Quantum mechanical postulates are (a) states of a quantum system form a separable Hilbert space H for multiparticle systems tensor products of these, (b) observables of a system form an algebra Obs of self-adjoint operators on H, and (c) the measurement process is an assignment mu(s,K) that is a probability measure on the real line.

I don’t know whether J Von Neumann was part of the crew that actually put down these postulates but I remember his book on Foundations of Quantum Mechanics to be quite abstract as an undergraduate in 1991-95 and since I did not pursue physics then I had no real feel for how this abstract machinery translates into measurement process for actual experiments. But I have been working on the S4 model for the past decade on and off and now that I consider how the universe must actually work, as an evolving hypersurface of a four-dimensional sphere, it is quite an achievement to produce a linear theory of this sort that became successful in development to quantum field theory. The apparent stochastic phenomena in the actual universe must be due to a continuous movement of the entire physical universe in an EM phase dimension that is immense, the scale of the entire universe in size these EM phase circles — and they are metric but obviously this is not pursued yet today but I am sure in the future they will. So in this fluctuating hypersurface measurement of subatomic particle characteristics is a tricky business as we know from the experience that physicists have had since the 1920s when these issue occupied science. Every single particle in the universe and every single atom is fluctuating in S4 and measuring apparatus is designed by physical world beings and physical world equipment and originally we are considering measurements of position and momentum of particles and we have Heisenberg’s uncertainty principle from the situation. It is true that quantum mechanics is fooled by randomness and the universe is governed by deterministic laws behind the veil, but at the same time one must marvel at quantum mechanics because it is a LINEAR THEORY IN A NONLINEAR UNIVERSE THAT HAS SUCCEEDED. That’s AMAZING.


This is in the end not so much a criticism of quantum field theory — and by this I mean the established standard model of electroweak and strong forces rather than the large number of variations of quantum field theories that are not directly established consensus view — as much as an idiosyncratic perspective I have developed over the past decade since I began thinking about the S4 model.  For much of that time I was not primarily concerned with quantum field theory because originally I was excited by a unification of electricity and magnetism and the fact that it is a static model that can explain the distance-redshift relation of Hubble and my focus had been on trying to convince people that the expansionary cosmological models are wrong.  But of course in the past four or five years I have been interested in moving slowly towards understanding the small scale properties of objects in the S4 geometry since I became confident from the fits of redshift-distance that the cosmological constant problem disappears in this geometry.  Then I am returning to the issue of quantum field theory because in fact this is our strongest physics model and S4 model differs from some of the major features of the electroweak model for example.  I read Steven Weinberg’s popular book on Dreams of a Final Theory and I don’t have training in physics from Princeton where I studied mostly mathematics.  But now in my middle age I am learning quantum field theory from the perspective of my S4 model and here are my thoughts at this point of why I think quantum field theory has failed to resolve the cosmological constant problem.

The cosmological constant problem cannot be solved without recognizing that each of the foundational pieces that went into flat space quantum field theory from quantum mechanics, special relativity, building up mechanics of multipatricle scattering cross sections and so on were too empiricist in outlook to reach the right description which is that the physical universe is a continuously moving hypersurface of a fixed eternal static round four sphere of radius approximately 3246 Mpc and the deep empiricism of physics has produced a good linear approximation to reality by arduous methods that obscure a classical universe where the geometry of space is not being evident in the flat Minkowski space development of quantum field theory whose empirical achievements are tremendous but cosmological constant problem cannot be satisfactorily resolved by the concepts in quantum field theory that sees objects like photon and fermions through a complicated lens of quantum fields rather than the clear lens of fixed geometry of space and classical wave equations on it. The intuition from quantum fields lead to the 120 orders of magnitude divergence from cosmological constant for its estimate of the energy of the vacuum for this reason and not for any other obscure reason.

Einstein was right about quantum mechanics: Nature is not described by a linear theory where position and momentum can be related by Fourier transform on the FLAT Minkowski space. So you look at the sequence of things that go from quantum mechanics to quantum field theory for QED and now Zulf tells you that reality is S4 and absolute time. From Zulf’s perspective the first mistake is linearity of quantum mechanics because the physical universe is going to be a continuously moving hypersurface that stays embedded in S4. Then of course while S4 model gives you the reason why we have wave-particle duality for matter and photons cleanly as solutions of Dirac and Maxwell’s wave equations on S4, quantum mechanics does not work out right as a description of Nature and you moved to adding relativity to it and adding also the idea that you will use the quantum mechanics techniques to fields. Now Zulf says a photon is a global solution of a wave equation as is a fermion. Zulf looks at quantum field theory which is building up from the flat space foundations and adds quantization of fields following the paradigm developed of canonical commutation relations between position and momentum on flat space and generalizes it straightforwardly to fields and Fock introduces the modeling of multiparticle fields as polynomials in creation and annihilation operators. These developments are syncretic and close to experiments so they are perfectly REASONABLE for development of quantum field theory but Zulf says this is a very arduous way of getting to a LINEAR APPROXIMATION of reality which is not based on flat Minkowski space at all. REALITY says Zulf is that the universe is a fluctuating continuously evolving hypersurface of a fixed radius round four-sphere and these ardous developments from quantum mechanics to quantum field theory with focus on producing good fits to experimental data are complicating the actual description of Nature which is much simpler than all this. One could go backwards and take a hypersurface M of S4 and take the tangent space at a point T_x M of the physical universe and probably get quantum field theory QED to be a particular approximation of physics on the TANGENT SPACE of the physical universe at a point. On the tangent space, you CAN pretend that position (on the tangent space) and momentum satisfy the canonical commutation relations where observables are thought of as operators and the rest of the rigmarole of quantum field theory but this is still approximating something much simpler on S4 which Zulf claims is NATURE.

Ok I get it. What QFT is doing is approximating S4 classical fields using clever ‘creation’ and ‘annihilation’ operators on flat Minkowski space. This is tractable computationally but that is NOT a fundamental description of Nature. Nature is going to be a classical theory for hypersurfaces of a scaled round four-sphere where the physical universe is moving hypersurface. This type of ‘creation-annihilation’ mechanism is like a flat approximation to a curved hypersurface of S4 universe. This might get you a good phenomenological theory which it is and has produced extremely successful QED but this is not a fundamental theory of Nature.

Look the physical universe is a hypersurface of a scaled round four-sphere and the PHASE SPACE is the cotangent bundle of S4 restricted to the hypersurface. Why would position and momentum be related by a Fourier transform? This would be true if the world were flat but it’s not. It’s an S4 universe. Quantum mechanics has taken the accidental feature of Minkowski flat space where you can get the cotangent space by taking Fourier transforms and made this into some law of Nature. That’s not the right thing to have done. Of course then you can take the quantum mechanics ideas and do MICROLOCAL ANALYSIS on manifolds in general but S4 is special because THAT is our actual universe not general manifolds.

Look the physical universe is a hypersurface of a scaled round four-sphere and the PHASE SPACE is the cotangent bundle of S4 restricted to the hypersurface. Why would position and momentum be related by a Fourier transform? This would be true if the world were flat but it’s not. It’s an S4 universe. Quantum mechanics has taken the accidental feature of Minkowski flat space where you can get the cotangent space by taking Fourier transforms and made this into some law of Nature. That’s not the right thing to have done. Of course then you can take the quantum mechanics ideas and do MICROLOCAL ANALYSIS on manifolds in general but S4 is special because THAT is our actual universe not general manifolds.

I need a short concise development of quantum field theory as practiced by the physicists today. This looks good. Peskin and Schroeder is too long winded. What I need to understand is exactly what is inferred about the PHOTON from pretending that electromagnetism has a U(1) local gauge invariance in contradiction to Zulf’s S4 model where electromagnetism does not have actual U(1) local gauge invariance. This looks good for that.

I know that in QED the U(1) gauge invariance of electromagnetism is used to infer properties of the photon but this is not right. A photon is a solution of a global wave equation for a 1-form on S4 cosmos that simultaneously acts as ETHER for photons. So I will have to dig into this aspect of QED. I think if we can just modify QED enough so that it correctly fits into S4 cosmos, we might just get a good description of Nature that satisfies Zulf. The U(1) gauge invariance of electromagnetism that is apparent will be a subtle geometric phenomenon where the hypersurface that is the physical universe moves in S4 in a particular way and gives us the impression that electromagnetism has a U(1) invariance but this is not right.



zulfikar.ahmed@gmail.com <zulfikar.ahmed@gmail.com>
8:16 AM (11 minutes ago)

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Ladies and Gentlemen,

Special relativity is one of the most highly confirmed physical theories and so it might seem outlandish to question it. But since S4 model gives us a unification of space and EM phase in a compact static cosmos with actual measurement of cosmological constant reproducing Planck’s constant and quantization of energy and matter in the model as a derived quantity from static space geometry the most parsimonious description of time is a global time because we have here an ether-substitute. Ether in the late nineteenth century was considered some substance in the physical universe through which EM waves propagated. My model tells me that Ether of this type is wrong but we should consider the entire universe as ether including an electromagnetic phase direction. What are the correct Maxwell’s equations for a static S4 cosmos (scaled so it’s curvature is the measured cosmological constant Lambda=1.11 x 10^(-52) m^(-2))?

This is how we can get the correct Maxwell’s equations: let A be a differential 1-form on a round four-sphere. We are considering classical electromagnetism and in a moment I will tell you why this is sensible and also why our results on special relativity that are highly confirmed may be set aside for absolute time. The Maxwell’s equations in this case will simply be the wave equation D’Alembertian(A)=0 for 1-forms A on S4. This is an equation for the EM 4-potential in standard quantum field theory for example but without any relativistic correction. If you restrict this A to a hypersurface of S4, i.e. the physical universe, you can verify that the restricted A will satisfy the standard Maxwell’s equations on the hypersurface but you won’t need a gauge condition because this is not a U(1) gauge invariant description of electromagnetism. Now using this I can ask — what is a photon? A photon can be described in my model as a component of eigenspace decomposition of the 1-form A in terms of the Laplace operator acting on 1-forms on a round four sphere. Thus we will have discretization of photons by frequency as we all know from early 20th century discoveries forming the basis of Planck and Einstein’s original quantum discoveries. But I will claim that a photon is a global object on S4 with wave particle qualities observed locally. The wave qualities are obvious and the particle qualities will be described from mathematical examination of the eigen 1-forms of the Laplace operator on a 4-sphere.

We have a similar description of fermions as solutions of a classical Dirac wave equation.

Now let me explain why Special Relativity (SR) might be true in terms of new concepts with Absolute Time. You can consider Absolute Time as time as seen from Light’s reference frame where light is global on S4. Then you can ask whether local time frames of two massive bodies in inertial motion in the physical universe will have their own local time and the answer is sure, and SR is the theory of how from one reference frame to another the laws of kinematics are adjusted to ensure speed of light is constant in their local reference frames. But these laws are not necessary in the presence of an absolute time and existence of an ether where photons have classical description.

Now let me move on to the issue of quantum field theory and standard model of electroweak and strong interactions. This is one of the most successful theories in modern physics but it faces an enormous problem with explaining the energy of a vacuum which is the cosmological constant: the estimates of energy of vacuum by quantum field theories are 120 orders of magnitude off from the measured value. My simple model can serve as the basis for a modification of standard model where quantum fields may not be necessary because these classical solutions have the wave-particle duality and necessary to re-examine the quantum field theories in due time. The cosmological constant problem may seem like a small crisis at a moment when so many of the internal consistency issue of standard model have been resolved but a re-examination of the basis of quantum theory in a static eternal cosmos offers us possibilities of quantum physics that is much more clear and coherent and might be the right way to both simplify the approaches of quantum field theory as well as produce a classical theory of the same phenomena without losing the achievements and insight of quantum field theory. My model is a good starting point that auto-resolves the cosmological constant problem and it is one where we do not have classical ether but we have a nice substitute – an extremely beautiful 4-dimensional spherical model.

Thanks for your time.

Zulf Ahmed


The Universe is Static Eternal in Light’s Clock. Light does not see relative motion of Matter to keep its Clock. Obviously. Now model the universe as S4 x R with time in Light’s clock. All the time dilation phenomena take place from the frame of reference of matter say in inertial movement relative to each other. What is wrong with Absolute Time here?

Now you have a classical model of a photon with Absolute Time as clock and using the following Maxwell’s equation on S4 x R. Using Light’s clock as time:

A(x,t) is a 1-form on S4 x R

A(x,t) solves D’Alembertian(A) = 0

A(x,t) acts as the EM potential 4-vector at every point in spacetime

That’s a global Maxwell’s equation. Solve the global Maxwell’s equation, decompose the solution in terms of eigenvectors of the Laplace operator on 1-forms on S4. Call each of the solutions which will be approximately an oscillating eigenform 1-form of the Laplacian a PHOTON. Now you can look at the SAME UNIVERSE from the frame of a moving massive body in the universe and find that other moving bodies in the universe SEEM to follow Special Relativity Rules. That’s fine but Light does not care about these Special Relativity Rules necessarily and you can calibrate the clock of EVERY SINGLE massive body in the entire cosmos to the Absolute Clock and then what SR is going to tell you is that relative to a DIFFERENT Clock that is not calibrated to the Absolute Clock that other inertial massive bodies will show time dilation. That may be true but that does not mean that such an SR would be giving you a fundamental laws of Nature.

The spectrum is computed here.  The exact formulae are probably worked out somewhere.

Take a 1-form A on a round four-sphere scaled so cosmological constant matches Lambda=1.11 x 10^(-52) m^(-2). The Maxwell’s equation will be D’Alembertian(A) = 0. For every hypersurface M of the sphere as physical universe A restricted to M will satisfy the Maxwell’s equations for the hypersurface. This is clear from the covariant description of EM where the Maxwell’s equations are described by D’Alembertian(A|M) = 0 and a gauge fixing condition such as d_mu A^mu = 0. We need not put in special relativity into this Maxwell’s equation and we will recover classical Maxwell’s equation in the hypersurface M. This implies then that in the S4 model you can have Maxwell’s equations with a fixed speed of light. If matter is grossly described by classical Dirac wave equation then speed of matter is totally independent of speed of light. In this model, Absolute Time makes perfect sense and we have S4 itself as ETHER. Now you may think that since SR is highly established that this has got to be a toy model, but I distrust the various tests of SR at the moment. There are many theoretical models that violate SR in the published literature. SR arose at a time in the history of science when 3D ether was culled from science. Since S4 model provides a 4D ether I will hold on to Newtonian Absolute time in the face of apparently massive amount of experimental confirmation of SR. I am sure the right coherent physics will show the problems with all these experiments in time. Without a coherent unified physics theory we will not be able to see correctly what the problems might be. Certainly Poincare and Einstein were perfectly right that pushing Galilean relativity where light and matter are localized point particles following billiard ball models would make us accept SR because in such a way of looking at the world SR provided an extremely strong solution to what to do when ether did not exist. However, my model has a substitute for ether through which both matter and light propagate and therefore for me it is a hard decision to throw out Absolute Time in the model.

You would not be invited to join the sacred cult of PHYSICISTS if you did not sell your soul to special relativity in the first place.  You’d go through years and years of training where special relativity is grilled deep into your psyche as what we know about the universe.  This alone makes me highly skeptical of experiments purporting to show more and more precise tests of time dilation effects of special relativity.  For most physicists Einstein is their great hero.  So you will have to excuse me for being skeptical of large numbers of physicists gathering to do experiments on time dilation.  Time dilation is a RELIGIOUS FAITH of these large groups of physicists.  What will they do, overthrow their fundamental faith about how the universe works since 1905.  They are very jealous of this special knowledge — it is common for them to deny credit for Lorentz transformations to Henri Poincare who articulated a Lorentz transformation law before Einstein as well.  I adore Einstein as well but I am not a professional physicist and I don’t believe Special Relativity is right.  If I were a professional physicist I personally would be quite ready to keep showing results to reinforce it.  I will be quite honest.  No physicist in his right mind would push for results that violate Lorentz invariance.  It’s like asking a large group of devoted Muslims to give judgments about the divinity of Allah and then blindly accepting their judgment.  They would not be Muslims if they did not have this faith to begin with.

How can Special Relativity not be true?  I am constructing a model where Time is Newtonian Absolute and Special Relativity need not be true at a fundamental level.

EVERY photon in the universe is a global object. And speed of light is an intrinsic component of S4 Maxwell’s equation. Therefore speed of light is a special thing. Matter is not described by Maxwell’s equation. It is described by a classical Dirac wave equation. Therefore ‘speed calculus’ of matter follows some GALILEAN relativity principle. This ‘speed calculus’ will not have any relation to the speed of light at all and we do not NEED to bend time to get this because S4 model has a universal-size ether — ALL of it is ether in toto. Of course since current physics ACCEPTS special relativity the physicists are TRAINED to keep the faith and produce results that reinforce their beliefs in Lorentz invariance. Does not prove a thing to me. It’s a HOLY COW of physics. Untouchable by physicists. It’s drilled into their minds. It’s what MAKES them physicists this faith in these basic laws of physics laid down in the early 20th century. If you did not believe SR you would not be in the team doing tests of SR. Not compelling easily for me. No one is objective. If you go into a physics crowd and do not believe Special Relativity you’d be thrown out as an IGNORAMUS.