I am aware about different interpretations of quantum mechanics out there but would mostly like to see an answer from the perspective of Copenhagen interpretation (or relative quantum mechanics if you wish).
Let an observer being a man with brain consisting of molecules and atoms. According the basic principles of quantum mechanics each of these particles has a wave function.
The question is: is there a combined wave function of all those particles which constitute the observer? Can such wavefunction be (in theory) determined by the observer himself?
Since the observer cannot isolate himself from his own brain, this would mean that the wave function, at least the part which determines his thoughts is permanently collapsed (i.e. the measurement happens instantly once the state changes). Does this "permanently collapsed" wave function imply special physical properties of the observer's own brain?
Does knowing his own thoughts constitute a measurement? Which moment should be counted as the moment of the collapse of wave function when making measurements on own brain?
Pretend an observer tries to measure the wave function of his own brain by a means of an X-ray apparatus or other machinery and read his own thoughts. Would not his own knowledge of that measurement or its results invalidate the results thus making the whole measurement impossible?
Does the behavior of particles which constitute the observer's brain differ statistically (acoording his measurements) from the behavior of particles which constitute the brains of other people?
Is there a connection with quantum immortality here?
Answer
I have just found this interesting paper by Thomas Breuer from 1995:
https://homepages.fhv.at/tb/cms/?download=tbPHILSC.pdf
The paper seems to prove that for a system that includes observer himself there are quantum states which are indistinguishable by the observer however technical means he employs, while he can measure any such states in the brains of other people.
The paper claims this proves that not only quantum mecanics is not universal theory that is applicable to all objects in the universe, but that no such universal theory can exist.
It also follows that in the world that the observer himself observes there is hidden information in his brain which cannot be extracted and read by any means even with help of other people (while the same information can be easily extracted from the brains of other people).
I do not know however how to interpret it regarding the wavefunction. Does it mean the observer's wavefunction indeterminate, singular or inexistent?
UPDATE.
And this this paper says it all. There will be subjective decoherence once the observer wants to measure himself. So he will see himself in a mixed state while others in the same situation will be observed as if they were in coherent state.
Note that this position is often taken for quantum mechanics. According to many interpretations, as for example the one of Bohr, or the one of London and Bauer (1939) and Wigner (1961, 1963), or even perhaps19 the one of von Neumann (1932), the “true” observer (or his mind) cannot be described by quantum mechanics. These authors say that if quantum mechanics is universally valid at all, then it is so only in the relative sense that every observer can perhaps apply it to any selected part of the world, except himself. It supposedly applies to Schroedinger’s cat, Wigner’s friend and Wigner himself under the condition that they lose their status of observer and are observed by something or somebody else.
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