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Old Feb 19th 2011, 03:49 AM   #1
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What is spacetime

Hello. I keep reading about how the space time curved so choose or make deductions from the rotating mass.
It is therefore only the geometry of space time or traveled by some physical reality?
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Old Feb 20th 2011, 04:09 PM   #2
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Originally Posted by jaiii View Post
Hello. I keep reading about how the space time curved so choose or make deductions from the rotating mass.
It is therefore only the geometry of space time or traveled by some physical reality?
I'm sorry, I really can't make much sense out of the question. I'll give it my best guess.

The geometry of space-time gives us what are called "geodesics." A geodesic is the shortest distance between any two points in space-time. (Assuming you are just letting gravity take its course.) A geodesic, then, is the closest analogue to a "straight line" in a given metric space. For example, in the Cartesian xy plane in two dimensions a geodesic is, in fact, a straight line. But if we take our usual rubber sheet with a mass at the center we can easily see that the path an object takes is "curved" around the mass. The path can even curve around and meet itself as in the case of an orbit. The geodesics in this case are not what we would consider "straight," but still represent what we would call a straight line in that geometry.

I am, of course, being rather specific. To get a better idea, see this. It's a little Math intensive, but with this sort of Mathematics that can't be helped.

If that doesn't answer your question, please try to re-write it and I'll take another shot at it.

-Dan
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Old Feb 20th 2011, 11:21 PM   #3
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Thank you.
Your answer is quite precise and intelligible.
But still, I wonder whether there is any
device to display curvature of spacetime. For instance, a computer application or web page?

Thank you.
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Old Feb 21st 2011, 11:27 AM   #4
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Originally Posted by jaiii View Post
Thank you.
Your answer is quite precise and intelligible.
But still, I wonder whether there is any
device to display curvature of spacetime. For instance, a computer application or web page?

Thank you.
There's a neat little video here. There are also some computer generated "perspective" pictures floating around. I'll see if I can find any. The problem is that the space-time curvature is not just in the fourth dimension, it is in an imaginary fourth dimension. For example, the usual space-time metric is given as s^2 = x^2 + y^2 + z^2 - (ct)^2. But you can also look at it in a more "Euclidean" view point. Here s^2 = x^2 + y^2 + z^2 + (ict)^2, where i = sqrt(-1). (Switching to coordinates like these is called a "Wick" rotation.

-Dan

PS I'm moving this to the Special Relativity forum since we aren't talking about QM.
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Old Apr 1st 2011, 02:59 PM   #5
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Originally Posted by topsquark View Post
The geometry of space-time gives us what are called "geodesics." A geodesic is the shortest distance between any two points in space-time.
For this to be true it must be understood that the term "distance" as used here does not refer to spatial distance but refers to the integrated magnitude of the spacetime interval. And it need not be shortest. It need only have a "stationary" value. It could theoretically have a maximum value!!
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Old May 1st 2011, 02:25 AM   #6
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Originally Posted by Pmb View Post
For this to be true it must be understood that the term "distance" as used here does not refer to spatial distance but refers to the integrated magnitude of the spacetime interval. And it need not be shortest. It need only have a "stationary" value. It could theoretically have a maximum value!!

Hello Pmb. Nice to see you again after a couple years.

Even better, geodesics are suprizingly maximal when derived as the extremal solution to the path integral. All infinitessimal variations to the geodesic are of less proper time. I don't know why this is. Perhaps it has something to do with how time enters into it. See Sean Carrol, Lecture Notes on General Relativity, eq. 3.48.
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Old Mar 7th 2012, 04:51 AM   #7
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Originally Posted by topsquark View Post
The geometry of space-time gives us what are called "geodesics." A geodesic is the shortest distance between any two points in space-time.
The distance between two events on a geodesic is given by integrating the Euclidean metric you will get a statioary value for the integral and that will be one of te geodesics. If you intergrate the Minkowski metric between two points you will get a stationary value. Such a value is different than the Euclidean geodesics value.
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