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July 6, 2015 at 4:34 pm #2500
Counterfactual communication protocol
Lev VaidmanJuly 14, 2015 at 1:29 am #2712
Hi Lev, Thanks for this interesting contribution to the forum. I didn’t follow the controversy in your Refs [1-5] so perhaps I’m just ignorant of the context and hence missing the point. But my initial impression is that the whole question here is based on a kind of equivocation on the word “particle”. You define “counterfactual communication” as “communication without particles present in the transmission channel”. OK, so then is it “counterfactual communication” if I send morse code to my friend (on the other side of the lake) by means of ripples that propagate across the lake? Or is communication by means of information encoded in electromagnetic waves (taking here the perspective that classical Maxwellian electrodynamics is true, i.e., ignore photons) “counterfactual”? If the answer to those questions is “yes” then I suppose you are right that this simple setup involves counterfactual communication according to Bohm’s theory. But then I’d wonder why in the world I should care about this strangely and arbitrarily defined notion, “counterfactual communication”.
On the other hand, presumably, to whatever extent the idea of counterfactual communication is actually interesting, we should understand the word “particle” in your definition more broadly — basically as meaning “anything physically real”. In which case, obviously, sending messages using waves (water or electromagnetic) rather than particles, would fail to count as counterfactual communication. And in that case it seems like this setup, from the point of view of Bohm’s theory, would also fail to count — because although the Bohmian particle may not go through the arm of the interferometer that takes it past your mirror 1/2, *something* physically real (namely the “empty half” of the wave packet) does take that route. So there is a perfectly clear physical mechanism by which Bob’s choice about whether to place the mirror at 1, or 2, influences the subsequent motion of the particle.
That is, my reaction to your final question “Is it counterfactual according to the Bohmian perspective?” is “It depends on exactly what you mean — but surely there’s nothing puzzling here?!” But like I said, maybe I’m just missing what makes this puzzling…July 14, 2015 at 3:59 pm #2729
Dear Lev, Thank you once again for presenting such an interesting example. To answer to your question: ‘is this example counterfactual according to Bohmian mechanics ?’ I can say that factual means here classical. Your example is indeed counter intuitive on this you agree I think but by intuitive you only mean classical. And indeed due to the quantum potential or the empty wave Bohmian mechanics is not strictly equivalent to clasical physics. This is the same problem you mentionned in you previous examples discuss in ‘Can You Kill with an Empty Wave Bullet?’.
One point to add: your example is not fully quantum since Bob can select the output but can not superpose them in a coherent quantum way. To do that you will need entanglement with degrees of freedom of Bob. This is of course not very difficult to do but then you will certainly realize, like Hardy did in the 90’s with your famous interaction free protocol, that non locality and the time ordering of the differen processes can modify in even more counter classical ways the dynamics of the particles.July 14, 2015 at 5:38 pm #2731
Of course, communication with a water wave, or with a classical electromagnetic wave is not counterfactual. What I felt is that some Bohmians do not take quantum wave, and especially empty wave, in a strong ontological sense. Sometimes, wave is considered as a part of a physical law which governs the particle motion. My guiding principle of the presence of a particle in a particular place is the (weak) trace it leaves there. Empty Bohmian waves sometimes leave trace, and this is the case in the setup I proposed, so from my point of view is is not counterfactual.July 14, 2015 at 5:54 pm #2732
Thank You for the Comment. But why you say that Bob cannot superpose the message in a coherent way? He should put in the location 1 of the mirror, a 50:50 beam splitter instead, and a permanent mirror at location 2. This provides a coherent superposition of messages 1 and 2. Alice can arrange interference between them and measure the phase which Bob fixes. This modification is “Bohmian counterfactual” as well.July 14, 2015 at 7:30 pm #2741
Hi Lev, Thanks for the elaboration/clarification. I think we agree, about two things. First, yes, this setup probably should not be described as “counterfactual communication” according to Bohm’s theory since *something* (the empty wave) goes along the path through 1/2 and then causally influences the motion of the Bohmian particle below. And second, yes, I agree, different fans of Bohm’s theory (and perhaps sometimes the same one person at different times!) sometimes think/talk about the ontological status of the wave function differently. For me personally, one of the things that makes Bohm’s theory really attractive is the clear, intuitive, causal explanations it provides in exactly this kind of situation (similarly the 2-slit experiment, etc.). So I definitely tend to think of wave functions as physically real things — so much so that I am troubled by the ontological status of multi-particle (and ultimately the universal) wave function(s), and want to try crazy things like reformulating the theory so that only 1-particle wave functions appear as beables. That is to say, the things that attract me most to Bohm’s theory make it rather difficult for me to understand wave functions, not as physical waves, but instead as laws.
On the other hand, I can definitely understand the point of view of the people who (looking more at the fundamental formulation of the theory, in which there is only really one wave function, that of the whole universe) think of the wave function as more law-like (than beable- or field-like) in character. But then I am troubled at losing the intuitive/causal understanding of things like the 2-slit experiment and your example here. Of course, it’s not completely clear that one has to really choose one or the other. For example, one might say that the wave function of the Universe is best understood as a law, but then the one-particle (so-called “conditional”) wave functions that would figure in a Bohmian analysis of the 2-slit experiment, or your setup here, can perhaps be thought of as beable-/field-like. But to me that’s a bit weird. The “conditional wave function” in Bohm’s theory is just the universal wave function, evaluated at the actual (Bohmian) position of all the other particles. It’s like a single “slice” out of the Universal wave function. And… how can a single “slice” of a law, be a beable/field? That’s weird to me.
Anyway, yeah, if you are motivated here by the feeling that you sometimes get mixed signals or contradictory answers from Bohmians about whether one should think of wave functions as physical fields, or instead something like a law, that makes sense and I agree that this is worth discussing further. On the other hand, it should be noted here that these sorts of questions about how to understand the wave function aren’t as pressing for Bohmian mechanics as they are for some other theories — e.g., MWI/Everett, according to which the wave function is the only thing in the ontology. For Bohm’s theory, the matter we see around us (tables, chairs, trees, planets, etc.) is made of *particles* which are just unproblematically in 3D and can hence unproblematically build tables, chairs, etc.; the wave function has a somewhat secondary, background role; so it’s possible to understand quite a lot about what the theory says and how it works and how it explains the distribution of matter we observe, etc., without ever really resolving these questions about whether the wave function should be thought of as a law, or a field, or what. Whereas MWI/Everett, I think, has a long way to go to explain how we end up with tables and chairs and planets in 3D, starting *just* from a universal wave function.July 14, 2015 at 8:41 pm #2744
Thank You for the post. I think I agree with what you write, although I do not feel particular need for beables and for me wave function is ontology and the only ontology. I agree that MWI requires much more to explain our experience than Bohm, but the advantages of the MWI as a physical theory (no action at a distance, more economical in concepts) put it for me far beyond any competition.July 15, 2015 at 6:33 am #2756
Sorry Lev, My answer got lost in a parallel Universe (probably the bohmian demon).
I wanted only to say that entanglement will change all. If you use an additional BS then you are indeed in the regime that I am mentioning. But the main problem is now that Bohmian mechanics is strongly sensitive to contexts so that the time ordering of the operations and the way you are doing entanglement will make your dynamic even more counter-classical. In some case Alice will receive the particle coming from her mirror (like in your example) but in other the particle could come from Bob mirror. You mentioned already these problems in your cat paper years ago and Hardy did a lot in that direction as well. Bell was probably the first to see that of course.July 15, 2015 at 9:36 am #2759
Yes, there are many interesting subtle effects when the experiment involves entanglement. But my current simple proposal including introducing the beam splitter for coherent quantum signal does not involve entanglement. ALL particles Alice detects had no Bohmian trajectories passing through Bob’s site.July 15, 2015 at 10:25 am #2760
We agree, may be someone will try to develop a modified version of your protocol. This could be a nice exercice.July 15, 2015 at 1:29 pm #2769
Dear Lev, Two quick (and arguably off-topic) points about your previous comment to me above (#2744).
First, you seem to be using the word “beable” to mean something like “hidden variable” (i.e., stuff postulated to exist in addition to the wave function). I understand Bell’s term in a different way, though — as referring to whatever a theory says exists. So for you, as an MWI/Everett guy, it’s not that you don’t “feel a particular need for beables”, but, I think, rather, that you see no need for beables other than the wave function of the universe (which, for you, is the one and only beable). In a way this is just a pointless quibble about how to use a word, but I wouldn’t want there to be any kind of misunderstanding (on the part of other people reading this exchange) about the fact that MWI/Everett does postulate that the universal wave function (and only that!) is physically real, i.e., I’d say, a beable.
And then second (and relatedly) you indicated that you prefer MWI/Everett over Bohm in part because MWI/Everett does not include action at a distance. I have for a long time found this claim (which Everettians always make) very puzzling. “Action at a distance” refers, of course, to the sorts of faster-than-light causal influences (influences outside of the future light cone) that Bell took himself to have established. The point is that it really only makes any sense to apply this notion (or its absence, “local causality”) to physical goings-on in ordinary 3D physical space (or 4D spacetime). But I simply don’t understand how you can claim that MWI/Everett is a local theory in this sense (if that is what you meant to claim?), or what you would even take such a claim to *mean*, when it is so unclear (as I think you acknowledged?) how the beable posited by MWI/Everett (namely the universal wave function) relates to anything like a distribution of matter in 3D space / 4D spacetime. Do you have some specific model/idea in mind for how we go from the quantum state / wave function of the universe, to some kind of story about physical processes in 3D/4D to which notions like “local”, “action at a distance”, etc., can even be meaningfully applied? Or maybe when you say there’s no action at a distance in Everett’s theory, you don’t actually mean that the theory is locally causal (in anything like Bell’s sense) but you instead only mean something formal, like that the equations defining the theory’s dynamics respect Lorentz invariance. That I would probably agree with. But then to me it remains far from clear why I should care about that, or what it has to do with relativity theory (and its claims, e.g., about the structure of 4D spacetime), when it remains completely unclear what if anything the theory is even saying about physical goings on in 4D spacetime. Anyway, can you help me understand what you have in mind with this claim that Everett avoids the kind of nonlocality that is present in Bohm’s theory?July 15, 2015 at 1:55 pm #2770
I am ready for your semantics about beables.
About action at a distance. When I deal with a physical theory I assume a closed system and an external omnipotent creature which can test the theory making disturbances and observation of what is going on that system. So there is no issue of “free will”.
Nonlocality of Bohm is best manifested in its treatment of the EPR-Bohm system of two separated particles in a singlet state. If Bohmian position of the two particles in the EPR pair are in their upper half, then measuring spin of one particle will change the result of spin measurement of other particle immediately after.
In contrast, any local action in one place will cause no change in the complete local description (local density matrix) of other place. I describe it in detail in Quantum Theory and Determinism, L. Vaidman, Quantum Stud.: Math. Found. 1, 5-38 (2014) quant-ph 1405.4222.July 15, 2015 at 4:26 pm #2775
Lev, yes, in Bohm’s theory the nonlocality is clear: if you have a pair of entangled particles, the velocity of one of them (according to the theory) can depend on a free choice (say, about some external magnetic field that you might apply) at the location of the other one. That is, something over here (the trajectory of this particle) depends on some distant intervention, according to the theory. So it’s not locally causal.
The thing I don’t understand about MWI is: what *is* there “over here”, according to the theory, that might or might not depend on some distant intervention? What really exists, physically, “over here” (in 3D space) according to the theory? If all you have is a quantum state (or wave function) it’s just not clear what ontology there is, if any, in 3D space.
I think maybe you meant to suggest that the local (i.e., existing-in-3D-physical-space) ontology is the local density matrices. Is that right? So then the idea is that what exists physically, in 3D space, “over here”, is some local density matrix/operator, and then it’s easy to show that this isn’t affected by distant interventions. Have I got that right? Assuming so, I might have follow up questions (such as how I should understand a mathematical operator as a description of something physically real, and whether the local density operators *exhaust* the ontology even though they don’t capture all of the structure that’s in the wave function (which I thought was what the theory said was real), etc.). But maybe I’ll pause there and just make sure I’m on the right track so far.July 15, 2015 at 5:10 pm #2776
Yes, you are on the right track. Locally, there is only local density matrix. It captures all information about what is there. And it cannot be changed by action at a distance.
But, all local density matrices do not exhaust all the ontology. Wave function is more than this. And in some sense it is non-local (entanglement etc.). However, local density matrix is certainly real as it ALL what is in a particular location. If something in this location entangled with something in other location, local interaction might lead to entanglement to more systems, but no change happens nonlocally: no action at a distance!
I am preparing a talk “Ontology of the wave function”, Saig, July 22. If it will be recorded in some way I’ll send you a link.July 15, 2015 at 8:34 pm #2779
I would be very interested to hear your talk, so do send me a link if it’s recorded, etc. I hear what you are saying about the local density matrices, but presumably you can appreciate that there are further (subtle and challenging) questions. For example, if the local density matrix doesn’t exhaust the ontology, then it is hardly persuasive to say “the theory is local because interventions over there do not affect the density matrix over here”. And (as I have written about elsewhere) I think there are real questions about whether the local density matrices even capture the part of the ontology that I think you have in mind when you say that it is/captures “ALL what is in a particular location”. One of the crucial things that is real (in the sense of being there in the wave function) is that there are connections between terms in the local density operator over here, and the one over there. (That is, a certain “piece” of the density operator over here is, so to speak, “in the same world/branch” as a certain other “piece” of the density operator over there.) But, sort of by construction, the collection of local density operators leave precisely these connections out, and hence what they omit is in some sense exactly the thing that (in the context of other theories) causes problems for nonlocality. So the whole argument seems a bit like a swindle.
And then I really just don’t have any idea how I’m supposed to understand mathematical operators (associated with spacetime regions) as describing some physical “stuff”. If you tell me tables are made of particles, that makes sense as a possibility. Or a constellation of spacetime-point “flashes” — OK, that’s weird, but I can comprehend it. Or maybe a table is a table-shaped region in which some field has a different value from the background value. OK, yes, that makes sense as a possibility. But if you tell me a table is made out of mathematical operators that act on states in some abstract Hilbert space, I literally don’t know what you mean; I don’t understand what in the world it could mean for a table to be made of such things.
But maybe this is off-topic for this thread. =)July 15, 2015 at 8:55 pm #2780
First, I did not say local, I said that MWI has no action at a distance. The (nonlocal) connections you talk about are changed locally.
Operators are very far from reality. Ontology is the wave function, quantum states, not values of observables. According to my picture in your language tables are as GRW-m, only there are no collapses and density measured inside a “world” which is a vague concept which has to be carefully explained. These are LOCAL properties of the Wave Function.July 15, 2015 at 11:04 pm #2782
Ah, so you understand MWI/Everett as what Allori et al call “Sm” in this paper:
Is that right? I’m still a little confused by how you talk about the ontology, though. Do you think of the m-field as something like an emergent property of the wave function (such that it, the m-field, doesn’t count as an addition to the ontology beyond the wf)?July 16, 2015 at 5:21 am #2790
Exactly. I am aware that the founders of GRWm view it differently and in the paper you mentioned it is claimed that S0 and Sm are different, but I do not see it. The only ontology is the wave function. “m” is an emergent property which help us to understand world around us. If we want to add to physics ontology of the Universe our world ontology, “m” will be there.July 16, 2015 at 12:25 pm #2793
Thanks Lev, it is so refreshing to get clear and simple answers to these kinds of questions! I continue to have concerns about the view you’re advocating, and would love to continue probing you about them if you’re game, but I just wanted to say that it’s nice to get straightforward answers!
So, can you tell me about how you think of the wave function (quantum state) ontologically? There’s no way I know of to mathematically formulate the wf/qs such that it can be understood as just directly representing some physical things/stuff in the 3D space we take ourselves to inhabit (and if this were possible we wouldn’t be having this discussion about “m”, etc.!). For example, to the extent one thinks about the wave function as something like a physical field, it’s evidently a field in a very high dimensional (so-called) configuration space. Is that how you think of it? If so, the idea that the m-field (in 3D space) is just an emergent property of the wf, really concerns me. How can an emergent property of a thing that lives in one space, live in a different space? Where does the new (3D) space come from?? Or maybe instead I shouldn’t think of the emergence of the m-field in this way (as if it really comes into existence) but should instead understand emergence in a more psychological sense, as in: the m-field is “what the wave function looks like, to us, who are also built of it, from the inside” if that makes sense. That avenue also really worries me, as it seems to basically imply that the whole 3D world we ordinarily take ourselves to live in, isn’t actually real, but is instead a kind of delusion… It has a “brain in a vat” flavor to me. I wrote about some of these worries here
if anybody is really interested. But probably the short version above is enough to give the essence of the concerns. Can you shed any light on how you think about these things, Lev?
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