I read this description of Bell's theorem. I understand he's restating it slightly, so there may be incorrect assumptions there, or I may have some. I think Bell's theorem should lead to FTL communication, and I'll try to lay out my assumptions as to how, and propose an experiment. So:
- A and B are entangled photons.
- With 100% probability, if I measure A at X°, and you measure B at X°, our measurements will be opposite (mine will go through iff yours is absorbed). 3.
So this is the experiment:
- Generate A and B, and send B lightyears away.
Whoever's manning the experiment at B does the following:
1. If they want to send binary 1, measure B at 20°.
2. If they want to send binary 0, don't do anything.
Now whoever is at A measures A first at 0°, then (if it goes through), at 40°.
The results should be (it seems to me):
If 1 above, then B was absorbed with 50% probability and was transmitted with 50% probability. In either case, the probability of seeing A get transmitted at 0° and get absorbed at 40° is less than or equal to 11.6% (because the probability of case 1 or 2 in the article is 50% for the measurement at 20° times either the probability of A transmitted at 0°, or B transmitted 40° (which under assumption 2, is the same as A not transmitted 40°) so the probability of both must be less than or equal to 11.6%).
If 2 above, then the probability of seeing A get transmitted at 0° and get absorbed at 40° is 20.7%.
So A can determine a binary message from B, violating the no-communication theorem. If done with enough photons, you can send much longer messages.
I know it is far likelier that I've made a mistake here than that I've disproved the no-communication theorem, so what's wrong? If anyone doesn't understand the experiment, ask and I'll try to clarify.