As Einstein argued long ago, the quantum physics of his era - that is, the single-global-world interpretation of quantum physics, in which experiments have single unique random results - violates Special Relativity; it imposes a preferred space of simultaneity and requires a mysterious influence to be transmitted faster than light; which mysterious influence can never be used to transmit any useful information.
That's not quite right, there is no preferred frame and no influence is transmitted. Until the results of the spacelike-separated measurements are compared, one observer cannot know if the other even measured anything. All they know is that, if the other guy measured everything properly, the results must agree when they compare them later. You can visualize this outcome with collapse or with many worlds, whatever you are comfortable with.
I guess the confusion comes from the counterfactuals: people talk about the other measurement as if it were an objective reality before they learn about it. You can reasonably hope that the other measurement happened as planned, but you cannot know it for sure until you get the record of it some time later. Only then it becomes a part of your world.
Let's assume local laws of the universe, and the many worlds interpretation. How does the physics know which branch of the multiverse here corresponds to which branch of the multiverse there?
What exactly happens when I go from place A to place B, and then return to the place A? The whole universe is a superposition of many configurations. The place A (roughly speaking) is a superposition of many possible variants of the place A. What helps me to return to (a future of) the same variant of place A as I left? When I was in place B, in a sufficiently small time interval (distance between A and B, divided by c) both places were disconnected. And yet the universe somehow remembers to which branches of the place A do I belong.
Its probably a confused question, so please help me fix my intuition. (To avoid unnecessary branches of discussion, let's suppose that I agree with what is explained in the Sequences, although I probably misunderstood a few things. I just want to avoid unnecessary disclaimers like "assuming the WMI interpretation" in the responses.)
Perhaps the single most important thing to realize when adopting the (non-relativistic) MWI is that physical three-dimensional space is not the fundamental space of the theory. The arena in which the theory takes place is configuration space.
The sort of information you're looking for, about which physical space you return to, is encoded in configuration space and the Schrodinger equation. Even though the two different versions of point A you're talking about inhabit the same location in physical space, they inhabit distinct locations in configuration space, so the laws of quantum mechanics can distinguish between them.
Think of a simple case where you perform a spin measurement experiment at location A, and say that in your branch the measuring device at the location shows that the particle you measured was spin up. There will be another branch where the measuring device shows spin down, but this branch will have separated quite substantially from your branch in configuration space. Now your question amounts to this: if you leave location A and then return, why don't you return to find that you're in the other branch (the spin-down one). Looking at things from the configuration space perspective, the question doesn't seem all that troubling. This other branch is in a totally separate region of configuration space. Moving around in physical space won't jump you across configuration space to this other branch. The Schrodinger equation is local in configuration space. All that happens when you move around in physical space is that your branch (the one with the spin up measurement) moves around with you in configuration space. Since you always stay within that branch, returning to location A will reveal that the detector still shows spin up.
Perhaps what I say in this comment about "worlds" in MWI not being places might also help. You can't move out of your world (your branch) by travelling far enough in physical space.
Perhaps the single most important thing to realize when adopting the (non-relativistic) MWI is that physical three-dimensional space is not the fundamental space of the theory. The arena in which the theory takes place is configuration space.
Of course, this pretty much destroys the "locality" argument.
When a quantum coin-flip happens at A the universe splits everywhere at the same time. So position B is also split. But it doesn't know that it's split because the two universes look the same in the area around B. It takes time for the changes at A to propagate to B. If in the meantime a quantum coin-flip occurs at B then the universe(s) split again, now going up to four universes total. The universe is split into four everywhere, but at A two of the pairs look the same, and at B a different pairing looks identical.
When a quantum coin-flip happens at A the universe splits everywhere at the same time.
If you believe in relativity, that can't be true. And in fact some MWI people speak explicitly of splitting as starting locally and then spreading along the lightcone. But I don't think anyone has a working description of this, because those secondary, tertiary... quantum coin-flips would be happening and that means that the splitting light-cone has to develop new propagating splits of its own.
The union of relativity and quantum mechanics is an amazingly challenging subject, and the extension of MWI to the relativistic domain even more so. Since you don't have absolute time, you don't have a unique wavefunction of the universe evolving in time, and you can't reduce everything to a unique flow of amplitudes through configuration space. The prototypical QFT calculation is a sum over histories, in which whole relativistic histories get amplitudes, not just static, instantaneous spacelike configurations. It almost suggests a new MWI in which there's no splitting, just a stack of self-contained histories, but as usual, I don't see how to independently justify a phenomenological Born rule from this.
Also, the actual practice of QFT contains so many other hacks - complexified variables, analytic continuations - and so many bizarre transformations and re-representations of the math have been discovered in recent years (the twistor renaissance, the Hopf algebra of diagrams, AdS/CFT duality) that I expect the final answer to be something very different to what anyone imagines.
I agree that the problem of extending MWI (and for that matter, any interpretation of QM) to quantum field theory is a very difficult one. There is good reason to think that one of the central tenets of MWI -- wavefunction realism -- will not survive the transition. I said in a response to Villam's question that the fundamental ontology of the MWI is a universal wavefunction on configuration space. This is the view promoted by Eliezer in his QM sequence. It's an elegant view, but unfortunately its appeal falls apart when you start looking at QFT.
Part of the problem is that in QFT there is no precise configuration space. Particle number isn't conserved in the theory, and particles (being non-fundamental) do not have precisely defined masses, charges and positions. It is very different from the simple case where we can construct a space consisting of the exact configuations of a fixed number of particles.
Also, unlike in non-relativistic QM, operators in QFT are associated with particular regions of space-time. For instance, there are separate field operators associated with every space-time point. Physical space-time is much more entangled with the fundamentals of the theory than it is in non-relativistic QM.
So I think the QM sequence should be accompanied by a huge caveat. The form of MWI advocated there is (I think) the best interpretation available for non-relativistic QM. However, many of the basic lessons of the sequence no longer apply when we are dealing with QFT. And the true physical theory is likely to be a lot closer to QFT than non-relativistic QM. I still think our best bet is to build a broadly MWI-like non-collapse interpretation for QFT, but I suspect it will look quite different from the MWI we all know and love.
Is there any papers that asses this problem ? I can't say I've heard any proponents of MWI acknowledge problems with relativity?
Thanks for explanation. So I guess the question is still open (of course, the word "open" refers to our maps, not to the territory). If I understand it correctly:
relativity assumes that the universe is local in space
quantum physics assumes that the universe is local in configuration space
and the problem, as I see it, is we don't even have a nice definition of "configuration space" that wouldn't violate the assumption of space locality.
If I understand it correctly, some people are trying to fix this by replacing configuration spaces by histories of the universe, but... imagining a history of the whole universe up to the specific point of space-time as a fundamental particle of physics, that feels wrong. Well, maybe it is right -- we should not rely on our intuition derived from macroscopic events -- but maybe we just didn't find a better solution yet.
The form of MWI advocated there is (I think) the best interpretation available for non-relativistic QM.
That's a matter of taste, since there is no way to resolve this except on aesthetic grounds.
However, many of the basic lessons of the sequence no longer apply when we are dealing with QFT.
Indeed. Including the quote in the OP, which makes no sense as stated.
our best bet is to build a broadly MWI-like non-collapse interpretation for QFT
Or else, dispense with interpretations and do physics instead.
That's a matter of taste, since there is no way to resolve this except on aesthetic grounds.
MWI is not empirically equivalent to all other interpretations of QM. It makes different predictions from the Copenhagen interpretation, for instance. Even if this were not the case, we distinguish between empirically equivalent theories on scientific grounds all the time. Neo-Lorentzian theory is empirically equivalent to the special theory of relativity, but I think (and most scientists agree) that there are good non-empirical grounds for preferring the special theory. You may call these criteria "aesthetic", but that doesn't alter the fact that they are part of the standard explanatory toolbox of physics.
Or else, dispense with interpretations and do physics instead.
Part of doing physics is figuring out the actual structure of our universe, and interpreting QFT is crucial to that task. Physics isn't just about doing calculations.
Part of doing physics is figuring out the actual structure of our universe, and interpreting QFT is crucial to that task. Physics isn't just about doing calculations.
I agree with you, but I'd like to note the irony of this against your username.
You're right. I have had this discussion with you a number of times before. I'm not very good at keeping track of usernames, so I didn't realize this. Sorry, I didn't mean to come across as tediously piling on.
Since you don't have absolute time, you don't have a unique wavefunction of the universe evolving in time, and you can't reduce everything to a unique flow of amplitudes through configuration space.
Hmmm, you're right. (Of course I could just pick a favoured reference frame, but that's inelegant. Timeless physics might work too (I think?), but the sequence reruns will get to that question in due time.)
Also, we had a similar discussion here.
EDIT: Would you agree that what I said was the same as what Eliezer is saying in the QM sequence?
EDIT2: Okay, my brain's just melted. What does it even mean for a QM theory to obey SR? I don't know how to apply Lorentz transformations to a wavefunction.
I don't know how to apply Lorentz transformations to a wavefunction.
The wave function is a scalar in the regular QM, so it is unchanged under the Lorentz transformations. Unfortunately, the Schrodinger equation is inherently non-relativistic.
The Klein-Gordon and Dirac equations were the early attempts to "relativize" the Schrodinger equation. It didn't work that well until the wave function was replaced with quantized fields. Those quantized fields become photons, electrons and other particles in a certain approximation. Unfortunately, the math gets quite hairy in a hurry.
The wave function is a scalar in the regular QM, so it is unchanged under the Lorentz transformations.
Eh? If I have a scalar field phi(x) in classical physics and I rotate the universe by pi/2 (an active transformation) the field not changes to phi(Mx) where M is the linear map that rotates the universe by pi/2 in the other direction. This changes phi, no? I know that if phi were a vector field then we would have the additional change that the vector rotates as well (i.e. we get M^(-1) v(Mx)), but the scalar field phi still in some sense changes.
If I wanted to check if my theory was invariant by rotations by pi/2 I would take a field that satisfied my equations, apply the above transformation to it, and see if it still satisfied my equations. What analogous transformation could I apply to a wavefunction to check if my theory was Lorentz invariant?
(Also, isn't the wavefunction also a scalar in QFT?)
This changes phi, no?
Definition of a scalar). In other words, if you change your coordinate system, a value of the scalar field at a given point in spacetime (now described by the new coordinates) is still the same number. Whereas a vector will, in general, have different components.
(Also, isn't the wavefunction also a scalar in QFT?)
No. To quote wikipedia, "probability conservation is not a relativistically covariant concept", because the particle number is neither conserved, nor is a covariant quantity. I.e., different observers can disagree on the number of particles, which violates the definition of a scalar. Thus the wavefunction (from which probability is derived) is not a useful concept in QFT and is replaced by fields living in the Fock space, not in the Hilbert space.
When a quantum coin-flip happens at A the universe splits everywhere at the same time. So position B is also split.
This is incorrect. "World-splitting" propagates at the speed of decoherence, and this is not instantaneous.
"World-splitting" propagates at the speed of decoherence, and this is not instantaneous.
Decoherence is just another word for interaction.
I think its a little more specific than that. "Decoherence" refers to spontaneous system-environment interactions that suppress interference. But I don't see what that has to do with the point I was making. World-splitting occurs at a finite speed set by the speed of these interactions.
My (poorly worded, convoluted and implicit) point was that propagation speed of an interaction is something we should be able to measure. Would you propose an experiment in which the decoherence propagation speed is measured?
There is no single universal rate at which decoherence propagates. The details will depend on the structure of the system and its environment. What we can say is that the speed of light sets an upper limit on the speed at which interactions can propagate, so decoherence will propagate at a finite rate.
As for measuring decoherence rates in specific cases, this has been done. Take this paper, for instance. The authors couple Be-9 ions prepared in superpositions of their energy eigenstates with various types of reservoirs, representing different environments. They then measured the coherence of the ion's state at different times, determining the rate at which the superpositions decohere given different environments and different interaction strengths. Is this the sort of experiment you were looking for?
As for measuring decoherence rates in specific cases, this has been done.
I thought we were discussing the (hypothetical) decoherence propagation rate, not the time it takes for a quantum system to decohere in the lab, which has nothing to do with relativity. It is even measured in different units (inverse seconds vs. meters/second). So no, this experiment is not what I was asking about.
The claim I made was that world-splitting is not instantaneous. The fact that systems decohere gradually establishes this (if you buy that "world-splitting" is just a consequence of decoherence). I'm not sure I see your worry. Perhaps you can indicate what, specifically, you think is wrong with my initial claim?
This strikes me as an odd thing to say, given the context. You raised what I presume is a criticism of the point I was making. I am trying to clarify the nature of the criticism, since I don't see the problem yet. If I am able to recognize the force of the criticism, then surely we would have have got somewhere in this conversation. If you realize that the criticism does not work, we would have got somewhere as well. So why do you think we are not getting anywhere? Your comment just leaves me confused.
I can interpret it in a few ways:
(1) "I think our disagreements are sufficiently fundamental that discussing this within the constraints of a blog combox is unlikely to be productive." It seems to me the particular disagreement at issue, though, isn't all that fundamental, and can be settled rather quickly once we are both clear on what is being disputed. If you think I am wrong about this meta-point, could you at least give an indication why?
(2) "I do not think you are engaging in good faith, so continuing this is a waste of my time." All I can do is assure you that I am in fact engaging in good faith. I am very interested in this stuff, and potentially learning more about it is far more valuable to me than "winning" some internet argument.
(3) "You do not possess knowledge sufficient to understand my point, and I do not have the patience to explain it to you." Given your complaint elsewhere about dilettantes promoting the MWI, I suspect this might be what you intend. I think your point about dilettantism is valid, especially on this site, but it does not apply to me. I have peer-reviewed publications on the foundations of quantum mechanics (not on MWI specifically, but still).
(4) "I realize that my argument doesn't work, but I don't want to admit it." This is a very uncharitable interpretation of your intent, and I mention it only for the sake of completeness. I doubt this is what is really going on.
(5) "I don't want to talk about this anymore because I'm bored/busy." If this is the case, please say so (or just don't respond with anything). I have no problem with people saying this to me, and I will of course refrain from engaging with you further on this.
Which of these is the right one? Or is it something else? I would really appreciate a more informative response from you, because if your actual intent is captured by (1), (2) or (3), it would be beneficial for me to know.
I have peer-reviewed publications on the foundations of quantum mechanics (not on MWI specifically, but still).
I would be interested to see them, provided they were in physics journals (except for the Foundations of Physics, which often publishes stuff that can only be very charitably described as physics), and not in philosophy journals (my opinion of those happens to coincide with that of Feynman).
As for the immediate reason, I pointed out a rather elementary problem with units, which you did not address. Given that we cannot even agree on how propagation rate is defined, I do not see how we can make further progress.
I would be interested to see them, provided they were in physics journals (except for the Foundations of Physics, which often publishes stuff that can only be very charitably described as physics), and not in philosophy journals (my opinion of those happens to coincide with that of Feynman).
Fair enough. I will admit that the only physics journal in which I am published is in fact Foundations of Physics. You may not see this as a worthwhile venue for publication, but I hope that it will at least absolve me of the charge of dilletantism. I'd also point out that while in the past Foundations has had a reputation for encouraging mild crackpottery, its reputation has substantially improved since Gerard 't Hooft (I think probably the most insightful contemporary physicist) took charge. My publication in the journal was in the post-'t Hooft era, for what that's worth. I'd point you to my paper, but I'd like to retain a little anonymity here.
I disagree very strongly with you on the value of (scientifically informed) philosophy, but that is probably a topic on which we genuinely will not get anywhere, so I'll drop it.
That said, your response was (as I predicted) beneficial. I take it you are expressing surprise (or perhaps skepticism) at my claim to some degree of expertise. When I comment on physics, I try to balance signalling that I know what I'm talking about against being informal and accessible. Perhaps I'm not getting the balance right.
As for the immediate reason, I pointed out a rather elementary problem with units, which you did not address. Given that we cannot even agree on how propagation rate is defined, I do not see how we can make further progress.
Your point about units seems irrelevant to what I was saying. My comment was not intended to be non-responsive. I was trying to make clear what I was actually claiming, in the hope that it would also make clear that the units worry isn't a problem. Maybe I'll try again, at slightly greater length.
Look, here's the dialectic: Someone said that in MWI, world-splitting is global and instantaneous. I responded that it isn't, since "world-splitting" is just a consequence of decoherence, and decoherence takes time and relies on system-environment interactions, which are constrained by relativity.
At no point do I commit myself to measuring decoherence rates using units of velocity. I did speak of decoherence propagating, and this is what I meant by it: When a system decoheres its dynamics are no longer unitary. But the dynamics of an informationally isolated system are always unitary, so for a system to decohere, it must exchange information with its environment. Relativity constrains the (spatial) propagation of information.
Whether or not a particular quantum process has led to "world-splitting" is, in a sense, relative to an observer. Say I'm observing a Stern-Gerlach experiment. The spin state of the particle decoheres through interaction with the measuring device, From my perspective, though, this doesn't correspond to a splitting into two worlds with different spin measurements until information from the measuring device propagates to me. This will take a (slight) additional amount of time. To you, standing outside the lab, there wouldn't have been world-splitting until some portion of that information propagates to you; again, at finite velocity. Until that point, the whole particle-measuring device-me system will be in a state of superposition relative to you. So if we are dealing with localized systems, and we assume that information propagates through space at finite velocity, world-splitting can also be (crudely) thought of as propagating through physical space.
But I should emphasize that this in fact a crude approximation. I'm glossing a number of complications in this sketch. But these complications do not affect my main (in fact, sole) point: world-splitting in MWI is not global and instantaneous. Perhaps you think I'm making some bigger claim here, like MWI is a spatio-remporally local or relativistically invariant interpretation. I am not claiming anything of the sort. I don't even think the ordinary notion of spatial locality is well-defined in the MWI framework (since physical space is non-fundamental), and I made a comment above explicitly saying that MWI in its current form cannot be easily reconciled with relativity.
First, I did not mean your personally when I was talking about dilettantes who learned from other dilettantes. I meant the people who read the QM sequence as their only in-depth math-free introduction to QM and took it as a self-evident truth, compartmentalizing away everything EY said about guessing the teacher's password and such. Again, as EY keeps saying, a belief feels like truth from the inside, so it is extremely hard to argue with such people. I am well aware that this applies just as much to me, as to everyone else, having been burned by false beliefs before multiple times.
I agree that under 't Hooft FoP gotten better, though it is still more philosophy than physics, hence my reservations.
At no point do I commit myself to measuring decoherence rates using units of velocity. [...] To you, standing outside the lab, there wouldn't have been world-splitting until some portion of that information propagates to you; again, at finite velocity.
I find these two statements in contradiction. If you can measure the degree of decoherence and pinpoint when something is, say, "50%-decohered", then you can take two observers at two points in space who measure it and calculate the propagation velocity as (x2-x2)/(t1-t1). If you cannot do that, then propagation of decoherence is not ontologically fundamental and is just a feel-good picture.
But these complications do not affect my main (in fact, sole) point: world-splitting in MWI is not global and instantaneous.
My point is that it makes no sense at all to talk about the "world-splitting process" as anything in any sense "real".
Now, I do not expect you to agree with me, that is why I tried to drop the issue. And the reason I do not expect you to agree with me is a pragmatic one (pun intended): actions speak louder than words. And by "action" I mean an experiment differentiating between our points of view. That's why I asked you how such an experiment would look. Until this is settled, we can continue back and forth with little hope of coming to an agreement. It might or might not work out better in person, though my observations of metaphysical debates between some rather smart people makes me skeptical that it would.
Today's post, Spooky Action at a Distance: The No-Communication Theorem was originally published on 05 May 2008. A summary (taken from the LW wiki):
Discuss the post here (rather than in the comments to the original post).
This post is part of the Rerunning the Sequences series, where we'll be going through Eliezer Yudkowsky's old posts in order so that people who are interested can (re-)read and discuss them. The previous post was Bell's Theorem: No EPR "Reality", and you can use the sequence_reruns tag or rss feed to follow the rest of the series.
Sequence reruns are a community-driven effort. You can participate by re-reading the sequence post, discussing it here, posting the next day's sequence reruns post, or summarizing forthcoming articles on the wiki. Go here for more details, or to have meta discussions about the Rerunning the Sequences series.