Wave-Particle Duality (partial) — Rob Spekkens

0:00 From one step to the other step. And so that's, even though in each run of the experiment, there's a matter of fact about which may the particle win. So in a given run of the experiment, let's say this is the object state. Well, that tells me that it was occupied on the left and vacuum on the right. So it really went this way. But nonetheless, I get this dependence on the phase I put in my beam splitter because of this code. So, I'm not going to, this is just a synopsis of the things I've said. Only one mode is occupied inside the interferometer at any time, not both of them, so it really went one way. The type of occupying mode and the type of vacuum at the end of the ports are being able to determine which output port is going to be occupied, and so the type degree of freedom is like a discrete phase that determines where it's going to go. speaking, we have the number and phase observables being well-defined in a toy theory, and all we have is a restriction on whether they can be measured simultaneously. They can't. So, just like the other toy theory said, look, spin z and spin x are both simultaneously well-defined, and simply can't know their value simultaneously, this theory says this discrete number and phase variables, they're both simultaneously well-defined, and they determine the behavior of systems moving them simultaneously. So, roughly speaking, the picture is that these systems, ontologically, they have both a wave aspect and a particle aspect. They have an occupation number, and they have a phase. But all we have is a restriction on how much we can know about those two things simultaneously. That's the idea. There's no time for me to go through the quantum eraser, but you can explain the qualitative features of that experiment as well. And I made all these beautiful diagrams to explain to you, but no doubt. They are beautiful. So, let me wrap up. I can add to my list of accomplishments of these sorts of toy theories various weight particle phenomena, such as spatial interference, the Elitzer-Beidman bomb testing problem, quantum erasers, delayed choice experiments, and certain features of Lucian's, some experiments proposed designed to demonstrate the reality of empty waves in von der Broyen theory. Although, as of a few days ago, I'm starting to wonder about

2:30 how well the PQC did this. There's some question marks here. So anyway, the bottom line is that these, from the perspective of my research program, these are not the phenomena to focus on. They're not going to help me get at what I'm missing. So I should focus on other phenomena. But there may be other sort of wave-particle-duality type phenomena, things that I haven't reproduced here So, remember the approach, there'll be, I'm hoping that there might be an assetization wherein one of the actions restricts how much any observer can know, the other involves some fundamental change to what we assume about quantology. Let me lead you with the big open questions. The biggest one is, if you claim that quantum states are states of knowledge, then what's that knowledge about? clearly it's not local non-contextual invariables, but that doesn't exhaust the set of things that could possibly be the case about the universe. So I have some thoughts on what the right flavor might be for that, but it's an open problem. And then secondly, as I mentioned earlier, ultimately we really want to derive this epistemic restriction from some sort of principle about the constitution of observance. So thanks for your attention. Thank you, Rob. Well, it is now 11.30, but I take it we are willing to go cut into the coffee break a bit. I suggest we start with the idea that we will do 10 minutes of that, and we'll see how that works. So, Bernita? Do you want to go first? Go ahead. I have one remark and one question. The remark is that it seems to me that the concept of locality is not unambiguous. The concept of locality is not in the usual discussion and in your approach, because it's obvious that any field theory is local. So in this sense... Right. So what I meant... But on the other hand, there's a problem that there's no code to it and has a local state. It's obviously another sense of local. I meant neither of those. I meant it in the sense of Bell locality. So Bell, in one of his papers, formulates a notion of local causality, which says that essentially, if I'm doing a measurement here and a measurement there, then if I condition on some slice of the backward

5:00 light cone here, and I ask what are the probabilities for different events occurring here and conditions on some slice in the backward light cone. Further conditioning on what happens over here won't update my probabilities. So basically, the backward light cone screens me off from any other influences. So all causes should come from the backward light cone, essentially, what bell locality encodes. So that's what I was saying, that these theories are bell local, and so they certainly don't violate any value qualities. But what's a bit surprising is that a lot of people have essentially suggested that things like are instances of non-locality just as violations of Bell inequality are. They didn't state it in the sense that this is a rigorous proof, but people sort of have to speak that way, that the only way one could hope to explain things like Lister Weidman in the context of realist interpretation is by positing non-local influences a la Bell. So you should... This shows that that's not true. That's right, this shows that that's not true. So you should be able to accommodate some kind of Bell inequality Yes, you can do that. So that would be a feature that I can't reproduce. Violations of inequality certainly would not be reproduced by these theories. So, and this was my remark, but I also have one question. Where do you have your trust that finally you will end up with a consistent axiom system? Well, I sort of take that to be part of the definition of axiotization. would be a consistent axiomatization. That you end up with an inconsistent axiomatization. Would you then say that the program is made? I would say an inconsistent axiomatization is no axiomatization at all. I think there is a model that the axioms are supposed to apply to. But I don't have a set of axioms. But there is theory already working. There is a consistent axiomatization. Yeah, I guess if it introduced quantum mechanics then clearly the axiom would have to be consistent because otherwise I would derive contradictions and that wouldn't be quantum mechanics. Howard? Yeah, so I was wondering a couple of things. One was just I wanted to comment on the extent to which the vacuum type is playing an analogous role

7:30 to the pilot of the And the other thing is I was wondering if you're worried that when you start changing things to get more of these other quantum phenomena that you don't have in the toy theory, that then problems might come up with not having some of the phenomena in the toy theory does. So in answer to the first question, it's very different from the pilot wave explanation of wave-particle duality. because the pilot wave explanation says I do a measurement on this wing of the Mach sender and that changes the quantum state and that therefore changes the pilot wave that's seen by the particle which is traveling along the other arm. And so that's a genuinely non-local influence. Whereas in this theory, the type of vacuum in our fight, you think of that as sort of phi, a phase degree of freedom that can only take two values, zero or pi. And so the code when you get the beam splitter is both zero, both pi, if so go left or you have different phases if so go right, and so those are local tags that instruct the particles how to move, so that's the difference So it's a big difference that the influence has to propagate to the beam splitter and that's what happens, and that's precisely why these experiments don't violate building qualities, it's because there was always the possibility of a ghost particle making it from this to the beam splitter to tell it how to behave, and this is just saying that we don't need ghost particles, if you take the epistemic degrees of freedom underlying the vacuum, and those are the very degrees of freedom that carry the information. In answer to your second question, I'm not terribly concerned about losing all the advantages that I got from the first axiom by coming up with a second axiom, because my sense is that the second axiom will involve the nature of the ontology, whereas the first axiom is about what observers know of that ontology, and those seem to me to be independent things. I guess the worry, though, is that when you do the next step of the program, which is your principle of epistemic restriction from the ontology that you might find that it doesn't work. You've got a nice promising axiomatization but given what you assumed about the ontology you can't explain the behavior of observers. There's a possibility for trouble there. So, first a comment. I'm not sure I agree with your typization of the bone interpretation. The bone interpretation is actually local for a single possible experience experiment.

10:00 And you can see that by looking at this diagram. The influence complicates through the way to the region of experience. It's something not local when you have, say, a two possible experience. Let me just talk quickly. I was thinking of describing this as two modes, and that's why I'm thinking it's a two-system scenario. You could maybe look at the electromagnetic version, but there is the single particle version. Yeah. That's interesting because if you try to do the single particle group here, you get something non-local. Right. Okay. That's interesting. And my question was, well, if you're going to actually try to produce, say, quantum theory for example, for a qubit, then we know that we'll have to have not just four object states, but any kind of four underlying object states. So, in that case, it seems it's not so clear in the knowledge balance principle, can you have issues with how a knowledge balance principle about living on top of the head in a number of optic states and reproduces the pictures that you've got here? I certainly won't be able to reproduce the pictures. Yeah, well, that happened. You have a much bigger group there. Yeah. So, is your question how can I imagine recovering at least as much as what I've got here using an infinite number of optic states? Yeah, yeah. Yeah, so I guess the honest answer is I anticipate that one of the assumptions that goes into this very framework is going to have to go, namely the idea that I can think of a qubit as having some intrinsic degree of freedom about which I have a lot of knowledge, and that's going to be replaced by thinking of it as having an intrinsic degree of freedom is wrong. it's really that all of its degrees of freedom are extrinsic, its relations to everything else. And so I don't really know how I'm going to be able to reproduce any of this in that context because I'm not going to be talking about knowledge of, you know, the properties of the thing that got spit out of the preparation device, but it's going to be knowledge about something much more diffuse, namely relations with everything else.

12:30 And so I have a feeling that really what it's going to have to do is the whole framework is going to have to change, and I won't be able to answer your questions to express these relational types of ideas. Alexi? Yeah, thanks. I'm somewhat surprised to hear that you're hoping that your second axiom would provide some insight about the nature of phantic states. Because it seems to me that, especially given this list of missing parts, and to know that, well, I myself have an epistemic second axiom, anyway, it seems to me that there is still room of those things or parts of those things within the framework. So there is a limit, but maybe there's something else about information that we can add as an axiom to reproduce more of those. So I think before we move or don't move to any ontological axioms, there is clearly, and the list shows it, there is clearly room for axioms within the epistemic framework. I think that's true if you're thinking of an axiomatization as something that might be operational, might be realist. So if you're in an operational context, then clearly I can say, well, one of my axioms is a restriction on how much I know about, say, the outcomes of measurements. And then I can add a number of other axioms which might be information.