BigFatBeardo

Edit: It turns out that I got a few things wrong in this post. See the response by /u/bobotheking for some corrections

I'm taking a course on quantum mechanics now, and although I could never explain it as well as Dr. Greene, I'll tell you what I know about this.

You've probably heard of the principle of superposition. It's the idea that a quantum particle can be in more than one state at once. Take, for instance, quantum spin. Electrons are spin-1/2 particles, which means that if you measure their spin along any axis, you'll get one of two answers: spin up or spin down.

So let's say you measure the spin of an electron, and you find that it is spin-up. According to the traditional ideas of measurement, the electron was already in spin-up before we measured it. The measurement didn't change anything; it merely revealed a property that the electron already had.

But this is not what quantum mechanics says. Quantum mechanics says that the electron was in both states at once, until you measured it. Then, it was forced to take on one or the other value.

Which is correct? The traditional view, or the quantum mechanical view? We never actually observe any electrons that are in both spin states at once. When measured, they are always found to be in either one state or the other. The question is, before the measurement took place, do we accept the quantum mechanical view that the electron was actually in both states at once? How could we possibly test such a thing.

Well, there was a physicist named John Bell who came up with a brilliant way to test it, and some experiments were conducted based on his ideas. I won't get into a lengthy explanation of them, but it suffices to say that the results of the experiments heavily supported the quantum mechanical view that the electron is in BOTH states at once, UNTIL measured, at which point it is (for some reason) coerced to choose one state or the other.

And it turns out that this idea of superposition doesn't just apply to spin -- it applies to everything. For instance, before you measure the location of an electron, it is everywhere at once. Only when you measure it, is it forced to take on a definite position.

The position that it ultimately decides to take on, when measured, is probabilistic, but it doesn't have the same probability everywhere. There is usually a very high probability that you'll find the electron within a certain very tiny volume of space, and the probability is near-zero everywhere else. So the fact that it is probabilistic should not be taken to mean that you will literally find the electron anywhere. In theory, if you're measuring the location of an electron emitted from an electron gun in your laboratory, it could be found on the other side of the moon, but in practice the probability of this is so small that it never really happens.

Ok. So let's extend this idea of superposition to not just spin and location but also paths of travel. By analogy, you could say that the traveling electron is in a superposition of paths. Some are direct (close to what is called the "classical path" -- the path that a particle would take according to classical mechanics). Some are indirect, going to the moon and back before arriving at its destination.

But, when you measure the electron, you cause the superposition to collapse, just as before, and the electron is forced to take on a single path.

Now, the crazy thing is, all of the paths have the same probability. The probability is a positive number between 0 and 1 that says how probable it is that a certain path will be chosen. A probability of 0.5 means that the path has a 50% chance of being chosen. The crazy thing I'm saying here, though, is that all of the paths have the same probability, which sounds crazy.

Quantum mechanics has a weird quantity, though, called the probability amplitude. The amplitude is like the square root of the probability. Since it's a square root, it need not be positive, and it doesn't even have to be real. A probability amplitude can be any complex number, as long as the square of its modulus is between 0 and 1.

And it turns out that, even though all of the paths have an equal probability, they do not all have the same probability amplitude. Specifically, they differ by a phase. When you add up the probability amplitudes for each path, you find two things:

a) The paths that are close to the "classical" path tend to re-enforce one another. b) The paths that stray far from the classical path tend to cancel each other out.

So in the end, the probability of finding the particle very far away from the classical path is very small. Small particles like electrons can stray a little bit, but it's not too far before the probability becomes too small. Heavier objects, like a grain of sand, can't stray by any measurable amount before the probability becomes near-zero, which is why those objects seem to behave in a classical way.

So I think the answer is that the electron doesn't travel to the moon and back faster than c. There are infinitely-many paths. There's a direct, classical path that perhaps takes nanoseconds. There is a path that takes the electron out to the moon, and perhaps that path takes days. There is a path that goes to the edge of the galaxy and back, and that takes trillions of years.

But when you actually go to measure the position of the electron, the various paths are going to interfere in such a way that you're hugely, hugely likely to find the electron somewhere near the classical path.

If you found it on another path, it wouldn't be so far away that it'd violate the speed of light or anything.

Jackie Treehorn wants to talk to the deadbeat Lebowski.

My daughter really, really wants to know, "Does watching that much TV really rot your brains?"

Bonobo is amazing. Animals is one of my favorite songs ever.

I currently work in simulation, making training simulators for heavy construction equipment. I'm also pursuing a degree in Physics. If I wanted to seek a career in space simulation, do you think that would be possible? Or do they usually want people who have experience in space (cosmonauts such as yourself)?