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Copenhagen cracked? [Apr. 18th, 2003|01:30 pm]
John
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.
linkReply

Comments:
[User Picture]From: wcg
2003-04-18 02:34 pm (UTC)
This page lists the three major quantum interpretations and some of their ramifications.

The Copenhagen Interpretation is, as you note, a statistical interpretation. The thrust of Bohr's argument in formulating it was that physics is a science of measurement, and that talking about where something might be without measuring it is meaningless within the parameters of physics.
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[User Picture]From: johnpalmer
2003-04-18 03:02 pm (UTC)
Thanks for the link; I'll be spending some time there someday soon.

It does confirm what I'd puzzled out today: that "many worlds" requires actual, honest-to-goodness worlds, and not my thought-up 'theoretical other worlds'.

It was weird, because I'd long been annoyed at the Copenhagen interpretation, but, right now, it seems that it's a better model for my world view, even though I had been sure it wasn't. I feel almost like I should be apologizing to someone....
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[User Picture]From: jodawi
2003-04-18 07:50 pm (UTC)
my great idea of a year or two ago that is now living at the bottom of some pile was something along the lines of explaining nonlocality as a many universes thingy where the universe splits off at each decision point into two universes, and that decision propagates at the speed of light - when the decision wave washes over the observer, the universe that is consistent with the observer's universe is the one that is 'selected' for that observer. to make this something other than babble, i went to the local university bookstore and looked at cohen and tanouudji however that's spelled and got very very sleepy, and realized i wasn't interested in spending the years needed to determine if it was viable or random nonsense. my current theory is that an old black woman somewhere (hm, part native american, part chinese too) will work this all out and get a nobel prize in 23 years. the end. tune in next week when grammar and capitalization.

but, right now, it seems that it's a better model for my world view, even though I had been sure it wasn't. I feel almost like I should be apologizing to someone....

in 1992ish, i got depressed because einstein had been proven wrong more or less. later i decided i liked that better. currently i decide that it's possible to influence the quantom randomness, making it not random but just potential, but i have zilch to back that up.
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[User Picture]From: 98
2003-04-18 02:56 pm (UTC)
It has been a long time since I worried about stuff like this but I recall vaguely that Bell's Theorem indicates that a hidden variable theory can not predict observed quantum mechanical behavior unless some other reluctant assumptions like nonlocality are made.

The Copenhagen interpretation, which I grew up on, is admittedly somehow unsatisfying but easy to apply and successful in practice.

The many-worlds interpretation makes its devotees feel more comfortable but IMO is just a sugar coating around the exact same calculations and the fact that we do not fundamentally know how that quantum weirdness works.
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[User Picture]From: pernishus
2003-04-18 03:38 pm (UTC)
John, is there a difference between a "many-worlds" interpretation and a "some-worlds" one? I remember Fred Hoyle's "October the First Is Too Late", which seemed to me to be a many-worlds viewpoint, but with consciousness determined by an extra-universal 'spotlight' illuminating individual world states: even in random order of illumination, each pigeonhole would have the 'past' and 'future' implicit in that pigeonhole, so that we, as prisoners within the pigeonholes, would have the impression of an ordered set of transitions from pigeonhole to pigeonhole whatever the order of illumination. Can there be 'semi-determinate' states? I'm not exactly sure what I mean, yet -- but I'll hope to make a more coherent comment presently.

John Barnstead
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[User Picture]From: greyman
2003-04-18 04:32 pm (UTC)
I don't have a problem with "many worlds" except that it is philosophically unsatisfying. Sure, I can supposed the existence of a universe for each possible outcome of an event, and some entertaining science fiction stories have been based on the idea. It seems to be a neat if self-deluding way of resolving paradox.

As I was researching for this: click on Supermodeling for Skeptics I ran across the idea that the "many worlds" model also includes the idea that the multiple possible universes can interfere with each other.

Now, c'mon. If it's a universe, how can it interfere with another completely different universe? This seems like a huge violation of the idea of "Least Hypothesis."

I do subscribe to the Copenhagen interpretation, but I don't put a lot of stock in it. It's just an explanation of reality, not reality.
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[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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[User Picture]From: kightp
2003-04-18 07:59 pm (UTC)
So this is what you get up to in my kitchen while I'm at work.

Heavens.

I don't want to think about what you might be up to in the bedroom, love.
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