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?
Best Answer
A measurement is a type of entanglement. If you measure a photon at the opening of a slit in a double slit experiment then you can think of there being a spin state at this opening. If the photon passes through it the spin changes direction. So the wave function for the photon in the double slit experiment is $$ \psi(x)\rangle~=~C(e^{ikx}|1\rangle~+~e^{ik(x’)}|2\rangle) $$ where the x and x’ denote the different paths through the two slits. If you compute the modulus squared you get $$ \langle\psi|\psi\rangle~=~|C|^2(2~+~e^{ik(x’-x)}\langle 1|2\rangle~+~ e^{-ik(x'-x)}\langle 2|1\rangle) $$ The exponential terms give the interference between the superposed states $|1\rangle$ $|2\rangle$ which have a nonzero overlap $\langle 1|2\rangle~\ne~0$. We now consider the coupling of a spin to this $$ \psi(x)\rangle~\rightarrow~C(e^{ikx}|1\rangle|+\rangle~+~e^{ik(x’)}|2\rangle|-\rangle) $$ which serves as the detector. Since $\langle +|-\rangle~=~0$ if you compute $\langle\psi|\psi\rangle$ the interference term is gone. This gives a reason for why one can’t measure which slit the particle travels through. We have replaced a superposition of states type of nonlocality with an entanglement. Now in doing this we have not addressed the question of how one actually observes the spin. One might presume we entangle some other states and do so up some “chain.” This of course leads to the Schrodinger cat problem. A cat or a human being, our brains and the like are not described well as single quantum systems. In fact they are messy thermal systems with high entropy. This is one problem with the whole idea of quantum consciousness, which never got out of the starting gates as a serious physical problem.