The Possibility of Unification via a Global Adynamical Organizing Principle by Michael David Silberstein and W. M. Stuckey

Florin,

Welcome to the dark side :-) I will respond to specific statements/questions, but let me start with a general explanation.

Whether you like BW or not, this is the case concerning the spacetime of GR (which subsumes SR):

"There is no dynamics within space-time itself: nothing ever moves therein; nothing happens; nothing changes. In particular, one does not think of particles as moving through space-time, or as following along their world-lines. Rather, particles are just in space-time, once and for all, and the world-line represents, all at once, the complete life history of the particle."

[This Geroch quote is cited in the FoP paper.] It may be true that consciousness is fundamental and free will is no illusion; GR does not bear on that. It is a mathematical formalism rendering a lossy mathematical description of reality. By "reality" I mean an integral, coherent description of perceptions couched in a single spacetime frame (this doesn't rule out extra dimensions or a multiverse). I don't believe physics is the be-all-end-all of knowledge. What is "REALLY" going on? I don't know. I'm just looking for a coherent, integral, lossy mathematical description of physics experiments and their outcomes (subset of all perceptions) couched in spacetime. Whether BW is true as regards consciousness, for example, does not bear on physics. My search for a description in spacetime is not consistent with other approaches or desiderata. I can appreciate that and the fact that there are others pursuing such options.

By "MP" I mean the inconsistent time evolution of the state vector in Hilbert space, i.e., unitary versus collapse (non-unitary), necessary to render an outcome (probability). As you said, MP can be avoided if you subscribe to a multiverse because you simply ignore the collapse postulate. Otherwise, as far as I know, this problem is unavoidable for those using "differential equations," i.e., the dynamic view., in QM. Conversely, MP doesn't exist in the path integral approach because you're computing directly the transition amplitude (or partition function in Euclidean path integral) between a specific initial state and specific final state. What is there to collapse? Where is decoherence? It's a spacetime view where "nothing happens."

I've found that many physicists do not like this spacetime view, preferring instead dynamical stories (entities interacting via forces in space as a function of time). The only way I can see to salvage the dynamical picture is via causal non-locality (again, to accommodate space-like separated, correlated experimental outcomes which violate Bell's inequality), and indeed this is employed in Bohmian Mechanics. I chose the alternative, i.e., constitutive non-locality as explained in the arXiv paper (Figure 8), because I favor relativity of simultaneity over a preferred frame in SR. The biggest pragmatic advantage to my approach is that I'm motivated to seek a formalism fundamental to QM whereas most interpretations of QM are just that. So, let me address your specific comments/questions.

"what happens after decoherence?"

There is no decoherence, there is no collapse. Nothing happens in spacetime. What we mean by probabilities is explained in the FoP paper (essentially standard "relative frequencies" as in all physics, just couched per subsets of spacetime).

"One thing that looks suspicious is the K4-NRQM because this clearly does not satisfy the Lorenz transformation"

Correct, Schrodinger's equation is not Lorentz invariant, so if someone has an interpretation of QM requiring M4, you should be suspicious! What we're pointing out in our paper is that the spacetime isn't necessarily Galilean either, i.e., it doesn't necessarily respects absolute simultaneity. The transformation equations lack the gamma factors found in the Lorentz transformations, but the time transformation equation contains a displacement term and that term is responsible for RoS. All this is explained in our FoP paper, but it was all published earlier in the papers I cited. We only used their results to justify our interpretation of QM.

"I am very familiar with the path integral approach, but I have never worked in this area myself."

I'm using path integral because, as I stated supra, I wanted to develop a constitutively non-local, adynamical formalism under QFT and the discrete path integral approach is very well suited for this (see our arXiv paper).

"About the BW interpretation, I simply cannot agree with it. In this interpretation there is no freedom and all future history is pre-determined."

Again, whether reality is "pre-determined" or not doesn't bear on mathematical modeling per physics. That is an issue for the study of consciousness proper, rather than the coherent integration of perceptions (and physics is only concerned with a small subset of those, i.e., its experiments). In all honesty, Florin, I believe the hard problem of consciousness, reductionism, and Godel's incompleteness theorem pretty much force us to view consciousness as fundamental. And in that case, a BW model of physics does not violate sensibilities that concern most of its critics. But, as I say, that is not an issue for physics, so we needn't discuss it here :-)

Mark

Florin,

I better clarify this statement, "There is no decoherence, there is no collapse. Nothing happens in spacetime." There are "decoherence" experiments and those experimental configurations and outcomes are certainly couched in spacetime. I'm saying that there is no "quantum/screened-off system" in spacetime. All we have in spacetime are Sources, beam splitters, mirrors, diffraction gratings, polarizers, detectors, non-screened off particles (amenable to worldlines), etc. These things don't exhibit "quantum" behavior, e.g., entanglement, interference, etc., unless you introduce causal or constitutive non-locality. Bohmian Mechanics chooses causal non-locality. I would say backwards causation chooses to violate causal locality by allowing causation to be bi-directional in time. RBW chooses constitutive non-locality.

It seems to me that you can avoid this discussion altogether if you couch your interpretation in configuration space, and I have the impression that's where you're coming from.

Much of this is semantics, I'm afraid. But continued dialogue will help us overcome language barriers.

Mark

Mark,

I would like to say something memorable form Star Wars related to the fact that I was really busy at work recently and I had to ignore FQXi for a bit, but funny quips can be easily misinterpreted, so I pass. Besides, I could not find anything really funny, besides: "busy at work I've been, nice to be back it is"

I have nothing to say about consciousness, but I feel really strongly about free will. Let's just say I've got tired of "happiness is understanding necessity" during communism in Eastern Europe. Plus, imagine a trial defense for murder with: "yes your honor, but all is just a block world universe, it was mathematically proven, and I was destined to kill that person, it's really not my fault."

"I'm just looking for a coherent, integral, lossy mathematical description of physics experiments and their outcomes (subset of all perceptions) couched in spacetime."

I did not get the lossy part. What do you mean by it?

"By "MP" I mean the inconsistent time evolution of the state vector in Hilbert space, i.e., unitary versus collapse (non-unitary), necessary to render an outcome (probability)."

Here I have something to say. Point one. Take your quantum liar experiment. Consider also the C clicks and perform your bell inequality analysis twice: first on all experiments, and second only on the subset of acceptable D clicks. In the first case there are no violations, in the second there are. But the subset of events where violations are present occur also in the case without violations, and beauty is in the eye of the beholder. This is similar with the quantum eraser. In other words, the interpretation of the wavefunction depends on the experimenter's point of view, and this is why Roveli is right. This only makes sense in the Bayesian formalism.

Point two.

Q: Why do we not see interference in the macroscopic world? A: because interaction with environment causes decoherence?

Q: why we do not see superpositions in macroscopic world? A1: This cannot be explained only by Bayesian reasoning. A2: because of the superselection rules. Superselection rules are violations of non-relativistic QM. This is a circular explanation: they are not there because they cannot be there. (or they are there but each live in a separate world. - believe that, sure we do - Sorry I could not help being Yoda again) Space, time, locality, superselection rules are concepts outside non-relativistic QM. Space, time, and locality are concepts inside relativistic QM. By a leap of faith, I conjecture superselection rules should also come from inside relativistic QM.

Q: are any arguments for RBW which cannot be explained by Bayesian reasoning? A: no. (or at least not yet from the papers I read). Conclusion: RBW cannot (yet) conclude it does solve the MP. Just like superselection rules, the concept of an event is not definable inside non-relativistic QM. Solving MP requires defining what an event is.

"There is no decoherence, there is no collapse"

Yes there is decoherence and it has experimentally been observed.

"essentially standard "relative frequencies" as in all physics, just couched per subsets of spacetime"

The relative frequency approach is intuitive, but not mathematically feasible. You simply cannot derive any proof from it because your series has to go to infinity. The right "philosophy" is Kolmogorov's axioms.

"I'm using path integral because, as I stated supra, I wanted to develop a constitutively non-local, adynamical formalism under QFT and the discrete path integral approach is very well suited for this"

Again, just like the frequentist approach, the path integral is not a rigorous approach either, mathematically speaking. It does work, but so does umbral calculus for example. All I am saying it is just too shaky a ground to build upon.

"There are "decoherence" experiments and those experimental configurations and outcomes are certainly couched in spacetime"

Then ignore my earlier comment.

"It seems to me that you can avoid this discussion altogether if you couch your interpretation in configuration space, and I have the impression that's where you're coming from."

The configuration space is Schrödinger's interpretation. I am using Heisenberg's interpretation because I am working in the algebraic approach to QM, and all operators' algebras are in Heisenberg's interpretation.

"Much of this is semantics, I'm afraid. But continued dialogue will help us overcome language barriers."

Most of it, yes, but not all. I mentioned earlier the Connes and Rovelli's result. Connes proved that the "time parameter" is independent of state in the context of measurement theory, spectral theorem, and von Neumann's algebras and this is big and I believe it kills the BW interpretation. Your second roadblock is "the free will theorem" of Conway and Kochen. Again I am agreeing with the R in RBW, but not with BW. Fell free to ignore my points of views, but you need to present a clear rebuttal on how Connes' and Conway's results are explained in a BW interpretation, before your interpretation is to become accepted by the rest of the physics community.

Florin

Hi Michael,

"1) Textbook NRQM which includes only: the claim that QM applies to everything, Schrodinger dynamics, the Eigenstate-eigenvalue link and the Born rule leads to the measurement problem (MP)."

I agree.

"2) If you want to solve the MP head-on you must modify NRQM in some way such as Bohm or GRW. Otherwise, you can go Everett or some kind of statistical interpretation-SI. If you think Rovelli's relational interpretation is an exception to this please explain how, how EXACTLY does this interpretation solve the MP then."

I disagree.

Bohm is looking backwards towards the CM ideals and is not a viable solution. GRW is technically not quite standard NRQM, but this may be a way to go forward if no other solutions to MP are found. If we strictly agree with (1), GRW should not be considered. Everett is not falsifiable and is not science. Rovelli does not solve the MP, it only points out that the wavefunction is a relational object and is a nice way to introduce Bayesian reasoning.

My take on this is that a solution to MP is best found in relativistic QM by looking for ways to generalize Gleason's theorem. Gleason is based on von Neumann algebras which define a statistical measure, but this does not quite work in non-commutative geometry framework. I do know how Born rule generalizes to relativistic QM and there must be another way (different than Gleason) to derive Born rule in NRQM that is better suited to the relativistic QM setting.

Relativistic QM is still QM and any solution to MP in relativistic QM should be applicable to NRQM as well.

Yesterday I had searched the literature and found out that Zurek may have found a solution to the MP in the context of NRQM using "environment--assisted invariance = envariance" (http://arxiv.org/abs/quant-ph/0405161) This looks promising and it does resonate with my way of thinking, but I need some time to asses if this is indeed a valid solution.

"Moving to RQFT by itself doesn't solve the MP."

I agree with a caveat: the solution of MP may be simpler there.

"Environmental interaction (decoherence) makes QM systems behave classical FAPP but does NOT solve the MP."

I agree, but now Zurek has this new idea of envariance and he uses this to derive decoherence from it.

5) Nothing in QM (including the free will theorem" of Conway and Kochen) gives any reason to believe in free will (FW). Note: Conway and Kochen don't think their theorem establishes FW and there are now SEVERAL papers showing that the theorem doesn't entail FW. Belief in free will is maybe motivation for not liking BW but isn't an argument against it. Note that FW is equally screwed by mere dynamical determinism and indeterminism!

I partially agree/disagree. Yes, FW theorem presupposes experimenter's free will in arranging the orientation of his measurement device, so technically this does not prove FW completely, but is surely it is very likely.

"Note that FW is equally screwed by mere dynamical determinism and indeterminism!"

Of course I am aware of those arguments and this is why classical mechanics is at odds with FW. QM is qualitatively different because of 2 things: 1. the experimenter is free to choose what he wants to measure, and 2. the measurement outcome does not exist before the experiment (no hidden variables). So this is neither fully deterministic, nor fully chaotic. Still this is not a proof of FW, I am only restating the gist of Conway's argument.

"6) Merely using the path integral approach doesn't solve the MP either. Likewise for the Heisenberg approach."

I agree.

PART II

"You claim: Connes' and Conway's result refute a BW interpretation, and further that this is accepted wisdom on the part of the physics community. Please explain in DETAIL why this is true. "

In BW there are no genuine choices and from everyday life we do know free will is a reality. Still, this is only handwaving. What Conway's result prove is that nature posses FW if the experimentalist has it. Not a complete proof for FW, but for the remaining original assumption of Conway's result we can then turn to experiments and see if there are any "conspiracies" ever present stopping us to do whatever experiments we choose. Because there are none, I think this completely settles the FW question and now the burden of proof is upon you to show that BW interpretation is compatible with FW. I do not see how this can ever be achieved, but anything is possible until proven impossible.

"Are you talking about this citation: A. Connes and C. Rovelli, Von Neumann algebra automorphisms and time-thermodynamics relation in general covariant quantum theories, arXiv:gr-qc/9406019 (1994)? I have looked at this and I don't see how it refutes a BW at all--is your whole argument based on this paper from 94; Stuck you should see for yourself and respond directly. Florin you say: Connes proved that the "time parameter" is independent of state in the context of measurement theory, spectral theorem, and von Neumann's algebras and this is big and I believe it kills the BW interpretation. Even if this is true (Stuck check this out) please explain EXACTLY how this rules out BW."

Yes, that is the paper. See also the references inside. There are two basic interpretations of time. One is the standard NRQM interpretation: time as a parameter. Why there should be this parameter, we do not quite know, but it is, and this is fully compatible with a BW interpretation. I would say that this is a gross oversimplification of the notion of time.

From Connes and others, here comes the richer notion of time. As an emergent phenomenon, time is compatible only with hyperbolic evolution equations and Cauchy initial value problems. No elliptical PDEs , no index theorems, no global self-consistency conditions.

Before Connes, there was no solid mathematical justification for time as an emergent phenomena. There were clues, but not a proof. Now again, the same scenario from FW applies. If you want BW to be accepted, then you have to prove that BW is compatible with time as an emergent phenomenon. Yet again, I do not think this is possible, but that does not mean anything because I am not working in this approach. In my (possible wrong) view, emergent = now = initial value problem.

"I suspect that the strongest argument you could have here is that perhaps certain algebraic approaches, if true, lead to certain conclusions, if there are theorems based in algebraic approaches PROVING that BW is ruled out or that a SI of the wave function is impossible that would be news to most of the people that I know. "

To the best of my knowledge, there are no such theorems in the algebraic approaches.

"You say: A BW interpretation is time independent [by the way, is that necessarily true?]"

That is my understanding of it, see my answer above. What you need to do is to prove me wrong. I do not think this is possible though, but it is only an opinion at this point.

"You say: A BW interpretation is time independent [by the way, is that necessarily true?] and this runs aground of the Tomitza-Takesaki theorem which provides a God-given time parameter. Please explain this or tell me where to look. Are you saying this theorem proves that there has to be a preferred frame of reference? "

Please excuse the sloppy formulation, but here is the gist. There are no preferred frames of reference, but "now" is qualitatively different from "future" because "now" is emergent from "past" and "future" did not "emerge" yet.

"2)That all statistical interpretations-SI (including ours) are committed to deriving superselection rules from a Bayesian interpretation which is impossible. So again, please explain in DETAIL why all SI are committed to a Bayesian account of the wave function and why our account in particular can't explain or isn't consistent with superselection rules. I'm not sure I'm getting you here, for example, how does this relate to our claim that:

This is similar with the quantum eraser. In other words, the interpretation of the wavefunction depends on the experimenter's point of view, and this is why Roveli is right. This only makes sense in the Bayesian formalism. "

For a Bayesian interpretation in QM see: http://arxiv.org/abs/0706.2274

"3) Please explain this claim in detail and why this tells against RBW:

Space, time, locality, superselection rules are concepts outside non-relativistic QM. Space, time, and locality are concepts inside relativistic QM. By a leap of faith, I conjecture superselection rules should also come from inside relativistic QM. "

Those are only facts, not claims against RBW.

"4) Please explain this claim also:

The relative frequency approach is intuitive, but not mathematically feasible. You simply cannot derive any proof from it because your series has to go to infinity. The right "philosophy" is Kolmogorov's axioms. "

There are several approaches to probability: Laplacean principle of indifference, frequentist approach, Kolmogorov's approach as a model. I was only stating that to infer consequences one uses either a model (Kolmogorov), or reasons by knowledge gain (Bayesian - Laplace's approach) but one cannot say anything definite in the frequentist approach because there is always the possibility of counterexamples as the infinite series goes to infinity.

Cheers,

Florin

Florin,

"I have nothing to say about consciousness, but I feel really strongly about free will."

I'm not concerned with preserving the notion of "free will" in the formalism of physics.

"I did not get the lossy part. What do you mean by it?"

Here is a definition from the internet: "A term describing a data compression algorithm which actually reduces the amount of information in the data, rather than just the number of bits used to represent that information." See the Rickles essay.

"Take your quantum liar experiment. Consider also the C clicks and perform your bell inequality analysis twice: first on all experiments, and second only on the subset of acceptable D clicks. In the first case there are no violations, in the second there are. But the subset of events where violations are present occur also in the case without violations, and beauty is in the eye of the beholder. This is similar with the quantum eraser. In other words, the interpretation of the wavefunction depends on the experimenter's point of view, and this is why Roveli is right. This only makes sense in the Bayesian formalism."

There is still the mystery of single-particle interference with C clicks but, yes, the MZI does not entangle the atoms unless there is a D click. You can look at this as a state preparation as in any experiment. For example, you don't get 100% entangled down-converted photons from laser-pumped crystals. So what? You simply use the pairs that are so entangled because that's the QM state you're testing. The experimentalist must always adjudicate correlation events in some manner, but I haven't heard anyone challenge the phenomena on that basis since the early 90's. We're well past that.

"Q: why we do not see superpositions in macroscopic world? A1: This cannot be explained only by Bayesian reasoning. A2: because of the superselection rules. Superselection rules are violations of non-relativistic QM. This is a circular explanation: they are not there because they cannot be there. (or they are there but each live in a separate world. Space, time, locality, superselection rules are concepts outside non-relativistic QM. Space, time, and locality are concepts inside relativistic QM. By a leap of faith, I conjecture superselection rules should also come from inside relativistic QM."

It seems you want to resolve the mysteries of NRQM by appealing to formal structures in violation of NRQM. That would only make sense if NRQM made predictions that were NOT observed. Violations of Bell's inequality are predicted by NRQM and observed accordingly by experiment.

"Q: are any arguments for RBW which cannot be explained by Bayesian reasoning? A: no. (or at least not yet from the papers I read). Conclusion: RBW cannot (yet) conclude it does solve the MP. Just like superselection rules, the concept of an event is not definable inside non-relativistic QM. Solving MP requires defining what an event is."

Again, the MP (as I defined it previously) is a non-starter for the path integral approach because the formalism assumes a specific experimental outcome ("event"). That's pretty trivial, I don't know how else to explain it to you. This does not solve the MP in the dynamical approach. As I said, I don't see a solution to the MP there. Nothing you've said here bears on these facts.

"I mentioned earlier the Connes and Rovelli's result. Connes proved that the "time parameter" is independent of state in the context of measurement theory, spectral theorem, and von Neumann's algebras and this is big and I believe it kills the BW interpretation. Your second roadblock is "the free will theorem" of Conway and Kochen. Again I am agreeing with the R in RBW, but not with BW."

I read the Connes paper, it does not prove that a dynamical approach is fundamental, they assume it and investigate a thermodynamic manner by which it may be instantiated. They tacitly assume globally hyperbolic spacetime structure in their approach to constructing their "hypothetical time parameter," but even if GR turns out to be so constrained by quantum gravity, one has not discounted BW. Everything Geroch said about the spacetime structure of GR holds, whether it admits a Cauchy hypersurface or not. For us, "BW" merely means it is valid to use future boundary conditions as in the path integral approach; BW in general is metaphysics. How BW bears on consciousness per free will does not threaten the relevance of a path integral approach. Again, we're looking for a formalism fundamental to quantum physics (NRQM and QFT) that is amenable to constitutive non-locality and the path integral over graphs is doing a great job for us. We've only to marry it up to GR to have quantum gravity and since we can do that uniquely via Regge calculus, we're in a strong mathematical position.

"Fell free to ignore my points of views, but you need to present a clear rebuttal on how Connes' and Conway's results are explained in a BW interpretation, before your interpretation is to become accepted by the rest of the physics community."

Having presented RBW at conferences such as "New Directions in the Foundations of Physics" and published it in FoP and SHPMP, I can readily testify that feedback from the foundations community is strongly against a BW perspective. Not because it can't work technically, but because, apparently, it threatens free will. You are in the majority, Florin. The results you cite in no way threaten our approach, as we've explained. But, we are resigned to the fact that because there is such strong emotional opposition to the metaphysical implications of a path integral approach (as elucidated in our FQXi essay), we will find very little support for the RBW program until it delivers more than an interpretation. We can live with that :-)

Mark

Mark,

""I did not get the lossy part. What do you mean by it?"

Here is a definition from the internet: "A term describing a data compression algorithm which actually reduces the amount of information in the data, rather than just the number of bits used to represent that information." See the Rickles essay."

I know what lossy means. I did not understand why it was applicable in your statement.

Ha, ha. This reminds me of a discussion in the movie Airplane.

"-The passengers are sick. We need to get them to a hospital."

"-What is it?"

"-It's a big building with doctors, but that's not important right now."

"There is still the mystery of single-particle interference with C clicks but, yes, the MZI does not entangle the atoms unless there is a D click. [...] but I haven't heard anyone challenge the phenomena on that basis since the early 90's. We're well past that."

I was not challenging anything here. I was only making a case for the Bayesian interpretation. If that got misunderstood, please ignore my comment.

"It seems you want to resolve the mysteries of NRQM by appealing to formal structures in violation of NRQM. That would only make sense if NRQM made predictions that were NOT observed. Violations of Bell's inequality are predicted by NRQM and observed accordingly by experiment."

I do not see which violations you are talking about. Take space for example. Yes, the concept of locality is independent of unitary groups, but one does have a position operator in NRQM and there is no "violation" here. In NRQM one has to introduce the concepts of space and time as independent axioms. Not so in relativistic QM. In RQM the Lorenz symmetry is inherent and follows from the unique realization of the abstract rules of QM. No need to postulate space and time in RQM as we need to do it in NRQM.

"Again, the MP (as I defined it previously) is a non-starter for the path integral approach because the formalism assumes a specific experimental outcome ("event"). That's pretty trivial, I don't know how else to explain it to you. This does not solve the MP in the dynamical approach. As I said, I don't see a solution to the MP there. Nothing you've said here bears on these facts."

I actually agree with your statements above, but you misunderstood my criticism. In your model of reality, the MP is indeed a mute point. But from all I've seen, your model can be mapped into another model where MP is not solved. This means that your paradigm is too restrictive. Is like saying that x^2 +1 = 0 is impossible to be solved in real numbers and from here arguing that is impossible to be solved in general. Of course you can turn this argument around and say that your interpretation is superior precisely because you do not have any MP.

"They tacitly assume globally hyperbolic spacetime structure in their approach to constructing their "hypothetical time parameter,""

If this is the perception of the paper, then they explained it wrong.

Let M be a von Neumann algebra in a Hilbert space.

There is an exact sequence:

1 -> Inn(M)->Aut(M)->Out(M)->1

The Tomita time evolution \sigma_t^{\phi}in Out(M) does not depend on the choice of state \phi

The time parameter in Cones' theory defines an "orientation". This orientation is algebraic and global in nature. Equivalently, Alfsen, Hanche-Olsen, and Shults defined a geometric local orientation in a C* algebra. The two concepts are very much related and they guarantee the preservation of the phase in QM.

The only reason one cannot declare victory and state that time has a QM origin is that we are lacking a quantum gravity theory. But we no longer need to postulate global hyperbolicity from the beginning. The results above are not as well known as Conway's free will result, but in my opinion they are just as big a roadblock to your interpretation as free will is.

"Having presented RBW at conferences such as "New Directions in the Foundations of Physics" and published it in FoP and SHPMP, I can readily testify that feedback from the foundations community is strongly against a BW perspective. Not because it can't work technically, but because, apparently, it threatens free will."

Fortunately in science popularity and being right are separate things. Good luck to you in proving new results.

Florin