This is only true for local hidden variables. It is possible to explain this with hidden variables in broader sense. Which you could also call hidden connections.
"This is only true for local hidden variables. It is possible to explain this with hidden variables in broader sense. Which you could also call hidden connections."
Can you explain further?
The reason I ask is that, it would appear quite sound and logical (based on our knowledge of discrete objects in the real world) to say that the electron goes through either slit 1 or slit 2 in all cases, but this is not accurate.
The reason is this:
When an observation is made, then it can be determined which slit the electron went through; in this case, it always goes through one slit or the other.
However, this observation is impossible to make without simultaneously disturbing the electron and destroying the interference pattern; that is to say, the resulting arrival distribution curve is not equal to the arrival distribution curve that is generated when no observations are made.
Therefore, how can it be determined which slit the electron will go through, while at the same time, not destroying the interference pattern?
To me, this is one of the "mystery of mysteries" of our universe.
There is a perfectly good theory which allows one to have electrons just going through one slit at a time. It has a few names: de Broglie-Bohm theory/pilot-wave theory/Bohmian mechanics. The idea is that we have a wave AND a particle. The wave goes through both slits and interferes. The particle travels along the wave, like some wood on the ocean.
Unlike an ocean wave, the quantum wave exists in 3N dimensional space where N is the number of particles in the universe (fundamentally) or the number of relevant particles in an experiment (practically). When an observation is made of which slit it went through, the environmental variables get entangled with the experimental system and separate the two branches of the wave functions (kind of like 2d waves that become separated vertically) and thus they can no longer interfere. The particle, always there and traveling along the wave, no longer is on a wave with an interference pattern. The system is no longer isolated from the environment and the behavior changes as a result.
The weirdness is not the hidden variable (position of the particle!), but rather the quantum wave function. It lives on configuration space, meaning that, in theory, it uses the configuration of all the particles of the universe at a single time. This somewhat contradicts relativity. Bell, once he saw Bohm's theory, realized that nonlocality is the central issue. He tried to do better. He failed and then proved that nature itself is simply nonlocal. No one likes it, but that is simply the way nature is. Relativity lost to quantum nonlocality.
As for randomness, one can prove in Bohm's theory that it is impossible to know the precise location of a particle. The best we can do, theoretically regardless of technology, is the quantum mechanical rule of psi-squared probability.
The theory has global existence and uniqueness of solutions which classical mechanics does not even have. It agrees completely with standard quantum predictions. It is not very magical. It can even be derived more easily than the Schrodinger equation itself. In fact, all one has to do is assume that one has particles with positions and the guiding equation can be derived from at least five entirely different points of view.
