On 31/10/2022 18:08, Phillip Helbig (undress to reply) wrote:
> Reality is complex, but examples---sometimes even from professional
> physicists---such as a disk broken in a "random" way (the jagged edges
> of each are "correlated"---yes, I really did see that used as an
> example) are too simple and misleading and don't grasp the essential
> concept.
>
> Here is something in-between. It's wrong, but more involved than the
> simple examples. Showing why real correlation is "more" than this might
> help to understand it.
>
> Imagine that a vector can have any orientation between 0 and 360
> degrees. If it is between 270 and 90, the measurement result is "up".
> If between 0 and 180, "right", 90 and 270 "down" and 180 and 360 "left".
>
> Two correlated vectors have opposite directions.
>
> If I measure one to have "up", then I know that the other is "down", but
> can't say whether it is "left" or "right". And so on. But if I measure
> it to be "right", I know that the other is "left", but can't say whether
> it is "up" or "down". I am also free to choose which 90 degrees
> correspond to, say, "up".
>
> That model explains many popular presentations of quantum correlation,
> but what is the "more" which is actually observed? Is such a model the
> simple hidden-variable model mentioned above?
>
In a way it is. You only have to specify a probability distribution of
the hidden variables as Bell did in his famous paper in Physica and
assume "locality". Then you have what he calls a "local realistic
hidden-variable theory".
The point of all the debates on the EPR paper, which is just
philosophical and not science, be cause it doesn't provide any
quantitative prediction which can be tested empirically. This has been
achieved by Bell with his inequality based on a set of spin measurements
on a system of two entangled spins 1/2.
The point, which distinguishes QT from any such "local realistic
theories" is that the measured single-particle spin components are not
taking determined values due to the preparation of the two-particle
system in an entangled "Bell state", which is a pure state such that the
single-particle spin components are maximally uncertain, i.e., the
reduced statistical oparator of each single-particle spin is simply
describing ideally unpolarized particles, i.e., the single-spin density
matrix is 1/2 \hat{1}. Nevertheless the measurement of any combination
of spin components is strongly correlated. If you measure both spin
components in the same direction it's (for the singlet Bell state) 100%
sure that if you measure "spin up" for one particle, the other must come
upt with "spin down" and vice versa.
Choosing a set of measurements of spin components in different
well-chosen directions you find violations of Bell's inequalities and
thus disprove local realistic theories.
My interpretation is that, what you have to give up is "realism", i.e.,
the assumption that there are hidden variables which make all
observables determined no matter in which state the observed system is
prepared in.
On the other hand locality is obeyed by relativistic quantum field
theory. In fact it's one of the important fundamental building blocks
underlying such QFTs, i.e., the assumption that operators that represent
local observables must commute at space-like separation of their
arguments. Particularly all local observables must commute with the
Hamilton density at space-like separation of their arguments and thus
there cannot be any causal connection between space-like separated
events. Particularly if the spin measurements on entangled particles
discussed above are made at space-like separated "measurement events"
("detector clicks") one can be sure that, within local relativistic QFT,
there cannot have been any causal influence of one measurement on the other.
--
Hendrik van Hees
Goethe University (Institute for Theoretical Physics)
D-60438 Frankfurt am Main
http://itp.uni-frankfurt.de/~hees/