# Is this derivation of the Born rule circular in any way?

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PeterDonis
Mentor
Is this circular?

I don't know about circular, but it seems invalid. On p. 3, right column, they argue that any sequence of results from a binary measurement (i.e., only two possible results, ##0## or ##1##) will give a probability 1/2 in the limit of large numbers. But according to the MWI, that's not the case; according to the MWI, if we do the measurement ##N## times, every possible sequence of ##N## bits will be a term in the superposition that results. Most of those sequences do not have half ##0## and half ##1## bits, or even close to it.

The unstated assumption that is being used in their heuristic reasoning is that only one result occurs for each measurement. They even say measurements are made by "a detector of discrete nature that is found only in one state at a time". But under the MWI, this is false; every result occurs every time a measurement is made, each possible result being one term in the superposition that comes out of the measurement interaction. So it is simply not true in the MWI that a "discrete" detector (one that gives results from a discrete set instead of a continuous one) is "found only in one state at a time".

In other words, the paper claims to derive the Born rule from the MWI, but what it's actually doing is making an assumption that's inconsistent with the MWI.

I don't know about circular, but it seems invalid. On p. 3, right column, they argue that any sequence of results from a binary measurement (i.e., only two possible results, ##0## or ##1##) will give a probability 1/2 in the limit of large numbers. But according to the MWI, that's not the case; according to the MWI, if we do the measurement ##N## times, every possible sequence of ##N## bits will be a term in the superposition that results. Most of those sequences do not have half ##0## and half ##1## bits, or even close to it.

The unstated assumption that is being used in their heuristic reasoning is that only one result occurs for each measurement. They even say measurements are made by "a detector of discrete nature that is found only in one state at a time". But under the MWI, this is false; every result occurs every time a measurement is made, each possible result being one term in the superposition that comes out of the measurement interaction. So it is simply not true in the MWI that a "discrete" detector (one that gives results from a discrete set instead of a continuous one) is "found only in one state at a time".

In other words, the paper claims to derive the Born rule from the MWI, but what it's actually doing is making an assumption that's inconsistent with the MWI.
Interesting. I found another one that uses time symmetry https://arxiv.org/pdf/1505.03670.pdf . It looks to me that the MWI can use this to derive the Born rule.

PeterDonis
Mentor
It looks to me that the MWI can use this to derive the Born rule.

I don't think so. This paper makes the same unstated assumption the other one did: that measurements have single results. The MWI violates this assumption.