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!