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Physics: What is space?

MattusMaximus said:
Touche. But it also speaks to the inferiority of our mathematics to describe reality, at least it does in the context of certain kinds of math.
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In my opinion, the only possible explanation for the effectiveness of mathematics in describing physical reality is that mathematics is not invented, but discovered. So I agree that at any time, we might not have discovered enough mathematics to be able to describe everything. But I see no reason to believe that we can't some day.
 
Badly Shaved Monkey said:
paximperium said:
Good point. I was just wondering if there was anything more...should I ask "What is time" now?
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I know! I know!!.
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I was hoping that this would be a link to a Dilbert strip that I tried to find myself. Dogbert explains what time is, and it went something like this (while showing slides with images of what he was talking about):

"Imagine a donut being shot out of a cannon, rotating, and close to the speed of light. Time is like that, except for the cannon and the donut".

This explanation is another classic:



sol invictus said:
The history of physics - and certain theoretical considerations now - make it clear that our current models cannot be reality (because they're not self-consistent). They're either an imperfect model for some non-mathematical reality, or an imperfect model for the true mathematical "reality".
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The current theories may be even less than that. We're so used to thinking about theories as approximate descriptions of some aspect of reality that it's sometimes hard to imagine that they could be anything else, but the defining property of a theory isn't that it describes something. It's that it makes predictions about results of experiments. (At least according to my definition :)). So a theory could just be an algorithm that tells us how to compute probabilities of possible results of experiments without using concepts that represent things that "exist in the real world".

The Hilbert space of QM may be an accurate representation of the universe (which would then consist of many worlds, corresponding to different subspaces), but it also may not be.

Virtual particles is probably a good example of a concept that's very useful in the algorithm, but may not correspond to anything in the real world.

Because of these things, I no longer consider the words "model" and "theory" to be more or less synonymous. Most theories consist of axioms that tell us how to interpret the mathematics of a mathematical structure ("the model") as predictions about the results of experiments. (Example: SR. The model is Minkowski space, and the theory of physics is defined by a bunch of axioms like "What a clock measures is the proper time of the curve in Minkowski space that represents its motion"). There may also be theories that don't even include a model. They would be pure algorithms. QED is like that right now. (As I understand it, making sense of products of operator-valued distributions (the interaction terms) is a major difficulty in 3+1 spacetime dimensions). But that may be temporary. We might still find a model that's appropriate for a nicer formulation of that theory.

sol invictus said:
In my view, math is just a symbolic representation of the rules by which the world runs itself. If we could figure out all the rules and write them down, it would be pretty reasonable to call that theory (or its solutions) "reality". But whether that's possible is anyone's guess.
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This is my view too. I would just like to add that even if we do find those rules, there wouldn't be any way to prove that we have found them. All we could do is to keep improving our attempts to falsify the theory and fail consistently.

MattusMaximus said:
The problem with people insisting that their "mathematics is reality" is that reality doesn't necessarily correspond to that math. ...
So much for the "true reality" represented by Euclid's geometry.
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There's also the possibility that the "true reality" is all of mathematics, which would imply among other things that there are lots of universes with different properties, some of which can sustain intelligent life, while others can't. That would of course be even harder to support experimentally than the claim that one particular mathematical model is an exact representation of our universe.
 
sol invictus said:
In my opinion, the only possible explanation for the effectiveness of mathematics in describing physical reality is that mathematics is not invented, but discovered. So I agree that at any time, we might not have discovered enough mathematics to be able to describe everything. But I see no reason to believe that we can't some day.
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Perhaps. I suppose this is, at some level, what the search for GUTs is all about.
 
paximperium said:
There are mathematical concepts to describe space and time and its characteristic...but what it is?
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Did you not believe what I said in #6, since you're asking again? :) Science can't answer that question, and therefore nothing can. Mathematical concepts that can be used to predict the results of experiments is the best kind of answer we can ever hope to find.
 
Fredrik said:
This is my view too. I would just like to add that even if we do find those rules, there wouldn't be any way to prove that we have found them. All we could do is to keep improving our attempts to falsify the theory and fail consistently.
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That's not necessarily the case. People have managed to prove some extremely surprising and non-intuitive things... Godel's incompleteness theorems come to mind. So I think it's perfectly conceivable that one could prove that some theory is complete or unique, say in the sense that's it's either exactly correct or totally wrong.

There's also the possibility that the "true reality" is all of mathematics, which would imply among other things that there are lots of universes with different properties, some of which can sustain intelligent life, while others can't. That would of course be even harder to support experimentally than the claim that one particular mathematical model is an exact representation of our universe.
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Math is a set of rules for how to manipulate or relate things. It doesn't really tell you which things to consider. So perhaps there is something extra - the initial conditions, as it were - necessary to complete the picture, even if you knew what the exact theory was.
 
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