In general, I don’t see much evidence that physicists who argue against MWI actually have the kind of understanding of probability theory necessary to make their arguments worth anything.
Physicists have something else, however, and that is domain expertise. As far as I am concerned, MWI is completely at odds with the spirit of relativity. There is no model of the world-splitting process that is relativistically invariant. Either you reexpress MWI in a form where there is no splitting, just self-contained histories each of which is internally relativistic, or you have locally propagating splitting at every point of spacetime in every branch, in which case you don’t have “worlds” any more, you just have infinitely many copies of infinitely many infinitesimal patches of space-time which are glued together in some complicated way. You can’t even talk about extended objects in this picture, because the ends are spacelike separated and there’s no inherent connection between the state at one end and the state at the other end. It’s a complete muddle, even before we try to recover the Born probabilities.
Rather than seeing MWI as the simple and elegant way to understand QM, I see it as an idea which in a way turns out to be too simple—which is another way of saying, naive or uninformed. Like Bohmian mechanics, conceptually it relies on a preferred frame.
The combination of quantum mechanics with special relativity yields quantum field theory. In quantum field theory, everything empirically meaningful is conceptually relativistic. In your calculations, you may employ entities (like wavefunctions evolving in time) which are dependent on a particular reference frame, but you can always do such calculations in a different frame. An example of a calculational output which is frame-independent would be the correlation function between two field operators at different points in space-time. By the time we reach the point of making predictions, that correlation function should only depend on the (relativistically invariant) space-time separation. But in order to calculate it, we may adopt a particular division into space and time, write down wavefunctions defined to exist on the constant-time hypersurfaces in that reference frame, and evolve them according to a Hamiltonian. These wavefunctions are only defined with respect to a particular reference frame and a particular set of hypersurfaces. Therefore, they are somehow an artefact of a particular coordinate system. But they are the sorts of objects in terms of which MWI is constructed.
The truly relativistic approach to QFT is the path integral, the sum over all field histories interpolating between conditions on an initial and a final hypersurface. These histories are objects which are defined independently of any particular coordinate system, because they are histories and not just instantaneous spacelike states. But then we no longer have an evolving superposition, we just have a “superposition” of histories which do not “split” or “join”.
At any time, theoretical physics contains many ideas and research programs, and there are always a lot of them that are going nowhere. MWI has all the signs of an idea going nowhere. It doesn’t advance the field in any way. Instead, as with Bohmian mechanics, what happens is that specific quantum theories are proposed (field theories, string theories), and then the Everettians, the Bohmians, and so on wheel out their interpretive apparatus, which they then “apply” to the latest theoretical advance. It’s a parasitic relationship and it’s a sign that in the long run this is a dead end.
I will provide an example of an idea which is more like what I would look for in an explanation of quantum theory. The real problem with quantum theory is the peculiar way its probabilities are obtained. You have complex numbers and negative quasiprobabilities and histories that cancel each other. The cancellation of possibilities makes no sense from the perspective of orthodox probability. If an outcome can come about in one way, the existence of a second way can only increase the probability of the outcome—according to probability theory and common sense. Yet in the double-slit experiment we have outcomes that are reduced in probability through “destructive interference”. That is what we need to explain.
There is a long history of speculation that maybe the peculiar structure of quantum probabilities can be obtained by somehow conditioning on the future as well as on the past, or by having causality working backwards as well as forwards in time. No-one has ever managed to derive QM this way, but many people have talked about it.
In string theory, there are light degrees of freedom, and heavy degrees of freedom. The latter correspond to the higher (more energetic) excitations of the string, though we should not expect that strings are fundamental in the full theory. In any case, these heavy excitations should cause space to be very strongly curved. So, what if the heavy degrees of freedom create a non-time-orientable topology on the Planck scale, giving rise to temporally bidirectional constraints on causality, and then the light strings interact (lightly) with that background, and quantum-probability effects are the indirect manifestation of that deeper causal structure, which has nonlocal correlations in space and time?
That’s an idea I had during my string studies. It is not likely to be right, because it’s just an idea. But it is an explanation which is intrinsically connected to the developing edge of theoretical physics, rather than a prefabricated explanation which is then applied in a one-size-fits-all fashion to any quantum theory. It would be an intrinsically string-theoretic derivation of QM. That is the sort of explanation for QM that I find plausible, for the reason that everything deep in physics is deeply connected to every other deep thing.
Either you reexpress MWI in a form where there is no splitting, just self-contained histories each of which is internally relativistic
Huh? This is what I’ve always¹ taken MWI in a relativistic context...
Just kidding. More like, since the first time I thought about the issue after graduating (and hence having an understanding of SR and QM devoid of the misconceptions found in certain popularizations).
Anyway, I’ll have to read the works by ’t Hooft when I have time. They look quite interesting.
In 1204.4926 the idea is that a quantum oscillator is actually a discrete deterministic system that cycles through a finite number of states. Then in 1205.4107 he maps a cellular automaton onto a free field theory made out of coupled quantum oscillators. Then in 1207.3612 he adds boolean variables to his CA (previously the cells were integer-valued) in order to add fermionic fields. At this point his CA is looking a little like a superstring, which from a “worldsheet” perspective is a line with bosonic and fermionic quantum fields on it. But there are still many issues whose resolution needs to be worked out.
Physicists have something else, however, and that is domain expertise. As far as I am concerned, MWI is completely at odds with the spirit of relativity. There is no model of the world-splitting process that is relativistically invariant. Either you reexpress MWI in a form where there is no splitting, just self-contained histories each of which is internally relativistic, or you have locally propagating splitting at every point of spacetime in every branch, in which case you don’t have “worlds” any more, you just have infinitely many copies of infinitely many infinitesimal patches of space-time which are glued together in some complicated way. You can’t even talk about extended objects in this picture, because the ends are spacelike separated and there’s no inherent connection between the state at one end and the state at the other end. It’s a complete muddle, even before we try to recover the Born probabilities.
Rather than seeing MWI as the simple and elegant way to understand QM, I see it as an idea which in a way turns out to be too simple—which is another way of saying, naive or uninformed. Like Bohmian mechanics, conceptually it relies on a preferred frame.
The combination of quantum mechanics with special relativity yields quantum field theory. In quantum field theory, everything empirically meaningful is conceptually relativistic. In your calculations, you may employ entities (like wavefunctions evolving in time) which are dependent on a particular reference frame, but you can always do such calculations in a different frame. An example of a calculational output which is frame-independent would be the correlation function between two field operators at different points in space-time. By the time we reach the point of making predictions, that correlation function should only depend on the (relativistically invariant) space-time separation. But in order to calculate it, we may adopt a particular division into space and time, write down wavefunctions defined to exist on the constant-time hypersurfaces in that reference frame, and evolve them according to a Hamiltonian. These wavefunctions are only defined with respect to a particular reference frame and a particular set of hypersurfaces. Therefore, they are somehow an artefact of a particular coordinate system. But they are the sorts of objects in terms of which MWI is constructed.
The truly relativistic approach to QFT is the path integral, the sum over all field histories interpolating between conditions on an initial and a final hypersurface. These histories are objects which are defined independently of any particular coordinate system, because they are histories and not just instantaneous spacelike states. But then we no longer have an evolving superposition, we just have a “superposition” of histories which do not “split” or “join”.
At any time, theoretical physics contains many ideas and research programs, and there are always a lot of them that are going nowhere. MWI has all the signs of an idea going nowhere. It doesn’t advance the field in any way. Instead, as with Bohmian mechanics, what happens is that specific quantum theories are proposed (field theories, string theories), and then the Everettians, the Bohmians, and so on wheel out their interpretive apparatus, which they then “apply” to the latest theoretical advance. It’s a parasitic relationship and it’s a sign that in the long run this is a dead end.
I will provide an example of an idea which is more like what I would look for in an explanation of quantum theory. The real problem with quantum theory is the peculiar way its probabilities are obtained. You have complex numbers and negative quasiprobabilities and histories that cancel each other. The cancellation of possibilities makes no sense from the perspective of orthodox probability. If an outcome can come about in one way, the existence of a second way can only increase the probability of the outcome—according to probability theory and common sense. Yet in the double-slit experiment we have outcomes that are reduced in probability through “destructive interference”. That is what we need to explain.
There is a long history of speculation that maybe the peculiar structure of quantum probabilities can be obtained by somehow conditioning on the future as well as on the past, or by having causality working backwards as well as forwards in time. No-one has ever managed to derive QM this way, but many people have talked about it.
In string theory, there are light degrees of freedom, and heavy degrees of freedom. The latter correspond to the higher (more energetic) excitations of the string, though we should not expect that strings are fundamental in the full theory. In any case, these heavy excitations should cause space to be very strongly curved. So, what if the heavy degrees of freedom create a non-time-orientable topology on the Planck scale, giving rise to temporally bidirectional constraints on causality, and then the light strings interact (lightly) with that background, and quantum-probability effects are the indirect manifestation of that deeper causal structure, which has nonlocal correlations in space and time?
That’s an idea I had during my string studies. It is not likely to be right, because it’s just an idea. But it is an explanation which is intrinsically connected to the developing edge of theoretical physics, rather than a prefabricated explanation which is then applied in a one-size-fits-all fashion to any quantum theory. It would be an intrinsically string-theoretic derivation of QM. That is the sort of explanation for QM that I find plausible, for the reason that everything deep in physics is deeply connected to every other deep thing.
Huh? This is what I’ve always¹ taken MWI in a relativistic context...
Just kidding. More like, since the first time I thought about the issue after graduating (and hence having an understanding of SR and QM devoid of the misconceptions found in certain popularizations).
Anyway, I’ll have to read the works by ’t Hooft when I have time. They look quite interesting.
In 1204.4926 the idea is that a quantum oscillator is actually a discrete deterministic system that cycles through a finite number of states. Then in 1205.4107 he maps a cellular automaton onto a free field theory made out of coupled quantum oscillators. Then in 1207.3612 he adds boolean variables to his CA (previously the cells were integer-valued) in order to add fermionic fields. At this point his CA is looking a little like a superstring, which from a “worldsheet” perspective is a line with bosonic and fermionic quantum fields on it. But there are still many issues whose resolution needs to be worked out.