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Teginder,

"In order to describe dynamical evolution the theory depends on an external classical time, which is part of a classical spacetime geometry."

The point I make in my entry is that the classical timeline is an effect of the underlaying dynamic, such that it isn't the present moving from past to future, but the changing configuration of what is, that turns future into past....

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Teginder,

"In order to describe dynamical evolution the theory depends on an external classical time, which is part of a classical spacetime geometry."

The point I make in my entry is that the classical timeline is an effect of the underlaying dynamic, such that it isn't the present moving from past to future, but the changing configuration of what is, that turns future into past. Not the earth traveling the fourth dimension from yesterday to tomorrow, but tomorrow becoming yesterday because the earth rotates. Duration is simply what happens within the present, between events, not a property external to the present. This makes time an emergent effect of action, similar to temperature. So without an external dimension of time, there can be no dimensionless point on this timeline. A frozen point in time would be equivalent to a temperature of absolute zero; the complete absence of motion. It would be like trying to take a picture with the shutter speed set at zero. The result would not be a frozen moment in time, but nothing. Which means an entity, micro, or macro, cannot be isolated from its action. That macroscopic table only exists because of the dynamic activity sustaining it. So, effectively, the particle is actually just a really small wave.

Consider this exchange from an interview with Carver Mead;

"So how did Bohr and the others come to think of nature as ultimately random, discontinuous?

They took the limitations of their cumbersome experiments as evidence for the nature of reality. Using the crude equipment of the early twentieth century, it's amazing that physicists could get any significant results at all. So I have enormous respect for the people who were able to discern anything profound from these experiments. If they had known about the coherent quantum systems that are commonplace today, they wouldn't have thought of using statistics as the foundation for physics.

Statistics in this sense means what?

That an electron is either here, or there, or some other place, and all you can know is the probability that it is in one place or the other. Bohr ended up saying that the only statements you can make at the fundamental level are statistical. You cannot grasp the reality itself, only probabilities related to it. They really, really, wanted to have the last word, and the only word they had was statistical. So they made their limitations the last word, saying, "Okay, the only knowledge that there is down deed is statistical knowledge. That's all we can know." That's a very dangerous thing to say. It is always possible to gain a deeper understanding as time progresses. But they carried the day.

What about Schrodinger? Back in the 1920s, didn't he say something like what you are saying now?

That's right. He felt that he could develop a wave theory of the electron that could explain how all this worked. But Bohr was more into "principles": the uncertainty principle, the exclusion principle--this, that, and the other. He was very much into the postulational mode. But Schrodinger thought that a continuum theory of the electron could be successful. So he went to Copenhagen to work with Bohr. He felt that it was a matter of getting a "political" consensus; you know, this is a historic thing that is happening. But whenever Schrodinger tried to talk, Bohr would raise his voice and bring up all these counter-examples. Basically he shouted him down.

It sounds like vanity.

Of course. It was a period when physics was full of huge egos. It was still going on when I got into the field. But it doesn't make sense, and it isn't the way science works in the long run. It may forestall people from doing sensible work for a long time, which is what happened. They ended up derailing conceptual physics for the next 70 years."

.........

"So early on you knew that electrons were real.

The electrons were real, the voltages were real, the phase of the sine-wave was real, the current was real. These were real things. They were just as real as the water going down through the pipes. You listen to the technology, and you know that these things are totally real, and totally intuitive.

But they're also waves, right? Then what are they waving in?

It's interesting, isn't it? That has hung people up ever since the time of Clerk Maxwell, and it's the missing piece of intuition that we need to develop in young people. The electron isn't the disturbance of something else. It is its own thing. The electron is the thing that's wiggling, and the wave is the electron. It is its own medium. You don't need something for it to be in, because if you did it would be buffeted about and all messed up. So the only pure way to have a wave is for it to be its own medium. The electron isn't something that has a fixed physical shape. Waves propagate outwards, and they can be large or small. That's what waves do.

So how big is an electron?

It expands to fit the container it's in. That may be a positive charge that's attracting it--a hydrogen atom--or the walls of a conductor. A piece of wire is a container for electrons. They simply fill out the piece of wire. That's what all waves do. If you try to gather them into a smaller space, the energy level goes up. That's what these Copenhagen guys call the Heisenberg uncertainty principle. But there's nothing uncertain about it. It's just a property of waves. Confine them, and you have more wavelengths in a given space, and that means a higher frequency and higher energy. But a quantum wave also tends to go to the state of lowest energy, so it will expand as long as you let it. You can make an electron that's ten feet across, there's no problem with that. It's its own medium, right? And it gets to be less and less dense as you let it expand. People regularly do experiments with neutrons that are a foot across.

A ten-foot electron! Amazing

It could be a mile. The electrons in my superconducting magnet are that long.

A mile-long electron! That alters our picture of the world--most people's minds think about atoms as tiny solar systems.

Right, that's what I was brought up on-this little grain of something. Now it's true that if you take a proton and you put it together with an electron, you get something that we call a hydrogen atom. But what that is, in fact, is a self-consistent solution of the two waves interacting with each other. They want to be close together because one's positive and the other is negative, and when they get closer that makes the energy lower. But if they get too close they wiggle too much and that makes the energy higher. So there's a place where they are just right, and that's what determines the size of the hydrogen atom. And that optimum is a self-consistent solution of the Schrodinger equation."

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Dear Angelo, Tejinder and Hendrik,

I think the criterion for this departure from linear QM may come with horizon scales. The de Broglie wave equation tells us the wave length of a particle with momentum p is λ = h/p. If we use the momentum p = mc (thinking in a relativistic sense of p = E/c) we may estimate the wave length for a Planck momentum particle p = m_pc = 6.5x10^5gcm/s, for...

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Dear Angelo, Tejinder and Hendrik,

I think the criterion for this departure from linear QM may come with horizon scales. The de Broglie wave equation tells us the wave length of a particle with momentum p is λ = h/p. If we use the momentum p = mc (thinking in a relativistic sense of p = E/c) we may estimate the wave length for a Planck momentum particle p = m_pc = 6.5x10^5gcm/s, for m_p the Planck mass. The wave length for such a particle is then 1.0x10^{-32}cm, which is close to the Planck length scale L_p = sqrt{Għ/c^3} = 1.6x10^{-33}cm.

A quantum system is measured by a reservoir of states. The superposition of states in that system is replaced by entanglements with the reservoir of states. The standard measuring apparatus is on the order of a mole or many moles of atoms or quantum states. This then pushes the effective wavelength of this measurement, or maybe more importantly the time scale for the reduction of quantum states measured to an interval shorted than the Planck time T_p = L_p/c. This might mean that measurement of quantum systems, and associated with that the stability of classical states (the table not being in two places at once & Schrodinger’s cat) involves this limit that is associated with quantum gravity.

John Wheeler discussed how there may be different levels of collapse. With gravity there is the collapse of a star into a black hole. He then said this may be related to the “collapse” (to use an over played buzzword) of a wave function. He said the dynamics of black hole generation and the problems with quantum measurement might well be related, or are two aspects of the same thing. It might also be pointed out there are theoretical connections between QCD and gravitation, where data from RHIC and some hints with the heavy ion work at the LHC, that gluon chains or glueballs have black hole (like) amplitudes similar to Hawking radiation.

In an ideal situation it might the be possible to maintain a system with around 10^{20} atoms in a quantum state. A reduction of such idealism may reduce this to a lower number. This does leave open the question of how the physics of superfluidity, superconductivity and related collective overcomplete or coherent states fits into this picture.

My essay is not related to this topic directly, though my discussions on replacing unitarity with modular forms and meromorphic functions could have some connection.

Good luck with your essay.

Cheers LC

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As noted at the beginning of your article:

"The principle of linear superposition...Along with the uncertainty principle, it provides the basis for the mathematical formulation of quantum theory." You then suggest that it might only hold as an approximation.

I view the problem rather differently. Fourier Analysis is the actual mathematical basis for quantum theory. Superposition and...

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As noted at the beginning of your article:

"The principle of linear superposition...Along with the uncertainty principle, it provides the basis for the mathematical formulation of quantum theory." You then suggest that it might only hold as an approximation.

I view the problem rather differently. Fourier Analysis is the actual mathematical basis for quantum theory. Superposition and the uncertainty principle are merely properties of Fourier Analysis. In other words, they are not properties of the physical world at all, but merely properties of the mathematical language being used to describe that world. Even the well-known, double-slit "interference pattern" is just the magnitude of the Fourier Transform of the slit geometry. In other words, the pattern exists, and is related to the structure of the slits, as a mathematical identity, independent of the existence of waves, particles, physics or physicists.

For the better part of a century, physicists have been misattributing the attributes of the language they have chosen to describe nature, for attributes of nature itself. But they are not the same thing.

Fourier Analysis, by design, is an extremely powerful technique, in that it can be made to "fit" any observable data. Hence it comes as no surprise that a theory based on it "fits" the observations.

But it is not unique in this regard. And it is also not the best model, in that it assumes "no a priori information" about what is being observed. Consequently, it is a good model for simple objects, which possess very little a priori information. On the other hand, it is, in that regard, a very poor model, for human observers; assuming that it is, is the source of all of the "weirdness" in the interpretations of quantum theory.

Putting Fourier Analysis into the hands of physicists has turned out to be a bit like putting machine guns into the hands of children - they have been rather careless about where they have aimed it. Aiming it at inanimate objects is acceptable. Aiming at human observers is not.

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Dear Authors,

Thank you for an interesting essay.

Maybe I am missing something, but, on the face of it, there may be some contradiction between the following statements in your essay:

1). "When one considers doing such an interference experiment for bigger objects such as a beam of large molecules the technological challenges become enormous."

2)."However when we look...

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Dear Authors,

Thank you for an interesting essay.

Maybe I am missing something, but, on the face of it, there may be some contradiction between the following statements in your essay:

1). "When one considers doing such an interference experiment for bigger objects such as a beam of large molecules the technological challenges become enormous."

2)."However when we look at the day to day world around us linear superposition does not seem to hold! A table for instance is never found to be `here' and `there' at the same time. In other words, superposition of position states does not seem to hold for macroscopic objects. In fact already at the level of a dust grain, which we can easily see with the bare eye, and which has some 10¹⁸ nucleons, the principle breaks down."

So if technological challenges are enormous for large molecules, one would think they are downright prohibitive for dust grains or tables, so the principle does not break down, but we just cannot solve the technological challenges to demonstrate it for such objects? The following analogy may be appropriate: we cannot demonstrate reversibility for large objects (e.g., when we break a vase), furthermore, thermodynamics is based on irreversibility, but that does not mean that reversibility fails for large objects.

Another remark. For what it's worth, I expect interference to exist for arbitrarily large objects. My reasoning is based on the following almost forgotten ideas of Duane (W. Duane, Proc. Natl. Acad. Science 9, 158 (1923)) and Lande (A. Lande, British Journal for the Philosophy of Science 15, 307 (1965)): the direction of motion of electron in the interference experiment is determined by the momentum transferred to the screen, and this momentum corresponds to quanta (e.g. phonons) with spatial frequencies from the spatial Fourier transform of matter distribution of the screen. So I tend to make the following conclusion: when the mass of the incident particle increases, the momentum transferred to the screen remains the same, but the angle of deflection of the incident particle becomes smaller, as its momentum is greater. So the mass of the incident particle is in some sense an "external" parameter for the interference experiment.

Thank you

Best regards

Andrey Akhmeteli

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Please:

I show by experiment in this essay contest how quantum theory is an approximation. My experiments refute the Born rule. A singly emitted gamma-ray should go one way or another at a beam splitter, but I show coincident detection exceeding chance. Similarly for an alpha-ray. This supports the Loading Theory, which was misrepresented and misunderstood for ~70 years, which is why no...

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Please:

I show by experiment in this essay contest how quantum theory is an approximation. My experiments refute the Born rule. A singly emitted gamma-ray should go one way or another at a beam splitter, but I show coincident detection exceeding chance. Similarly for an alpha-ray. This supports the Loading Theory, which was misrepresented and misunderstood for ~70 years, which is why no one considers it. There are two problems:

(1) There are accepted experiments that may be adjusting things to favor QM, and also that researchers have not looked for certain artifacts. A good example is macromolecule diffraction. I do not expect a macromolecule could load up. My experiments and analysis indicate the universe is not crazy and that macromolecules are real particles. But atoms can take on either a wave state or a particle state. My enhanced version of the Loading Theory can explain wave-particle duality up to at least atoms. Physicists may think a macromolecule is neutral, but it is easily charged. It is very likely that many experiments are looking at field deflection effects. To further back my claims, I analyzed one of the Vienna experiments in my essay, and cite several anomalies that do not fit diffraction theory.

(2) The other problem is that my work is so sensational that you are not likely to take it seriously unless other physicists examine it. I have been offering to demonstrate to physicists for 10 years and have performed public demonstration of the gamma-split experiment with little recognition. What I have is for-real and I go with full confidence to face any scrutiny. I made an offer to demonstrate to FQXI people in Brendan Foster's blog on the essay contest.

Please be careful: I do not need to be the one to say bad things about physicists who embrace quantum weirdness because they are invested in it. Now we have a good experimental reason to resolve the paradox instead of embracing it. The history that has misled generations of physicists is in my essay. We no longer need acts of desperation, like superluminal magical collapse of the wave function, etc.

Please see A Challenge to Quantized Absorption by Experiment and Theory. Also please see Ragazas' paper that supports the Loading Theory.

Thank you, Eric Reiter, September 12, 2012.

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Dear Angelo, Tejinder, and Hendrik,

You present a very good idea, all the more so because of the very realistic possibility of experimental verification in the near future. I don’t know if it’s right, but the case you present for pursuing this direction is quite convincing. Indeed, I hope it’s wrong, because it would wreck some of my own ideas about quantum gravity! The universe...

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Dear Angelo, Tejinder, and Hendrik,

You present a very good idea, all the more so because of the very realistic possibility of experimental verification in the near future. I don’t know if it’s right, but the case you present for pursuing this direction is quite convincing. Indeed, I hope it’s wrong, because it would wreck some of my own ideas about quantum gravity! The universe is oblivious to such considerations, however. A few questions and comments:

1. Presumably this provides an arrow of time, since collapse is irreversible, but perhaps time in this sense fades out of the picture on the fundamental scale where the superposition lifetime becomes infinite?

2. I’m sure this has been addressed, but it seems that there might be some issues involving things like locality and “microscopic constituents” of “macroscopic systems.” Roughly speaking, how does a microscopic system “know” if it is supposed to preserve its own superposition or recognize that it is part of a larger system, which must collapse? One of the main points of the decoherence explanation of the measurement problem is that one must consider microstate, apparatus, and environment simultaneously. I am wondering how this all fits together.

3. You mention Adler’s view that it’s the wrong approach to quantize classical dynamics. This may be correct, but it seems to me that it is simply a choice of assumptions: does one start with the correspondence principle, in which case classical physics is viewed as a limit of quantum theory, or does one start with the superposition principle, in which case quantum theory is built up from classical alternatives? Perhaps the experiments you mention will settle this one way or the other.

4. I will have to look at your reference by Oreshkov et al., to see exactly what they mean by “order.” Again, this might wreck my own ideas if it is right.

5. I don’t expect that you will agree much with my own approach, but if you’re interested to see the motivation for my questions, my submission is here: On the Foundational Assumptions of Modern Physics.

Thanks for the interesting read. Take care,

Ben Dribus

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It's not clear to me that you have adequately considered the possibility that the linearity of QM is conventional (or axiomatic, if you will)? The linearity of probability measures, for example, is /axiomatic/ for disjoint events. I suggest that our practice is to use operators to model the statistics of datasets that we obtain from experimental preparations and measurements /on the conventional...

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It's not clear to me that you have adequately considered the possibility that the linearity of QM is conventional (or axiomatic, if you will)? The linearity of probability measures, for example, is /axiomatic/ for disjoint events. I suggest that our practice is to use operators to model the statistics of datasets that we obtain from experimental preparations and measurements /on the conventional assumption/ that the Born Rule determines expected values (and probabilities). If we were to use a different Rule, we would model given data using different density and measurement operators; unless there were other changes to the axioms, I suppose the relationship to probability theory might be rendered problematic, which we would presumably avoid. [Although it's extreme nitpicking, I note that QM is perhaps more properly called bilinear, insofar as expected values are linear both in the states and in the measurement operators. A given totality of experimental datasets has to determine both the density operators and the measurement operators. Quantum Theory as a whole is more than just Hilbert spaces and the Born rule, including as it does elaborations such as heuristics for choosing a Hamiltonian for a given Physical situation, but it seems to me that such overlays are not relevant here.]

The rhetorical thrust of your final section's title, "WHY IS QUANTUM THEORY APPROXIMATE?" seems excessive, insofar as for any given finite and finite-accuracy experimental datasets we can in principle construct arbitrarily precise Hilbert space models for that data, particularly by using ever larger Hilbert spaces. I don't suppose that any other mathematics would be different in the respect of accuracy, albeit different types of models might be more or less parsimonious.

Since these are prejudices that I have held for some time against ideas such as you have expressed in your essay, I will welcome an effective rebuttal.

Peter Morgan.

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Dear Angelo Bassia , Tejinder Singhb, and Hendrik Ulbrichtc,

The answer to your essay question is "no". Quantum linear superpositions are only valid as approximation to an underlying stochastic nonlinear theory. I am glad to find so many points of agreement between our respective approaches; however, I would object to some few points.

First, I would object to the claim that the...

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Dear Angelo Bassia , Tejinder Singhb, and Hendrik Ulbrichtc,

The answer to your essay question is "no". Quantum linear superpositions are only valid as approximation to an underlying stochastic nonlinear theory. I am glad to find so many points of agreement between our respective approaches; however, I would object to some few points.

First, I would object to the claim that the linear superposition principle is valid for fullerene molecules. The superposition principle applies to the electronic part but not the nuclear framework. Precisely the no-applicability of the linear superposition principle to this molecular entity, as a whole, is the basis for the existence of a well-defined molecular shape, with each Carbon atom vibrating around a well-defined position. In fact, as chemists know very well, the application of the linear superposition principle of quantum mechanics to the full molecule (electrons more nuclei) is at odd with the experimentally well-tested concept of molecular shape.

It is very interesting that you discuss the CSL model because your nonlinear equation (1) can be derived from the generalized Schrödinger equation in section (3) of my essay, in the specific case when there is only one Lindblad operator and this is given by

we recover your (1).

Precisely in my essay I emphasized how this kind of generalized nonlinear equation solves the old Schrödinger-cat paradox because prohibits that a cat was in a macroscopic superposition of a live-cat and a dead-cat. It was a delight to discover that you use (1) for essentially the same.

A difference with the CSL approach is that here the generalized nonlinear equation in my essay is derived from a more general Liouvillian approach. I would add that the explanation for the nonlinearity is not related to any hypothetical gravitational effect of the kind assumed by Penrose and others [*], but has a very different physical origin. However, it is true that nonlinearities depend on the size of the system and that is why cats are not found in superposition states.

Due to size limitations for this contest, I could not discuss all the details, but in my subsequent paper positive phase space quantum mechanics (here and thereafter denoted by "PPPQM") I offer additional details and theorems of the Liouvillian approach mentioned in my Essay. It is remarkable that this new formulation/interpretation of quantum theory has an alternative matrix representation (I am going to prepare a paper on this; here and thereafter denoted by "MQM"), and that we can find resonances with the trace dynamics mentioned in your Essay. I will discuss some similarities but also fundamental differences.

In the general case, MQM deals with matrices whose elements are ordinary complex-valued functions obtained from the quantization rule in PPPQM. It is interesting that trace dynamics also deals with such matrices.

The non-commutative structure of the matrix phase space is here derived, as in trace dynamics.

A fundamental difference is that the general equations of motion in MQM are not obtained from an action principle as in trace dynamics. The action principle and Hamiltonian-like equations for the matrices are valid only in the 'pure' case limit. The trace dynamics analogue of Liouville’s theorem is valid in the same limit. The consideration of a much more general kind of equations allow us to study far-from-equilibrium phenomena.

It is again interesting that both approaches introduce their corresponding generalization of the Poisson brackets. Although, I do not know what is the interpretation for trace dynamics; references that I know merely introduce the generalized Poisson bracket using the trace formula; maybe you could explain this to me! In MQM the matrix generalization of the Poisson brackets has a clever interpretation in terms of Fréchet derivatives.

Congratulations by your high ranking in the finalists score. I wait you will win some of the prizes.

[*] Their arguments about hypothetical superposition of spacetimes are traced to an incorrect interpretation of general relativity plus an inconsistent quantum gravity approach.

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