timmdeeg said:
Two particles, A and B, are entangled.
It's conceptually clearer to describe this as a system of two particles in an entangled state. See below.
timmdeeg said:
The measurement of A yields spin-up.
Again, it's conceptually clearer to say that the system of two particles is measured and particle A is measured as spin-up about a given axis.
timmdeeg said:
What happens to B in that instant of time?
The system of two particles is now in an unentangled state. The state of the non-local system has changed, as result of the measurement. The particles are now independent, although each is in an eigenstate of spin about a given axis.
timmdeeg said:
a) is B still a quantum object and as such doesn't possess definite spin properties before measurement?
There's no problem with a particle being in an eigenstate of spin about a given axis. The measurement of the entangled system has effectively done that to both particles. The spin about other axes is indeterminate - as it would be with any measurement of spin about a given axis.
timmdeeg said:
b) has B the definite property spin-down even prior to its spin measurement?
Again, this is no different from any measurement of a particle. After the measurement, the particle is in an eigenstate of spin about that axis. Repeated measurements of spin about the same axis must result in the same outcome.
It seems to have been a common theme recently that people asking about QM don't realise that systems in an eigenstate of a given observable will have a definite measurement outcome for that observable. This is not something where entanglement contradicts the rest of QM.
timmdeeg said:
What means action on a distance in this context, if at all?
It has no meaning, since QM says nothing about any action or mechanism to enforce correlation between measurements. The simplest position is to treat the quantum state as a non-local, mathematical object that allows you to calulate the probabilities of measurement outcomes. And, sometimes, those probabilities can be 0 or 1.
Again, there has been a common misconception recently that a probability of 0 or 1 somehow contradicts the probabilistic nature of QM. It doesn't. Probabilities of 0 or 1 are precisely what you get in the case of an eigenstate of the measured observable.