consider a electron, it has location, rotation, momentum,etc
we can describe it with a N dimension vector with each dimension
representing one of the above qualities. obviously N is small for a
electron but big for a cat. just imagine in a 1000 dimensional space, the
dot product of two 5-dimensional subspace vectors is likely to be 0 : the
probability for the 5 non-zero coordinates to meet 955 0s is much
larger than to meet with the other 5 non-zeros. that's what i mean
by most likely to be orthognal.
there are 2 ways to deal with your problem, both need to sacrifice
some basic propoties of the classical view of the universe. anyway
local realism does not exist.
if we sacrifice locality, Einstein's relativity and ignore the idea that nothing
travels faster than light, then your experiment can be explained
by some "hiden variable theory"---- this is to give up the world to
save a photon
if we sacrifice realism and accept any of the quantum mechanics point
of view, then we dont have a problem at all because before we do our
measurement, the photon does not exist, talking about its path is meaningless
it can simultaneously choose any path and it is at any path at the same time
This is crazy, how can anyone who doesn't know physics know this much!
Credit to Hazelina Yeo.