Saturday, August 28, 2021

Why is quantum mechanics weird? The bomb experiment.

[This is a transcript of the video embedded below. Some of the explanations may not make sense without the animations in the video.]

I have done quite a few videos in which I have tried to demystify quantum mechanics. Because many things people say are weird about quantum mechanics aren’t weird. Like superpositions or entanglement. Not weird. No, really, they’re not weird, just a little unintuitive. But now I feel like I may accidentally have left you with the impression that quantum mechanics is not weird at all. But of course it is. And that’s what we’ll talk about today.

Before we talk about quantum mechanics, big thanks to our tier four supporters on patreon. Your help is greatly appreciated. And you too can help us, go check out our page on Patreon or click on the join button, right below this video. Now let’s talk about quantum weirdness.

First I’ll remind you what’s not weird about quantum mechanics, though you may have been told it is. In quantum mechanics we describe everything by a wave-function, usually denoted with the Greek letter Psi. The wave-function itself cannot be observed. We just use it to calculate the probabilities of measurement outcomes, for example the probability that the particle hits a screen at a particular place. Some people say it’s weird that you can’t observe the wave-function. But I don’t see anything weird with that. You see, the wave-function describes probabilities. It’s like the average person. You never see The Average Person. It’s a math thing that we use to describe probabilities. The wave-function is like that.

Another thing that people seem to think is weird is that in quantum mechanics, the outcome of a measurement is not determined. Calculating the probability for the outcome is the best you can do. That is maybe somewhat disappointing, but there is nothing intrinsically weird about it. People just think it’s weird because they have beliefs about how nature should be.

Then there are the dead-and-alive cats. A lot of people seem to think those are weird. I would agree. But of course we don’t see dead and alive cats.

But then what’s with particles that are in two places at the same time, or two different spins. We do see those, right? Well, no. We actually don’t see them. When we “see” a particle, when we measure it, it does have definite properties, not two “at the same time”.

So what do physicists mean when they say that particles “can be at two places at the same time”? It means they have a certain mathematical expression, called a superposition, from which they calculate the probability of what they observe. A superposition is just a sum of wavefunctions for particles that are in two definite states. Yes, it’s just a sum. The math is easy, it’s just hard to interpret. What does it mean that you have a sum of a particle that’s here and a particle that’s there? Well, I don’t know. I don’t even know what could possibly answer this question. But I don’t need to know what it means to do a calculation with it. And I don’t think there’s anything weird with superpositions. They’re just sums. You add things. Like, you know, two plus two.

Okay, so superpositions, or particles which “are in two places” are just a flowery way to talk about sums. But what’s with entanglement? That’s nonlocal, right? And isn’t that weird?

Well, no. Entanglement is a type of correlation. Nonlocal correlations are all over the place and everywhere, they’re not specific to quantum mechanics, and there is nothing weird about nonlocal correlations because they are locally created. See, if I rip a photo into two and ship one half to New York, then the two parts of the photo are now non-locally correlated. They share information. But that correlation was created locally, so nothing weird about that.

Entanglement is also locally created. Suppose I have a particle with a conserved quantity that has value zero. It decays into two particles. Now all I know is that the shares of the conserved quantity for both particles have to add to zero. So if I call the one share x, then the other share is minus x, but I don’t know what x is. This means these particles are now entangled. They are non-locally correlated, but the correlation was locally created.

Now, entanglement is in a quantifiable sense a stronger correlation than what you can do with non-quantum particles, and that’s cool and is what makes quantum computers run, but it’s just a property of how quantum states combine. Entanglement is useful, but not weird. And it’s also not what Einstein meant by “spooky action at a distance”, check out my earlier video for more about that.

So then what is weird about quantum mechanics? What’s weird about quantum mechanics is best illustrated by the bomb experiment.

The bomb experiment was first proposed by Elitzur and Vaidman in 1993, and goes as follows.

Suppose you have a bomb that can be triggered by a single quantum of light. The bomb could either be live or a dud, you don’t know. If it’s a dud, then the photon doesn’t do anything to it, if it’s live, boom. Can you find out whether the bomb is live without blowing it up? Seems impossible. But quantum mechanics makes it possible. That’s where things get really weird.

Here’s what you do. You take a source that can produce single photons. Then you send those photons through a beam splitter. The beam splitter creates a superposition, so, a sum of the two possible paths that the photon could go. To make things simpler, I’ll assume that the weights of the two paths are the same, so it’s 50/50.

Along each possible path there’s a mirror, so that the paths meet again. And where they meet there’s another beam splitter. If nothing else happens, that second beam splitter will just reverse the effect of the first, so the photon continues in the same direction as before. The reason is that the two paths of the photon interfere like sound waves interfere. In the one direction they interfere destructively, so they cancel out each other. In the other direction they add together to 100 percent. We place a detector where we expect the photon to go, and call that detector A. And because we’ll need it later, we put another detector up here, where the destructive interference is, and call that detector B. In this setup, no photon ever goes into detector B.

But now, now we place the bomb into one of those paths. What happens?

If the bomb’s a dud, that’s easy. In this case nothing happens. The photon splits, takes both paths, recombines, and goes into detector A, as previously.

What happens if the bomb’s live? If the bomb’s live, it acts like a detector. So there’s a 50 percent chance that it goes boom because you detected the photon in the lower path. So far, so clear. But here’s the interesting thing.

If the bomb is live but doesn’t go boom, you know the photon’s in the upper path. And now there’s nothing coming from the lower path to interfere with.

So then the second beam splitter has nothing to recombine and the same thing happens there as at the first beam splitter, the photon goes both paths with equal probability. It is then detected either at A or B.

The probability for this is 25% each because it’s half of the half of cases when the photon took the upper path.

In summary, if the bomb’s live, it blows up 50% of the time, 25% of the time the photon goes into detector A, 25% of the time it goes into detector B. If the photon is detected at A, you don’t know if the bomb’s live or a dud because that’s the same result. But, here’s the thing, if the photon goes to detector B, that can only happen if the bomb is live AND it didn’t explode.

That means, quantum mechanics tells you something about the path that the photon didn’t take. That’s the sense in which quantum mechanics is truly non-local and weird. Not because you can’t observe the wave-function. And not because of entanglement. But because it can tell you something about events that didn’t happen.

You may think that this can’t possibly be right, but it is. This experiment has actually been done, not with bombs, but with detectors, and the result is exactly as quantum mechanics predicts.

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