A Question on two-particle systems in Quamtum Mechanics

[firewolfsm]

So I was reading Quantum Mechanics and Experience and the author described a situation with two random, separated, electrons. If we take two incompatible properties, in his case, hardness and color (doesn't matter what they are) we measure color on one electron, if it is white, then the hardness of that electron is uncertain, while the color of the OTHER electron is known to have the opposite value, black, 100% of the time.

So if we measure the color of one electron, we also know the color of the other. This does not effect the other electron. My question is, if we measure the color of one, and the hardness of the other, wouldn't we know the specific values of both properties for both electrons? That's definitely not allowed so I'm curious to know what I'm missing.

 

[Biftheunderstudy]

This sounds a little bit like the Pauli Exclusion Principle, but I think more information is needed to clarify. Electrons are elementary particles and thus only have a few properties such as mass, charge and angular momentum. Is it a bound electron?

 

[f95toli]

First of all, if you have two "random" electrones nothing in particular happens, they just behave (more or less) like classical particles and their properties are NOT correlated in any way. Hence, there is no way to gain information about one by measuring the other.

However, if we have two entangled electrons (and I am pretty sure this is what you are refering to) things change. Due to the entanglement their properties are correlated meaning we can create situations whereby we can learn something about particle A by measuring B (this is usually done via some conservation law).

Now, about your question. If we take two properties (lets call them X and Y) that do not commute (which I guess is what you call "incompatible") something interesting happens.
Lets assume that we have two entangled particles A and B that have two non-commuting properties X and Y (such as position and momentum). Let us also assume that we want to come up with a way to measure BOTH X and Y. Since X and Y do not commute we can -by definition- not measure particle A and get the values for both of them at the same time.

But, since A and B are entangled (and therefore have values of both X and Y that are correlated) one could naively assume that it would be possible to e.g. measure X of particle A and then measure Y of particle B and then-since their properties are correlated- be able to deduce both X and Y for A and B.

This turns out to be wrong (which is what you were missing).

What happens is that if we measure X of particle A we ALSO affect the properties of particle B in such a way that it is impossible to precisely measure Y, i.e. the uncertainty principle holds EVEN if the particles are separated.
This is sometimes called "spooky action over a distance" since it sort of gives the impression that the two entangled particles are "talking" to each other. Moreover, this interaction is -as far as we know- "instantaneous" although it STILL turns out that no information is actually travelling faster than the speed of light; i.e. special relativity is still correct.

This is one of the big mysteries of quantum mechanics. It is one of those things that we can describe without any problems using math and it has been experimentally verified countless times. However, I don't think anyone truly understands it, it is simply too weird and too different from the kind of situations we are used to in our daily lives.

 

[firewolfsm]

Thanks f95toli, that helped.

One more clarification, this still stands if you make the measurements simultaneously right? Would it just be impossible to get a result from the measurement?

edit: wow, I really should have read more of this book before asking (although I still have the question above). Apparently the reason causality still stands is because a measurement on electron 1 does not change the probability of any measurement on electron 2.