Particle Physics Research Papers

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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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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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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Revision to cleanroom standard: ISO 14644 Parts 1 and 2

by Tim Sandle

Cleanrooms are highly controlled environments, defined by the air quality, and where certain physical and microbiological requirements need to be met. Air quality is achieved through a combination of airborne particulate control, such as... more

Table 1: Cleanroom classification examples. With cleanroom A, which has a size of 200 square metres, the number of locations was 15. With the revised version, it has laces eee OD) Ni: Bas Rae AT lA eh Atm aeAe LAK BRAS BD ane ef

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Atoms Radiation and Radiation Protection

by Florencio Dorado

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A REPORT ON COMPLETION OF STUDENT industrial work experience scheme

by John Jay

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

by Rute Melo

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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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Topological String Theory \\ An Introduction

by Dr. J. M. Ashfaque (MInstP)

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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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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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Boyd Nonlinear Optics Third Edition

by Itzel Reyna

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The Dictatorship of Value. Teaching and Research in the Planetary University

by Gino Zaccaria

In what sense do we speak of the planetary university? This essay belongs to a more comprehensive, still unpublished reflection that the authors have been developing over the past years while teaching and doing... more

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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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Environmental Monitoring Risk Assessment

by Tim Sandle

This paper explores current trends in the application of risk assessment to the practice of environmental monitoring by examining the following key areas: a) Determining the Frequency of Monitoring: Using the concept of risk assessment... more

Non-Numerical Risk Assessment Example 9te: Where growth is detected on the operator who placed the air sampler at Grade A, and this is shown to be the same micro-organism, the category of risk is increased by one (i.e.: low becomes medium and medium becomes high).

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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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Marion Classical Dynamics 5e Solution

by HISU OH

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CLASSICAL MECHANICS

by JANARDHAN H P

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

by sanury nury

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Effective field theory

by Antonio Pich

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Yung-Kuo Lim. (ed.) Problems and Solutions on Atomic, Nuclear and Particle Physics for U.S. PhD q.pdf

by Akshay SB

Yung-Kuo Lim. (ed.) Problems and Solutions on Atomic, Nuclear and Particle Physics for U.S. PhD

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SCHRÖDINGER'S PHILOSOPHY OF QUANTUM MECHANICS. Chapter 4: Towards a new ontology

by Michel Bitbol

After the birth of quantum mechanics Schrödinger raised two questions which, he thought, can only be addressed from a philosophical viewpoint. Question 1: can one frame a new ontology in strict correspondence with the symbolic system of... more

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The Magnetic field of the Electric current

by George Rajna

2011

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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Quantum-Vortex Electron Formed From Superluminal Double-Helix Photon in Electron-Positron Pair Production

by Richard Gauthier

A superluminal quantum-vortex model of the electron and the positron is produced from a superluminal double-helix model of the photon during electron-positron pair production. The two oppositely-charged (with Q = ±e sqrt (2/α) = 16.6e)... more

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Preprint typeset in JHEP style -HYPER VERSION Quantum Field Theory University of Cambridge Part III Mathematical Tripos

by ChangHwi Park

These lecture notes are far from original. My primary contribution has been to borrow, steal and assimilate the best discussions and explanations I could find from the vast literature on the subject. I inherited the course from Nick... more

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Entangled Double-Helix Superluminal Photon Model Defined by Fine Structure Constant Has Inertial Mass M=E/c 2

by Richard Gauthier

Two spin-½ charged half-photons, each composed of one helically-circulating electrically-charged superluminal energy quantum, compose a double-helix photon model of total spin 1 hbar and of diameter D = λ / π where λ is the photon's... more

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Dirac's The Evolution of the Physicist's Picture of Nature - Scientific American 1963 Article

by Raghav Govind Jha

The axiomatic basis of theoretical physics cannot be extracted from experience but must be freely invented -A. Einstein

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Supersymmetric Field Theories: Geometric Structures and Dualities

by Dr. J. M. Ashfaque (MInstP)

Book by Sergio Cecotti

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HOW EINSTEIN’s GENERAL RELATIVITY BENEFITS AS BLACK HOLES TURN BALL OF FIRE

by Abhas Mitra

Article prepared for the souvenir of the Reunion of the Alumni of Uttarpara Govt. High School, West Bengal, India

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Dark matter and dark energy from quark bag model

by Maxim Eingorn

2013

We calculate the present expansion of our Universe endowed with relict colored objects - quarks and gluons - that survived hadronization either as isolated islands of quark-gluon "nuggets", or spread uniformly in the Universe. In the... more

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An Innovative Interpretation for Parallel Universe

by G. Udhaya Sankar and

The theoretical view of universe is the most interesting topic of debate since past 20 th century, in which its origin to existence and how it will goes to finished off is remained as a question, and there is no ensure evidence to prove... more

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Symmetry and Particle Physics

by Deepti Devi

The simplest electromagnetic process consists of the absorption or emission of a photon by an electron: The electromagnetic interactions are weaker than the strong interactions. They occur in the interactions between electrically charged particles, such as charged leptons, mediated by photons.

Electron-positron annihilation can also produce particles such as charmonium or bot- and there are also smaller contributions to this process from multi-photon exchanges. Electron-positron interactions are also mediated by electromagnetic interactions and there are also smaller contributions to this process from multi-photon exchanges.

The gauge bosons W~ carry electric charge and they can change the flavour of quarks.

The flavour changes within one family are dominant; e.g.

In any process in which a photon is exchanged, it is possible to have a Z° boson exchange. At low energies, the electromagnetic interaction dominates; however at high energies and momenta, the electromagnetic and weak interactions become comparable. The unified theory of electromagnetic and weak interactions is Weinberg-Salam theory. exchange. At low energies, the electromagnetic interaction dominates; however at high

Consider 7N scattering. The scattering is described by a S-matrix, which, in processes dominated by strong interactions is taken to be isospin invariant: [J;,S] = 0 and so by Schur’s lemma

for m1, m2, m3 € Z. It follows that 2\/3q € Z. It is particularly useful to plot the sets of eigenvalues (p,q) as points in the plane. The resulting plot is known as the weight diagram. As the representation is assumed to be irreducible, there can only be finitely many points on the weight diagram, though it is possible that a particular weight may correspond to more than one state. Moreover, as 2p € Z, 2\/3q € Z, the weights are constrained to lie on the points of a lattice. From the effect of the raising and lowering operators on the eigenvalues, it is straightforward to see that this lattice is formed by the tessalation of the plane by equilateral triangles of side 1. This is illustrated in Figure 1 where the effect of the raising and lowering operators is given (in this diagram (0,0) is ¢ weight, though this need not be the case generically). The weight diagram has three axes of symmetry. To see this, recall that if m is a weight of a state in an irreducible representation of £(SU(2)) then so is —m. In the context o! the three £(SU(2)) algebras contained in £(SU(3)) this means that from the properties of the algebra in (4.7), if (p,q) is a weight then so is (—p,q), i.e. the diagram is reflectior symmetric about the line @ = 5 passing through the origin. Also, due to the symmetry ot the £(SU(2)) algebra in (4.8), the weight diagram is reflection symmetric about the line @ = & passing through the origin: so if (p,q) is a weight then so is (5(p+v39q), $(V3p—q)). And due to the symmetry of the £(SU(2)) algebra in ((4.9) the weight diagram is reflectior symmetric about the line 0 = a2 passing through the origin: so if (p,q) is a weight then sc is (3(p — V3q), 5(—V3p — 9). Using this symmetry, it suffices to know the structure of the weight diagram in the sector of the plane § < 6 < 5. The remainder is fixed by the reflection symmetry. NA 4a) lee kL RK been nde ned Q£ OTTIO\ coc ee le, AL, UD LUO ee,

Having established the existence of a unique highest weight state |), we can proceed to obtain the generic form for the weight diagram. Recall that the highest weight j of an irreducible representation of £(SU(2)) is always non-negative. By acting on |w) with the lowering operators E™, one obtains three irreducible representations of £(SU(2)). Non- negativity of the highest weight corresponding to the £(SU(2)) irreducible representation generated by E! implies that the highest weight must lie in the half-plane to the right of the line @ = 4, or on the line @ = 5:

As the highest weight must lie in all three of these regions, it must lie in the sector <6< § relative to (0,0), or at the origin:

This case is illustrated by Proposition 26. Each weight in this triangle corresponds to a unique state. Proof ire no states outside this line, as these points cannot be reached by applying lowerin; yperators. Then, by using the reflection symmetry, it follows that the outermost state: yom an equilateral triangle with horizontal base. Each lattice point inside the triangl sorresponds to (at least) one state which has this weight, because each lattice point in th riangle lies at some possible weight within the £(.SU(2)) representation given in (4.7) und from the properties of £(SU(2)) representations, we know that this has a state wit] chis weight (ie. as the £(SU(2)) weight diagram has no “holes” in it, neither does th /(SU(3)) weight diagram). ew 171

Proposition 27. Each weight in this triangle corresponds to a unique state. Proof Now, using (4.11) it is straightforward to show that

This case is illustrated by The multiplicities of the states for these weight diagrams are more complicated than for the triangular diagrams. In particular, the weights on the two edges of the hexagon leading off from the highest weight have multiplicity 1, because these states can only be constructed as (E!)" |) or (E2)™ |). So by symmetry, all of the states on the outer layer of the hexagon have multiplicity 1. However, if one proceeds to the next layer, then the multiplicity of all the states increases by 1. This happens until the first triangular layer is reached, at which point all following layers have the same multiplicity as the first triangular layer. Then, by using the reflection symmetry, it follows that the outermost states form @ hexagon. Each lattice point inside the hexagon corresponds to (at least) one state which has this weight, because each lattice point in the hexagon lies at some possible weight within the £(SU(2)) representation given in (4.7), and from the properties of £(SU(2)) representations, we know that this has a state with this weight (i.e. as the £(SU(2)) weight diagram has no “holes” in it, neither does the £(SU(3)) weight diagram).

The highest weight is then at (4, 5 alm + 2n)). The outer n layers are hexagonal, whereas the n + 1-th layer is triangular, and all following layers are also triangular. As one goes inwards through the outer n+ 1 layers the multiplicity of the states in the layers increases from 1 in the first outer layer to n+ 1 in the n+ 1-th layer. Then all the states in the following triangular layers have multiplicity n + 1 as well. We will prove this in several stens.

By using the commutation relations, it is straightforward to prove the identities

This representation is denoted 3. It will be convenient to define the following states in the 3 representation. This representation is denoted 3. It will be convenient to define the following states

The highest weight state is e? with weight (3, fe) All weights have multiplicity 1 except for (0,0) which has multiplicity 2. The weight diagram is a regular hexagon: 4.3 Tensor Product Representations Suppose that dj), dz are irreducible representations of £(SU(3)) acting on Vi, V2 respec- tively. Then let V = Vi ® V2 and d = d; ®@1+1® dbz be the tensor product representation of £(.SU(3)) on V. In general d is not irreducible on V, so we want to decompose V into a direct sum of invariant subspaces on which the restriction of d is irreducible.

Plotting the corresponding weight diagram gives The raising and lowering operators are E! m LE = €2 m @®1+1@e}. The highest weight state is u®u with weight (1, a): Applying lowering operators to u ® u it is clear that a six-dimensional irreducible representation is obtained. The (unit-normalized) states and weights are given by

This representation is called 6. Removing the (non-vanishing) span of these states from the tensor product space, one is left with a 3-dimensional vector space. The new highest weight is at (0, a) with corresponding state wala ®u—u®d) (this is the unique linear combination- up to overall scale- of d® wu and u ® d which is annihilated by all the raising operators). This generates a 3. The states and their weights are which has the following weight diagram trom the tensor product space, one is left with a 3-dimensional vector space. ‘The new

with weight diagram The raising and lowering operators are FE? = e7’ @1@1+1@e2@141816ef. There are six weights of multiplicity 3, and the weight (0,0) has multiplicity 6. The highest

Note that the highest weight is now (5, V3), This weight has has multiplicity 2. It should be noted that the subspace consisting of linear combinations of d®u@u, u®d@u and u ® u ®@ d which is annihilated by all raising operators E”” is two-dimensional and is spanned by the two orthogonal states veld Qu@utuS@d@u— 2u@u®d) and va(d QuSQu—uSd@u). By acting on these two states with all possible lowering operators, one obtains two 8 representations whose states are mutually orthogonal.

There is also a J = 0 meson singlet 17’. The vector meson octet has B = 0 and J = 1. The (J3, Y) diagram is

We have shown that mesons and baryons can be constructed from qq and qqq states respectively. But why do gq particles not exist? This problem is resolved using the notion of colour. Consider the A** particle in the baryon decuplet. This is a u®u@®u state with i= 3. The members of the decuplet are the spin 3 baryons of lowest mass, so we assume that the quarks have vanishing orbital angular momentum. Then the spin J = 3 is obtained by having all the quarks in the spin up state, i.e. u T ®u T @u 7. However, this violates the Pauli exclusion principle. To get round this problem, it is conjectured that quarks possess additional labels other than flavour. In particular, quarks have additional charges called colour charges- there are three colour basis states associated with quarks called r (red), g (green) and b (blue). The quark state wave-functions contain colour factors which lie in a 3 representation of SU(3) which describes their colour; the colour of antiquark states corresponds to a 3 representation of SU(3) (colour). This colour SU(8) is independent ot the flavour SU(3). MhRnanR nA Aam nhenwmern awn AlAR wmnpstmn) £R mramncen nemtantann Atnpnmnmnmnntnn (AL we neeennan ni

The leptons are also spin 1/2 fermions and can be arranged into three families The quarks carry a fractional electric charge. Each quark has three colour states. Quarks Hadrons are made from bound states of quarks (which are colour neutral singlets).

Typical hadron lifetimes (valid for most decays) via the three interactions are summarize below: with the notable exceptional case being weak neutron decay, which has average lifetime 1036. 1.2.4 Typical Hadron Lifetimes 1.3 Conserved Quantum Numbers

Proposition 4. Suppose that G is a matrix Lie group and that v,w € T.(G) and V, W are the left-invariant vector fields defined by Vg = Lgxv, Wg = Lgxw. Then the matrix associated with |[V,W]e is the matrix commutator of |b, w] where 6 and w are the matrices associated with v and w. By definition, the matrix associated with [V, W] is

Exercise: Suppose that [v, w] = 0. Show that e’e’ = e’t

For this tensor product the quark content/weight table is as follows:

The states and weights of these two 8 representations are summarized below:

Removing these weights from the weight diagram, we are left with a singlet 1 with weight (0,0). The state corresponding to this singlet is

can be written as a product of rotations around the spatial co-ordinate axes

Differentiate this constraint and set t = 0 to obtain

where here D,, is the adjoint covariant derivative. Note that by the Bianchi identity

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“Gravitational Waves”: Great Discovery or Blunder? The I.S.S. (Inertial Simultaneous Synchronization) as Mach’s Unification of Gravity, Electromagnetism and Quantum Mechanics. The “Mathematical Universe” as an Impulsive Dirac Delta Function/Distribution. (+ Addendum)

by Alberto Miatello

Alberto Miatello " Einstein's relativity work is a magnificent mathematical garb which fascinates, dazzles and makes people blind to the underlying errors. The theory is like a beggar clothed in purple whom ignorant people take for a... more

Alberto Miatello " Einstein's relativity work is a magnificent mathematical garb which fascinates, dazzles and makes people blind to the underlying errors. The theory is like a beggar clothed in purple whom ignorant people take for a king... its exponents are brilliant men but they are metaphysicists rather than scientists " (Nikola Tesla) Abstract This study is the first expounding, in a new exciting manner, that a Theory of Everything(TOE) unifying all the fundamental forces with gravity at 10^-43 seconds after the Big Bang, can be worked out within the I.S.S. (Inertial Simultaneous Synchronization), namely by applying and improving the " holistic " concept of universal Inertia-as proposed firstly by Ernst Mach – instantaneously connecting the inertia of all bodies in the universe, irrespective of their distance. This paper proves that this mechanism of ISS can unify gravity, electromagnetism and Quantum mechanics, by treating them as " action-at-a-distance " phenomena – as experimentally evidenced by the instantaneous propagation of gravity, electromagnetic fields such as Coulomb, and entangled particles in QM – arising in different forms from the same universal and original Inertia. It enables to do so by simply surrendering the wrong Einstein's concepts of universal constancy of light speed (c) within a frame of relativistic space and time – rather handling c as a variable velocity inversely proportional to the size and radius of the universe , in a frame of absolute time – while keeping only the mass-energy equivalence (E=mc²) as a relativistic valid concept. This paper proves that Newtonian/ " classical " and Quantum mechanics are correct physical interpretations of the universe and coherent epistemological systems, and they can easily be matched, sharing the same concepts of absolute time while the " observer " is always someway involved in the described universe/phenomena, whereas relativism introduces " metaphysical " or false concepts such as the mass " warping space-time " of GR + c as an absolute constant of SR. Thus, any attempts to " reconcile " QM with General Relativity (such as string theory) are bound to fail, as GR is simply incorrect and self-inconsistent. Results of this work are fully in agreement with Guth's theory of inflationary universe. Furthermore, this study explains the 68% " dark energy " in the universe that has been discovered in the last decades, as simply the positive difference ΔE between the energy in today's universe where c<c' than that of previous universes. And finally, this work introduces new concepts of gravity and ISS as impulsive signals propagating as a Dirac delta (δ) function/distribution, while the universe itself can be better thought as a " point mass " (new concept of " singularity ") surrounded by nothingness (= true vacuum) and quickly expanding " ad infinitum " after the Big Bang as a Dirac δ function/distribution.

lowever, this effect can simply be explained by the well-known “Magnus effect”, i.e. the spinning and eflecting effect on a round body by fluids (usually air) in which it travels. This effect causes a backlash and downward deflection of the bodies traveling in fluids, and it is also accompanied by the “dragging” — as a ortex — of the fluid matter/energy surrounding the rotating body, which cumulates in fluid “layers” around it nd makes the mass of the rotating body to increase.

(2004 Indian Ocean Tsunami. Credit : Photo Gabriel Andres Trujillo) Thus, it makes no sense to call as “gravitational waves” the signals allegedly coming from rare and extraordinary cosmic events, which have nothing to do with the “ordinary” phenomenon of gravity (attraction between masses of bodies whatever ) as we all know and are experiencing in our everyday life, and in our universe.

However, the fundamental stability of our Solar System is clearly admitted not only by the great astrophysicists in the past, such as Kepler, Newton, Laplace, Eddington, but it has recently been recognized even by modern astrophysicists — as Jacques Laskar — who nevertheless are claiming in their recent papers that the motion of planets in our Solar System can be defined as “chaotic”: “...At the same time, 99% of the trajectories will behave in a similar way as in the recent past millions of years, which is coherent with our common understanding that the Solar System has not much evolved in the past 4 billion years’ [17]

(Hafele and Keating aboard the airliner, in October 1971, during their famous experiment) In October 1971, the American scientists J.C. Hafele and R.E. Keating performed an experiment, with some atomic clocks, in order to test the validity of the relativistic postulates regarding the alleged “slowing” of time, experienced by bodies in motion. They flew the globe twice, Eastward and Westward, aboard a commercial airliner, and then they compared the times of three sets of special cesium-beam atomic clock supplied by Hewlett-Packard, with those showed by clocks in their Washington laboratory. [23] The result of this experiment was presented by many academic papers as a Sort of “triumph” for the relativistic predictions, and the differences between the flying clocks and the clocks grounded in the Washington laboratory were considered an experimental confirmation of the relativistic prediction about the “slowdown of time” by bodies in motion, that Einstein epitomized in his famous thought experiment of the “twins paradox”, showing a different aging in two twins, one of them flying for years aboard a spacecraft at a speed near to c , and aging more slowly than his twin living on Earth.

This important conclusion is evident because if c were dependent upon a “retarded potentials” and “time-dependent” equation, such as this one:

However it is not so difficult to prove that it is physically impossible for us, living in the Milky Way, to decide whether the universe is expanding or contracting. This argument is not so “eccentric” after all, because Rubino is correct when he remarks that if a second parachutist is jumping from the airplane a few seconds after a first colleague, and then a 3™ parachutist jumps a few seconds after the 2™, this latter will see that the first and the 3™ parachutists are drifting away at growing velocity from him, although they are all “converging” to the ground.

(Credit source of image: http://www.tpub.com/neets/book10/39b.htm )

Guth’s model is perfectly in agreement with mine, where light speed is changing according to the universe radius/size, and where the first singularity was a Dirac 5, surrounded by nothingness, possessing no energy/mass in inertial terms, and tending to infinity when the Big Bang was starting, with the speed of light quickly slowing down as the radius was expanding.

(Image source: Copyleft : Feynman Diagram. Wikipedia Creative Commons ) However, the first experimental refutation of Dirac’s theory was in 1947, after the Lamb-Retherford experiment on the hydrogen microwave spectrum, discovering the so called Lamb shift, [92] namely the difference in energy between energy levels *S1/2 and 2P1/2 of the hydrogen atom, that Dirac equation did not predict, because the latter did not consider interactions between electron and vacuum, and so in Dirac equation there were no difference between the energy levels above. electron of present time with its anti-particles moving backward in time, and coming from future to present/past , and possessing —E negative energy, with a “retro-causality” and reverse of the “arrow of time”, i.e. the cause of anti-particle’s motion was in the future, whereas the effect (i.e. annihilation) was in the past. [89] that was shared also by Archibald Wheeler (1945) [90] and by the Nobel laureate Y oichiro Nambu

Nevertheless, Einstein’s “mathematical” rooted belief is challenged by the “common sense” idea shared | humans that all of us perceive time as clearly distinct from space where our bodies live and move, and abo all we perceive “the arrow of time”, [104] we clearly feel the difference among now, yesterday, 1-2-3 yea ago, etc., among living beings that age and die, and nobody feel “space-time” as a new, specific “entity different from space and time alone. It is highly enlightening — in this respect — what the Harva astrophysicist David Layzer [105] wrote in his article of 1975 in Scientific American, where he clear suggested why the initial conditions of the early universe, and its expansion, were so important to establi: once forever a forward arrow of time. It is quite revealing — in this respect — that no scientist, philosopher, psychologist, writer, artist, etc., ever mentioned such bizarre idea of “space-time” as a “fusion” before the end of XIX century. Aristotle was clearly defining time as “the measure of movement with respect to “before” and “after” “, having clear in his mind the notion of time as “arrow” with a succession of distinct instants.

if we take the whole rectangular major area, whose sides are At and ti-F’ - within which the impulse function S$ variating - and we take also the point F’ on top of the curve as the most distant point of body’s mass from he source of impulse, then we can easily realize that our impulse/force can 100% fully reach with the lighest intensity just the nearest points of the side on which the force is being applied along the side At, whereas on the most distant and opposite side of the body the force/impulse is lower, due to the opposite ‘eaction of the body according to the 3% Law of dynamics.

Now, if we assume that a = g, and we look what happens when a gravitational field is acting on the same body’s mass, we can easily realize that the gravitational field is instantaneously propagating (as g propagates at infinite speed) on the whole body’s mass, as in diagram C__, and all the points (i.e. atoms and molecules) are equally reached by g it in the same way.

Diagram above is visually evidencing the motion of a body/particle “P” (red vector) as a succession of 3-D spaces (space 1 + space2 +...space n) in which it is always possible to locate its position through the coordinates x,y,z. The rapid succession and superposition of 3-D spaces creates our perception of motion and time as a new distinct entity.

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Physics for Chemists

by yusna iin frantina

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Solucionario Fisica Serway 7MA vol 2

by John Oviedo

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Nobel Prize on Hoax . Rally Against Nobel Prize 2017 ( physics and Physiology on Fiction and Illusion ) -- Paper Published on 28.10.2017 - 25 days after prize declared

by vijaymohan das

Time is consciousness ( Time mindness or Atomic genes , TM ) present in CCP ( thought script of Anti mind particles ) While Space is Void which is Nothing . How could space create ripples ? A Fake Mathematical Theory of Space Time... more

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Inflation due to quantum potential

by Maxim Eingorn

2015

In the framework of a cosmological model of the Universe filled with a nonrelativistic particle soup, we easily reproduce inflation due to the quantum potential. The lightest particles in the soup serve as a driving force of this simple,... more

Both these functions are shown in Fig. 1 (blue and orange curves re- spectively). Red and purple curves correspond to the classical case with- out quantum effects when all terms containing exponential functions are dropped and H = A€~3/?, @/a = — (A?/2) €-%. Finally, the green vertical line € = & = (p1e)/° signifies the end of inflation. So there are inflationary expansion (with the positive acceleration) for € < € and traditional expan- sion (with the negative acceleration) for € > €., as it certainly should be.

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Maggiore

by quantum theory

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Solved Problems on finite potential well

by allen maleba

Given here are solutions to 15 problems on Quantum Mechanics in one dimension. The solutions were used as a learning-tool for students in the introductory undergraduate course Physics 200 Relativity and Quanta given by Malcolm McMillan at... more

The equations relating the speed v, momentum p, de Broglie wavelength 4, wave number k, total energy
E, kinetic energy K, angular frequency w and group velocity vg for a relativistic particle of mass m are:
In a region of space, a particle with mass m and with zero energy has a time-independent wave function
where A and L are constants.
Solution

The stationary state wavefunctions ~,,(a) are solutions of Eq. (20) and are orthonormal:

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Sol FUS 12

by Raul Sosa

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Kepler 3 rd Law Explanation (a claim against Nobel Prize board decision-in physics -2018

by Gerges Tawadrous

A claim against Nobel Prize Board Decision – in Physics -2018 Best Greetings I send this paper as a claim to the Nobel Prize Decision Board - for their decision - for Nobel Prize in physics 2018 Of course I have nothing against the... more

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Theory of Everything – 4 Dimensional String Theory

by George Rajna

2013

New ideas for interactions and particles: This paper examines the possibility to origin the Spontaneously Broken Symmetries from the Planck Distribution Law. This way we get a Unification of the Strong, Electromagnetic, and Weak... more

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