dimensional point-to-point connection mistakenly assumed and thus afforded by the intrinsic nature of the space-time continuum. In other words, Kaluza utilized a higher embedding dimension, but mysteriously retained the intrinsic nature of space-time curvature. Thus he used a fundamentally flawed mixed intrinsic/extrinsic model of physical reality. Klein’s idea that quantification in the fifth-direction of space will quantize the lower four- dimensional space-time is valid, but only under the newly specified geometrical conditions that render our normal three-dimensional space real. Quantizing surfaces point-by-point into the single field

Each intersection represents a dimensionless point in 3-D space and there is no space between points

The geometrical points in space or space-time about which the quantum would then be considered action or actionable points in space around which the fundamental unit of change determined the quantized three- dimensional ‘sheet’ that is our experiential material world.

Since the higher dimension is extended to at least as great a distance as the other three dimensions of space (the Einstein radius of the universe), the final quantum number would be nearly infinity in this case. The normal laws and theories of physics that apply in three-dimensional space would be strictly limited to the three-dimensional ‘sheets’. However, the only three-dimensional ‘sheet’ that is characterized by curvature is the primary or fundamental ‘sheet’ (quantum ground state of n=1) so while the theories and laws of physics influence only three-dimensional extension within the ‘sheets’, the laws must be modified for non-ground This quantizes the space-time curvature and unifies the space-time continuum of general relativity and the quantum world. The fundamental ‘sheet’ where the single field is on average densest would account for the n=1 quantum state or ground state of a static universe defined by its static curvature, T,, = G,,. However, higher quantum states can be attained dynamically on a point-by-point basis. Higher quantum states, for n=2 to n = nearly infinity, would appear like pages in a book stacked one on top of the other both above and below the primary n=1 ‘sheet’.

This is why Kaluza’s cut-transformation which is the mathematical equivalent to cutting a splice across the three-dimensional ‘sheet’ perpendicular to the fourth direction (and thus around the particles three- dimensional boundary) yields electromagnetism. a strain in the three-dimensional space surrounding the particle that science observes and interprets as the electrical field.

Whereas points through the surface from point-to-point between such bound like particles would be quite weak even though it transmits the point-by-point ‘stress’ of stretching in the higher expanded fourth dimension of space to the outer surface of the particle in three-dimension space. Obviously, these two internal forces that are the geometrical or structural equivalents to the outer forces of strains associated with the gravity and electric fields are just the strong nuclear force (or field) and the weak nuclear force (or field). This structural switch of roles, whereby the external weak force (gravity) becomes the internal strong force and vice versa, explains exactly how and why the internal weak nuclear force has become associated with the stronger external force of electricity and recast as the electro-weak force in earlier unification schemes. However, a great deal more physics is now implied by the geometrical structure of space-time curvature. Within the particle, the surface of curvature and the point-by-point stretching stress due to expansion in the fourth direction change roles in a sense. The internal particle ‘force’ due to the surface tension becomes by far the stronger of the two internal particles ‘forces’. While a particle is outwardly spherical in three-dimensional space, it is inwardly three-dimensional surface an exponentially curved in the fourth direction of space which would form a strong surface to surface ‘force’ of attraction with another like patticle.

in free space these four-dimensional extensions become the magnetic vector potentials, Dark Energy and shotons depending on the characteristics of any given situation, but when packaged under the metric curvature surface they become inertia and the stress source of the magnetic field strength that manifests in ither moving or stationary particles. If a frve-dimensional space-time continuum representing the single ield is used to interpret Einstein’s equation then no additional term is necessary for Dark Matter, since it 1: ncorporated into the anti-symmetrical portion of the complex tensor. The additional anti-symmetric term iso results in a ‘twist’ in each dimensionless point in three-dimensional space as opposed to the symmetric erm of the tensor which represents the normal Riemannian metric or extension-based geometry of space- ime curvature in the higher embedding dimension of space. vs oa | te, ie ye oF sas a a Y a | te, a cf TT. 1m . Pa 7 The additional or anti-symmetric term — Einstein called it a non-symmetric form in his final attempt to develop a unified field theory — represents a point-geometry as opposed to the normal Riemannian metric, which is an extension-geometry. This point-geometty can account for Dark Energy, inertia, the magnetic vector potential and photons, all of which are represented as points in three-dimensional space extended in the fourth dimension of space as one-dimensional lines (Kaluza’s A-lines).

we Each time the curvature in the fourth direction of space drops by the ‘effective width’ of three-dimensional space (it experiences a quantum drop of ryx or about r,/137) such an equilibrium position is established. This structure turns the continuously sloping curvature into energy ‘steps’ on which the electrons move up and down the curvature as they absorb and emit energy in the form of electromagnetic waves. These equilibrium positions occur at distances of n°R, from the center of the nucleus where n=1, 2, .3 and so on. The quantity R, is the Bohr radius of the hydrogen atom and is equivalent to h/2xm,ca or 5.29 x 107" meters. These orbital positions or steps end when the curvature from the nucleus merges with the collective The prescribed — allowed or restricted — electron orbits already exist structurally in the space (along the urvatute) surrounding the nucleus before the electron jumps into (or out of) another orbital position. In ne sense the positions are etched into the curvature in the local space near nuclei by the quantum onditions of existence, but in another sense they are the product of a physical negotiation between the ucleus and the orbiting electrons. Otherwise, they are virtual until an electron falls into any particular orbit. ‘his point would never have been made with regard to previous theories or theoretical models of the orbits, yhich Bohr only defined after the fact by electromagnetic and quantum considerations alone. The positions where the orbits occur are gravitational (curvature) equilibrium positions between the en |e | a ae ae a: cn fe) a ae ae a) ee ae ee oe Te ae en (i rn i es) erie, a ae

This equation readily implies a quantum structure for the orbits such that

The ‘sheet’ which serves as our common three-dimensional space is represented by principle quantum number one. The ‘sheet’ curves spherically in the macroscopic domain to render the Riemannian curvature of our three-dimensional universe as a whole as proposed by general relativity, while there are three basic forms of curvature in the smallest possible local portions of the ‘sheet’ at the quantum level. They define the primary elementary particles.

Under those special conditions where a gamma ray of the correct energy comes close to a nucleus (or other object corresponding to sharply curved space) and actually surrounds the nucleus (touches all sides of the nucleus simultaneously) the quantum stress in the space-time continuum creates the particle and its anti- particle. Of course the last condition is having the proper energy to create the curvature in the ‘sheet’, so curvature packages energy in a sense. This process occurs because the ‘photon’ which is equivalent to an ‘A. line’ or longitudinal portion of the light wave cannot exist at two different places in three-dimensional space simultaneously, such as both sides of the nucleus simultaneously. So, pair production could not have occutred before the inflationary period ended with the creation of elementary particles and can only occur afterwards when the proper quantum and geometrical conditions are met. vn wal El Sd a | - fe = Pe og 7 * oe 7 <: 1 , 2 Wa ca | Pe lost as gamma rays that have no curvature. The annihilation works like opposing wave pulses traveling in opposite directions along a single tightly stretched string. The only difference is that the two pulses in the string cancel each other only momentarily and the energy that they carry continues as before and the pulses reemerge after the collision still traveling as they were before they collided. Annihilation is the same as the oppositely directed pulses cancelling out, however, unlike the pulses in the string the particles covert to energy when they make contact and thus disappear. Pair production creatino anti-narticle/narticle naires onerates in the onnosite wav and could not have

The collision thus results in an inward pressure of -1/3 along the direction of motion and outward stresses of +2/3 and +2/3 of the electrical charge along the remaining two dimensions or directions of space inside the target proton. This configuration thus accounts for the —1/3, +2/3 and +2/3 electrical charge of ‘quarks’ from which the proton is constructed according to the Standard Model. This dimensional model of ‘quarks’ also explains why ‘quarks’ can never be found outside of the particles and nuclei in which they reside, solving one of the major dilemmas associated with ‘quark’ theory. TH: 2d so anche: bon ldbin “SAaandél? Bimdel weedbizre Geneiinwe méetendiimnd wl the donde ohEo I ole rteien| -~-Lhnéene

Yet how can this be so? Quite beyond the obvious question of what is a one-dimensional string and how could it vibrate (?) within the one dimension that it supposedly occupies, the Calabi-Yau bundles fill ‘discrete’ points in space for which no simple connection or connecting property has ever been defined. That is why there are literally millions upon millions of possible different superstring theories. You can put

The distance does not really seem to matter, big or small, since its only purpose is to weaken the effect of the gravitons traveling between the two branes. The bulk seems to have no other purpose than the convenience it affords the model by accounting ‘or the distance between the two branes. The bulk seems to be no more than a mathematical device that w only mandated to justify the distance between the two branes. The branes themselves have no other featur han the fact that they are platforms upon which to place material reality, at least in the case of the primary ot real-world brane. Unlike a normal membrane in three-dimensional space, the branes seem to be one- sided and the single side of each brane is facing the other at a constant distance. In one version of the Randall-Sundrum (RS) Braneworld, dubbed RS-1, the branes are a few centimeters apart, while they are -xtremely distant, but not quite infinitely far apart, in RS-2. In still another version, the RS-1 branes are a rety large distance from one another and infinitely far apart in RS-2.

The bulk can then be closed and defined as a single-polar Riemannian embedding manifold. If curvature is then returned to the primary ‘sheet’, the Randall-Sundrum model corresponds quite nicely with the single field model which has been developed within this paper. This correlation is important because it demonstrates that other scientists, even when they are working from false premises, are slowly approaching the same model as here proposed. ptt 17 wine oe

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Electromagnetic Theory of Everything

by George Rajna

2015

This paper explains the magnetic effect of the electric current from the observed effects of the accelerating electrons, causing naturally the experienced changes of the electric field potential along the electric wire. The accelerating... more

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Qft-schwartz

by fjsdkl fdjksl

This is an example of the spin-statistics theorem. I think it’s the simplest way to see the connection between anti-symmetrization and Lorentz invariance. This just indicates that the boosts are not unitary transformations. To get something new, recall that for the Pauli matrices, 0; and a3 are real, and o2 is imaginary

Note that this doesn’t depend on what n x is, this is just a phase space integral. There is no mention of temperature or of equilibrium — it is true for any values of nx.

Note that these matrices do not commute, so the order we do the rotations and boosts is important. We will only very rarely need an actual matrix representation of the group elements like this, but it is helpful to see it. Nuv 1s known as the Minkoswki metric. So Lorentz transformations preserve the Minkowskian inner pro- pv duct

Now assume ¢ > 0, then we pick up the pole at k = — ie. For e~’*” we close the contour up and miss th pole, so this term gives zero. For e’*” we close the contour down and get We will use this implicitly all the time. When a field theorist thinks “box” he thinks “— k” If you are not familiar with contour integration, please see Hitoshi Murayama’s notes on Contour Inte- grals, which I have made available. We can also reproduce this result by taking the limit m— 0 of a mas- sive vector boson.

This is just good-old time-independent perturbation theory written in a funny language of propagators. So you see that we have been using Green’s functions and propagators to do perturbation theory all along. We call this old-fashioned perturbation theory. we have added an ie to the denominator to make sure there aren’t any unwanted singularities. It is not important for now. In practice, this E — Hp means take the difference between the energy of the excited state and the energy of the ground state.

Let’s try another example: an electron scattering off another electron. In this case, the states are free elec- trons, so they are momentum eigenstates and we can now be exact about the amplitudes. The diagram for this process is Say the intermediate photon has energy Fy, and the incoming electrons have energies #, and EF and the outgoing electrons have energies F3 and Ey. We need to calculate the transition matrix elements 5.5 Coulomb’s law from OFPT

We have dropped the ie, which is fine as long as s,t,u are not equal to m?. For that to happen, the inter- mediate scalar would have to go on-shell in one of the diagrams, which is a degenerate situation, usually contributing only to 1 in the S-matrix. The ie’s will be necessary for loops, but in tree-level diagrams you can pretty much ignore them.

s,t and wu are great because they are Lorentz invariant. So we compute M?(s,t, u) in the CM frame, and then we can easily find out what it is in any other frame, for example the frame of the lab in which we are doing the experiment. So you see s,t,u can be very useful and we will use them a lot! As we say in the previous example, s,t and u correspond to particular diagrams where the propagator has invariant mass s, t or u. So we say s-channel for annihilation diagrams. In these the intermediate state has pe, =s>0. The t- and u- channels to scattering diagrams

For the classical case, we just took J, = 5,06°)(a), to simulate a point charge. For the Feynman diagran case, we replaced J by some interaction J =e@A¢, so that the point charge is now thought of like a scala: field, which is the non-relativistic version of an electron. Diagrammatically I think it is helpful also to see more directly why the Feynman rules and the classical perturbatior theory are the same. Starting with a Lagrangian with a cubic interaction In classical field theory, we found a perturbation expansion that looked like

where 6; are 6 numbers, corresponding to the 6 angles Ary, 9x2, Oyz, Gry, Brz, Byz and Aj are called genera- tors. For the regular, vector, representation above, the generators are The group itself is a mathematical object independent of any particular representation. To extract the group away from its representations, it is easiest to look at infinitesimal transformations. We can always write these group elements as

Non-unitary representations of the Lorentz group are ok for fields, but not for particles. Particles must transform under unitary representations of the Poincare group, so that we can construct physical ampli- tudes with them. As Wigner showed, and we discussed when we introduced gauge invariance, unitary rep- resentations and are characterized by mass and spin. This spin indicates a representation of the 3D rota- tion group, which is unitary. Since the group element is the exponential of the generator A =e, unitarity requires that \} = , that is, that A be Hermetian. Looking back at our explicit 4D representation for the Lorentz generators, we see that the rotations

In the Weyl representation, the Lorentz generators are These are block diagonal. These are the same generators we used for the e 0) and (0, ) representations above. It makes it clear that the Dirac representation is reducible, it is the sum of a left-handed and a right-handed spinor representation. - ra. oa % , gow . 47 nro.

That is, we rotate 360 degrees and we’re back to where we started. How do we exponentiate a matrix? The standard trick is to first diagonalizing it with a unitary transfor- mation, do the rotation, then transform back. This unitary transformation is like choosing a direction, except it is purely mathematical as the direction must be complex! Se a

Thus a 27 raation does not bring us back where we started! If we rotate by 47 it would. So we say spinors are spin > . What does | this mean physically? I have no idea. There are plenty of physical conse- quences of arsiec being spin 5 =, but this business of rotating by 27 is not actually a physical thing you can do. As an aside, note that the factor of 2 is determined by the normalization of the matrices, which is set by the Lie Algebra. For each representation by itself, this would be arbitrary, but it is important fo1 expressions which combine the representations to be invariant.

We have chosen a normalization here, which amounts to

where the square root of a matrix means diagonalize it and then take the square root. In practice, we will always pick p along the z axis, so we don’t really need to know how to make sense of these formulas. But they are useful because they are explicitly Lorentz covariant so we can manipulate them cleanly.

We would like to calculate the unpolarized cross-section. There are two diagrams:

This is the Klein-Nishina formula. This is first calculated by Klein and Nishina in 1929 and was one of the first tests of QCD. Tx Athaw waren hla Now we want to integrate over w’ to enforce the energy constraint E’ + w’=m-+w. But we have to be a little careful because E’ and w are already constrained by the electron’s on-shell condition The delta function fixes the 3-momenta when we integrate over d°p4, leaving the energy constraint

We can also generalize it for many p;, so that ap? = p;a;jp; = PAP, with A a matrix. If we diagonaliz A then the integral is just a product of integrals over the p;, so we just get the product of all the factor: above. That is, 14.2 Gaussian integrals

Figure 15.1. Casimir energy function f(a)= 2a| Evor(a) - M71] for a hard cutoff A=1, with L=1000. The line is — eh, Thanks to David Simmons-Duffin for this plot. Putting back in the fh and c, we found that the Casimir force in 1 dimension is

One of the best tricks is the Feynman Parameter trick. Here’s a bunch of integrals that we will need (see Peskin and Schroeder for the derivations) The reason these are useful is that they let us complete the square in the denominator 16.2 Wick Rotations A nice way to do Minkowski integrals, like the ones above, is to observe that once the te factors are put in, they look like Regularization Schemes and Tricks

and so on. Lhese formulas are all derived 1n section 0.9 OF reskin and ocnroeder. The Wick rotation can only be justified if the integral is convergent. Well, if it’s not convergent, it is useless to Wick rotate anyway, since you will still get infinity. But the technical problem is the divergence can indicate the presence of new poles that invalidate the contour rotation. Keep in mind that the Wick rotation is just a trick to do these integrals. There is nothing physical about it.

If we insert our scalar bubble in the middle, we get If this expression looks a little funny, keep in mind that g is not a number in ¢° theory but has dimen- sions of ,/mass. This actually makes ¢° a little more confusing than QED, but not insurmountably so. 2 Let’s just simplify things by writing the whole thing in terms a new t-dependent variable g? = = which is dimensionless. Then _. 1 ... fF Oo

In d dimensions (using k#k” > Sige), the integral becomes It looks like this integral is much more badly divergent than the ¢° theory — it is now quadratically instead of logarithmically divergent. That is, if we cut off at k = A we will get something proportional to A?. This is not a problem — the same thing happened for the Casimir energy, where we saw we could reg- ulate with a heat-kernel regulator or a zeta-function regulator. Instead, we will use dimension regulariza- tion, which shows nicely why the integral isn’t as badly divergent as it seems.

Note that we moved the reference value of the charge from p= 0 to p= me. This is natural, because the simple log dependence in this formula comes from the limit p>> m_-, so near p= me we should match on to the exact formula with the p/m_ corrections. In any case, the difference between the effective charge at p=M™Me and p=0 is very small, they are both e = /4ra ~ 0.3 up to a? corrections. We will eventually re- derive this formula for the effective charge using the renormalization group, which is a more general method. But the Landau pole singularity is unavoidable in QED. We can actually include higher order corrections to the effective electric charge without much more work We now know the result of the whole series 17.5.3 running coupling

This result was first obtained by Julian Schwinger in 1948. This calculation was critically important his- torically for convincing people that the loops in QED had physical consequences. At the time of Schwinger’s calculation, the best measurement was ge = 2.00236 + 0.00006 which is in remarkable agree- ment with Schwinger’s answer.

Actually, we only computed the p?g” part of the expression. Peskin and Schroeder compute the rest. In any case, we could have guessed the form by the Ward identity. Note that So that this is a projector. For simplicity, we will just drop the p“p” terms, since we can always put them back in the end by asking that the Ward identity be restored.

F, on the other hand controls the gross interactions of the electron with the photon. It is the part that leads to Coulomb’s law. Thus the electric charge measured in Coulomb’s law is proportional to erF{(0). So we have to set F\(0)=1. That is, we demand

Or with the current, simply the current matrix elements G7 with an extra photon. The graphs are We will do the loops first, then the real emission graphs, and then show that we can take m1 — 0 after then are combined into the full cross section da(ete- > ut u~(+7)). We take m,.=™,, for simplicity. In addition to the loop corrections to the 4-point function, to cancel the infrared divergences, we will need to calculate also real emission graphs. These are the tree level contributions to a 5-point function If you find this operator language confusing, don’t worry about it. In the end, we will have calculated the full ete~ — pty. The current language just lets us break the problem into pieces, so we can see what’s important at each stage, but if you prefer to think about doing it all at once, go right ahead!

What about 2-loop and higher loop 1PI graphs? We can show they are finite by induction. When we add a loop, we can add either a photon propagator or a fermion propagator. If we add an internal photon propagator, it must split two fermion lines, so the new loop has two additional fermion propagators as well. By the definition of 1PI, loop momenta go icing all internal lines. So for k >> p;, where p; is any external momentum, each internal line will get + — or =. So the matrix element gets modified to 22.2.3 renormalizability to all orders

So we find a (divergent) shift in g proportional to the mass of the fermion M. This is fine if M~ g, but if parametrically it’s really weird. As M gets larger, the correction grows. That means that the theory is sensitive to scales much larger than the scale associated with g. So, There is a radiative correction from the loop of ¢. This is UV finite, proportional to g? and not particu- larly interesting. A more important radiative correction comes from the loop of the fermion.

We don’t know exactly what the interaction Hamiltonian H;,; is, but it’s got to have something to con- nect the initial and final atomic states and some creation operator or annihilation operator to create the photon. So it must look like

We say that the Lorentz transformations which are continuously connected to the identity transforma- tion are Proper Othonchronous Lorentz transformations. They can be characterized by Obviously time = (t,0,0,0) is timelike and (0,x,0,0) is spacelike. Whether something is timelike or space- like is preserved under Lorentz transformations since the norm is preserved. If it’s norm is zero we say it is lightlike

This is the same as the free solutions to Maxwell’s equations, equation (3.23) but instead of a, being a function, it is now the creation/annihilation operator for that mode. The factor of /2w; has been added for later convenience, and in fact guarantees the A(x) is Lorentz invariant. The connection with Eq. (3.23) should be considered only suggestive, and this taken as the definition of an operator A(x) constructed from the creation and annihilation operators a, and aj. Now let’s get a little more precise about what this Hamiltonian means. The natural generalization of

Here dII is the region of final state momenta we are looking at. It is proportional to the product of the differential momentum d?p; of each final state and must integrate to 1. So

The «x integral gives a 5°)(p + k) in the first term and a 5@)(p — k) in the second term. Either way, it forces Wy =Wpy and so we get and we have an expression for ap(0o) — ap(— 00). Note that all the initial states have a!’s and — oo’s and P the final states have aj,s and + oo’s. This leads to a very important trick. We can rewrite the S-matrix element as

Let’s warm up by calculating this time-ordered product in the free theory. We start with the free field Wnoratnr

8.1.1 perturbative solution for Dyson’s series

The Dirac equation follows from this Lagrangian by the equations of motion It is in this sense that people sometimes say the Dirac equation is the square-root of the Klein-Gordon equation. a a a ee

Next, let’s calculate the propagator for a Dirac spinor. 12.3. Dirac Propagator Where as always the energy is always positive and determined by the 3-momentum w, = \/p?+m?. Note the convention that o(a) gets both u and v and w gets @ and ©. It might have made sense to use u and U in w, but since when we found the free states, v were the negative frequency solution, this way of assigning u and v to 7 and w is consistent. This is just a convention.

you will use this last one a lot! You can remember the signs because adjacent indices give + and the other one gives —. Before begging the QED calculations, let’s derive some useful identities about y matrices. We will often need to take traces of products of y matrices. These can be done simply using the cyclic property of the trace

Since the particles are not all of the same mass, we have to use the more general formula for the differen- tial ernee eactinn

As far as QED is concerned, a proton and a muon are the same thing, up to the charge, which gets squared anyway. So let’s start with e~z~ ~ ep. The amplitude is given by a t-channel diagram

Now let’s take the limit m, >> m- to get the Rutherford answer, but including relativistic corrections. This means we can treat the proton mass as infinite, but have to treat the electron mass as finite to go from the non-relativistic to the relativistic limit. Then the center of mass frame is roughly the protons rest frame, so

We want to calculate M?, which includes the 4 terms, from the t-channel and u-channel diagrams squared and their cross term. Let’s just evaluate one piece, in the high energy limit, to see what’s involved. Take 13.4.3 t-channel term

This has a singularity at 0=7a. That is where the photon and electron bounce off each other and go back- wards. The mass of the electron cuts off the singularity, but still the scattering amplitude gets very large as 9~7. The cross section is 13.4.6 high-energy behavior

So this is a nice way of calculating time-ordered products. 14.6.1 Current shorthand Well, the left hand side doesn’t care whether I write ®(21)®(x%2) or ®(a#2)®(x1), since these are classical fields. So what would determine what order I write the fields on the right? We see it must be something that makes the fields effectively commute, like the time-ordering operator. We’ll do another check once we get a a little more experience playing with the path integral. ae a -— /< of; Vem ox oF

I’m not sure how legitimate this is. It’s really hard to define the path integral mathematically, but at least this convergence factor sounds believable. In any case, we knew we had to get the time-ordered product out, so this is the correct answer.

We can also compute higher order products 14.7.1 4-point function

- - So Fermionic path integrals seem like they would be really hard and confusing, but in the end they are quite simple and you can mostly just forget about the fact that there this a lot of weird mathematics going into them. 14.12 Schwinger-Dyson equations An important feature of the path integral is that it tells us how the classical equations of motion are mod- ified in the quantum theory. These are known as Schwinger-Dyson equations. Consider the correlation function of w (x1)w(ax9):

The important point is that this only depends on f(0), that is, the propertires of the energy spectrum near w~ 0, i.e. in the infrared. So,

Now the p term should vanish by the Ward identity. This is easy to see because A and the integral mea- sure are symmetric in 7+ y but the p” term is antisymmetric. And we don’t care about the 7“ term for the magnetic moment, Fb.

The real emission graphs are easy to compute. However, the phase space integrals with a massive photor can be somewhat tedious. This analysis is taken from Rick Field’s book “Applications of perturbative QCD”. With a massive photon, this gets modified. There are both explicit factors of m. that come into the matrix elements, but also factors of m. in the phase space integrals to make a cross section. The result is 20.4 Real-emission: Final state radiation

Instead, it is conventional to add the IR divergence into your subtraction terms so that What are we to make of the / integral, which doesn’t have any structure in it besides the infinity? If we wick rotate and do the phase space integral, we find

As a rough estimate, the total cross section is at least as big as the cross section for forward scat- tering,. So, The s channel exchange diagram gives

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Magnetic Universe Theory A Top-Down Review of Phases of Magnetic Theory Development, with accompanying historiography and comparison with Unified/Aether Field Theories including EPEMC

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My God, He Plays Dice! How Albert Einstein Invented Most Of Quantum Mechanics

by Bob Doyle

2019, My God, He Plays Dice! How Albert Einstein Invented Most Of Quantum Mechanics

Is it possible that the most famous critic of quantum mechanics actually invented most of its fundamentally important concepts? In his 1905 Brownian motion paper, Einstein quantized matter, proving the existence of atoms. His... more

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Advance Quantum physics

by dan xu

Figure 1.1: Basi c setup of scattering experiments. Target scattering (left): a beam of elec- tromagnetic radiation (or massive particles) characterized by a set of quantum numbers k and energy ¢(k) responds by emi is emitted by a source (9) and directed onto a target sample. The sample tting radiation according to some distribution P(k’, e’(k’)’), which is, in turn, recorded by a detector (D). Notice that the emitted radiation can, but need not, contain the same type o f particles as the source radiation. For example, light quanta may trigger the emission of electrons (photoemission spectroscopy). Collider scattering (right): two particle beams generated by sources S and S’, respectively, collide in a scattering region. The detector, placed outside the beam axes, samples the products (particles and/or radiation) generated in the scattering process.

1.3 Differential cross section (definition)

is infinitely extended in space. This does not sit comfortably with the intuitive picture of localized ‘particles’ scattering off a target. Formally, a particle is described by a quantum mechanical wave packet, i.e. a spatially localized superposition of momentum eigenstates. Once the scattering theory of individual plane wave eigenstates of Ho has been developed the scattering of wave packets may, hence, be constructed by superposition principles (cf. M.L. Goldberger and K.M. Watson, Collision Theory, Chapter 3 (New York: John Wiley, 1964); R.G. Newton, Scattering Theory of Waves and Particles, Chapter 6 (New York: McGraw-Hill, 1966).) However, the complications that come with this after-step can be avoided as long as we restrict ourselves to the consideration of wave packets of (near) definite momentum p and spatial extension R much larger than the characteristic extension Ry of the scattering region. ——) 1 = oe er re er es er 7 crow f ef rm a ok “1 1 1

Figure 1.2: On the length scales relevant to a wave package scattering process. Discussion, see text. such that upon removal of the scattering potential V > Oit smoothly reduces to a solution of the ‘unperturbed’ equation Hy|¢) = E|d) of the same energy. To understand the rational behind this agenda, imagine the scattering process from the perspective of the incoming parti- cles (states). Upon approaching the scattering region, the latter effectively see the emergence (switching on) of a scattering potential, and energy conservation requires that they smoothly evolve into scattering states, i.e. solutions of the full equation at the same energy. A formal solution to this problem may be proposed as follows:

The final one-dimensional integral is tabulated and the result readily gets us to (1.24). (Readers familiar with the theory of complex functions may find it instructive to compute the integral by the theorem of residues.)

Let us, then, consider the Lippmann-Schwinger equation for the retarded scattering state, Eq. (1.7), in a real space representation:

turns out to be independent of angles, i.e. the scattering off a d-potential is purely isotropic

a i Finally, notice how the Yukawa scattering amplitude illustrates the general principles on scattering wavelength 27/k vs. potential extension Ry ~ ji! discussed above. The first panel in the figure above shows a plot of the Yukawa potential in the xz plane, in arbitrary units, where z is the direction of the incident beam. The second, third, and fourth panel, resp., then show the intensity of the scattered wave amplitude, amaelt(k, k’)|? (again in arbitrary units.) Values r < k~! are blocked out, as the asymptotic spherical wave form of the

Comparison with the definition of the scattering amplitude, Eq. (1.26) then leads to the identification

An increase in the scattering potential may lead to a reduced, or ever vanishing scattering cross section.

i.e. a state first evolved to the infinite future under the free dynamics, and then evolved back under the full dynamics. We now claim that the physical information on the scattering process is encoded in the matrix element

2.1 Second quantized model Hamiltonians: two examples

The Hamiltonian defined by Eqs. (2.30), (2.31) (2.32), and (2.33) provides the formal basis for the description of many light/matter interaction phenomena. For example, the quantum theory of the laser can be formulated in this description. In this section, we will explore the physics of light/matter interaction on a simple phenomenon: when an atom is excited by a coherent light field, it will cyclically absorb and emit photons. The ensuing oscillatory emission profiles are called Rabi oscillations. They play a fundamental role in many phenomena of quantum optics.

Now, the ‘natural’ matrix U to choose in the present context follows from the familiar iso- morphy of the Lie algebras so(3) and su(2) of the groups SO(3) and SU(2), resp. The correspondence between the two algebras is expressed by the table CHAPTER 3. RELATIVISTIC QUANTUM MECHANICS

Finally, interpreting p,, as eigenvalues of linear operators p,, it may be written as (3.22). The historical derivation of this equation, different from the one discussed here, is reviewed in the info block below. The construction above is different from the historical derivation of the Dirac equation. In fact, Dirac’s original derivation is much shorter, and rather elegant at that. However the price to be payed is that, unlike with the derivation given above, the physical principles behind the mathematical structure of the equation remain opaque. Still, it is rewarding to recapitulate Dirac’s original line of arguments: For the reasons outlined in section 3.2, Dirac was after an equation linear in the four-momentum operator. He thus started from an ansatz

where in the second equality, we added 0 = im —im. Unlike with the Klein-Gordon equation the Dirac density 7° = wy°w = wiw is positive, i.e. our problem of negativ particle densities is gone! 3.4.2 Dirac’s way out

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136253314-physics-of-vibration-and-waves-solutions-pain-141001200006-phpapp01

by sanury nury

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String Theory

by einstein hafis

with Daniel Robbins, PhD in Physics Learn: • The basic concepts of this controversial theory • How string theory builds on physics concepts • The different viewpoints in the field • String theory's physical implications

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Calendars with Olympiad display and eclipse prediction on the Antikythera Mechanism

by Tony Freeth and

2008, Nature

Figure 1| The ‘instruction manual’. Previously identified inscriptions reveal remnants of an instruction manual, describing the Mechanism’s cycles, dials and functions, as seen in two examples from the Mechanism’s back door. a, Polynomial texture mapping of fragment 19 shows fine surface detail, with text about 2 mm high. Highlighted in red are “76 years, 19 years” for the Callippic and Metonic cycles (Supplementary Box 1), and “223”, for the Saros cycle (Supplementary Box 2). b, X-ray CT of fragment E reveals text about 2 mm high. Highlighted are “on the spiral subdivisions 235”, confirming the Metonic dial (Supplementary Box 1); and “excluded days 2...”, the final “K” presumably standing for the number 20—part of the 22 excluded days round each of the five turns of the Metonic calendar—though “B” that would complete “KB” (22) remains speculative. The month names and order in Greek regional calendars vary widely'®. The months on the Mechanism belong to one of the Dorian family of calendars, with practically a complete match (11 or 12 names) with Illyria and Epirus in northwestern Greece and with Corcyra (Corfu)—all Corinthian colonies. The calendars of Corinth and its other important colonial foundation, Syracuse, are poorly

documented. Seven of the Mechanism’s months, however, coincide in both name and sequence with the calendar of Tauromenion in Sicily, which was probably originated by settlers from Syracuse in the fourth century Bc. The Mechanism’s calendar is thus from Corinth or one of its colonies. Moreover, the estimated date of the Mechanism falls after the Roman devastation of Corinth (146 Bc) and Epirus

Figure 4 | The glyphs. A selection of the 18 known eclipse prediction glyphs (Supplementary Notes 4). Left, the raw data; X-ray CT for glyphs 20, 25, 26 and 131, and polynomial texture mapping for glyph 178. Right, the text traced in red. Most of the glyph symbols were previously decoded®. &, SELHNH (Moon); H, HAIOZ (Sun); H\M, HMEPAY (of the day); o\’, «po (hour) and the text that follows is the eclipse time in hours. Here we add N\*, NYKTOX (of the night), as seen in glyph 131, and the identification of index letters at the bottom of each glyph in alphabetical order. In the consecutive glyphs 20, 25 and 26 the index letters E, Z and H can be seen. (Z is always written on the Mechanism as an | with long serifs.) Some of the glyphs have unexplained bars over the index letter, as in glyphs 131 and 178. The index letters have profound consequences for the design of the glyph sequence.

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Fisica quantistica: i modelli originari dell'universo

by Fabio Marzocca

Il secolo scorso ha indubbiamente rappresentato per la ricerca scientifica un periodo di estremo interesse: sembrava fossero raggiunte e superate quelle che classicamente erano ritenute le frontiere della conoscenza. Gli scienziati hanno... more

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Electromagnetic Frequency Patterns that are Crucial for Health and Disease reveal a Generalized Biophysical Principle: the GM scale

by Hans Geesink and

Solitons or polarons, as self-reinforcing solitary waves, interact with complex biological phenomena such as cellular self-organization. Such soliton models are able to describe a spectrum of electromagnetism (EM) modalities, that can be... more

Solitons or polarons, as self-reinforcing solitary waves, interact with complex biological phenomena such as cellular self-organization. Such soliton models are able to describe a spectrum of electromagnetism (EM) modalities, that can be applied to understand the physical principles of biological effects in living cells, as caused by endogenous and exogenous electromagnetic fields, on the basis of quantum coherence. A bio-soliton model was earlier developed by us, that enables to predict which eigen-frequencies of non-thermal EM waves, are life-sustaining and which are, in contrast, detrimental for living cells. The particular effects of the proposed coherent wave pattern are exerted by a range of EM-wave eigen-frequencies of one-tenth of a Hertz till Peta Hertz, representing a pattern of twelve bands, that can be positioned on an acoustic frequency scale. The discrete pattern was revealed by a meta-analysis of 219 published papers of biological EM-radiation experiments, in which a spectrum of non-thermal EM fields were exposed to living cells and intact organisms. In follow-up studies, we analyzed 120 articles on cancer-promoting and inhibiting EM fields, of which the frequency patterns fully confirmed the inferred model. Finally we analyzed experimental data out of 27 recent publications on laser mediated radiation therapy, for a spectrum of disorders such as traumatic brain injury, depressive disorders and neurological defects, confirming the general predictive force of our life algorithm. It is postulated that long-distance control of cellular morphology and fine tuning of cellular networks by soliton-waves, is instrumental in providing a morphogenetic field that maintains cellular health. The latter also may have played a role in the initiation of first life in biological evolution. The particular parametric resonance may provide positional information and cues to regulate organism-wide system properties like anatomy, control of reproduction as well as gene expression and repair. In addition, potential damaging effects of non-ionizing electromagnetic fields on life systems can be counteracted by dedicated phyllosilicate (clay) nano-materials, that were shown by us to exhibit semi-conducting EM field properties. A related protective technology was designed on the principle of toroidal trapping, since torus geometry adequately generates a coherent field of frequencies and thereby induces coherent oscillations of macromolecules. Our papers, collectively, picture the rapidly growing and dynamic field of molecular electromagnetics, that currently shows promising clinical effects in the treatment of various sincere, and often, chronic diseases.

Figure 1: EM radiation frequencies, that were experimentally applied to living cells in vitro and in vivo as derived from 219 separate biological studies. All of the particular frequencies (green and red dots) were plotted on a logarithmic scale, according to an acoustic algorithm of which the calculated values are depicted on the X-axis. For clarity, points are evenly distributed along the Y-axis. The meta-analysis of the 219 biomedical reports, showed 12 apparent frequency bands of life-sustaining frequencies (148 green points), as opposed to detrimental frequencies (77 dots in red) positioned in between the beneficial frequency bands. The mean values of the green bands differ less than 1 % from the calculated acoustic values derived from the music-theoretical algorithm. Figure 1: EM radiation frequencies, that were experimentally applied to living cells in vitro and in vivo as derived from 219 separate biological studies. All of the particular frequencies (green and red dots) were plotted on a

Figure 2. Cancer frequencies. EM field frequencies that were experimentally applied to living cells systems, in 120 studies are plotted on a logarithmic acoustic scale, are found to be patterned in 12 apparent frequency bands of coherent frequencies that were reported to inhibit/retard cancer (green points) and decoherent frequencies able to initiate or promote cancer or being measured directly in cancer tissue (red squares), that evidently are positioned between the cell-sustaining coherent frequency bands. Numerical values on the logarithmic X-axis represent frequencies according to the chosen acoustic algorithm as in fig 1.

Figure 3: Geometric Chladni patterns of water set in motion by sound, induced on a vibrational plate (A); Vibration of a Chladni disk, Matlab., W. Xiao, 2010 (B); Frequency response plot of a Chladni plate (University of Illinois, 2015 (C); Vibrational geometric patterns of sand particles measured by Chladni, 1787 (D)

Figure 4. Example of phyllosilicate-layers, with tetrahedral and octahedral structures, as present in natural clay material. The material have been shown to act as a semiconductor, that can absorb EM radiation and transmits coherent discrete EM frequency bands. Instrumental in this property are clustered water molecules that provide resonance cavities (left above) and various doped inorganic cations such as Ca2+, Na+, Mg2+ etc. Figure 4. Example of phyllosilicate-layers, with tetrahedral and octahedral structures, as present in natural clay

Figure 5. The supposed components of the electromagnetic cell structure and potential interactions with external forces and fields as depicted in the various insets

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