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

      Thank you Eric for your remarks. We are trying to understand your essay and the one by Ragazas.

      Regards,

      Authors

      Dear Ben,

      Thank you for your interesting and important comments.

      1. The answer here depends on the stand one has towards collapse models. If one considers the stochastic collapse dynamics as an intrinsic feature of nature, then collapse models define an arrow of time, given by the direction along which pure states become statistical mixtures. Since for material particle lambda is always finite, their dynamics always contains an arrow of time.

      On the other hand, if one considers collapse models as phenomenological models emerging from an underlying theory, like the dissipative dynamics of a (classical) particle in a bath is, with respect to the underlying Netwonian dynamics, then there is no in-built arrow of time.

      2. The behavior of a system (like in any theory) depends on its state, in this case on its wave function. If the wave function is entangled with a larger system, then it will evolve in a certain way (typically, enhancing the collapse rate); If on the other hand the wave function is factorized from the rest of the world, it will evolve as an isolated system. Whether the system's wave function is entangled or factorized, depends on the previous history of the system.

      3. In our view, it would not be a matter of choice whether to obtain a quantum theory from quantizing a classical theory, or derive it from an underlying theory. One cannot assume classical mechanics, define quantum mechanics from that, and then derive classical mechanics. IT is not logical. We agree with you that if experiments show departure from quantum theory in the mesoscopic regime, the need for an underlying theory will be strongly indicated.

      Looking forward to reading your essay.

      Regards,

      Authors

      Thank you Sreenath, for your remarks; we look forward to reading your essay.

      Authors

      8 days later

      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

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        • Post #57

        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.

          Thank you Alan. I left a short comment on your post.

          Tejinder

          Thank you for your kind remarks Tom. Could you possibly give a brief gist of your essay - meaning, what the key points are? I have tried reading it, but some pointers from you will be helpful.

          Regards,

          Tejinder

          Many thanks Peter. Hope to read your essay soon.

          Regards,

          Authors

          • [deleted]

          • Post #62

          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

              Dear Frank,

              We have no issues with classical mechanics, of which the equation F=ma is a part. Our point is that quantum theory predicts that the classical world should behave in a certain way, and it apparently does not behave that way [superpositions are not seen in the classical world]. And in our view this calls for an [experimentally falsifiable] explanation. The explanation we discuss possibly involves gravity.

              We do not have anything specific to say here about electromagnetism.

              Authors

              • [deleted]

              • Post #68

              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?

              Dear Peter,

              Thank you for your comments. We whole-heartedly agree that linearity is axiomatic to quantum theory. Our point is: this axiom of linearity leads to a dynamical equation [the Schrodinger equation] whose predictions do not agree with what we see in the macroscopic world around us. The Schrodinger equation predicts that we should be able to observe linear superpositions of position states of macroscopic objects. Why then do we never observe such superpositions? This is the central question. [The quantum measurement problem, the origin of probabilities and the Born rule, while fundamentally important, are secondary to the afore-mentioned central question].

              It may be that this central question can be answered without modifying quantum theory, or without altering its predictions. Thus it may be that macroscopic superpositions are not seen because of decoherence accompanied by the branching of the universe into many worlds. Or it may be that Bohmian mechanics underlies quantum theory.

              We are instead considering an experimentally falsifiable answer to this central question, namely that the axiom of linearity has to be given up. To us, the fact that the assumed renunciation of linearity can be tested by ongoing experiments is of great importance. For the first time since the inception of quantum theory, we have concrete quantitative models which explain the absence of macroscopic superpositions, and whose empirical predictions differ from those of quantum theory, and which can be confirmed or ruled out in the laboratory.

              We do not quite understand what you meant in your second paragraph. A stochastic non-linear modification of quantum theory gives experimental predictions which disagree strongly with predictions of quantum theory, in the mesoscopic and macroscopic regime. For instance, in a noise-free matter-wave interferometry experiment for particles having mass of million amu, if an interference pattern is not seen, this will certainly imply that quantum theory fails for this system. We do not see how the situation can be saved by enlarging the Hilbert space, keeping in mind that the experiment is disagreeing with the assumption of linearity.

              Authors

              Dear Vladimir,

              By `rethink of how we comprehend quantum theory' we meant that quantum theory is an approximation to a deeper theory, in the same spirit in which Newtonian mechanics is an approximation to special relativity, and Newtonian gravitation is an approximation to general relativity.

              By `rethink of how we comprehend the structure of space-time' we meant that space-time geometry as described by special and general relativity is an approximation to a more fundamental description of space-time. This is because an aspect of quantum theory such as instantaneous collapse of the wave-function might possibly be inconsistent with the way we are accustomed to describing space-time geometry.

              We do not yet have at hand a complete description/understanding of what this underlying space-time structure might be. We are working at it, from various angles. For one possible line of thought, please see one of our recent papers

              http://arXiv.org/abs/arXiv:1203.6518 [to appear in Foundations of Physics].

              Regards,

              Authors