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Author Topic:   What is "the fabric" of space-time?
Chiroptera
Inactive Member


Message 25 of 327 (457855)
02-25-2008 9:09 PM
Reply to: Message 24 by fallacycop
02-25-2008 8:49 PM


To be more precise, space-time is a manifold - that is, it is a four dimensional object that has a certain shape. The fact that the shape isn't completely flat is what we call "warped". This "warping" of space-time -- the fact that in places it is very much not flat -- is what we experience as "mass".

Mass doesn't warp space-time. Rather, mass is the warps in space-time.


If I had a million dollars, I'd buy you a monkey.
Haven't you always wanted a monkey?
-- The Barenaked Ladies

This message is a reply to:
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Replies to this message:
 Message 27 by Calypso, posted 02-26-2008 1:41 AM Chiroptera has replied

  
Chiroptera
Inactive Member


Message 30 of 327 (457920)
02-26-2008 10:46 AM
Reply to: Message 27 by Calypso
02-26-2008 1:41 AM


This is an interesting question.

Disclaimer: I do not have any real experience with GR. From the physics side of my education, GR requires a knowledge of differential geometry, which is not part of the standard curriculum for physics students even at the graduate level. It is mostly those students who are specializing in GR who end up studying it.

On the math side, I did take a course in differential geometry. But I never really got an intuitive feel for what a non-positive definite metric "looks like" (I can "visualize" an n-manifold with a positive definite metric), nor did I ever see physics applications. So, my "explanation" is going to consist of what I understand from the math side.

Manifolds automatically come already curved. In fact, it is how the manifolds are curved that distinguishes them. The curvature is basically the shape. The only significant difference between a sphere and an oblate ellipsoid is that the curvatures are different. If I hand you a sphere, it is already curved -- that is what makes it a sphere.

So, when our universe is modelled by a Lorentzian 4-manifold, it has to come with some shape. In the physical GR model, mass density is a parameter (or one of several parameters) that is part of the mathematical equations that describe the curvature.

Now the interesting question is: is there some physical quality called mass that forces the otherwise flat manifold to curve? Or is does the manifold already come curved, and our experience of mass simply how we percieve this curvature? This becomes a metaphysical question, about how exactly we are going to interpret the mathematical equations to make sense of what we actually observe.

But in the end that's all we have: the mathematical models, a way of interpreting the results of calculations in terms of potential observations, and some measure of how close the potential observations match up with our actual observations. The actual ontological nature of the universe is, I suspect, beyond what science can really answer.


If I had a million dollars, I'd buy you a monkey.
Haven't you always wanted a monkey?
-- The Barenaked Ladies

This message is a reply to:
 Message 27 by Calypso, posted 02-26-2008 1:41 AM Calypso has taken no action

  
Chiroptera
Inactive Member


Message 176 of 327 (459752)
03-09-2008 6:16 PM
Reply to: Message 175 by Silent H
03-09-2008 6:07 PM


Re: A bit of history.
Hi, H.

I've been asking about whether our current math is a model of the underlying reality, or just a useful tool.

I'm not sure what you mean here. I think of a model as a tool, so I'm not sure what you mean here.


...Onward to Victory is the last great illusion the Republican Party has left to sell in this country, even to its own followers. They can't sell fiscal responsibility, they can't sell "values," they can't sell competence, they can't sell small government, they can't even sell the economy. -- Matt Taibbi

This message is a reply to:
 Message 175 by Silent H, posted 03-09-2008 6:07 PM Silent H has replied

Replies to this message:
 Message 177 by Silent H, posted 03-09-2008 6:59 PM Chiroptera has replied

  
Chiroptera
Inactive Member


Message 178 of 327 (459768)
03-09-2008 7:08 PM
Reply to: Message 177 by Silent H
03-09-2008 6:59 PM


Re: A bit of history.
Heh. cavediver* and I disagree about how real the mathematics really is. I tend to be pretty anti-Platonic.

One theoretical question I keep trying to get at (though hopefully not ad nauseum) is whether it might be possible for a different mathematical approach to be found based on totally different conceptions for how the phenomena function, or even different concepts using relatively the same math?

And I've had similar questions in regards to determining how real the mathematics is. Suppose that we come across an intelligent alien species which clearly has an advanced technology. Suppose that this species has developed its science and technology through a historical development of theories that in every stage were utterly incommensurate with our mathematical theories. Would that imply that mathematics really isn't real, but simply a useful tool that one simply uses as a tool to concisely denote complicated abstract concepts?

Conversely, suppose that we meet a lot of advanced alien races, and everyone of them has developed their science and technology through concepts and mathematics that, once deciphered, are clearly analogous to ours. Would this imply that there is something real about mathematics after all?

Or is this not what you are asking?

*Speaking of good grammar -- if someone's handle isn't capitalized, is it nonetheless proper to capitalize it at the beginning of a sentence?


...Onward to Victory is the last great illusion the Republican Party has left to sell in this country, even to its own followers. They can't sell fiscal responsibility, they can't sell "values," they can't sell competence, they can't sell small government, they can't even sell the economy. -- Matt Taibbi

This message is a reply to:
 Message 177 by Silent H, posted 03-09-2008 6:59 PM Silent H has replied

Replies to this message:
 Message 179 by Silent H, posted 03-09-2008 9:18 PM Chiroptera has taken no action

  
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