The Predictable Universe
Even with Einsteinian modifications, Newtonian mechanics stipulates that no elementary particle can alter its own momentum or position, and that all changes are dictated by the interactions between multiple particles. (I.E. a particle stays in constant motion until affected by the force of another) Hence the position and momentum (linear and angular) of every elementary particle can only be altered by other particles, and nothing more. And since a multi-particle object (a macro-object) is just a collection of elementary particles, a macro-object is subjected to the same universal laws, and hence moves according to the interactions between multiple individual particles.
Let us consider a simple three-particle (A, B, and C) example in a vacuum in space free of external forces (such as gravity). Momentum is necessarily conserved because of Newton's laws, and kinetic energy is also necessarily conserved because elementary particles only interact elastically. There may be gravity (very small) and electrostatic attraction between the particles, but they are the only things that affect each other. Given the initial state (momentum, position, mass and electrostatic charge maybe) of each particle, by simple mechanics, a diligent worker can determine the complete state of each particle a time t later. It's as simple as solving a few three-row augmented matrices (after setting it up, of course). This can be said for a 4-particle system, a 5-particle system, and by extension, a n-particle system.
Hence, because this simple analysis involving three particles does not degrade as N increases, we can substitute the number of particles in the universe for N and provide the states of each, and in effect, we have the equation of the universe as a function of t. Unfortunately, it would take more than the number of particles in the universe to represent this system of equations, and unless we have an infinitely-fast (instant) calculator, by the time the matrices are computed, the states would have already changed. Hence, although predicting the future is practically impossible by all means, it is theoretically possible given the initial states of each particle in the universe. It's not a matter of whether anyone can predict the future (they can't); it's a matter of whether the future is defined.
The state and future of the universe is completely determined by the state of the universe now. The states of all the particles in the universe conspired together to make me compose this.
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This sort of reminds me of
This sort of reminds me of that Heisenberg Uncertainty Principle argument we had a few months ago. This is the same thing I was talking about, how it is theoretically possible to predict the future of the universe, or extrapolate the past, but can't realistically be done (due to not only Heisenberg, but the limits of computer technology).
Since this is theoretical, and every one of the 10^80+ particles in the universe is calculated (position and momentum), with almost instantaneous speed, what would happen if you could look up the future? What if you looked up your future 5 minutes from now, and did something different from what was predicted?
I don't think it's wise to
I don't think it's wise to think about practically impossible things. It'll just be pure speculation because we wouldn't know anything about what's beyond the unsolvable equation :P
It's like... what happens when you go faster than the speed of light? Albert Einstein's modifications would give you negative discriminants (under the square root) so you'll end up being imaginary?
Well, a lot of what we
Well, a lot of what we speculate now can become reality in the future, or not. There might be ways around Heisenberg's principle that we have no grasp on currently, or a great discovery could change things to make this a reality. If not, I think it's a good scenario for a sci-fi movie.
There's no way around the
There's no way around the uncertainty principle in practice. Theoretically, someone outside of our three (or four) dimensions could determine both at the same time, but that's not possible for us to do.
Maybe I'm overlooking
Maybe I'm overlooking something, I might have to do more research. Basically what I picture is something analogous to predicting a planet based on movements of a star, how you can't really observe the planet with light, or whatever, but you can make inferences that if developed, could have a reasonable degree of accuracy. If the particles of that size truly affect nothing to some analogous degree like that, then they could probably be overlooked when making the calculation without causing significant error. Or maybe by using what we can fully observe, we can make conclusions about what we can't.
I don't have as strong a knowledge base in quantum physics as I do in a lot of other areas, so if there's something blatantly wrong with that, let me know. I might have to consult....Wikipedia.
Somehow, exactly 1 year (to
Somehow, exactly 1 year (to the day) later, this was brought up again, so again, if something above is wrong, tell me. But another scenario, let's say that the computer guessed everything it couldn't find out, and happened to get it all right. Or by whatever means, it did obtain all the information it needed (because what I was trying to get at back then was that the means of obtaining the information is completely irrelevant to what I was saying, practicality has nothing to do with it).
So what does this say about free will? If an omniscient computer tells you what you're going to do, and you do something different, doesn't this make determining the future impossible, since this obviously couldn't be calculated, even if the calculations happened infinitely fast?
Well, obviously the thing
Well, obviously the thing compiling information into a model of the future can't interact with the things that the "compiler" (if you will) is examining. Why? Because there's no way to use N particles to cover the whole future--position and momentum at the very least--of N/2 or more particles. So, to have a computer that can model the entire universe of N particles, the computer itself must have AT LEAST 2N particles--just for basic memory--assuming each particle stores one "package" of information.
What I'm saying is, what you describe (someone doing contrary to what the prediction machine says he'll do) is not possible because the prediction machine can't possibly model a future that includes itself.
That was confusing, I admit, but the bottom line is, since the prediction machine can't interact with the thing it's predicting, there's no way the machine itself can alter the future of which it's predicting.
I think you're arguing more
I think you're arguing more along the lines of how the machine works, instead of assuming it works, which is crucial to the thought experiment. While what you mentioned still results in the same conclusions, I'm saying it doesn't matter, even if each particle could somehow hold billions of pieces of information, where it would have enough information to predict itself, it still can't predict its own interaction with the universe. So even without the bounds of needing more particles for information that the computer contains, it isn't possible to predict the future if it interacts with the universe.
So, we agree that an observer cannot predict its own future.
Since the universe entails everything that exists, including any omniscient observer, even if physically detached from everything else, while still knowing the information needed to predict everything else, since the observer cannot predict the observer, it cannot predict everything in the universe. Any extension of another observer observing both the universe and the original observer runs into this same conflict, so there no way to really objectify knowing everything about the universe. The other possibility is that one omniscient observer knows everything about the universe and the other observer, and the other observer knows everything about the universe and the original observer. Obviously, this cannot happen, because if you have one observer knowing everything about another observer who knows everything about the first, then the first observer knows everything about itself, which for the reasons above is impossible, you end up in an infinite regression. I think I brought up the two omniscient chess players in the Origin thread, same idea.
Hopefully that wasn't too confusing, but the ultimate conclusion is that not even an omniscient observer can predict the entire universe, so the universe is not entirely predictable or deterministic.
So I disagree with the ultimate premise of this blog. There always has to be some sort of exception to predicting the universe.
On the other hand, if we declare that the omniscient observer does not count as part of the universe, then we assume by the cause and effect philosophies that we've known our whole lives, that it can be predicted. I tend to disagree that we can really know that. Physics is based on this assumption, not the other way around, so it is really only based on the hope that our observations are consistent in that way, which really isn't basing it on anything sound at all. I generally assume that that's true, however, as do most people, I'd imagine.
So if the question comes down to whether an observer, who knows everything about a certain closed system can predict what happens, the answer is probably yes. If the question is whether the entire universe is predicable, the answer is no.
What makes the universe
What makes the universe different from a closed system?