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Subject:A Great Quantum Mechanics Explanation
Time:06:17 pm
This was actually posted by someone in a discussion about Watchmen which was started by Roger Ebert. I'm trying to find a link. It's one of the best explanations I've seen of the various mind-bending concepts of Quantum Mechanics and also a bit about why it is often seen to disagree with Einstein's Relativity (which they never did adequately explain in my Modern Physics class which covered both of these theories).

Eric M. Van wrote:

"There really is spooky action at a distance, apparently instantaneous communication of information between widely separated particles."
I really hate to wade into the waters of attempted pithy lay explanations of QM concepts, but I really feel like I should put a stop to what is the all-too-common interpretation of the nonlocality of the EPR "paradox". That is to say:

Information cannot be transmitted faster than light because of quantum entanglement.

Einstein rightly worries about violating local causality because local causality is absolutely fundamental to Relativity Theory. Local causality cannot be violated and Relativity to still be true.

Yet QM implied quantum entanglement (which Van described earlier).

A little backstory on this... You've probably heard the famous Einstein quote "God does not play dice with the universe". This was his essential criticism of quantum mechanics. He was never comfortable with QM because it was most essentially says that the universe we experience is entirely probabilistic at the most fundamental level. Einstein still thought in terms of classical Newtonian "billiard ball" physics, which quantum mechanics denies. Thus, his "dice" comment.

His (with Podolosky and Rosen) thought experiment involving the apparent violation of local causality because of quantum entanglement was basically a reductio ad absurdum attempting to refute QM by way of showing it was incompatible with Relativity (and, whether or not contemporary physicists held Relativity to be irrefutable, they certainly felt local causality to be fundamental).

However, it took a few years, but eventually there was a definitive answer to the EPR paradox that showed that local causality isn't really violated.

In short, you can say that changing say, the spin of an entangled particle here will change, instantly, the spin of its entangled particle some distance away (any distance would violate causality, but for clarity, think a light year or something—many science fiction writers use quantum entanglement vis a vis the EPR Paradox as their rationale for faster-than-light communication across space), but there's a problem: because of other aspects of QM, particularly Heisenberg Uncertainty (which I'll deal with in a minute), when you're observing a particle, there's a built-in uncertainty about, say, the spin of that particle on a moment-to-moment basis. In short, if you were watching an entangled particle and observing its spin, you'd see it constantly changing, whether its entangled partner was being changed by experiments, or not. The changes would be random. The experimenters, a light year away, would be making changes in the spin of the entangled particle that will be masked by the random changes that will happen anyway.

The only way to extract information out of the paired particle will be to compare observations of both particles, at which point you could identify how the experimenters changed the spin and the other particle echoed that change. And there's the rub: to compare the observations, you'd need to transmit that information across that distance by some other method...that is equal to or less than the speed of light and obeys local causality.

At this point, whether local causality has been violated becomes a philosophical question. You can't ever claim that local causality has been "violated" except after-the-fact, by virtue of acting in the world in ways which don't violate local causality. Arguably, only when you compare the observations does the experienced reality come into being where local causality seems to have been violated.

Dangit, there's so much here to be explained...

Okay, look: the reason local causality was so important to Einstein and fundamental to Relativity is that violating it—in fact, actually postulating instantaneous "action at a distance"—is a violation the very basic premise of Relativity. Relativity in its most basic sense says that there's no such thing as absolute space or absolute time. That is to say, you can't say that a point in space is exactly somewhere and you can't say that a moment in time is the same for the entire universe. With regard to time, in other words, there is no such thing as a universal "now". You can't say that "two things happen at the same time" in an absolute sense. You can say that they happen at the same time, relative to each other. You can say that two points in space have some distance, relative to each other. And that's it. There is no absolute space or absolute time. This is what makes relativity so fundamentally counter-intuitive, contrary to our everyday experience of reality.

Einstein didn't just randomly make this up and then see what it might mean. He came up with this because there had been a number of disturbing experiments, one in particular, that seemed to call deeply into question our notion of absolute space. He came up with relativity as he tried to understand how to interpret these weird experimental results.

So, this is the problem: quantum entanglement, when it is said to violate local causality, implicitly violates the relativity of time. If you can "instantly" change one thing a distance away by changing something here, then you have a way of defining an absolute instant moment in time that's true for the entire universe. If EPR worked, then Special and General Relativity would be proven false.

And while it's true that quantum mechanics is the first most successful physical theory in history, Relativity is second. Toppling Relativity today would be the equivalent of Einstein toppling Newtonian physics in his time. It's a big deal. You can see why Einstein would personally have some trouble with the implications of his thought experiment. That's why he thought that it proved QM false. But my explanation of what would actually happen explains why both Relativity and QM survive the EPR Paradox.

And the way in which EPR doesn't violate local causality, not really, is extremely familiar to particle physicists: it's exactly the sort of thing they dealt with right at the very beginning of the development of QM and in the experiments they performed.

The foundational experiment in quantum physics is the famous "two slit experiment". It's pretty easy to explain, and if you really want to have a lay understanding of what the weirdness of QM is, then you need to understand the two slit experiment.

Imagine a very sophisticated emitter of light that can emit as little as one photon at a time. Photons are the particles of light. This emitter is a "gun", pointed at something like, say, photographic paper. A single photon isn't really enough to expose the paper, but bear with me.

Okay, so you have that gun pointed at the paper. Now, photons, like all these quantum elementary particles, don't move in exactly straight lines like billiard balls. If you point your photon gun, the photons that come out average in something close to a straight line, but because of Heisenberg Uncertainty (remember I mentioned it?), it's only an average. Individual particles vary probabilistically.

HU is simple, and fundamental. It says that we can't know both the position and momentum of a particle at the same time. In fact, it says that the more we know of one, the less of the other. (This wades into deeper waters, but the usual explanation of this is the commonsensical "you can't measure something without changing it" idea. However, this is a practical way to interpret HU, but it's not exactly true. HU is stronger than that. It's epistemological. It's saying exactly what it's saying: you can't know both at the same time. Or, it's saying that both don't exist at the same time in the sense that they both have definite values. It's a mistake to think that HU is a statement of a measurement problem. It's more than that.)

So, photon aimed with out gun "scatter" probabilistically. You fire the gun at the film a lot, you get a nice dark, exposed spot.

So, now we place a lead plate between the gun and the film. The plate has a small hole in it. We fire the gun for a while. What do we see? We see an exposed circle of film behind the hole in the plate. Now we put two holes in the plate, side by side, and fire the gun for a while. What happens?

Well, this is the rub. It took a very long time for anyone to think of light as being made up of particles (well, actually, if you go back to the Greeks, you find the Greek atomists did think of light as being made of particles, like everything else, but that's only a historical curiosity). Why? Because light actually seems to be made up of waves, like water waves. Light "flows" around corners. That's diffraction. Light does all sorts of things that waves do. It's why we have rainbows.

If you imagine our photon gun as a water gun pushing water waves in a tank, and you think of the steel plate; then you can imagine the little waves that will come through the single hole in the plate. It may be hard to visualize this, but if those waves "exposed" something like our film, they'd make a circle, just like the photon and the single hole did.

Now think about having two holes. With waves, the water wave will go through both holes at the same time, and the pattern they will make on the other side of the steel plate will be two waves, which will interfere with each other (where one has peaks and the others have troughs). Again, if you has something like film to record how those two waves impact it, you'd see a classic "interference pattern". Not two circles. That's the important thing, here.

And if you have your photon gun, two holes in the lead plate, and film behind the plate, you'll see that interference pattern after you fire your photon gun for a bit.

But remember that I said you could fire a single photon with the gun? That implies that this is a particle, the photon. Didn't we say that light acted like a wave? Yep. Which is weird.

Here's where it gets weirder.

Since we can fire only one photon at a time, then we can build a little device to attach to each of the two holes in the lead plate so that we can tell which hole each photon goes through when one goes through the lead plate. Now we fire lots of photons.

What shows up on our film? Not the interference pattern we had before when we didn't know which hole the photons each went through. Now, while we're checking to see which hole each photon goes through, the whole thing changes. We see two circles on the film, and not an interference pattern.

This is the essential weirdness of the two-slit experiment and the essential weirdness of quantum physics:

When we force light to act like it's made up of particles—by checking to see which hole each particle goes through—it acts like it's made up of particles. When we don't, it acts like a wave. In acting like a wave, a single particle emitted from the gun will go through both holes at the same time (because it's a wave).

When the gun emits a particle, that photon doesn't "know" whether we have a detector on the hole in the plate, or not. It leaves the gun, and...is it a wave or a particle?

You might say that when it gets to the plate, and there's a detector there, then it "decides" that it's a particle. That's one way of thinking about it. Except that what happens is that if you can tell that it's a particle, it will always have been a particle.

I've read about some interesting thought experiments that make this point much more viscerally. For example, you can imagine light leaving a very distant galaxy that is partly occluded from our view by, say, a black hole. Because of "gravitational lensing", the light will bend around the black hole the same way that light waves bend in a lens. And this is true for each individual photon. So, you say that a particular photon actually went around the black hole like a wave would...all around it. Now imagine a device that can detect a single photon here on Earth detecting on of those photons from that distant galaxy. Now, because we force it to be a particle, by looking for it in a way that presupposes particles, then we've forced it to have acted like a particle. In that case, it's always been a particle...meaning that it now went to the side of the black hole. If we don't look for a particle, it the light will act like a wave. Just like our photon gun...that distant galaxy is exactly the same thing, doing the same thing; and the black hole is acting sort of like that lead plate. 

And the point here is that the photon passed that black hole millions of years ago. Yet, we only just now check to see if it's a particle or a wave. What we do now, makes it true a million years ago.

Doesn't that violate local causality? Well, no, no more than EPR does. Because there's no way to check.

Now we have the famous Schroedinger's Cat. That was another attempt at a reductio. I won't explain it, it's just the same sort of thing except it takes this to a seemingly absurd degree—you have a cat that lives or dies on the basis of observing whether something acts like a particle. The thought experiment implies that you can't say that the cat lives or dies until someone opens the box and checks...until that point, the particle has acted like a wave, and so the cat exists in a wavelike both dead and alive until the box is opened. QM theorists said, before that thought experiment (and still do, mostly) that the probabilistic weirdness of QM only exists at the microcosmic level, that the probabilities of macrocosmic things, like cats and people, involve so many particles that the probabilities work out to be so close to certainty that everything is solid and things are exactly in one place (and not spread out in many places at once) and so forth. The Schroedinger's Cat thought experiment is an example showing that this sort of QM weirdness can "invade" the world we live in.

In a very contrived circumstance, of course.

So, anyway. Dealing with seemingly paradoxical things began at the very beginning of QM. QM always threatened things like local causality because of the kinds of weirdness I've described. However, and importantly, in all the history of modern physics, all of these weird things have been reconciled. And they usually come down to, well, observation. You can't observe things, or compare observations of things, in ways that violate local causality and the speed of light and whatnot. Since QM basically says that things exist in an indeterminate state until you observe them, it avoids trying to say what is happen "at the same time" of two entangled particles at a distance.

I don't think that M. Van understands that the EPR paradox doesn't actually violate local causality, because pretty much all lay people, notoriously including science-fiction writers, don't understand this.

I don't recall the name of the commenter who said this, but it is the best thing to keep in mind when trying to understand quantum physics: it's math. All narrative descriptions of QM are inadequate attempts to talk about something that only can be talked about with anything approaching real comprehension by using math. Words don't suffice, words are misleading. QM goes so far outside our intuitive experience of reality, that our words are not only insufficient, they are misleading.

Don't trust non-physicists' explanations of QM. Including mine. If you care to understand it at all, then read a source that has that primary, reliable, mathematical comprehension who will then, at least, mangle it minimally when he/she describes it to you. When you trust people like me, you're two degrees of separation from comprehension using a tool, language, that is inherently misleading on the topic.

That said, I believe that it's a pity that the philosophical implications of QM have languished for so many years, now. At it's birth, there was a huge burst of enthusiasm in grappling with what it means, by physicists and knowledgeable non-physicists, alike. That was the period of Schroedinger's Cat and other famous thought experiments. That period lapsed. The implications are too weird and it wasn't proving to be very fruitful to grapple with this with language and the usual tools of philosophers. It led to lots of badly-informed popular misunderstandings, too, which continue to litter bookstores everywhere. But there are a few physicists who still work on the philosophical questions inherent in QM. I asked one that I met what kind of response he gets from his fellow physicists for this work. He told me that it's slightly disreputable, but they tolerate it because he does other, more respectable, particle physics work.

As someone with an education in both the history and philosophy of science, I do think that some of the issues inherent in contemporary physics are worth thinking about by the non-physicist. Particularly, I believe that both Relativity and QM point right at epistemology. I don't think it's an accident that the two basic physical theories we have developed over the history of physics—both of which are fantastically successful at describing the universe we live—are built upon the foundation of marking out the essential limits of knowledge. Relativity demolishes the "God's Eye" view of the universe that we intuitively believe—that there is a "now" for the universe, that everything exists in exact relationships with everything else (in space), that theoretically we could know the exact state of the universe in a given moment. Relativity demolishes this for things like spaceships traveling very quickly, planets, and other macroscopic things. But QM takes this limiting of knowledge down into the fundamental particles; where, here too, we see that mostly we can't know much at all, and very little with certainty.

If you want something to spend late nights considering, in amateur philosophizing, then consider that the history of western science is that we started with some fundamental assumptions, built from those for thousands of years, and the elaborate structure we've built has turned on itself, ouroboros-like, and called into question (or radically redefined) those very basic assumptions upon which we founded this whole process. The most basic things we thought we knew, we learned, after assuming them, we either didn't know or radically misunderstood. What does that mean? What does that tell us about our comprehension and experience of the universe?

That's the question I'd like to ask Dr. Manhattan. If he existed.

Sorry for the length. I hope you read it. 

Ebert: I'm going to post it now and read it bright and early. I feel like I've returned to college. It's a good feeling.

And then SalmonOfDoubt posted this in the Penny Arcade forums, of which I am very fond.  Sometimes, you've just gotta put Quantum Mechanics in perspective.  And if you've seen Watchmen, you understand why there is so much discussion of glowing blue quantum dongs.

Imagine, if you will, a seven dimensional penis which can project beyond time, and even through solid matter. This metadong can be everywhere and nowhere at once, its exact physical state is constantly in flux. You might think of this scenario as somewhat emasculating, because if someone asks you (for example) if you have the balls to do something, you have to very earnestly reply that you might or you might not, it's kind of a quantum thing. On the other hand, ask that motherfucker if he can have sex with anyone who ever existed, ever, even if they were trapped inside a safe. See what I'm talking about? With an infinite wang, this and much more is possible. Well, I guess I should say probable. It's kind of a quantum thing.

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