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.
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.
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.)
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?)
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.
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.
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.