The most interesting question to me is - what happens when one of the entangled particles get annihilated. If the other one does too, instantly, then we can use that to communicate faster than light.
No. If you annihilate one of the particles, the other particle continues "unaffected". Whatever you do to one of the particles, the other particle continues "unaffected".
Quantum mechanic is a little more complex, so it is difficult to explain what "unaffected" really means.
It's clearer with an example. Let's suppose that you and I have each one a particle that is a half of an entanglement particle pair:
* If you don't do anything with your particle, for each measurement that I can do there are some possible results with some probabilities.
* If you do any measurement to your particle, for each measurement that I can do I have exactly the same possible results with the same probabilities.
* If you do annihilate your particle :( , for each measurement that I can do I have exactly the same possible results with the same probabilities.
* Whatever you do with your particle, for each measurement that I can do I have exactly the same possible results with the same probabilities.
In that sense my particle is "unaffected". I can't do any measurement to know what you have done with your particle. So you can't use your particle to transmit information to me.
The strange effect is that if we later meet and compare notes, we will see that the results you get with your particle and the results I get with my particle are related. Some measurements always are equal, some have the opposite value and some are related in more complex ways.
Each measurement (yours and mine) alone are perfectly normal. The strange effect appears only when the result are compared.
Hmm, this somehow defies common sense (but of course, its quantim mechanics, so thats a given!).
You are saying that, if theres an entangled pair, they cannot be used to transmit information that couldn't be otherwise transmitted via "conventional" means. However, if you performed the measurements, and then compared notes you will find that somehow, it looks like the measurements were "synced"?
How does it work this way? that is, how could it be the case that those measurements can be related, but you can't use that relation to transmit informatino?
> How does it work this way? That is, how could it be the case that those measurements can be related, but you can't use that relation to transmit information?
In a simple example, both people measure for example the spin in the x axis of the particles that travel in the z direction. Each has a 50% probability of obtaining "up" and a 50% probability of obtaining "down". But in every case the get the opposite result, so each one has a random number generator that is synchronized with the other. But each one alone has only a random number generator.
Lest suppose that someone try to use that to create an intergalactic first person shooter for two players :). Using the "synchronized random number generator" it is possible to make the bots move exactly in the same way in both players computers, but they are only "synchronized random number generator" so it's impossible for one player to know what the other player has done (unless they wait until the information arrive in a conventional way, with a speed <=c, but that would be a very big laaaag).
But this is only part of the story, because this process can be simulated with a central "random number generator" that sends the signals to both players.
The strange property is that if both players "magically" decide begin to measure the spin in the y direction, they will have the same 50% chances and always get the opposite result. Another possibility that avoids magic is that one of the players continues measure spin in the x direction and the other players begins to measure the spin y direction. Now each one has a "random number generator" that is independent of the other "random number generator", so each player has no clue about what the other player result. It's not useful for a IFPS, but it's useful as a physic experiment.
(And one of the problems with quantum mechanics is that you can't measure the spin in both directions, you must choose one. It's a little more complicate, but I don't' want to enter into the technical details.)
But this is only part of the story, because this process can be simulated with a central "random number generator" that generate two random numbers and then sends the signals to both players, one for the x direction and one for the y direction. This is a simplification of the "hidden variable theory", that says that the particles "know" in advance what to do if they are measured in for the x direction and in the y direction, in spite of that you can't measure both.
In the experiments the idea is that the measurements/player decide which direction to use while the particles are flying, so they don't have enough time to communicate (at <= light speed) and agree what the result would be. They have to be in accordance from the start (hidden variable theory) OR they have to communicate faster than light OR something even more strange.
Really, to do the measurements it's possible to choose not only the x or y axe, but any direction in that plane. So for every direction each player has a "random number generator", but they are not independent. If one measure in the x direction and the other at 45º the probability that the results agree in some number in between 50% and 100%. The 50% is for orthogonal directions that have independent results, the 100% is for the same direction that has ever the same/opposite result, and for the other angles there is a formula to calculate the value. To simulate this you need a lot of hidden variables, or at least a few an a formula to calculate the result for each direction, or any other variation of this idea. There are many possible proposal, some are more simple and some are more complicated, so the idea is to put all of them in the "hidden variable theory" bag and forget for a moment the details.
The problem is that Bell proved that for any "hidden (local) variable theory" some inequality holds. This inequality ignores the details of the specific theory, so it's not possible to invent a more complex "hidden (local) variable theory" that breaks the inequality. When the same calculations are evaluated using the quantum mechanics the result is a value that for some angles is allowed by the Bell inequality but for other angles the value is forbidden by the Bell inequality. So there is a different prediction of some measurement using the quantum mechanics and any "hidden (local) variable theory".
And it is possible to do this experiment and calculate a value for every angle. And the result is that for the problematic angles the result agrees with the quantum mechanics predictions and don't holds the inequality that is predicted from any "hidden (local) variable theory". So we must eliminate all the "hidden (local) variable theory". (For the non problematic angles the result agrees with the quantum mechanics predictions again, and holds the inequality as expected because they are not problematic).
Entanglement is a lot more superficial / complex than that.
QM is so differnet than how we are used to dealing with things the only really useful way to understand it is the Math it's based on. But, decoherence is the hart of a lot of the spooky voodo that really trips people up so it's a much better place to start than the 'cool' vs. trying to extrapilate based on the odd stuff that goes on.
http://en.wikipedia.org/wiki/Quantum_decoherence
PS: Also, avoid thinking at the large and small scales at the same time. Sensors really are just more fields and particles just like everything else. Also, decoherence is not an all or nothing event it's more a sliding scale between wave and particle.
