4 ms·

If I have two bases |O_up> and |O_down>, representing the observer in the state of having measured an up spin and a down spin respectively, what is wrong with t

• effie 8y ago
  It does not work as written. How is |O_up> defined in terms of the basis of the global Hilbert space? There is infinity of directions in space which we can choose as the defining axis of the ket |O_up>. You could calculate the inner product for any of them. Does that mean that the inner product is typically zero and to get a non-zero probability, one has to talk not about probability of possible results of measurement, but about probability on the space of possible measurement setups? If so, why bother with the concept of quantum measurement at all? Why not just say any configuration of the world from some measurable set has probability int |psi|^2 dq? That would be the other, non-projection Born rule (or interpretation of psi), which doesn't have the problem of preferred basis and does not need it to be chosen by the classical apparatus.