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Decission Theory and Quantum Self-Measurement

by Alan Givré 1 min read22nd Dec 20194 comments

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Most Quantum Mechanics are formulated from a point of view of Causal Decission Theory, as can be seen from the Noncontextuality/counterfactual indefiniteness of Kochen-Specker Theorem.

Now, this creates a chatastrophe when the Observator needs to be analized through a physical lense. That is, Self-Measurement is terribly paradoxical.

Things go so badly that one needs to conclude that the following axiom is incompatible with the Law of Noncontradiction and Quantum Mechanics. According to Frauchiger and Renner:

https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6143649/

Suppose that agent A has established that

Statement A(i): “I am certain that agent A′, upon reasoning within the same theory as the one I am using, is certain that x = ξ at time t.”

Then agent A can conclude that

Statement A(ii): “I am certain that x = ξ at time t.”


How can we create a Quantum Theory of Self-Measurement that is compatible with Updateless or Functional Decission Theory (I don't know the difference between the two), which I deem more realistic for physical reasons.

I ask you this because I consider you the experts on Decission Theory. The answer to this question may have consecquences on my personal research in biophysical processing of information.

If you need clarification on Quantum Theory and its No-Go theorems to answer this question tell me.

Thank you on advance!!!!

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Most Quantum Mechanics are formulated from a point of view of Causal Decission Theory

No, Quantum Mechanics is a chimera of the unitary evolution and the measurement postulate (sometimes disguised or motivated), it has nothing to do with decision theories.

as can be seen from the Noncontextuality/counterfactual indefiniteness of Kochen-Specker Theorem

The KS theorem states that there are no local hidden variables independent of the observer, nothing more. For a model that postulates such a dependence, see for example superdeterminism, https://en.wikipedia.org/wiki/Superdeterminism and https://arxiv.org/abs/1912.06462.

How can we create a Quantum Theory of Self-Measurement that is compatible with Updateless or Functional Decission Theory

This will have to wait until someone really smart figures out how to resolve foundational issue of unitary evolution vs non-linear and non-unitary measurement.