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JG11
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JG11 said:Is this circular?
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 said: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.
JG11 said:It looks to me that the MWI can use this to derive the Born rule.
The Born rule is a fundamental principle in quantum mechanics that predicts the probability of measuring a particular outcome in a quantum system. It states that the probability of obtaining a certain measurement is equal to the squared magnitude of the quantum state's coefficient. It is important because it provides a way to calculate and predict the behavior of quantum systems, which is crucial for understanding and studying the microscopic world.
The Born rule is derived from the principles of quantum mechanics, particularly the wave function and its collapse upon measurement. It is also based on the concept of superposition, where a quantum system can exist in multiple states simultaneously. By applying mathematical equations and principles, such as the Schrödinger equation and the inner product, the Born rule is derived.
Some argue that the derivation of the Born rule is circular because it relies on the assumption that the wave function represents physical reality. This assumption is based on the Born interpretation, which states that the wave function is a probability amplitude, and is used to derive the Born rule itself. Therefore, some argue that the derivation is circular and cannot be proven without assuming the Born interpretation.
The implications of a circular derivation of the Born rule are still a topic of debate among physicists. Some argue that it undermines the fundamental principles of quantum mechanics and raises questions about the validity of the theory. Others argue that even if the derivation is circular, it does not affect the predictive power of the Born rule, which has been experimentally verified numerous times.
Currently, there is no definitive answer to whether or not the derivation of the Born rule is circular. Some researchers are exploring alternative interpretations of quantum mechanics, such as the many-worlds interpretation, which may provide a non-circular derivation of the Born rule. However, until there is concrete evidence or a consensus among physicists, the circularity of the Born rule's derivation remains a topic of ongoing discussion and debate.