Entangled particles

So we have two particles (A and B) that are entangled.

From what I understand, entanglement isn't destroyed, it is only obscured by subsequent interactions with the environment.

Particle A goes zooming off into outer space.

10 years later, Particle B becomes incorporated into my brain.

The day after that, an alien scientist measures the entangled property on Particle A.

This will have some immediate non-local effect on Particle B won't it?

And since B's state has been altered (in some sense), and it is part of my brain, then my brain state has been altered as well, hasn't it?

Maybe only a tiny amount, obscured by the many environmental interactions that the two particles have been subjected to since the initial entanglement, but in a way that is real and at least conceivably significant.

And if that is true, then to the extent that mental states supervene on brain states, my mental state would also have been altered by non-local effects.

Or is that wrong?

Thanks!

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– HDE Apr 23 '11 at 19:43

From what I understand, entanglement isn't destroyed, it is only obscured by subsequent interactions with the environment.

Depends on how you view it. There is an explanation of quantum measurement (called decoherence) in which this is true. I will not be using that explanation in this post because it's unnecessarily complicated.

This will have some immediate non-local effect on Particle B won't it?

Nope. When an alien scientist measures particle A, it does not have an effect on particle B. Specifically, it does not induce any sort of change in particle B that can be detected.

Of course, we would say that the quantum state of particle B (technically: the combined quantum state of the pair AB) has changed, but changes of this nature in the quantum state can't be detected. For example, suppose the entangled state, written in a basis of energy levels, is

$$|\psi_1\rangle = \frac{1}{\sqrt{2}}\left(|1\rangle|2\rangle + |2\rangle|1\rangle\right)$$

so that if particle A has an energy of 1 (in unspecified units), particle B will have an energy of 2, and vice versa. Suppose the alien scientist measures the energy of particle A to be 1. The state of the pair AB becomes

$$|\psi_2\rangle = |1\rangle|2\rangle$$

Then, the next day, when your brain measures the energy of particle B, it will get 2 as the result. But as far as your brain is concerned, the energy of particle B could have just been 2 all along. Or it could have had some arbitrary probability distribution with 2 as one of the possible results. The fact that the state changed from $|\psi_1\rangle$ to $|\psi_2\rangle$ has no effect, and could not have been detected by your brain.

And if that is true, then to the extent that mental states supervene on brain states,

If by that you mean that your thoughts are determined by quantum states, that's definitely false.

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So there are non-local effects on the brain - but these effects are random and not distinguishable from local quantum randomness. When the alien makes a measurement on Particle A, he is changing the state of the entangled A-B pair. But since the outcome of his measurement is random, it's effect on Particle B is random - and afterwards Particle B's behavior is entirely consistent with what it could have been even without the measurement. Though Particle B's behavior after the measurement is possibly not what it would have been if the alien scientist had not made his measurement? – David Feb 1 '11 at 16:51
@David: that's not a bad way to put it, mostly. But it would be better not to think of the measurement on A as having an effect on B. When you use the word "effect" it implies some sort of causal connection, but you can't really link a cause to an effect where entanglement collapse is concerned. Also, the question of what particle B's behavior would have been if the alien scientist had not made his measurement is not really a meaningful question to ask. – David Z Feb 1 '11 at 17:55