Is Quantum Linear Superposition an Exact Principle of Nature? by Angelo Bassi, Tejinder Singh, and Hendrik Ulbricht

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.

Dear authors,

When reading your excellent essay, a (perhaps silly) question compes to my mind. You write: "Suppose one has prepared in a controlled manner a beam of very large identical molecules...". What I wonder is: Mustn't there be an upper limit where the very large (hence comlex) molecules can no longer be assumed to be positively identical? Might the lack of controlled identity be the limit where linear superposition no longer holds? Might it be a question of molecular complexity, rather than size/weight?

Best regards!

Inger

Thanks for that. I don't yet have a mathematical model in the case of measurement: am thinking about it. The first step is to look at state vector preparation, which is an analogous non-unitary process, involving a projection operator depending on the local macro context. With that in place, the steps to a contextual measurement model - maybe with a new universal constant, as you say - may become clearer. But the essential comment is that the local measurement context may be the "hidden variable" (it's non-local as far as the micro system is concerned, so the non-locality criterion is satisfied). It's hidden simply because we don't usually take into into account.

George

Dear Authors,

You are tackling one of the elephants in the physics room, and as George Ellis commented above this one is hard to sweep under the rug.

Your solution of Continuous Spontaneous Localization [CSL] seems like a good idea to me.

My own work points to the Planck mass as the upper limit of all quantum phenomena including superposition. See my essay for two methods that show this. My essay is "An Elephant in the Room". This is a different elephant than yours (there are plenty of elephants to go around).

Here is a vague outline of an experiment that I believe can be performed that would correlate with your theory:

1. Chose a crystal like diamond to investigate. This is done because diamonds are considered to be a single molecule independent the number of carbon atoms.

2. Create bins of diamonds with increasing numbers of carbon atoms up to the Planck mass.

3. Test these diamond bins via the University of Vienna for the property of interference.

4. I suspect that interference phenomena will gradually decrease with mass and will disappear at the Planck mass. This experiment (if it can be performed) should provide confirmation of your theory.

Good to see you in this contest.

Don Limuti

Inger,

Your question is not silly at all. It is very near the heart of the issue. One need only go a little bit deeper to arrive at "the issue."

What is the significance of the particles all being "identical" in the first place? If they remain, forever identical, then they cannot change with the passage of time. If they cannot change with the passage of time, then they cannot store any information whatsoever, within their internal structure.

But a larger entity, constructed from a number of such identical particles, can store information, by the relationships (like distances) between them. Entities that store information, can behavior towards other entities in a "symbolic" manner, and not just a "physical" manner. Even a tiny virus particle has genetic information stored within it, that enables it to exhibit such "symbolic" behavior.

What is the significant difference between "symbolic" and "physical" behavior? It is this: in the latter, observed data measurements are treated as "real numbers", in the former, they are treated like "serial numbers." Real numbers have most significant and least significant digits. Serial numbers, like credit-card numbers do not; change one digit anywhere, and it symbolizes someone else's account number; introduce one genetic mutation, and it may code for a different protein.

All the "interpretations" of mathematical models in physics have assumed that entities only interact "physically." That is true for entities devoid of any information storage capacity, like subatomic particles. But it is not true of macroscopic entities, especially human observers. Physical behaviors can be viewed as encoded into the equations. But symbolic behaviors are coded into the initial conditions. By ignoring the exact (individual digits) of the initial conditions of the information stored within complex entities, physicists has thrown the baby out with the bath-water.

All the supposed "weirdness" in the "interpretations" of quantum theory, derives from the fact that physicists have failed to take into account that human observers interact "symbolically" with their experiments, as well as "physically."

Dear Robert,

Thank you very much for your enlighening reply! You gave me more than a hint of the role of information theory in physics, which I would like to follow up further. I entered this essay contest in order to have the opportunity to ask some silly questions to people that are more knowing than me - and kind enough to answer. See, if you like, my essay "Every Why Hath a Wherefore".

You saved my day!

Inger

Dr. Singh and Colleagues:

You ask an important fundamental question about quantum linear superposition. But implicit in that question is the assumption that linear superposition should be universal. Instead, I would suggest that linear superposition applies ONLY to primary quantum fields such as electrons and photons. Please see my essay "The Rise and Fall of Wave-Particle Duality", http://fqxi.org/community/forum/topic/1296. In this picture, Quantum Mechanics is not a universal theory of all matter, but rather a mechanism for generating localized particle properties from primary continuous fields, where these localized (but not point) particles then follow classical trajectories (as derived from the quantum equations). Composites of fundamental fields such as nucleons and atoms are localized composite objects WITHOUT wave properties of their own, and hence completely without linear superposition. Beams of neutrons or atoms do not require de Broglie waves for quantum diffraction from a crystal lattice, which instead reflects quantized momentum transfer between the beam particle and the crystal. Remarkably, this reinvisioned quantum picture is logically consistent and avoids quantum paradoxes. Even more remarkably, this interpretation seems to be virtually new in the history of quantum theory, although it could have been proposed right at the beginning. The FQXi contest would seem to be an ideal venue to explore such concepts, but this has drawn relatively little attention.

Thank you.

Alan M. Kadin, Ph.D.

I don't think decoherence solves the measurement problem per se. It does indicate how superpositions of a quantum system are teken up by a reservoir of states in entanglements. This then reduces the density matrix of the system to a diagonal matrix which correspond to probabilities. Decoherence does not tell us which outcome actually happens.

I framed this within the decoherence perspective. It seemed as if the criterion for the sort of nonlinear quantum physics would happen when the time of the state reduction occurs at a time comparable to the Planck time. This can happen for a system with approximately 10^{18} amu or proton masses. This might be the maximal size at which a system can have quantum properties.

Cheers LC

Dear Dr. Bassi and Dr. Singh,

It was a pleasure to meet you at the Quantum Malta conference and I am delighted to see that you have made what is in my view one of the two most important features of quantum theory the subject of your paper.

I agree with the belief that quantum superposition does not hold for macroscopic objects (but for different reasons which are outlined in my paper) and am glad that the predictions of CSL are being put to the experimental test. I just hope that it won't take 20 years, as you suggest in your paper, to test the theory in an adequate regime.

All the best,

Armin

Hi Tejinder,

Can you point me to information on testing particles for interference (that I would understand)?

In the essay (http://www.fqxi.org/community/forum/topic/1403) I logically derive the Planck mass (via two methods) as the ultimate mass for a particle. This does not mean there are any particles in nature that can make it to this mass. I define particle as an object with mass that shows the property of interference. It does not surprise me that real particles never get close to the Planck mass.

This is why I was interested in diamonds. They are peculiar because they are hard crystals that are thought to be quantum mechanical at all sizes. I think they have a chance of getting close to the Planck mass.

Let me know what you think,

Thanks,

Don L.

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

Hi, Post above was by Don Limuti, and not anonymous. Time-out got me.

Hi Tejinder,

Thank you. http://in.arxiv.org/abs/1109.5937 was very good. There is a lot of "art" and science in these measurements.

Here is conclusion of my essay:

Particles can never be accelerated to "c" because they hit their respective Vmax values first and can not be accelerated further. This is because particles are characterized by their Compton wavelength and at Vmax the Compton wavelength has shrunk to the Planck length, as short as anything can get. The Lorentz contraction (1-v2/c2)0.5 seems to indicate that that the velocity of a particle v can be taken to c but as shown in this essay it can only be taken to Vmax just short of c. Say goodbye to the elephant.

At Vmax all particles:

a. Have the same Compton wavelength which is the Planck length.

b. Have the same mass which is the Planck mass.

c. Have a Lorentz contraction that is equal to m0/Pm

d. Have a Schwarzschild radius that is two Planck lengths.

My contention is that quantum mechanics ends at the Planck mass. This does not mean we can find particles that have this super mass. This is why I am interested in diamonds and your essay which explores this most interesting mass zone from the Buckyball to the Planck mass. I suspect that a diamond with a mass below the Planck mass will show interference and a diamond above the Planck mass will not show interference.

Check out the logic for yourself: http://www.fqxi.org/community/forum/topic/1403

Thanks again,

Don L.