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.

This paper has been sent out to peer review.

Report of Referee A:

I have read the manuscript “Primitive Ontology in a Nutshell” by V. Allori. The paper is just what its title suggests: a brief summary of the Primitive Ontology approach that has been elaborated elsewhere by Allori and co-authors. There does not seem to be much novelty in the paper, but I think that is OK: thought of as a review paper whose goal is to make the PO approach more widely known and more deeply understood, a paper like this ought to exist and I will ultimately support its publication. But I think there are a number of ways in which the paper could be improved, and I would like to see the author consider some of them. So… in approximately decreasing order of seriousness… here are some suggestions/questions for the author to consider:

1. What, exactly, is the relationship between physics and metaphysics that the author, and/or the PO approach, assumes? I have the impression that a weird (and hardly plausible) “post-positivist” notion of metaphysics is being assumed here, in which physical theories saying nothing about what the world is like are proposed (based, presumably, on empirical evidence) and then it is the job of metaphysicians to come along and say something about what, according to the proposed theories, the world might actually be like. This, I suspect, is indeed how some philosophers of physics see their role. (We do, after all, live in a post-positivist world.) But I think this is absurd, and indeed contrary to the PO approach the author means here to clarify and endorse. Physics theories ought to say something about what the world is like! That, I take it, is a fundamental tenet of the PO approach. But then it seems that the point of the PO approach isn’t really, as the author describes it at one point, to show us how physics theories with clear ontologies “can be used as a guide to metaphysics”. Rather, in my opinion, the metaphysics is the primary thing: it is a metaphysical doctrine (along the lines of “matter in three-dimensional space really exists and is what all of our empirical evidence is ultimately *about*”) which undergirds the PO approach’s insistence that “any fundamental physical theory [have] a well-defined architecture, [at] the foundation of which there is the [PO], which represents matter.” Put it this way: it seems to me that the PO approach is fundamentally *normative* — it is not telling us what architecture physical theories do (historically/naturalistically) have, but rather telling us what architecture physical theories *should* have. And this “should” is based on certain metaphysical commitments. So, it seems to me, the PO approach isn’t fundamentally about how to extract metaphysics from physical theories; it is rather about how a certain set of metaphysical commitments leads us to demand that proper physical theories should have a certain architecture. I just think the whole idea would be clearer if this overall relationship among physics, metaphysics, and the PO approach, were straightened out.

2. At one point the author describes the notion of primitiveness (in “PO”) by saying: “some part of the ontology is `more important’ than other parts.” I find this (and related) formulation(s) problematically ambiguous. Are the parts of the ontology that are selected out as constituting the PO “more important” in a metaphysical/physical sense? That is, is it that the non-primitive elements of the ontology have some kind of secondary existence? Or is it instead that the PO is “more important” in some kind of epistemic sense, e.g., the primitive ontology is what we are somehow most directly aware of (in sense perception?) as against the non-primitive elements which are invisible (and hence have to be somehow inferred from complex abstract chains of reasoning)? If the former, I am skeptical, since I don’t know what it could possibly mean for two things to both really exist, but for one of them to be somehow metaphysically “more important” (more real??) than the other. (This worry is mentioned very briefly, alongside some others, in section 10; but to me the entire approach remains somewhat vague, confusing, unclear until this is explicitly addressed.) On the other hand, if the sense of primacy here is merely epistemic, I then don’t see how certain of the suggested implications (like that the non-primitive elements of the ontology can be thought of has having a nomological character) would follow or even relate. On these points, I would find it clarifying to see a concrete discussion, not just of classical particle mechanics and then quantum mechanics, but also of classical electrodynamics (CED). I gather that the ontology of CED includes (charged) particles as well as electric and magnetic fields. Which of these are part of the specifically *primitive* ontology? It is not clear to me, and all the possible answers seem to raise worthwhile questions. For example, the idea that the primitiveness of the PO is (basically) epistemic might suggest that the particles are the PO, and the fields are non-primitive. Does it then follow that electric and magnetic fields are not fully real, or not real in the same way that charged particles are real, or have a nomological (rather than a “material-field-ish”) character? (The author says in passing that electromagnetic fields can “arguably” be taken as part of the PO; but I have also heard advocates of the PO approach say that at least the magnetic field should not be considered part of the PO.) To me the PO approach starts to seem slightly awkward and cumbersome and ill-fitting in the context of this example (which in turn suggests to me that the PO approach is not really a kind of universal perspective on physical theories, but is instead just motivated by the particular concerns arising in quantum theory – in particular the fact that the quantum wave function, unlike the fields of CED, cannot really be understood as “material” at all because it doesn’t live in three-dimensional space). But I would love to be proven wrong by a fuller discussion of this and/or other helpful concrete examples. (What other examples? I also find the idea of treating momentum, in classical mechanics, as a non-primitive part of the ontology, somewhat puzzling. It seems we have some kind of direct sensory access to (average?) momentum, in the form of temperature. Should I conclude, after all, that the PO is primitive in a physical/metaphysical sense, rather than an epistemic one? So that might warrant further discussion. How about neutrinos? Are they part of the PO of standard particle theory? Higgs fields? Why? Why not? And re: physical equivalence, if the fields in CED aren’t part of the PO, does that make CED and Wheeler-Feynman physically equivalent? For me these sorts of questions deserve answers.)

3. Since “MW” (i.e., Everettian) approaches are so popular, I would find it helpful to actually engage a bit more seriously with its proponents in this paper, instead of just dismissing it as “incompatible with the PO approach”. Explain, briefly, why the Everettians don’t think they *need* a PO in their theory in order to achieve empirical adequacy. Explaining more about how and where and why PO-ism and Everett-ism fail to see eye to eye, will help make the PO approach (and its underlying assumptions and motivations) clearer.

4. I find the tangents about purely notational issues (e.g., the semi-colon, and the example of denoting classical mechanics as x_{deterministic}^{deterministic}, and basically all of section 11) sort of pointless and distracting. The intended audience for a paper like this shouldn’t be made to worry about notation. Pick a notation that gets the point across clearly and don’t let it become the focus.

5. I didn’t understand the reference in footnote 8 to “a theory like this with a [PO] of wave functions”. What theory? Did the author actually mean wave functions, or “fields, i.e., extended objects”? These are not really the same thing – and indeed, not even possibly the same thing, which is precisely why the author (in my opinion, correctly) insists that the wave function “is not a suitable primitive variable.”

6. I noticed a couple of ungrammatical pseudo-sentences, as in: “To specify what the ontology of a theory is amounts to select, among all the variables of the theory, are to be taken as representing what exists in the world.”

7. The paper ends rather abruptly. Maybe a final section to summarize / conclude?

To summarize/conclude, I think that this paper could and should become a valuable contribution to the foundations of physics literature. I would urge the editor to urge the author to consider improving it in response to some of the suggestions above. I don’t consider any of these mandatory and would generally leave it to the author’s discretion to decide exactly which sorts of improvements are most important and which are perhaps too daunting to raise in what is supposed to be a short summary paper. But I think at least some improvement in response to at least some of the suggestions/questions above would make for a much stronger, publishable paper.

Response to Referee’s comments

Further comments of Referee A:

Having read the revised version of “Primitive Ontology in a Nutshell” I think it would be fair to summarize by saying that, although a number of questions (along the lines of the ones I raised in my previous report) remain, it would be unfair to demand that full answers be squeezed into this particular Nutshell. With the acknowledgement of the questions and other minor revisions, I consider the paper essentially ready for publication, and look forward to the various elaborations promised in other forthcoming manuscripts by the author.

Finally, let me just note a couple of ungrammatical passages which should be fixed as the final version is being prepared:

“I will review what implication[s?] this approach has…”

“To specify what the ontology of a theory is amounts to select[ing] which variables…”

“…which variables are primitive and thus constitute[*s the counts as*] the PO of the theory.”

Accepted manuscript