Source Code (Page 2 of 2)

By the way, apparently my post the other day didn't go through, but this blew my mind.

He was Basquiat? Okay, he wins.

Everyone watch Basquiat.

I kind of hate myself for doing this. If I were sitting next to myself right now, I'd punch myself in the face.

During the commentary, you guys got on the topic of the so-called "many worlds interpretation" of quantum physics. Teague (I think it was) was like, "It's not about Spock with a goatee," and Mike was all, "Then what is it, bitch?" and there was a pregnant pause before Teague goes "I didn't build the fucking thing!"

Well … okay. So if you're interested, here's what y'all need to know about "many worlds." If I do this right, a few thousand words from now you'll have the gist of it, and you'll know why you should never, ever say the phrase "many worlds" ever again.

We're gonna start by talking about polarizers. You know what these are: they're like picket fences for light, a linear array of electrical conductors with teeny tiny gaps in between. When you put a polarizer in front of a lamp, the amount of light coming out of that lamp is cut by half, because the polarizer absorbs the other half.

What's happening way deep down at the smallest meaningful scale is this: Light comes in discrete quanta called photons. (You can also call photons "particles" and you won't be wrong, but they're fundamentally different from other kinds of particles we know about, so it's really better to call 'em "quanta" to keep those distinctions in mind.) A photon has, for reasons I'm glossing over here because they aren't important, a polarization vector that's perpendicular to its direction of propagation. Think about the mast on a ship. The ship goes forward, the mast points straight up, at a right angle to the ship's direction of motion. A photon's polarization vector is the same, only it can point in any direction in that perpendicular plane.

The reason why polarizers work is because photons — light quanta — that are polarized parallel to the gaps in the polarizer slide right through, and photons that are polarized perpendicular to the gaps get absorbed. Think about throwing a javelin through a picket fence; if you throw it straight, it goes right through the gap between the pickets, but if you throw it sideways, it bounces off.

So here's what we've got. We've got a lamp, which is spewing out javelins all over the damn place, all mixed up. Those javelins fly at a picket fence, and it turns out exactly half of them (for a sufficiently large number of javelins) are oriented such that they can slip through the gaps in the fence, and the other half bounce off of it. That's how a polarizer works.

But what happens when you throw just one javelin at the fence?

This is where things get a little strange. It turns out it is absolutely impossible to predict whether an individual photon will be absorbed by the polarizer or not. You can set up an experiment using a light source that emits only one photon at a time, and shoot those photons at a polarizer, and you find that it's a pure coin toss each time whether the photon will be absorbed. If you repeat that experiment a million times, you'll find that half a million photons were absorbed and half not, but that doesn't give you any information about what the million-and-first photon is gonna do.

If you like, you can imagine that every time a photon gets close to the polarizer, God flips a coin. Heads, the photon goes through. Tails, it gets absorbed. It's that arbitrary.

For this reason, quantum physics cannot deal with exact solutions. In classical physics, you model some system — a falling cannonball, say — and end up with a system of equations, and when you solve those equations you get numbers. Quantum physics doesn't use that method; instead, solving the equations that model a quantum system gives you probabilities. The equation that models a photon passing through a polarizer is real simple (well, relatively), and when solved it tells you that the probability amplitude of the photon being in the parallel state when it gets to the polarizer is one-over-the-square-root-of-two. You square the probability amplitude to get the probability; in this case, it's just one-half. So the equation tells you there's a 50/50 chance, which is what we knew empirically anyway.

Discovering that we could do equations this way was pretty revolutionary … but it was ultimately unsatisfying. Because the equations don't actually tell us what's going to happen. They tell us only what can happen, along with some numbers we can use to make aggregate predictions for sufficiently large cases. This equation in particular, for instance, tells us that half the time the photon will be absorbed and half the time it won't. That's well and good, but it doesn't tell us anything about any particular photon.

Or does it?

Teague mentioned Young's experiment on the podcast. Young's experiment is that thing where you put two holes in a card and shine a light through them. We know what happens if you shine a light through one hole; you see a spot on the wall, kinda fuzzy but well-defined. So if you shine a light through two holes, you'd expect to see two spots of light, right? Wrong, friendo. You see streaks of light (not five of them as Teague said, but actually an infinite number of them of exponentially decaying photon flux such that the ones on the edges end up having no photons in them at all so you can't see them). The light is acting like ripples on the surface of a pond; each photon is one ripple that hits both holes in the card simultaneously and makes ripples on the other side, and those new ripples pile up and cancel out so we see an interference pattern on the wall.

Back when Young originally did this experiment, he was all, "See? See? I told you light was a wave phenomenon! Suck it, Newton!" But that's obviously bullshit, thank you Einstein for figuring out the photoelectric effect that proved once and for all that light is a corpuscular phenomenon. So it was a big mystery: Light is definitely not a wave, but goddamn, it sure likes to pretend it is.

It took a hundred years (ish), and the invention of a whole new branch of physics, for anybody to solve this mystery. And truth be told, the "answer" we came up with is so fucked-up and incomprehensible that it caused more problems than it solved.

The answer's this: Every photon you fire through the apparatus passes through both slits in the card simultaneously. Where it actually ends up when it hits the wall is the result of the photon interfering with itself while its in transit. Through the lens of quantum mechanics, we can describe this in terms of probability: There are spots on the wall where the probability of the photon hitting are non-zero, and spots where the probability of the photon hitting are zero, and that's why we get streaks when we spray a bunch of photons through the apparatus. But we can only get that result by running the numbers such that each photon passes through both slits and then self-interacts on the other side.

So yeah. We just proved, with science, that shit can be in two places at once. That's messed up, right there.

But come on, this is light we're talking about. We already knew light was weird. Clearly this is not a universal thing, but rather just one aspect of how light is bizarre. Right? Guys? Right?

To prove that, we repeat the experiment, but instead of using photons we use electrons. Photons aren't matter; they aren't real in any meaningful sense. But electrons definitely are. So we repeat the experiment, expecting to see two spots on the wall instead of streaks, thus reinforcing our belief that the universe makes some kind of objective sense despite light being a little bitch.

Only no. We get a fucking interference pattern from the electrons too. Which means now we have actual particles of matter passing through two separate holes simultaneously. But okay, electrons are tiny, maybe that's what's weird. Repeat the experiment with helium atoms. Those fuckers do it too. Repeat the experiment with molecules of buckminsterfullere — a huge synthetic molecule, not occurring in nature, made up of 60 carbon atoms arranged in a geodesic sphere. Those fuckers do it too! On a subatomic scale, if an electron is the size of a baseball, a buckyball is the size of the solar system. Buckyballs are incomprehensibly vast at this scale, but dammit if they don't do weird two-places-at-once shit too.

None of this is remotely okay, and almost everybody in the field spent many years just ignoring it and hoping it would go away.

Almost everybody, I said. There was one guy in particular, a grad student at Princeton in the 50s named Hugh Everett, who woke up one morning and found himself with an opinion.

Everett started out by thinking about the polarizer, and about Young's experiment. He was bothered — like everybody else — by the inherent contradiction between them. In Young's experiment, the equations tell us that there's a 50/50 chance of the particle — photon, electron, buckyball, bowling ball, whatever — passing through each of the two slits, and in reality we find it actually does both. But with the polarizer, the equations tell us that there's a 50/50 chance of the photon being absorbed and a 50/50 chance of the photon passing through, and in reality we find it does either one or the other but never both.

Everett didn't like this, because it's a case where the exact same science gives us the exact same answer for two different experiments, but we get contradictory results. And he started thinking … what if the equations are right, and it's reality that's wrong?

Or rather I should say, what if it's "reality" that's wrong, because this is about to get into some very deep questions about what that word really means.

Everett's contention is this: When you shoot a photon at a polarizer, that photon both gets absorbed and passes through. When a polarizer absorbs a photon, a teeny-tiny electrical current flows through it; since the photon both does and does not get absorbed, this current both does and does not flow. If you hook up a very sensitive detector, you can detect that tiny electrical current, because the detector will go beep. Since the current both does and doesn't flow, the detector both does and doesn't go beep. And of course, if you're listening when the detector goes beep you'll hear it … and since the detector both does and doesn't go beep, you both do and don't hear it.

And you can model all that mathematically by including you in the equations that describe the experiment. (In approximation; it's not practical to model literally every subatomic particle and field that makes up your body, but we can rough it in just for fun.) When you do, you get precisely the answer you expect: There is a 50/50 chance that you'll hear a beep. Which is just what we observe when we do the experiment.

This all makes perfect sense, mathematically. It's the simplest thing in the world, really. The only problem with it is … if two people observe the same experiment, why do they always remember it playing out the same way? If there's a pure 50/50 chance that I'll hear a beep and a pure 50/50 chance that you'll hear a beep, then it's possible for me to hear it and you not (or vice versa), only that never happens. Either we both hear the beep or neither of us does, which is a big part of why we believe there's such a thing as objective, deterministic reality in the first place. So how does that jive with everything we said before?

Well, remember Young's experiment. We don't see two spots on the wall, nor do we see just one big blur; we see streaks on the wall, because the photon is interfering with itself, canceling out the chance that the photon will end up in some places. Let's extend our approximate model of the polarizer experiment a little further: I'm part of the system, and the equations tell me (rightly) that there's a 50/50 chance I'll hear a beep. If we add you to the system, there are now four possible outcomes: I hear the beep and you don't, you hear it and I don't, we both hear it, we both don't. But when you solve the equations, you find that the I-hear-it-and-you-don't and the you-hear-it-and-I-don't outcomes cancel out, just like those places on the wall where we see dark spots between streaks. In other words, when we're both part of the system, the probability that our experiences will differ is exactly zero. We can't predict whether we'll hear the beep or not, but we can say with certainty that we either both will, or we both won't.

And it's this insight that lay at the heart of Everett's doctoral thesis: the idea that the entire universe comprises a single quantum-mechanical system, and the way that probability distributions appear to collapse into definite outcomes is just a consequence of constructive and destructive interference between the parts of that system. There exists, in other words, a single mathematical equation which you could, in principle, write down and solve, that fully describes both the instantaneous state of and the future time evolution of the entire universe. That's why he titled his doctoral thesis "The Theory of the Universal Wavefunction."

So in summary, Everett's idea was this: It is a valid interpretation of the mathematics of quantum physics to say that everything which can happen does. Our subjective experience of the world contradicts this, telling us that things either happen or they don't, never both at the same time. But this subjective experience is just a consequence of constructive and destructive interference in the wavefunction that describes the entire universe, ruling out some possible outcomes (like two people disagreeing on whether a machine went beep) while permitting others. It's this self-interference — the universe interfering with itself — that creates what is essentially an illusion of classical, deterministic, objective reality.

Somefuckinghow, this idea got all bent and twisted into Spock-with-a-goatee. Oh, every time something can happen, a whole parallel universe is created where it did happen, so all possibilities are out there somewhere. There are, in other words, many worlds. Some have molested the idea even further: Somewhere out there, in one of the many worlds, there's a cubic light-year of pudding for some reason.

That is all pure, refined, weapons-grade bullshit. There is no validity to any of the previous paragraph. Nothing in Everett's work points in either of those directions, and there's nothing in quantum physics, or indeed in science period, to support those conclusions.

Instead, what has since come to be quite wrongly called the "many worlds interpretation" of quantum physics really just says that there's one big world — that is, the universe is a single system — and any experiment that attempts to isolate part of that world without taking the entire universe into account will inevitably result in an apparent boundary between the quantum-mechanical realm and the classical realm. If it were possible to solve the universal wavefunction — which it isn't — we would be able to see quite clearly that there is no such boundary, and everything we think of as classical mechanics is really just an uncountably vast number of degrees of freedom interfering with each other to create the illusion of determinism.

See? This is why I hate myself.

You're a good writer. I read that whole thing. And now I am smarter.

Also, now I am going to shoehorn that into my pilot for a time travel adventure TV show for JJ Abrams to produce. The working title is Sequence.

God does not flip coins.

To which Einstein replied, "FUCK YOU, NEILS! DON'T TELL ME WHAT TO DO! WHAT THE FUCK KIND OF NAME IS NEILS ANYWAY? MAYBE IF I COLLAPSE YOUR WAVE FUNCTION THERE WILL ONLY BE ONE OF YOU NAMED NEIL, LIKE A NORMAL PERSON!"

Einstein had little noted anger management issues.

Anyway, on a more legitimate note, a question: If the wave function of two people witnessing the double slit experiment is as you've laid out, how does the math work out if there are three people in the room? The possible scenarios are then:

1. All three hear the bell.
2. None of the three hear the bell.
3. Person A hears the bell, Persons B and C do not.
4. Person B hears the bell, Persons A and C do not.
5. Person C hears the bell, Persons A and B do not.
6. Persons A and B hear the bell, Person C does not.
7. Persons B and C hear the bell, Person A does not.
8. Persons A and C hear the bell, Person B does not.

That's still an even number of total possible outcomes; so long as the possible outcomes are an even number, does that mean the probabilities of different people experiencing different things always cancel themselves out? Somebody do math for me!

I'm now more curious than I was, but that's only half your fault.

Mostly, I just want you to write a textbook post haste. That was quite fun to read.

You can't really derive any of physics purely from first principles. You have to start with observations of the natural world — apples fall from trees — and then faff around with math for a few hundred years until you get the Einstein field equation.

This is one of those cases where we know something true and we want to build a mathematical model that tells us what we already know in the hopes that that model will also tell us other things, things we don't already know.

EDIT: Oh, also I just thought of something I neglected to include last night. Equations 4.1 and 4.2 should have a ± in them (because 1/√2 squared and –1/√2 squared both equal 1/2). That should ripple down through the rest of what I wrote, but it won't change anything because by that point in the evening I really just wanted to go to bed so I half-assed all the rest.

Point is, you have an answer you want that reflects reality, and you have a basic method that people smarter than you figured out (Heisenberg famously had the idea for the basics of this particular approach in a dream, and to the end of his life never could explain where it had come from any better than that), and the hard work is figuring out what goes in the middle, in between the pre-solved starting point and the ending you got by pointing your eyeballs at things.

Last edited by Jeffery Harrell (2012-03-02 14:02:39)

Skip that entirely. Binney's coursework is solid, but he's not a compelling teacher in that series. It's purely "Look at what I'm doing, then refer to the text to understand it."

If you want a better, qualitative introduction to quantum physics — or indeed, any branch of physics at all — look for Lenny Susskind's podcast series "The Modern Theoretical Minimum." It's on iTunes U. If you're a person of short attention span, you'll get frustrated, because he moves very methodically, but the upshot is that you almost have to try to get lost along the way.

Of course, the downside is that the whole series is something like 150 hours of video, so … yeah.

(Oh, another upside? Lenny happens to be the guy who finally figured out what black holes are, having to prove Stephen Hawking wrong in the process. The dude has street cred, and if he doesn't show up on the short list for a Nobel someday pretty soon, I'll be amazed.)

Last edited by Jeffery Harrell (2012-03-02 22:37:30)