How is quantum entanglement understood?

Question

I need enlightening on quantum entanglement. If the entangled pair of particles are, for simplicity's sake, a red and blue ball and I look at one ball and find it to be red then obviously the other one will be blue. Why is this mysterious? Can someone explain? Thanks, Kev.

Answer 1

Imagine a box with a red and blue ball. You are aware that there is a red and blue ball in the box, but you have your eyes closed when you pick and have them separated some distance away. Now, you don't know what those colors actually were on your left or right hand. It can be red or blue. If you open your eyes to look at your left hand, say you see a red ball. Then without looking at the right hand, you already know it must be a blue ball.

That's classical physics.

Let's take slightly more complicated example involving a quantum system with net zero spin, that consists of two electrons. From inference, the two electrons' spins add up to zero. Which means either electron has opposite spins to add up to zero, right? In quantum physics, as bizarre as it may sound, is probabilistic completely, and the two electrons in the box can each be both spin up and down at the same time.

You heard that right. And it has to do with the wavefunction. Because quantum physics is probabilistic, the two ball in the box system has a wavefunction that's the exact same for each of the two balls. To reiterate, each electron is in a mixed spin up and down state.

If you have your eyes closed, and have the two electrons separated, some distance apart, and then make a measurement on one of them, you can see that electron either spin up or down. It's no more in a mixed state. Now here's the important point. If the wavefunction is probabilistic, then after making a measurement, the wavefunction will modify to show a 100% probability for that electron to be in a spin up state.

Since the net spin of that quantum system initially known to be zero, then the other electron we didn't measure yet has to be spin down. But then, if the wavefunction for that electron was a similar probability distribution, then it should have collapsed as well to show 100% probability for a spin down state? In that case, how did this unmeasured electron know it has to collapse at this point? Did the spin up electron communicate information with this other electron? That's the spooky part of quantum entanglement. This wavefunction update.

I hope I didn't overload you with so much information.

Answer 2

There's actually nothing mysterious about the quantum entanglement. The only difference with the classical correlation is that when you get result tha one ball is red, what you know about the other ball is its quantum state $|blue\rangle$.

The difference is that this knowledge gives you not result for the measurement of the other ball but the probability distributions for these measurement results. In case of the color it's simple - you know that the other ball the result will be "blue". However, you may measure the incompatible observable (like coordinate with respect to momentum, or spin component $s_x$ wit respect to $s_z$). In that case you know probabilities but can't predict the result itself.

In the quantum theory all this is described in a very simple way. The "mystery" is when you try to imagine some fundamental classical physics from which the quantum mechanics must emerge (hidden variables). Then you can't explain the measurements for the incompatible observables unless those hidden variables behave in a strange way (admit superluminal signals and signals to the past from the future) All such strange behavior is not needed in the actual quantum theory, only when you try to push the hidden variable idea, but for some strange reason is always associated with the quantum theory in the popular science.