Amount of calculation isn’t so much the concern here as the amount of bits used to implement that calculation. And there’s no law that forces the amount of bits encoding the computation to be equal. Copenhagen can just waste bits on computations that MWI doesn’t have to do
And vice versa. You can do unnecessary calculation under any interpretation, so that’s an uninteresting observation.
The importantly is that the minimum amount of calculation you have to do get an empirically adequate theory is the same under any interpretation, because interpretations don’t change the maths, they just … interpret it.… differently.
In particular, a.follower many worlder has to discard unobserved results in the same way as a Copenhagenist—it’s just that they interpret doing so as the unobserved results existing in another branch, rather than being snipped off by collapse. The maths is the same, the interpretation is different. You can also do the maths without interpreting it, as in Shut Up And Calculate.
Copenhagen has to have rules for when measurements occur and what basis they occur in
This gets back to a long-standing confusion between Copenhagen and objective collapse theories (here, I mean, not in the actual physics community). Copenhagen ,properly speaking, only claims that collapse occurs on or before measurement. It also claims that nothing is known about the ontology of.the system before collapse—it’s not the case that anything “is” a wave function. An interpretation of QM doesn’t have to have an ontology, and many dont. Which, of course, is another factor that renders the whole Kolmogorov. Complexity approach inoperable.
Objective collapse theories like GRW do have to specify when and collapse occurs...but MW theories have to specify when and how decoherence occurs. Decoherence isn’t simple.
In particular, a.follower many worlder has to discard unobserved results in the same way as a Copenhagenist—it’s just that they interpret doing so as the unobserved results existing in another branch, rather than being snipped off by collapse.
A many-worlder doesn’t have to discard unobserved results—you may care about other branches.
I am talking about the minimal set of operations you have to perform to get experimental results. A many worlder may care about other branches philosophically, but if they don’t renormalise , their results will be wrong, and if they don’t discard, they will do unnecessary calculation.
MW theories have to specify when and how decoherence occurs. Decoherence isn’t simple.
They don’t actually. One could equally well say: “Fundamental theories of physics have to specify when and how increases in entropy occur. Thermal randomness isn’t simple.” This is wrong because once you’ve described the fundamental laws and they happen to be reversible, and also aren’t too simple, increasing entropy from a low entropy initial state is a natural consequence of those laws. Similarly, decoherence is a natural consequence of the laws of quantum mechanics (with a not-too-simple Hamiltonian) applied to a low entropy initial state.
MW has to show that decoherence is a natural consequence, which is the same thing. It can’t be taken on faith, any more than entropy should be. Proofs of entropy were supplied a long time ago, proofs of decoherence of a suitable kind, are a work in progress.
So once that research is finished, assuming it is successful, you’d agree that many worlds would end up using fewer bits in that case? That seems like a reasonable position to me, then! (I find the partial-trace kinds of arguments that people make pretty convincing already, but it’s reasonable not to.)
The other problem is that MWI is up against various subjective and non-realist interpretations, so it’s not it’s not the case that you can build an ontological model of every interpretation.
And vice versa. You can do unnecessary calculation under any interpretation, so that’s an uninteresting observation.
The importantly is that the minimum amount of calculation you have to do get an empirically adequate theory is the same under any interpretation, because interpretations don’t change the maths, they just … interpret it.… differently. In particular, a.follower many worlder has to discard unobserved results in the same way as a Copenhagenist—it’s just that they interpret doing so as the unobserved results existing in another branch, rather than being snipped off by collapse. The maths is the same, the interpretation is different. You can also do the maths without interpreting it, as in Shut Up And Calculate.
This gets back to a long-standing confusion between Copenhagen and objective collapse theories (here, I mean, not in the actual physics community). Copenhagen ,properly speaking, only claims that collapse occurs on or before measurement. It also claims that nothing is known about the ontology of.the system before collapse—it’s not the case that anything “is” a wave function. An interpretation of QM doesn’t have to have an ontology, and many dont. Which, of course, is another factor that renders the whole Kolmogorov. Complexity approach inoperable.
Objective collapse theories like GRW do have to specify when and collapse occurs...but MW theories have to specify when and how decoherence occurs. Decoherence isn’t simple.
A many-worlder doesn’t have to discard unobserved results—you may care about other branches.
I am talking about the minimal set of operations you have to perform to get experimental results. A many worlder may care about other branches philosophically, but if they don’t renormalise , their results will be wrong, and if they don’t discard, they will do unnecessary calculation.
They don’t actually. One could equally well say: “Fundamental theories of physics have to specify when and how increases in entropy occur. Thermal randomness isn’t simple.” This is wrong because once you’ve described the fundamental laws and they happen to be reversible, and also aren’t too simple, increasing entropy from a low entropy initial state is a natural consequence of those laws. Similarly, decoherence is a natural consequence of the laws of quantum mechanics (with a not-too-simple Hamiltonian) applied to a low entropy initial state.
MW has to show that decoherence is a natural consequence, which is the same thing. It can’t be taken on faith, any more than entropy should be. Proofs of entropy were supplied a long time ago, proofs of decoherence of a suitable kind, are a work in progress.
So once that research is finished, assuming it is successful, you’d agree that many worlds would end up using fewer bits in that case? That seems like a reasonable position to me, then! (I find the partial-trace kinds of arguments that people make pretty convincing already, but it’s reasonable not to.)
The other problem is that MWI is up against various subjective and non-realist interpretations, so it’s not it’s not the case that you can build an ontological model of every interpretation.