Quantum Entanglement

[LucasGB]

I know this is probably an extremely simple question, but anyway...

I shoot two particles towards each other. They collide, and then go their separate ways. Then I measure the position of particle A with full precision. This will allow me to determine with full certainty the position of particle B. A friend of mine is sitting somewhere else, sees particle B flying by and thinks to himself "I'm kinda bored, I'm gonna measure this particle's momentum". He does so, with full precision, and is thus able to determine the momentum of particle A, with certainty. We meet up later for drinks and discover that adding together what we discovered we have determined with full certainty the position and the momentum of both particles.

So what's wrong?

[ueit]

I know this is probably an extremely simple question, but anyway...

I shoot two particles towards each other. They collide, and then go their separate ways. Then I measure the position of particle A with full precision. This will allow me to determine with full certainty the position of particle B. A friend of mine is sitting somewhere else, sees particle B flying by and thinks to himself "I'm kinda bored, I'm gonna measure this particle's momentum". He does so, with full precision, and is thus able to determine the momentum of particle A, with certainty. We meet up later for drinks and discover that adding together what we discovered we have determined with full certainty the position and the momentum of both particles.

So what's wrong?

1. You cannot infer the momentum of A and the position of B unless the momenta of the colliding particles are exactly opposite in your (and yours friend) reference frame.

2. Assuming that the above is true, entanglement disappears after the first momentum measurement so your friend's result does not apply to your particle anymore.

3. It might be the case that the position/momentum of the particles, is not the same for both but the actual values depend also on the type of measurement performed on them.

4. There is nothing wrong with the determination with full certainty of the position and the momentum of both particles. You may think that uncertainty principle denies this possibility but in fact it does not.

[comote]

What you have described is called the EPR paradox. The answer, however strange it might seem, is that by measuring the state of the first particle you have in fact affected the state of the other particle. For more reading look up Bell's inequality.

[LucasGB]

2. Assuming that the above is true, entanglement disappears after the first momentum measurement so your friend's result does not apply to your particle anymore.

4. There is nothing wrong with the determination with full certainty of the position and the momentum of both particles. You may think that uncertainty principle denies this possibility but in fact it does not.

Thank you for both your replies.

2. Why would the entanglement disappear?

4. Isn't this exactly what the uncertainty principle is about?

[Pio2001]

the actual values depend also on the type of measurement performed on them.

Exactly the point.

LucasGB, you say "Then I measure the position of particle A with full precision. This will allow me to determine with full certainty the position of particle B."

Wrong ! What it allows you is to determine, not the position, but the result that would be found if, and only if the position of the other particle was immediately measured (QM postulate).

But if, in the meantime, the momentum of that particle is measured instead of the position, then the wave function is modified by the measurement, and you can no longer tell that if you measured the position of that particle, you would get the same result.

[LucasGB]

Wow, Quantum Mechanics is subtle. Thank you all for your help.

A little bit off-topic: what would you recommend as the best introduction to Quantum Mechanics? Is Griffith's book good?