The point seems so simple to me, I am having trouble expressing it… A wavefunction is the instantaneous state of a quantum system. It is extended spatially. In relativistic space-time, to talk about the instantaneous state of an extended object, you have to define simultaneity. This means choosing a particular decomposition of space-time into spacelike hypersurfaces that are treated as surfaces of simultaneity. In a relativistic universe, you cannot talk about finite time evolution of spatially extended wavefunctions without first breaking space-time into space and time.
In particle physics a la Copenhagen, there is no ontological commitment to wavefunctions as things that exist. They are just part of a calculation. But we are told that in MWI, the universal wavefunction is real and it is a superposition of worlds. As I have just argued, you can’t do what you want to do—study how this wavefunction evolves over time—without first breaking space-time into space and time, so that you have the hypersurfaces of simultaneity on which the wavefunction is defined. So it seems that belief in the wavefunction as something real, requires belief in an ontologically preferred frame, with respect to which that wavefunction’s time evolution is defined.
Hmm. Again, “the universal wavefunction is real” is part of the theory but “it is a superposition of worlds” is not, the latter is just a way to talk loosely about particular situations that sometimes come up. I don’t think that people in different inertial reference frames have to agree about how many worlds there are, indeed I don’t even think people in the same inertial reference frame have to agree about how many worlds there are. It’s not part of the theory. The only other thing that is part of the theory is some kind of indexical axiom, like I think one version is “if the complex amplitude for me having a certain brain state approaches zero, then the probability that I will find myself experiencing having that brain state also approaches zero”, or things like that, I think.
In my experience when physicists challenge a proposal as being inconsistent with relativity, they try to come up with an example where two people in different reference frames would make different predictions about the same concrete experimental (or thought-experimental) result. Can you think of anything like that? It seems like you have a different demand, which is “people in different reference frames cannot disagree about the value of ontologically primitive things” even if the disagreement doesn’t shake out as a concrete prediction incompatibility. If so (and sorry if I’m misunderstanding), I guess I just don’t see why that’s important. Why can’t something be both ontologically primitive and reference frame dependent? Like velocity, to take an everyday example. I don’t know if it’s ontologically primitive, (partly because I’m not sure what ontologically primitive means), but anyway, I don’t see why reference frame dependence should count against it.
I don’t think that people in different inertial reference frames have to agree about how many worlds there are, indeed I don’t even think people in the same inertial reference frame have to agree about how many worlds there are.
At this point I have nothing to say, because there’s no coherent concept of ‘world’ left to debate.
I think one version is “if the complex amplitude for me having a certain brain state approaches zero, then the probability that I will find myself experiencing having that brain state also approaches zero”
This could become a version of ‘many-minds interpretation’. But now you need to make ‘mind’ a rigorous concept. There has to be something exact in the ontology that corresponds to the specificity of what we see! - whether it’s a whole ‘world’, or just an ‘observer experience’. If everything other than the universal wavefunction is fuzzy and vague and a matter of convention, you no longer have a theory corresponding to observed reality.
Why can’t something be both ontologically primitive and reference frame dependent? Like velocity, to take an everyday example
The 4-velocity (considered as an invariant geometric object, rather than in terms of covariant components) is the fundamental entity.
there’s no coherent concept of ‘world’ left to debate.
Good! Maybe we’re on the same page there. “World” is not part of the theory and is not a well-defined concept, in my opinion.
now you need to make ‘mind’ a rigorous concept
Hmm, I guess I would propose something like “the complete history of exactly which neurons in a brain fire at which times, to 1μs accuracy, is a mind, for present purposes”. Then I would argue that different “minds” don’t exhibit measurable quantum interference with each other, or we can say “different minds are in different worlds / branches” as a casual shorthand for that, if we want. And there is a well-defined (albeit complicated) way to project the universal wavefunction into the subspace of one “mind”, in order to calculate its quantum amplitude, and then you can apply the Born rule for the indexical calculation of how likely you are to find yourself in that mind. Something like that, I guess. I haven’t thought it through very carefully, I just think something vaguely like that could work, with a bit more effort to iron out the details. I’m not sure what’s in the literature, maybe there’s a better approach...
The point seems so simple to me, I am having trouble expressing it… A wavefunction is the instantaneous state of a quantum system. It is extended spatially. In relativistic space-time, to talk about the instantaneous state of an extended object, you have to define simultaneity. This means choosing a particular decomposition of space-time into spacelike hypersurfaces that are treated as surfaces of simultaneity. In a relativistic universe, you cannot talk about finite time evolution of spatially extended wavefunctions without first breaking space-time into space and time.
In particle physics a la Copenhagen, there is no ontological commitment to wavefunctions as things that exist. They are just part of a calculation. But we are told that in MWI, the universal wavefunction is real and it is a superposition of worlds. As I have just argued, you can’t do what you want to do—study how this wavefunction evolves over time—without first breaking space-time into space and time, so that you have the hypersurfaces of simultaneity on which the wavefunction is defined. So it seems that belief in the wavefunction as something real, requires belief in an ontologically preferred frame, with respect to which that wavefunction’s time evolution is defined.
Is that any clearer?
Hmm. Again, “the universal wavefunction is real” is part of the theory but “it is a superposition of worlds” is not, the latter is just a way to talk loosely about particular situations that sometimes come up. I don’t think that people in different inertial reference frames have to agree about how many worlds there are, indeed I don’t even think people in the same inertial reference frame have to agree about how many worlds there are. It’s not part of the theory. The only other thing that is part of the theory is some kind of indexical axiom, like I think one version is “if the complex amplitude for me having a certain brain state approaches zero, then the probability that I will find myself experiencing having that brain state also approaches zero”, or things like that, I think.
In my experience when physicists challenge a proposal as being inconsistent with relativity, they try to come up with an example where two people in different reference frames would make different predictions about the same concrete experimental (or thought-experimental) result. Can you think of anything like that? It seems like you have a different demand, which is “people in different reference frames cannot disagree about the value of ontologically primitive things” even if the disagreement doesn’t shake out as a concrete prediction incompatibility. If so (and sorry if I’m misunderstanding), I guess I just don’t see why that’s important. Why can’t something be both ontologically primitive and reference frame dependent? Like velocity, to take an everyday example. I don’t know if it’s ontologically primitive, (partly because I’m not sure what ontologically primitive means), but anyway, I don’t see why reference frame dependence should count against it.
At this point I have nothing to say, because there’s no coherent concept of ‘world’ left to debate.
This could become a version of ‘many-minds interpretation’. But now you need to make ‘mind’ a rigorous concept. There has to be something exact in the ontology that corresponds to the specificity of what we see! - whether it’s a whole ‘world’, or just an ‘observer experience’. If everything other than the universal wavefunction is fuzzy and vague and a matter of convention, you no longer have a theory corresponding to observed reality.
The 4-velocity (considered as an invariant geometric object, rather than in terms of covariant components) is the fundamental entity.
Good! Maybe we’re on the same page there. “World” is not part of the theory and is not a well-defined concept, in my opinion.
Hmm, I guess I would propose something like “the complete history of exactly which neurons in a brain fire at which times, to 1μs accuracy, is a mind, for present purposes”. Then I would argue that different “minds” don’t exhibit measurable quantum interference with each other, or we can say “different minds are in different worlds / branches” as a casual shorthand for that, if we want. And there is a well-defined (albeit complicated) way to project the universal wavefunction into the subspace of one “mind”, in order to calculate its quantum amplitude, and then you can apply the Born rule for the indexical calculation of how likely you are to find yourself in that mind. Something like that, I guess. I haven’t thought it through very carefully, I just think something vaguely like that could work, with a bit more effort to iron out the details. I’m not sure what’s in the literature, maybe there’s a better approach...