We update our Relational Blockworld (RBW) explanation of quantum physics and argue that it provides a realist psi-epistemic account of quantum mechanics as called for by Leifer. RBW accomplishes this by employing discrete graphical amalgams of space, time and sources (“spacetimesource elements”) and an adynamical global constraint as ‘hidden variables’ that avoid the need for counterfactual definiteness in a realist account. Instead of an equation of motion governing time-evolved entities, the adynamical global constraint is used for computing the graphical transition amplitude whence a probability amplitude for our fundamental spacetimesource element. We begin with a largely conceptual and philosophical introduction to RBW’s most prominent features, i.e., adynamism, relationalism/contextualism, and the unmediated exchange of energy. This conceptual introduction includes a simple interferometer computation of the relative intensities found in a weak measurement that we compare with the authors’ computation per weak values. We use this to contrast our adynamical explanation of the experiment with the apparently dynamical, retro-time-evolved explanation of the authors’ Two State Vector Formalism. Next we use spacetimesource elements instead of paths in Dowker’s GHZ set-up to contrast RBW with Sorkin’s Many Histories account. We argue that rather than multiple paths per Many Histories, what is called for is no paths per RBW. The adynamical interpretation of these two quantum experiments, afforded by the global perspective, suggests that quantum mechanics might be underwritten adynamically. Thus, in the second part of the paper, we motivate an adynamical global constraint using coupled harmonic oscillators and then apply it to an analysis of the twin-slit experiment. This illustrates how the adynamical global constraint of our “modified lattice gauge theory” underwrites quantum field theory whence quantum mechanics. We conclude with a brief dismissal of the measurement problem and an RBW explanation of entanglement, environmental decoherence, quantum non-commutivity, quantum versus classical behavior, and the Born rule.

Here is the paper: Stuckey et al 2015 Revised. The paper has been revised per referee comments and Replies on the blog.

This paper has been sent out to peer review.

This is good stuff. It really help to position what you're doing against what others are doing.

I think it's right to say that the difference between yourselves and Price & Wharton is largely a matter of stress. They stress the backwards causation, you stress the acausal constraints. But they have the acausal constraints too, and you have the backwards causation (construed in a sufficiently deflationary manner).

A small point: on p.6 you suggest that any account that uses the statistical independence loophole is retrocausal. I don't think that can be right, because you can at least envision a conspiratorial theory with only past-to-future causation (Bell's "superdeterminism"). But what you say immediately after that sentence sounds right: global constraint models are retrocausal under a suitable analysis of causation.

On the difference between your model and TSVF: I guess I don't see the TSVF as particularly dynamical. Granted, you've got these two vectors that evolve forwards and backwards in time. I don't know how DFBV describe them, but it looks to me like they're a kind of heuristic -- what's real is the discontinuous photon trajectory (where the two vectors overlap). That is, you could construe DFBV and yourselves as proposing alternative methods of constructing one and the same thing. (Although I'm not exactly sure what the end result of your construction is -- see below).

On the specter of instrumentalism: What exactly is the ACGC a constraint on? Waves, particles, both? No -- you say "neither". You don't mean "nothing", right? In some places you say the source-sink energy transfer is unmediated, but then it does start to smell of instrumentalism -- the constraint is just a constraint on the detector clicks. In other places you say the constraint is a constraint on a spacetimesource element -- which looks like a spatiotemporal entity (or at least an entity that has a spatiotemporal aspect).

(Incidentally, it's not so clear that TSVF answers "waves" to the above question. They would certainly say "photons", but it's not clear what a photon is for them. It's whatever is represented by the regions of overlap of the two waves. Maybe it’s a spacetimesource element!)

(*This is good stuff. It really helps to position what you're doing against what others are doing.*)

Thanks for taking the time to read and comment on the paper, as always Peter.

(*I think it’s right to say that the difference between yourselves and Price & Wharton is largely a matter of stress. They stress the backwards causation, you stress the acausal constraints. But they have the acausal constraints too, and you have the backwards causation (construed in a sufficiently deflationary manner).*)

This part of the paper is due in part to valuable input from Ken Wharton who explained that our use of future boundary conditions is a form of retrocausation. In fact, Price refers to the “global constraint” nature of his Helsinki model and Wharton’s L = 0 constraint is spatiotemporally global (“all at once” to use his term).

(*A small point: on p.6 you suggest that any account that uses the statistical independence loophole is retrocausal. I don’t think that can be right, because you can at least envision a conspiratorial theory with only past-to-future causation (Bell’s “superdeterminism”). But what you say immediately after that sentence sounds right: global constraint models are retrocausal under a suitable analysis of causation.*)

We agree and will make that more clear.

(*On the difference between your model and TSVF: I guess I don't see the TSVF as particularly dynamical. Granted, you've got these two vectors that evolve forwards and backwards in time. I don't know how DFBV describe them, but it looks to me like they're a kind of heuristic -- what's real is the discontinuous photon trajectory (where the two vectors overlap). That is, you could construe DFBV and yourselves as proposing alternative methods of constructing one and the same thing. (Although I'm not exactly sure what the end result of your construction is -- see below).*)

TSVF is dynamical as we defined it because TSVF adds a new dynamical mechanism to the block universe whereas we do not – we use an adynamical global constraint (AGC) that requires no new dynamics, heuristic or otherwise. If TSVF embraced your deflationary interpretation of their account “as proposing alternative methods of constructing one and the same thing [an adynamical global constraint],” we would certainly welcome that. In that case, we would suggest to DFBV they should consider abandoning the redundant explanatory aspect of the two-vector formalism and rather state that their backward and forward-time-evolved wavefunctions (or whatever they are) constitute a spatiotemporally global constraint. Perhaps Lev Vaidman will offer input, in which case we will revise the paper accordingly. In any case one doesn’t need both a new dynamical mechanism and an AGC, and in the paper we argue why the latter ought to be fundamental. Given your take on TSVF it sounds like you agree.

(*On the specter of instrumentalism: What exactly is the AGC a constraint on? Waves, particles, both? No -- you say "neither". You don't mean "nothing", right? In some places you say the source-sink energy transfer is unmediated, but then it does start to smell of instrumentalism -- the constraint is just a constraint on the detector clicks. In other places you say the constraint is a constraint on a spacetimesource element -- which looks like a spatiotemporal entity (or at least an entity that has a spatiotemporal aspect).*)

The AGC constrains the probability amplitude for our beables, i.e., spacetimesource elements, which are spatiotemporal 4D ontological entities. Hopefully, we have clarified the role of the AGC in the non-mathematical outline of the twin-slit analysis below. The spatiotemporal distribution of detector clicks is in accord with the distribution of spacetimesource elements per the probability amplitude obtained in accord with the AGC. Again, a spacetimesource element isn’t *in* spacetime, it’s *of* spacetime, even while a distribution of detector clicks is viewed in the spacetime context of the experimental equipment and process from initiation to termination. This is RBW’s version of OSR in a block universe.

(*Incidentally, it's not so clear that TSVF answers "waves" to the above question. They would certainly say "photons", but it's not clear what a photon is for them. It's whatever is represented by the regions of overlap of the two waves. Maybe it's a spacetimesource element!*)

We should probably allow someone in the TSVF program to answer that. Again, if they will provide us with input, we will gladly revise our paper accordingly.

(*I still can't follow the details of the derivation of two-slit interference. Time to go back to school...*)

You are the exemplar target audience, so if you can’t follow the section on twin-slit, then we need to outline the formalism here. The computation is in three parts and the goal is to produce a non-relativistic, source-to-source QFT probability amplitude ψ for the spacetimesource element in the twin-slit experiment per our “modified lattice gauge theory” (MLGT). First, we use the transition amplitude for the Klein Gordon (KG) action in the non-relativistic limit to produce a propagator D(x – x') between point sources from the generating function W(J). Next, we relate D(x – x') to the probability amplitude ψ of the Schrödinger Equation (SE), even though the SE is homogeneous (has no source terms). Lastly, we discretize the transition amplitude of the non-relativistic KG action with source terms and use the adynamical global constraint (AGC) to find our MLGT counterpart to W(J), and thus ψ, for the spacetimesource element. A modification to the discretization process is required by the AGC since there is an undifferenced (non-relational) term ψ* in the non-relativistic KG action. The AGC also tells us which eigenmode of our difference matrix is relevant. Essentially, the second and third parts justify and explain our use of the propagator D(x – x') between point sources in non-relativistic QFT in computing the probability amplitude ψ for the spacetimesource element of the twin-slit experiment. [We should have limited the plots for the example to the physical range –π to π, as well.] This non-mathematical summary suffices to convey the content of that section conceptually, so we should have provided it in the paper.

Hopefully, the referees will give us a chance to make these corrections

A referee report has been received.

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