gogo_t said:
So the entanglement is quite unstable [or should I say not verry stable]? If this is so, then does it mean that in the sub-atomic levels entanglements appearing [being build] and disapperaing [being destroyed] all the time?
In a way, yes.
Kaldanis said:
Hi Aidyan, I posted in another thread about this but you've kinda cleared somethings up for me with your post.
So keeping with the sock analogy, you're saying that together they could produce green and it will remain green no matter the distance, until a measurement is made. My next question is how do you determine they are both green? I thought measuring it would instantly determine if it is red or blue, so how can you measure to tell it's green?
I appologise if this is hard to explain with such a stuipd analogy, my understanding of these things at this point is pretty basic.
This thing of "measuring will instantly determine" is a little bit too mystical.
What happens is not that the socks are 'green'. Neither of them is 'green'. They're just in a joint state of red+blue, what we should call a superposition, and we conveniently named this superposition 'green'. That basically means that each sock is red and blue at the same time (more or less what happens with Schrödinger's Cat), and furthermore, what's really impressive about this is that while the 'green system' doesn't interact with anything else (i.e. no outside particles happen to meet the system),
the socks can interact with themselves (that's what happens with the electrons in a double-slit experiment), because they are in what's called a 'coherent' system.
Now let's be clearer here. Measuring does
not alter the system itself in any way. If we define measuring in this particular case as a person opening the box and seeing the one sock, this is what happens. What happens is that what once was a coherent superposition of red+blue socks is now another superposition of 'red sock and human who saw red sock+blue sock and human who saw blue sock'. That is, you are superposed with yourself.
But of course, you yourself don't realize that. There is one 'you' who will only see a red sock, and there is another 'you' who will only see a blue sock. And because of that measurement, each of the 'you's will know what colour the other sock is.
And the analogy breaks down here, because in the sock case, if one sock is red, the other is definitely blue, and vice-versa. That is not so with entangled systems. It also depends on the "way" they are measured. I will take the example given earlier at the explanation of Bell's theorem.
In the example, they have a source that sends pairs of entangled photons (let's call them socks) to Alice and Bob, in different places. Alice and Bob each have a copy of a certain measuring apparatus, the SPOT, and depending on how the spot is positioned they can or cannot see each photon. Let's call 'blue' the state where one of them can see the photon, and 'red' the state where they cannot.
In this experiment, there is a multitude of entangled socks, one after the other. What is observed is that if Alice and Bob have the SPOT positioned in the same way, their results will seem completely random (half the times they will see red, half the times they will see blue, with no apparent order), but once they meet, they will see that the exact order of their results will match to a T.
Now, suppose Bob rotates his spot 90º. From that moment on, while the results will still appear random, once Bob and Alice compare their results, they will see that they are
all inverted, that is, whenever Bob saw Red, Alice saw Blue, and vice-versa.
Next step, suppose Bob and Alice's SPOTs are aligned again, but Bob rotates his 30º clockwise. From then on, they will see that 25% of their results disagree. That is, one out of four times Bob saw red, Alice saw Blue, but the other three times they both saw the same thing.
Suppose now Alice rotates her SPOT another 30º, except counterclockwise, so that there is an angle difference between both SPOTs of 60º. One should expect that then half their measurements would differ, right? Except this doesn't happen, and 75% of the time there is a difference in measurement.
This happens because the probability of a match is given by the cosine squared of the angle difference between both SPOTs, and that has to do with the Born Probabilities.
Let's explain what really happens. At first, before any measurement is made, we have an entangled, superposed state of two photons, each going in a different direction. Once they are detected, however, the superposition of states gets a little bit more complicated.
We have 'Alice sees red and Bob sees blue + Alice sees red and Bob sees red + Alice sees blue and Bob sees blue + Alice sees blue and Bob sees red'. These are the four possible different systems that happen. Once measurement was made, Alice and Bob became part of the superposed system. But that's not all. Because of the Born probabilities, not all four states are equally likely (although since all of them physically happen, likely isn't a good word here; let's just say that there's not an equal number of Alices and Bobs that fit in each state).
Actually, if we define chance as the
probability that Alice and Bob will find themselves in a given state, then there is a 3/8 chance of 'Alice red, Bob blue', a 3/8 chance of 'Alice blue, Bob red', a 1/8 chance of 'Alice red, Bob red' and a 1/8 chance of 'Alice blue, Bob blue'.
And if you then ignore Bob's result (i.e. if you don't ask Bob about his detection), then you have exactly 1/2 chance of 'Alice red' and 1/2 chance of 'Alice blue'. Once you know Alice's result, if you ask Bob, you know that there is a 3/4 chance of 'Bob disagrees with Alice' and a 1/4 chance of 'Bob agrees with Alice'.
That's... about it, I guess. I'm not sure I made myself perfectly clear, Quantum Entanglement isn't exactly easy to explain or understand :P
