Hi Fred
Just thinking about the expression si -> sf -> a.
As
si and
sf (=
a) are vectors they should be in bold, especially as you say you were trying to make more sense for the mathematicians.
I can understand the urge to insert Appendix in v5, as the '->' symbol makes me think of a classical '[asymptotically] tending to a limit' when in fact there is no 'tending to' in this case. This is one of the weird things about measuring an electron. Whatever the s value, the electron for Alice either immediately snaps from
s to
a with the emission of a single photon, or it doesn't emit a photon at all. (For simplicity I am just imagining the case where she either detects an emitted photon or there is no emitted photon.)
So on detection by Alice, an electron's states are instantly transformed from
s1 and lambda1 to
a and lambda_new. (And as an aside, as an electron changes handedness on detection, lambda_new does not necessarily equal lambda1?) But one can think of detecting an electron as peparing an electron for a new experiment. So
a and Lambda_new are appropriate for the newly prepared electron in a new experiment, whereas the old electron, i.e. the one participating in the Bell experiment, had states
s1 and lambda1.
However, since lambda1 is an unknown, information has to be built up statistically about the old electrons using the outcomes of Alice on many electrons all in terms of measurement results for which the newly measured electron vectors are
a.
So, after measurement, all Alice's vectors are a single vector
a. But before measurement there is a full range of vector directions:
s1.
And
s1 does not need to equal
a for an electron to emit a photon (otherwise there would be very few detections indeed).
That makes me think that the '->' symbol is a very confusing one.
Is there a symbol for 's1 snaps to a'?
PS Yes, website loading time is slow at the moment