OK, I try to bring in words what I like to understand - in a philosophical and mathematical sense ... Assuming that the paradigm "the observer determines (his) reality" is true - as was recently confirmed - I was wondering if there is a physical explanation and/or possibility so switch operators or transform operators into another operator. In the sense - if you have a certain (mental) filter - you see a situation with that bias - you can change your mental filter (if you are lucky) - by an act of "transformative insight" - and "see the world with other eyes". Now - is there a mathematical representation for this when applying an operator to the wavefunction? I know of course to rotate coordinates to have the eigenvalues in a different basis. Can this be somehow used to re-program an operator? Of course staying within the Heisenberg-limit.
There are an observation angle between the line of sight and the direction of the vector being observed and there is also an observation angle between the closing velocity of observed the line of sight. The cosine of both becomes dimensions of what ever vector or scalar quality you are observing.
See the PDF file below for details in regard to mass etc. and the closing velocity type cosine.
I am thinking eventually Donald Hofmanns conscious agents could be the thing in looking for - if thede can be transformed - have to look up the papers
Hi Thomas,
you might want to give a look at this paper (https://arxiv.org/pdf/1811.12420.pdf). In particular in Eq. 3 they describe the evolution of a density matrix in presence of a continuous (weak or strong) measurement by the observer. As you can notice, due to the fact that the quantum system is continuously projected in random states provided by the measurment outcome, the density matrix undergoes nonlinear stochastic dynamics. Due to this intrinsically stochastic nature, I am not sure whether this description in the Schrodinger picture can extend to similar formalism in the Heisenberg picture for the operators, but hopefully it will give you some lead!
Hi Thomas Ehmer ,
You said: " Assuming that the paradigm "the observer determines (his) reality" is true - as was recently confirmed (...) "
What do you mean by this? What we know is that the observation changes the state, not determines it - we can't "choose" it unless we disturb/prepare the system in a very specific way. By just observing, we can't "determine our reality". This is a common mistake made by people who try to use quantum physics to justify certain spiritual concepts. There is absolutely no evidence of the change of a system being related to the observer's mindset.
Anyway, in this case, changing the basis is usefull only if you whant to measure another thing. The operator itself is independent of the basis, what changes is its representation. And you cannot determine the eigenvalue unless you expand the state in the basis of eigenstates of the operator.
Hello Marcos Souza - i was referring to this work - observer dependent reality - its only a polarization of photons but nevertheles ... wiegners friend ... https://arxiv.org/pdf/1902.05080.pdf
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