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

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

Dear Dr. T P Singh,

Thanks for your beautifully written enchanting essay. It contains up to date information on QM and its various versions. I, too, have my own version of QM and to know this,please, go through my essay (http://fqxi.org/community/forum/topic/1543--Sreenath) and express your comments on it in my forum. It is continuation of my last year's essay.

In your essay, you have expressed your views with crystal clarity and also proposed an experiment to verify it. However, I feel that, currently there is lot of confusion in distiguishing between the classical world and the quantum one. This confusion,it appears,has arisen as a result of the failure to realise the seperate fundamental traits laying behind both worlds. If we realise this dichotomy then the results of your experiment become obvious before conducting it.

Best regards and good luck in the essay contest.

Sreenath

Dear Tejinder Singh and collaborators

Thank you for your essay, which presents a lot of material completely new to me. We seem to be thinking on the same lines.

I tried to describe a possible form for the kind of nonlinear theory which you suggest. It starts from the notions that

- space-time may have an asymmetric metric $g$ and an asymmetric connection $\nabla$.

From the metric, one can derive (at least) two interesting algebraic features. One is a model of the complex numbers, so $i^2 = -1$. The other is an element $R$ of a Hopf algebra discovered by Dubois-Violette and Launer. $R$ satisfies the "Quantum Yang-Baxter" equation.

$g$ and $\nabla$ are constrained by insisting that

- $\nabla i = 0$ and $\nabla R = 0$.

A solution is a pair $(g, \nabla)$ for which

- the Yang-Mills functional is stationary under all small variations of $g$ and $\nabla$ for which $\nabla i$ and $\nabla R$ are stationary.

There are other variants of this model.

A "particle" is a basic solution, an eddy in the geometry of space-time.

I have no evidence that real physics is like this, but it seems to offer all the apparatus one would expect: variational calculus, Hopf algebras. It fits naturally with general relativity. Solutions $(g, \nabla)$ may form a smooth manifold whose tangent spaces are the Hilbert spaces of quantum mechanics. If so, it seems likely that superpositions of states are unstable, as you suggest.

I would be glad to hear any views you may have on all this.

Best wishes

Alan H.

Angelo et al.

Fascinating essay. I disagree with proofs of Bells inequalities but that does no affect the substance, and I agree Optomechanics and Trace Dynamics, both consistent with my own fully mechanistic approach to causal unification, using a " radical rethink of how we comprehend quantum theory, and the structure of spacetime."

I suggest matter can be superposed in terms of additivity, i.e. fluids. Fine sawdust is additive, and at a larger scale 3 billion tables may be equally additive.

Have you considered superposition as long term macroscopic evolution subject to binding energy, so rigidity (viscosity) is the key variable?

And ref the twin slit molecular results; Have considered that molecules may propagate photons on surface interaction at the dense surface electron fine structure slit edges?

I've been discussing a simple causal re-interpretation of the measurement problem and the Copenhagen interpretation based on the mechanism of detection as 'sampling' and modulation discussed in my essay. I hope you'll get a change to read and discuss.

Best wishes

Peter

Tejinder,

You and your collaborators have done a superb job of explaining why continuous function physics is very much alive, even with all the success of quantum theory over the years.

Nice! Thanks for an essay I am sure to read a few more times.

I hope you get a chance to visti my essay site ("The Perfect First Question.")

Best,

Tom

Dear Angelo Bassi, Tejinder Singh and Hendrik Ulbricht,

I enjoyed your essay. It is very clearly written and accessible.I particularly like the thought provoking questions that you have at the beginning and where you end up, suggestion a possible need to reconsider the relationship of the wave function with space-time.It is good that you are able to propose detailed practical work that will support the presented idea. Good luck in the competition.

Thanks, Tejinder. I am honored that you ask.

The gist, following Wheeler ("it from bit") is that there is zero distance between a yes-no question and its answer, no matter how separated in time; in other words, a relativistic "finite and unbounded" reality does not have to be finite in time and unbounded in space -- general relativity suffers no loss of generality in a model finite in space and unbounded in time. The binary relation holds in either case.

This can be made rigorous:

For reasons explained in the essay, we assign positive-definite values 1/2 to yes, 1/4 to no; indefinite values of - 1/2 to not-yes and - 1/4 to not-no.

In a Bell-Aspect type experiment, 1/2 1/4 = 3/4 describes the upper limit of probability (75%) that Alice and Bob will have correlated answers, when they decide on a cooperative strategy in advance. Random correlations will fall to the average of correlations, 1/2, by the pair of equations:

1/2 1/4 - 1/2 1/4 = 1/2

- 1/2 - 1/4 1/2 - 1/4 = - 1/2

Because there is no negative probability, the prior assumption of a probability measure function adds a priori an extra sign, such that:

( 1/2) 1/4 - 1/2 1/4 = 1/2

- (- 1/2) - 1/4 1/2 - 1/4 = 1/2

So -- as it should be -- assuming that nature is fundamentally probabilistic, the singular average 1/2 applies in both cases. Underlying this calculation is the implied assumption of probability theory: the hypothesis of equally likely outcomes. That's why the extra sign, which brings with it the additional implication of a non-orientable space.

The contest asks us to identify and question foundational assumptions -- one of the most persistent of these is probabilistic measure. When we eliminate that assumption, what's left is topological orientability, left hand and right hand. That's the reason that I say the distance between question and answer is zero -- because orientability implies an additional degree of freedom by which no matter if the initial answer is yes followed by no (3/4)or not-yes followed by not-not-no, the outcomes is zero. (Thus, zero distance between question and answer, a result that can only come of topological analysis, where distance carries a different meaning than in ordinary geometry.) Thus:

1/2 1/4 - 1/2 1/4 - 1/2 = 0 (Left Hand, positive rotation in the plane)

- 1/2 - 1/4 1/2 - 1/4 1/2 = 0 (Right Hand, negative rotation in the plane)

The sign pair, and - -, are the same initial condition as the probabilistic model, except that the initial condition is compelled to be orientable, i.e., yes no (or not-yes minus not-not-no which is sign-reverse equivalent) such that an equal number of measurement events in the orientable space as the probability space, gives a zero remote outcome, implying Right Hand and Left Hand variables.

So instead of a probability average 1/2 for quantum correlated events, dependent on observer orientation and implying an observer-created probabilistic reality, we get a classical continuous wave function, with no probability function at all. The range of continuous values of the wave function are dichotomous correlated discrete values -- binary -- just as Wheeler said.

Therefore:

Local, physical information of a remote measurement outcome is compelled to originate from a point at infinity, because it's that singularity which distinguishes the nonorientable measure space of R^3 from the topology of S^3, the orientable space that is the source of continuous binary variables.

Hope this helps. I was just going to post the "gist," but I couldn't stop myself, because I think the argument is quite elegant.

Best,

Tom

Sorry, got logged off. The above is mine.

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.

Dear Dr's Bassi, Singh, and Ulbricht!

Physicists build their phenomenological model of the world ignoring the ontology. But besides the Empirical Standard of foundation of the Fundamental Knowledge required Ontological Standard of foundation. Quantum theory-operative theory, but not conceptual, theory without ontological foundation. Ontology displays dialectical thought to the fact that the whole world is Triune Superposition. What do you understand more broadly in your output «...radical rethink of how we comprehend quantum theory, and the structure of spacetime.»? What is your model of the structure of Space-Time? Thanks for your doubts! Sincerely, Vladimir

Hi Authors, fundamental gravitational and inertial equivalency and balancing (both at half strength force) fundamentally proves and demonstrates F=ma. A MOST IMPORTANT POINT -- DO YOU AGREE? (As acceleration is fundamentally balanced and averaged as well.) You will need to show this, in conjunction with the important fact that BOTH gravity and electromagnetism enjoin and balance visible and invisible space. Now, all of this is consistent with instantaneity and the fact that gravity cannot be shielded. You will need to show this too. As you well know, light is known to be quantum mechanical in nature, so all of the above necessarily involves balanced and equivalent attraction and repulsion as well. This will give you fundamental/true quantum gravity. My essay discusses and proves all of this. Can you review and rate it please?