Sunday, January 29, 2006

Particle/Wave II: Probabilistic Boogaloo

Moderator: Hello, and welcome back. Before you go any farther, you should probably read part one. No, really, do it. Also, everything you ever wanted to know about Quantum Physics can be found here. Okay, all good? Let's get back to the dialog.

Calvino: There's a moderator?

The Stoat: Apparently there was. Is. I feel strangely as if some chunk of my life has been removed, and yet here I am, arguing the same points as before, as if nothing had happened.

Calvino: Well, that could be because it's been a week since the end of the previous discussion, and you're not in fact real but a figment of the author's imagination, and therefore completely bound to the whim of an unseeable (unless he chooses to let you see him) and undefiable creator.

The Stoat: No, no, that's not it. It's some sort of metaphysical new state of being. A line has been crossed. We have been preternaturally altered, never to be the same again. I have flipped a coin and it has come up heads 100 times in a row, and it's entirely due to narrative.

Calvino: Ooookay. Whatever. We were talking about coin flips and quantum physics?

The Stoat: Well, right, I was saying that I'm skeptical of the idea of many universes being an explanation for a coin that is going to come up heads 50% of the time and tails 50% of the time.

Calvino: Can you, just for the sake of posterity, go over how you connect phenomenon of quantum physics to a coin flip, which is definitively a macro-level event?

The Stoat: Sure. Actually, you did it yourself when last we spoke, when you pointed out that the results of a regular coin flip were subject to the whims of tiny changes in atmospheric pressure. I'm actually going to argue, in fact, that any macro outcome that you would model as probabilistic is made up of (many) such quantum events.

Calvino: I'll save you the trouble. I'm perfectly prepared to accept this proposition. Clearly the coin flip is this way, not only in that it's subject to the environment, but the conditions that exist in your body--the muscles, the cells, the chemical signals between your brain and your extremities--at the moment you strike your thumb against the side of the coin in order to send it flipping end over end into the air. I might even be willing to make a case for the contrapositive being true--that is, things that seem to us absolute, like tides or seasons or the orbits of the planets, are non-probabilistic precisely because they aren't as affected by such things as the decay of carbon atoms or the existence of an electron in one place or another.

The Stoat: Good then. Someday we'll talk about chaos, and the fact that a quantum event could theoretically affect which side of the sun the earth will be on several million years from now. But for now, the model you describe is perfect.

Calvino: Last time you argued against the idea of multiple universes being an explanation for quantum events, or events in general that have multiple outcomes. That is, in the case of the coin flip that we interrupted so that we could talk about it, you tried to refute the idea that there's a universe in which it lands tails and a universe in which it lands heads.

The Stoat: That's right.

Calvino: It's not clear to me that you made this argument convincingly. I admit, on the surface the idea of many universes--and I acknoweldge that here "many" means "an ungodly large and incomprehensible number"--seems hopelessly complex, but that doesn't seem like enough to conclude that it's not a valid model of reality, or at the very least a useful one.

The Stoat: I grant that. Frankly, by the time I'm done this will be the least of your objections. My larger point is that I'm not to the point of making a rigorous argument yet. I'm not going to try and symbolically prove anything or write any equations. I'm only at the stage of making a proposition, or set of propositions.

Calvino: Okay. Then propose away.

The Stoat: All right. We were in the middle of that coin flip. Right now you would say that 50% of the time it's going to land heads and 50% of the time it's going to land tails. But if I won't let you have at least two universes, one in which the coin lands heads and one it which lands tails, what does that mean?

Calvino: I suppose it means that of the next ten flips, odds are that it'll come up heads about five times and tails five times.

The Stoat: No, no, we're not talking about multiple coin flips. We're talking about just this one, discrete flip. What does it mean to say that the result will be heads half the time and tails half the time?

Calvino: I don't understand what you're asking. This seems to be a pretty straightforward statement.

The Stoat: And I'm arguing that it's not. We've established and agreed that pre-flip, mid-flip, late-flip, and pretty much until it lands and we observe the results (when it does get kind of gray and have to do with things regarding cats and boxes) that the outcome of the flip isn't determined. But if you reject the idea that the universe somehow "splits" and there are multiple outcomes, there is no such thing as the coin coming out 50% heads and 50% tails.

Calvino: Look, this is stupid, and the only reason it seems like there's anything worth debating here is because this is a 50-50 proposition. If, for instance...well, okay, I'm thinking of a number between 1 and 100. If I ask you to guess what it is, I can say with as close as anything can be to actual, true, knowledge that you'll never....

The Stoat: It's 47.

Calvino: ...

The Stoat: ...

Moderator: Several moments of increasingly hilarious silence now ensue, followed at last by...

Calvino: Crap.

The Stoat: ...

Calvino: Okay, that was a bad example. I've got a hundred-sided die, and I'm going to roll it. I can say something about it: I can say that there's almost no way that it's going to come up 47.

The Stoat: Yeah, but you could say that about any number, including the number that's actually going to come up when you do roll it. I understand your frustration, but you're moving in a somewhat oblique direction to my argument. Here is what I am saying: when you say that the coin is going to come up heads half the time and tails half the time (or any way you want to phrase a statement on the probabilistic outcome of a discrete event), you are making a statement not about the event you're about to record, but about the nature of the results of an infinite number of those events--something I am, in fact, going to call the 'wave' of the flipped coin.

Calvino: Sure. I see that. But I'm still making an inference, based on that 'wave.' It sounds an awful lot like you're just saying I can't make a meaningful inference. This just doesn't sound right to me.

The Stoat: You aren't making an inference. You're making a statement about a wave. It's a wave, in fact, that is extremely well defined. The flip, on the other hand, is not defined at all.

Calvino: I just don't accept that. When the coin's in mid-air, isn't it 50% heads and 50% tails? That seems also extremely well defined.

The Stoat: Sure, sure. As long as it's a coin that's in mid-flip, or going to be flipped, or whatever (and you may make all manner of arguments about when that happens) it's in a superposition of states--50% heads and 50% tails if you like. But that's not information about what the outcome will be, that's a list of possible outcomes.

Calvino: Possible outcomes and their likelihood to occur!

The Stoat: It seems like that's true, but if there's no determinism--it wasn't predestined at any point to have a particular outcome, and there are no multiple outcomes--the universe doesn't split in two separate but equal universes in which each outcome occurs, what does that mean?

Calvino: It means that if I flip 100 coins...wait...crap....

The Stoat: Crap, exactly.

Calvino: I'm still hung up on the case of the hundred-sided die. I'd be stupid to bet on the next roll coming up 47. But that's a discrete event just like the coin flip. And there doesn't seem to be any getting around the simple fact that "not 47" is more likely than "47."

The Stoat: Well, for one, you've just lumped 99 outcomes together and are comparing them with one outcome. So 99 is indeed greater than 1, and I'm fine with that definition of "more likely." If, however, you want to say, "not 47 happens more of the time than 47," that's true, but again it's not a statement about one die-roll, it's a statement about many die-rolls--about the probability wave of a rolled 100-sided die.

Calvino: Hmm. Whether or not you've convinced me of anything at all here, I can't help but feel as if I've been robbed. I used to be perfectly happy having knowledge about individual outcomes, and whether or not you've proven that this was false belief on my part, you haven't given me anything new. It seems like the onus is on you to offer a better model. You've sort of hinted at some sort of particle/wave thing, but I haven't seen it yet.

The Stoat: I realize that. And I haven't even broached the subject of the coin flip having no outcome until somebody observes it. Frankly, I'm in a little bit of a quandary as to how to accomplish this and These dialogs are just too long. I should be writing a paragraph a day, rather than a treatise a week.

Calvino: So this dialog is just going to end, right here, with so much unresolved?

The Stoat: Yes. For today.

Next: More stuff! More things!
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Sam said...

For my feeble brain, this was the important bit:
You aren't making an inference. You're making a statement about a wave. It's a wave, in fact, that is extremely well defined. The flip, on the other hand, is not defined at all.
It seems to me you are rejecting a gigantic swath of the field of statistics, arguing in some ontological sense that inference is invalid - not that a particular inference fails, but that the entire project of inference fails.
I'm not sure what to make of that. Part of me thinnks it's far too broad, and casual a sweep, and that statistics does say some productive things. Part of me thinks it's spot-on.

Transient Gadfly said...

I think my failure here is what I state at the end, that I don't provide a replacement model. I think the problems with the current model (provided you indeed believe in non-determinism and that reality is fuzziness that only coalesces when an observation is made) are valid. But the whole thing is too opaque and takes to long, and I've taken on the task of trying to write journal articles in a blog. I'm having a small identity crisis at the moment. Surely soon I will blog about it.

Rebecca said...

I have just spent the last hour catching up on all of this. I must admit that I did not go to the wikipedia entries, but I did have fun with the light laser and slider thingy. ooo! pretty!

my comment is this, and I fully admit that what interests me may not have anything to do with what interests you or anyone else reading these posts and comments.

I've always been a bit intimidated by coin tosses, to be frank. how do you put it on your finger? what are the mechanics of getting it to flip perfectly? what's with the catching it, hiding it, and turning it over on the back of your hand? these things cause a certain amount of low-level worry in me, as if someone (the person doing the tossing?) might be able to determine what it is by performing all of these elaborate hand motions. a sort of agency in the coin tosser that is utterly absent from the discussion here.

but that's not actually what I want to say, as I don't believe the coin tosser has agency in determining the outcome of the toss. what I want to contribute is this: it's the moment after the coin is finished its toss and before you identify it as heads or tails--that's the moment of tension for me. it's about reading the iconography of the coin, right? isn't that about some sort of production of knowledge--something that your physics stoners might say "whoa" to in perfect Keanu Reeves fashion? if in the end, what determines the outcome of the toss is our reading of what is heads and what is tails (to the point that at the superbowl they actually have to identify for the captains of the teams which side of the oh-so-complex and ceremonial coin is heads and which is tails), then aren't we once again talking about an epistemology dependent on observation (freezing the particle and thus producing it), wherein that observation itself is not exactly a 100% clear, obvious thing with any objective reality? call me anti-empiricist if you will, but this strikes me as the root of the issue. what is observation anyway, if not reading?