bell's theorem
1. example with photons
- imagine you have a horizontal (A) and a vertical (C) polarized filter stacked on top of each other
- about half of the sunlight makes it through the horizontal filter, and none of this light makes it through the vertical filter
- So 0% make it through A and C
- imagine you add a 45 degree polarized filter (B) in between A and C
- Now 50% of the light makes it through B and 50% of the remaining makes it through C (25%) total
- Now imagine that before going through the filter, each photon has a hidden variable that says which filter they will pass through
- But this cannot be!
- A and C block 100% of the photons, so no photon can have the "pass A" AND "pass C" properties.
- A and B and C allow 25% of the photons, so at least 25% of the photons must have "pass A" and "pass B" and "pass C" properties
- contradiction!
- Question (mine): Does this preclude there being a "pass A and fail C" property, as well as a hidden "pass A and pass B and pass C" property?
- Answer (after thinking for a while): These proposed properties don't solve the paradox. Imagine a photon that has just arrived at C with these properties. How is C supposed to know whether this is a photon that has just passed through B and needs to be let through (with p=0.5) or whether this is a photon that has not passed through B and needs to be rejected (with p=1.0)? C needs to be, in some way, history sensitive, which leads us to our next point.
- It could still be that there is some hidden variable that is allowed to evolve based on history
- However, we can rule this out using entangled pairs (see EPR pairs), that are measured while being very far apart, so that any communication between them would need to be faster than light