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

    • [deleted]

    • 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

          Thank you for your reply, which I do find effective, even though my intuition directs me elsewhere. My comments in my second paragraph are too embedded in perhaps singular ideas about QM that I ought to have edited out and will not pursue here.

          I'm more an EFT person than a ToE person, but I nonetheless find CSL-type modifications of QFT somewhat uncongenial, although I do accept them as effective models, when pursued with enough care and detail. I suppose I would somewhat prefer 't Hooft-type models as alternatives to QM, if an alternative is to be pursued, indeed there are a few published papers of mine on random fields.

          FWIW, I am currently attempting to develop the consequences of other nonlinearities in QFT, without prejudice to your own intuitions. Higher interaction terms in a Lagrangian formalism, for example, are nonlinear in a sense, albeit they do not directly affect the axiomatic superposition of wave functions. Nonetheless, even the lowest order interaction term, the mass term, modifies interference patterns nontrivially, and the ways in which higher-order interactions modify interference patterns are not restricted purely to what the overall mass of an aggregate object may be. The experimental difficulty of being able to assert definitively that every possible effect of environmental decoherence on whatever interference pattern there may be has been adequately eliminated increases considerably when the aggregate object is large (though this way of putting the experimental situation accepts environmental decoherence as an explanatory move, which I think is awkward for your project; I see that on page 12 you explicitly require that decoherence has been "ruled out", which is, as just mentioned, difficult to ensure and even more difficult to be definitively certain of).

          Regularization and renormalization (and the presence of infinite numbers of virtual particles, in the usual way of talking about perturbative QFT) complicate intuitive understanding of interacting QFT, which I take to underlie QM (perhaps too uncritically, but hey ho). My own FQXi essay begins a discussion of a way of re-conceptualizing interacting QFT that I would hope might in time make it possible to discuss large aggregate objects more clearly (though that's obviously a large hope).

          Best wishes,

          Peter.

          Angelo, Tejinder, Hendrik.

          A real mechanism for 'Continuous Spontaneous Localization' or it's equivalent is discussed in my essay, which you hoped to read but may not have yet. CSL and the STR postulates emerge from the quanta, consistent with your prediction.

          An extension towards curved space time then also emerges. I'd still be very interested in your views on my rather ontological construction.

          I've now also looked through your recent arXiv paper, and think I agreed with the rather limited areas amongst the mathematics that I understood! There was more conceptual commonality with the foundations of my thesis than I'd expected.

          Very best of luck in the final run in. I think all the final 35 and more will be of high quality.

          Peter