Quantum theory, gravity, and the standard model of particle physics : using the hints of today to build the final theory of tomorrow by Tejinder Singh

GR physical systems are spatially separable into independent components. Three or more particle systems require cluster separability (macroscopic locality). System into subsystems, overall mathematical description reduces to descriptions of the subsystems (scattering problems with two or more fragments). QM allows entangled states (superpositions of product states) that require a fundamental irresolvable connection within empirical physical systems (two-slit diffraction, EPR paradox). Macroscopic locality is violated: Measuring the state of one slit in a double slit experiment obtains single slit diffraction patterns (quantum eraser experiments).

GR models continuous spacetime beyond conformal symmetry (scale independence) to symmetry under all smooth coordinate transformations - general covariance (stress-energy tensor re local energy and momentum) - resisting quantization. GR predicts evolution of an initial system state with arbitrary certainty. QM observables display discrete states. Heisenberg Uncertainty limits knowledge about conjugate variables in a system state, disallowing exact prediction of its evolution.

The Standard Model is a curve fit and massless. SM requires explicit insertion of 6 quarks', 3 leptons', W, Z, and Higgs bosons' masses); 3 neutrino masses and 4 parameters for the Maki-Nakagawa-Sakata matrix, electromagnetic and strong coupling constants, four parameters for the Cabibbo-Kobayashi-Maskawa matrix... The Higgs is absent. SUSY partners are absent; no solar axions (CERN Solar Axion Telescope). Protons do not decay (Super-Kamiokande). The Standard Model predicts what it already knows. U(1)xSU(2)xSU(3) or S((U2)xU(3))?

You conclude, "Perhaps its fair to say that in the end Einstein will turn out to be the winner after all. Unification will be achieved by a generalization of general covariance to the noncommutative case." That is 1931 teleparallel gravitation (Einstein, Cartan, Weitzenböck) with chiral anisotropic vacuum. Conservation of angular momentum through Noether's theorems fails. How would you test your contentions?

"Autoritätsdusel ist der größte Feind der Wahrheit," Albert Einstein, 1901.

Mr. Singh,

Thank you for an interesting essay.

One thing which I'll wager you *won't* view from the summit (unless it's a false summit) is a device which purports to be a working time machine. You'll find the reason for this assertion in my essay 'On the Impossibility of Time Travel,' which appears elsewhere among these collected essays.

If I correctly understand your thinking about the desirability of eliminating external classical time from quantum mechanics, I believe that you'll find my perspective on time to be consistent with that aim.

Dear Tajendra,

it is a pleasure to note some conceptual similarities between yours and my essay on this forum. You have used the term ' mesomic ' for the region of Physics where neither the classical nor the quantum physics is likely to be valid strictly. You have correctly indicated such a theory to act as a significant link in order to make Physics become comprehensive. As an experimetalist, my own essay indicates the missing link as one where the Planck's constant 'h' can neither be considered as negilgible nor its full significance is relevant in certain physical processes that have yet to be encountered experimentally on account of practical limitations. i am sure in the days ahead both theoretical people like you and the younger generation of experimental physicist will explore such possibilities specifically. i personal will welcome your comments on my essay too, if you can spare the time to go through it too!

Dear Tejinder,

First I want to congratulate you a very good essay. I have a few comments and questions.

You say: "there must exist an equivalent formulation of quantum mechanics, which does not refer to an external classical time"

And indeed there is one and moreover, the right way to understand it is in the non-commutative framework. Please see my essay: "Heuristic rule..." and Emile Grgin's essay: "A Historical Approach...". I am talking about the algebra of quantions. (You can see an overview of it at: arXiv:0901.0332, but ignore the second section, it is superseded by my essay as my understanding deepened after its publication).

One feature of this algebra is that it also has a "God-given time" and I was trying to read Connes archive paper (arXiv:math/1100193) but I could not find it. Is the reference correct?

This algebra generates a peculiar (non-commutative) state space that is no longer the usual Hilbert space and has a larger degree of freedom and no dimensionality as far as I can tell for now.

Another question I have is regarding the use of nonlinearity to explain the wavefunction collapse. Why we cannot understand the collapse simply as gaining knowledge in a Bayesian approach? I would expect that any nonlinear model of the collapse to be at odds with relativity.

Dear Tejinder,

Thank you for the updated archive reference, I look forward to reading it. For the second link, I was already aware of it and I even cite it in my essay. I concur, it will be wonderful if we arrive at the same destination coming from different perspective, and this validates further that we are on the right track.

Nonlinearity is indeed unavoidable, but I do not quite see it necessary to explaining the wavefunction collapse. If the collapse is due to nonlinearity (and conceivably this involves irreversibility), how can the quantum erasure (un-collapsing the wave function) be explained then? The Bayesian approach is much more natural. Suppose someone gives me a pair of gloves and I only look at one and see it is red. At that moment I know that its pair is red as well and there is no mystery in this knowledge gain process. You can object that this is not quantum mechanics, but the only difference between classical and quantum mechanics is that the pure state space is continuous and in QM even pure states are not immune to collapse.

The measurement problem is however not solved because one can show that there is no consistent mathematical description of a mixed classical-quantum system. So Zurek's decoherence and Bayesian's explanation of the collapse goes a long way towards solving the measurement problem, but not all the way. One has to show that either everything is quantum mechanical, or everything is classical mechanical. The proof is highly non-trivial even with Kochen Specker, or Bell, because of 't Hooft's program of emergent QM from a deterministic theory.

Florin

i have posted some comments in response to yours on my essay site. May be you see and then respond as you may desire

Dear Tejinder,

I am not a believer either in many worlds interpretation, although it is surprisingly widespread in conjunction with Wheeler-de Witt. I am much more inclined to accept Rovelli's relational interpretation of the wavefunction as observer-dependent. In classical mechanics one has a crisp difference between uncertainty and pure states. There the information gaining via the Bayesian interpretation is intuitive and non controversial because the pure states are safe from collapse. In QM the boundary is blurred and moreover for a given state one may even have nonunique decompositions of quantum mixtures. Quantum mechanics is first and foremost a different kind of statistical theory. Because of the Bayesian interpretation of the collapse as simply gaining knowledge there is no need for the many worlds interpretation (and therefore the wavefunction does not have an intrinsic ontological value).

I think that the right mathematical foundation of QM is not in state space, but in the algebra of observables. Here there is nothing un-intuitive and because of the GNS construction this formulation is well defined. (Also the Hilbert space is rather uninteresting because it is only determined by its dimensionality; the true action happens in the operator algebra.)

The measurement problem has two parts. First is the actual experimental setup and the freedom to choose what to measure (currently not captured by QM). Second, there is the actual interaction with the apparatus and the emergence of the superselection rules. Superselection rules are necessary to avoid inconsistencies on a classical-quantum system description, and they are definitely not derivable from a pure QM foundation.

I am currently not following Penrose's ideas of combining QM with gravity, but he may be on the right track. When I will have some free time I will try to understand his ideas. My intuition/speculation about superselection rules stems from the problem of force separation from the unification energy going down on the energy scale. If at high enough energies all interactions are unified, why is that at lower energies they no longer interact? This is also a kind of superselection rule prohibiting force mixing. If we can understand this mechanism then we are one step closer to understanding the measurement problem in general. So here is a wild idea. Maybe our whole universe is a giant relativistic (quantionic) wavefunction and the classical parts of our universe (including classical space-time) are just the manifestations of quantionic superselection rules.

Florin

Dear Professor Singh,

I enjoyed your essay. I particularly liked the concept of a mesomic region between quantum mechanics and classical physics. I believe I have a graph of this region that you may find interesting. It is located in the essay "Gravity from the Ground Up". I start with the concept of digital waves. This is where particles move digitally and therefore experience discontinuous space and time even though the space time fabric is continuous. So, time is not quite classical, but I do not think it is the timelessness you expressed for quantum mechanics. I am interested in any opinions you may have.

I also liked your ending quote by Einstein, and think it will be proven correct.

Thank you,

Don Limuti

Dear Tejinder,

From my viewpoint the problem is how do things stay together to make for a stable "hop". It is like a rigidity test in mechanics. Electrons are excellent hoppers because they have no parts. Protons may have parts, but when it hops it is rigid. Buckyballs C60 are big and distributed but the forces holding it together keep it rigid enough so that it hops and has QM properties. Nothing has been found to date that is bigger (more massive) than the buckyball that has QM properties.

At the Planck mass there are things like "fleas" that are far from quantum mechanical. So, the experiment would be to find a QM flea! It will be a ferocious flea.

Beyond the Planck mass I believe space time does not allow anything to hop.

I like it that you have given a name to these missing massive particles "mesoscopic Particles" and you abbreviate it m-mass. I think it is going to stick.

Best of luck,

Don L.

Dear Dr. Tejinder Singh

You wrote:

Consider, as a thought experiment, a Universe which has only quantum mechanical particles, such that their total mass-energy is much less than Planck mass. There is no longer a classical spacetime and no point structure, but in principle there is an equivalent reformulation of the quantum theory.

Consider a thought experiment that space-time is merely a math model and cosmic space itself is timeless. Physical time is run of clocks in timeless space. I see this thought experiment a possibility to resolve "action on distance" by gravity.

Gravity works between quanta of timeless space. Gravity is result of curvature of timeless quantum space. More mass is in a given volume of quantum space more space is curved. Curvature of quantum space depends on its density. More mass is in given volume of quantum space, less space is dense and more is curved. Density of quantum space Ds in a centre of massive object is Ds = 1/m, where m is a mass of stellar object.

Fg = G/Ds1 x Ds2 x r on square.

yours amritAttachment #1: 5_TIMELLESS_QUANTUM_SPACE.doc

Dear Tejinder,

1. You may want to contact these researchers in Vienna. This info came from the Physics World Archive.

"The interference pattern formed when a beam of electrons passes through a double slit is clear

evidence that electrons can behave as both waves and particles. This wave-particle duality lies at

the heart of quantum mechanics, but physicists remain intrigued by the boundary between the quantum

and classical worlds. Neutrons, atoms and small molecules have all shown quantum-interference

effects. Now Markus Arndt and co-workers at the University of Vienna have observed the wave-like

behaviour of carbon-60 molecules. The "bucky-ball" molecules are at least an order of magnitude more

massive than any other object where wave properties have been observed (Nature 1999 401 680)."

2. I did some "Googling" on "His Dark Materials" and found I had made a mistake. The university

involved is Oxford and not Cambridge. I could not discover weather Pullman actually met Penrose, but

they were linked in this article: http://www.telegraph.co.uk/technology/3340760/The-quest-for-dark-

matter.html

"Pullman's imaginary dark matter, Dust, is a name for what happens when matter begins to understand

itself. That's why it plays such an important role in the trilogy in which church scholars fret

that it could even bring down God. Pullman made a leap in inventiveness by making Dust "a way of

picturing human consciousness, the most mysterious thing in the universe".

Some of the inspiration for this idea lay nearby, in the university, in the controversial

suggestion of mathematician Sir Roger Penrose that consciousness is somehow linked with the yet-to-

be developed theory of quantum gravity, which will unite the quantum theory of the very small with

general relativity, the current theory of the very big (and gravity). "It is an extraordinary

idea," said Pullman."

3. I have been assuming that the transition from quantum to classical is gradual and that a buckyball is

not quite as good quantum mechanically as an electron. The transition to classical is complete at

the Planck mass. The m-mass region should contain a mixture of QM and classical stuff. These are just

my notions. What do you think?

4. If you think I can be of any help please let me know.

Thanks,

Don L.

i am fascinated with gravity as it seems to be the main mystry that lead the many we still have in Physics. Its connection with quantum mechanics is still doubtful. To me gravity may have different strengths and nature too, e.g both attractive and repulsive, depending on the sitaution faced in nature. After all , stong nuclear changes both its strength and nature as it encounters distances less than the nucleon size! At the level of cosmos it is difficult to plan test experiments and so also in a lab. on earth. Its long term manifestations are making us sense this inetraction , the first to emerge on the horizon, followed by strong, electromagnetic and nuclear weak. ay be gravity has different components too!

Dear Tajinder,

i await your response to some off beat suggestions i made for your mesascopic region studies on my essay site as also some others on your essay site. Perhaps

you have pressure on time that i do not have in my retired life.