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[SEQ RERUN] Spooky Action at a Distance
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):
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. Getting rid of the single global world dispels this mystery and puts everything back to normal again.
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.
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Comments (32)
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.
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.
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.
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.
Is there any papers that asses this problem ? I can't say I've heard any proponents of MWI acknowledge problems with relativity?
That's a matter of taste, since there is no way to resolve this except on aesthetic grounds.
Indeed. Including the quote in the OP, which makes no sense as stated.
Or else, dispense with interpretations and do physics instead.
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.
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.
If you think that's ironic, you should see how I live my life.
This particular dead horse has been pounded into dust already, so I'll disengage.
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.
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.
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.
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?)
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.
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.
The concept of "everywhere at the same time" is meaningless in a relativistic universe.
This is incorrect. "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?
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?
Sorry, I don't think we are getting anywhere...