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Copenhagen cracked? [Apr. 18th, 2003|01:30 pm]
So... today, I was in the kitchen, envisioning two dimensional shapes travelling through a third dimension of time as an analog to three dimensional objects travelling through a fourth dimension of time....

What, doesn't everyone do this from time to time?

Anyway, I was contemplating eternity, and thinking about looking into a universe from the outside. You see, if you're not *in* a universe, you're not constrained by its time or its space. To some degree this annoys me... it smacks of the ability to see the future in a deterministic way, and determinism violates free will.

So, I was trying to imagine a circle with a third dimension of time. If the circle just sat still, then it looks like an ordinary cylinder, straight up and down. If it moves, well, the cylinder bends, tracking the motion of the circle. If it moved three feet to the right in three seconds, you'd have a cylinder that's bent at a 45 degree angle, in a foot/second scale.

This isn't the annoying part. The annoying part is when you 'look up'. In theory, you can see the cylinder and it's bends and curves from 0, to its current time, to future times. The circle, to my mind, can't have free will. You can see where it's going to go; where it's going to go is no different, from your perspective, from where it's *been*. The circle can no more avoid its future than it can change its past.

Now, in quantum mechanics, questions about random events (like when a single atom of a radioactive substance decays) have at least two interpretations that I know of.

One is the "many universes theory". The idea is that universes split at each random event, into however many outcomes were possible.

I've heard that there's a 'hidden variables' theory, where we could know the outcome of random events, *if* we knew everything, but we don't... there are hidden facts that we can't grab a hold of. I think I've also heard that this theory is equivalent to another in some way... this is why I mention that I only know there are two for sure.

The final one I know is the Copenhagen interpretation (named after a place - don't make the mistake I made of assuming that there was this guy, Copenhagen, who won lots of support for his theory.) (For some reason, I also think that there's a "Copenhagen" brand of tobacco products, and it seems like there should be an awfully funny joke one can make about that.).

Anyway: The Copenhagen interpretation is the one that's famous in the Schrodinger's cat experiment. A cat is in a 'black box', so you can't see it. There is either a poison gas, or, for the soft-hearted-even-in-thought-experiments, some cat food, that will be released with probability .5 in an hour.

The Copenhagen interpretation is "the cat is both alive, and dead" (or "hungry and fed"); it's in a standing probability wave until you open the box and take a look."

(This isn't strictly speaking true. The cat has certainly observed what has happened, so the cat has collapsed its own probability wave. Still, it shows how strange the interpretation can seem.)

My interpretation is that the many worlds interpretation was right... the cat was alive in one hypothetical universe, and dead in another... and we just didn't know which universe we were in.

People like to mock the "Many worlds" theory, pointing out that suicide would be impossible. Point a gun to your head, pull the trigger... at least one version of you will exist where the gun misfired, or whatever.

This annoyed me because I didn't see any reason why these other universes had to be anything other than hypothetical. I didn't like the Copenhagen interpretation because I feel that whatever happened *had* happened... it wasn't still in flux just because no one looked at it.

And then, today, I was picturing my little circle. I pretended it had free will. At time t = 3 seconds, it was going to move, either to the right or to the left.

What would it mean that I couldn't look forward three seconds and *know* which way it was going to go? What would it require to allow free will for the circle?

Really, the "many worlds" with actual, multiple universes removes free will just like determinism does; in essence, it says both choices will be made. In this case, the circle will move left *and* it will move right, just not in the same universe.

So I imagined a hypothetical multiple universe... unmade choices don't really exist. What happens then, at time t=3 seconds?

We would look forward, and see the same universe, branching off in two directions... one where the circle went left, and one where it went right... we wouldn't know which one it was until we reached that time.

In short, we'd probably see a blurred 'future circle' moving in two different directions at once... until we arrived at that point and the circle decided.

The Copenhagen interpretation - that both are happening, in a probability wave - was a better model for "but we just don't *know*" than the many worlds one. It would include the "many hypothetical worlds", more or less. Without actual multiple universes, Copenhagen and many worlds would probably have the exact same properties, and it preserved free will in a manner that couldn't be questioned. There was only one universe, being shaped by our decisions. What those decisions *are*, we won't know until we make them.

Now, maybe I'll find out that this is absolutely not what the Copenhagen interpretation is and I'll be even more confused, but *damn* it felt good to puzzle this out.

[User Picture]From: claire
2003-04-18 06:03 pm (UTC)
I think you broke my brain. Which is OK since I'm not really using it for anything. I might have to read this again later when I'm caffeinated.
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