View Full Version : Spacetime curvature

Staticman

2011-Jan-16, 05:06 PM

Since Einstein's Generla relativity we have come to understand the force of gravity in geometrical terms as spacetime's curvature, my own way to understand this is to consider that what we feel as the force of gravity, is the tendency of the universe to maintain the curvature of spacetime locally (by extension if this local tendency is fulfilled in every local point of the universe I guess we could say it is fulfilled globally), and gravitational energy would be the energy spent by the universe to keep this equiibrium. And from Wheeler's "spacetime tells matter how to move and mattter tells spacetime how to curve", I understand that this spacetime curvature varies locally according to the specific local matter arrangement.

My question is, is it not possible then to define a global spacetime curvature (since according to relativity there is not an absolute time or space) in the same way that we are capable of defining a spatial curvature of the universe (that is thought to be flat or almost flat)?

Thanks

antoniseb

2011-Jan-16, 05:19 PM

I'm not sure I followed your description. Does this "tendency", expressed mathematically, reduce to Newtonian gravity in weak fields?

Ken G

2011-Jan-16, 08:29 PM

My question is, is it not possible then to define a global spacetime curvature (since according to relativity there is not an absolute time or space) in the same way that we are capable of defining a spatial curvature of the universe (that is thought to be flat or almost flat)?

Yes, that is possible, indeed that is really just what we do. The claim that "space is globally flat" is actually derived from the larger issue of the global spacetime curvature that you seek. The global spacetime curvature can be consistent with all kinds of spatial curvatures, it depends on what basis you are using to separate time and space (i.e., what coordinates or local reference frames you are using to cobble together your global description). When one is guided by the cosmological principle, one sees "comoving-frame coordinates" as especially simple, and when the global spacetime curvature is considered in those simple coordinates, that's where space comes out flat, while the time domain houses the cosmological redshifts.

Staticman

2011-Jan-16, 08:37 PM

I'm not sure I followed your description. Does this "tendency", expressed mathematically, reduce to Newtonian gravity in weak fields? Sure.

Yes, that is possible, indeed that is really just what we do. The claim that "space is globally flat" is actually derived from the larger issue of the global spacetime curvature that you seek. The global spacetime curvature can be consistent with all kinds of spatial curvatures, it depends on what basis you are using to separate time and space (i.e., what coordinates or local reference frames you are using to cobble together your global description). When one is guided by the cosmological principle, one sees "comoving-frame coordinates" as especially simple, and when the global spacetime curvature is considered in those simple coordinates, that's where space comes out flat, while the time domain houses the cosmological redshifts.

Ok, and this global spacetime curvature is constant or varies in time?

caveman1917

2011-Jan-16, 09:12 PM

Ok, and this global spacetime curvature is constant or varies in time?

It is prior to any choice of time coordinate, thus it cannot vary in time.

Ken G

2011-Jan-16, 10:50 PM

Sure.

Ok, and this global spacetime curvature is constant or varies in time?Like caveman1917 said, it varies over the spacetime manifold in a way that is very suggestive we might want to attribute the changes to the time coordinate.

undidly

2011-Jan-17, 01:52 AM

What are the units used to describe the curvature of spacetime?

Could it be degrees per kilometre?

Andrew D

2011-Jan-17, 07:00 AM

What are the units used to describe the curvature of spacetime?

Could it be degrees per kilometre?

No, it's not curvature in Euclidian space:

wiki link: intrinsic curvature (http://en.wikipedia.org/wiki/Curvature_of_Riemannian_manifolds)

wiki link: Einstein Tensor (http://en.wikipedia.org/wiki/Einstein_curvature_tensor)

Staticman

2011-Jan-17, 06:55 PM

It is prior to any choice of time coordinate, thus it cannot vary in time.

Like caveman1917 said, it varies over the spacetime manifold in a way that is very suggestive we might want to attribute the changes to the time coordinate.

And wouldn't this "no prior geometry" requirement in fact make the spacetime manifold curvature Time symmetric ?

Ken G

2011-Jan-17, 07:06 PM

And wouldn't this "no prior geometry" requirement in fact make the spacetime manifold curvature Time symmetric ?What is the "no prior geometry" requirement?

Staticman

2011-Jan-17, 10:48 PM

What is the "no prior geometry" requirement?

Oh, just GR general covariance. diiffeomorphism invariance or background independence, whatever you wanna call it. Freedom to choose metric and coordinates.

Ken G

2011-Jan-18, 05:23 AM

OK, then your question is around time symmetry. AFAIK, GR, like most of the fundamental equations of physics, is time symmetric. So I think it would require a pretty pathological time coordinate to break that symmetry. However, that just means the laws themselves don't include an arrow of time, it doesn't mean that the conditions we observe cannot unfold differently with time in the two directions (as with the expansion of flat space in comoving coordinates).

Staticman

2011-Jan-18, 10:59 PM

OK, then your question is around time symmetry. AFAIK, GR, like most of the fundamental equations of physics, is time symmetric. So I think it would require a pretty pathological time coordinate to break that symmetry. However, that just means the laws themselves don't include an arrow of time, it doesn't mean that the conditions we observe cannot unfold differently with time in the two directions (as with the expansion of flat space in comoving coordinates).

That's what I thought. But I guess at some point the 2nd law of thermodynamics enters the picture and time symmetry is broken, it is conserved at the quantum level though.

Ken G

2011-Jan-19, 04:45 PM

That's what I thought. But I guess at some point the 2nd law of thermodynamics enters the picture and time symmetry is broken, it is conserved at the quantum level though.It's a very interesting issue to what extent the second law breaks time symmetry, and to what extent it does not. In a sense, the arrow of time referred to in the second law boils down to "loss of specialness", but specialness is not a property of the universe itself, it is a property of how we think about the universe. In a very real sense, every possible state a system can have is just as "special" as any other, but our intelligence chooses to attribute different degrees of specialness that the universe itself, and its laws, may take no position on. But once we choose to draw such distinctions and categorizations, then the concept of entropy follows, and its tendency to increase is simply the observation that given our chosen categories, subsequent events will tend to favor the larger targets. Expressed that way, the break in time symmetry appears to follow quite clearly from our own language about what is happening, rather than from anything that is actually happening independently of that language.

Staticman

2011-Jan-19, 06:44 PM

It's a very interesting issue to what extent the second law breaks time symmetry, and to what extent it does not. In a sense, the arrow of time referred to in the second law boils down to "loss of specialness", but specialness is not a property of the universe itself, it is a property of how we think about the universe. In a very real sense, every possible state a system can have is just as "special" as any other, but our intelligence chooses to attribute different degrees of specialness that the universe itself, and its laws, may take no position on. But once we choose to draw such distinctions and categorizations, then the concept of entropy follows, and its tendency to increase is simply the observation that given our chosen categories, subsequent events will tend to favor the larger targets. Expressed that way, the break in time symmetry appears to follow quite clearly from our own language about what is happening, rather than from anything that is actually happening independently of that language.

I get a similar impression about this, the kind of reality "bias" that you explain is acting constantly to give us the sense of time passing. I've often considered entropy like an observer-dependent property of macroscopic systems that interact with the environment.

Ken G

2011-Jan-19, 09:48 PM

Yes, it's off-topic, but I'd say that's just precisely what entropy is.

caveman1917

2011-Jan-20, 12:29 AM

I'll just add that the weak force breaks time symmetry (though doesn't imply any 'arrow of time'), so it's not just the 2nd law of thermodynamics.

Perhaps a thread on "what is entropy" might be interesting. I could start one if you are interested in that discussion Ken?

Ken G

2011-Jan-20, 01:00 AM

Yes, I think that would be fascinating.

forrest noble

2011-Jan-20, 02:13 AM

Perhaps a thread on "what is entropy" might be interesting. I could start one if you are interested in that discussion Ken? I would start one in ATM if anyone were interested. It would post as a question but the answer would be entirely ATM :) , if not I would participate in a mainstream discussion of it if started here.

caveman1917

2011-Jan-20, 03:53 AM

Thread created (here (http://www.bautforum.com/showthread.php/111951-What-is-entropy)).

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