On 13-10-2025 03:56, Alan Grayson wrote:
Correct me if I'm mistaken, but as far as I know the wf has never been observed; only the observations of the system it represents. This being the case, in a large number of trials. Born's rulle will be satisfied regardless of which interpretation an observer affirms; either the MWI with no collapse of the wf, or Copenhagen with collapse of the wf. That is, since we can only observe the statistical results of an experiment from a this-world perspective, and we see that Born's rule is satisfied, so I don't see how it can be argued that the rule fails to be satisfied if the MWI is assumed. I think the same can be said about the other worlds assumed by the MWI, namely, that IF we could measure their results, the rule would likewise be satisfied.AG
I've scanned through part of this thread, so perhaps someone has already said what I'm going to say here. A special case of the Born rule is when measuring an observable A when the state is in an eigenstate of A. In that case you find the eigenvalue of A for that eigenstate the system is already in with 100% certainty. We can then exploit this fact to try to set up an experiment to verify the Born rule as a quantum experiment where the outcome is either 0 corresponding to the Born rule being falsified and 1 corresponding to the Born rule being verified. If we can then come up with such an observable for testring the Born rule, then if the Born rule is true, any quantum state should be an eigenstate with eigenvalue 1.
The problem here is that we can only ever do a finite number of measurements and we don't have a sharp rejection or verification of the Born rule. And there are then always exceptional states where the statistics will start to agree with the Born rule arbitrarily late. We can at most write down for any arbitrary integer an observable for repeating an experiment N times in a quantum coherent way where each individual measurement doesn't collapse the wavefunction (e.g. measurement conducted by a quantum computer and stored in that quantum computer), and only at the end we perform a measurement on the entire statistics stored in the quantum computer.
Suppose we set things up such that there is qubit that will take the value 1 if the hypothesis that the Born rule is false is ruled out at 99% confidence level. Then that qubit will be in a superposition of 1 and 0 and with N very large, the amplitude for 0 will be extremely small. But the amplitude for 0 will only become zero in the limit of N to infinity.
So, there is still a problem here, but at heart this is actually a problem with the very concept of probability, which is not well defined in physical contexts where one can only ever do a finite number of measurements:
https://www.youtube.com/watch?v=wfzSE4Hoxbc&t=1036s Saibal -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To view this discussion visit https://groups.google.com/d/msgid/everything-list/ca1579f01a0d59b8f90e88af95fd2da8%40zonnet.nl.
