B General Relativity and Gravity?

[ProfuselyQuarky]

We recently touched base with gravity in regards to general relativity and I'm a bit perplexed. So apparently (and correct me if I'm wrong) gravity is created when the mass of the universe warps, or bends, space-time. I've read all those analogies about a trampoline curving due to an object of mass, but (here's where I'm confused) doesn't a trampoline or blanket anything bend because of the presence of gravity? How can the warping of space-time cause gravity if gravity is the one causing the warping?

 

[Ibix]

https://m.xkcd.com/895/

 

[Ibix]

Less snarkily (sorry - it's been a strange couple of days), gravity changes the rules of geometry so that the definition of a straight line is replaced with a curve. Objects then follow curved paths because that's what they do in curved spacetime. The trampoline analogy doesn't really express this very well. But it's really not possible for a simple analogy to cover all the details.

 

[phinds]

To restate ibix's perfectly correct explanation but from a different point of view, objects in space-time follow straight lines, BUT those "straight lines" are what are called "geodesics" and when looked at from a Euclidean framework, they look curved.

 

[pervect]

The trampoline analogies tend to be a bit conceptually confused. I'm rather fond of the "Parable of the Apple", which explains gravity as geodesic deviation. I haven't seen any good popularizations of it though. The textbook original can be found by googling for ""Once upon a time a student lay in a garden under an apple tree reflecting on the difference between Einstein's and Newton's views". You should get a hit from "Gravitation, part 3 page 3" in the google books result.

The first thing that is needed to appreciate the analogy is to understand what a geodesic is. The ants are assumed to follow the most economical path on the apple, i.e. the curve of shortest distance lying entirely on the surface of the apple, i.e. a geodesic.

The second necessary mental leap is to understand that the apple does not represent space, but a space-time diagram. To appreciate this, it is very helpful to know the principle of extremal aging, often simplified as the principle of maximal aging. Matter moving through space takes a path through space-time that maximizes the proper time. It gets a bit confusing regarding the path of maximal aging as the "most efficient". It seems more like the least efficient. But it turns out that the details of the sign do not really matter, the point is that the path is an extremal path.

It's this second mental leap that's the hardest to convey. One might think of drawing space-time diagrams on the apple. Of course, one has to know what a space-time diagram is to appreciate this. Unfortunately it seems that the concept of a space-time diagram is abstract enough that it's just not appreciated, it seems to be (for instance) very difficult to get an interested poster to draw one.

If things go well, and both points are appreciated, then the result is this. The geodesic paths on the surface of the apple diverge due to the curvature of the apple. The geodesic paths through space-time diverge due to the curvature of space-time. We can regard this deviation as a tidal force. If we ignore time dilation as an apprxomation (it turns out to be not a very good approximation, unfortunately), we can regard the tidal forces as changes in an underlying force, called gravity.

 

[ProfuselyQuarky]

To restate ibix's perfectly correct explanation but from a different point of view, objects in space-time follow straight lines, BUT those "straight lines" are what are called "geodesics" and when looked at from a Euclidean framework, they look curved.

So it's a facade? They only "look curved", but not really?

 

[ProfuselyQuarky]

Less snarkily (sorry - it's been a strange couple of days), gravity changes the rules of geometry so that the definition of a straight line is replaced with a curve. Objects then follow curved paths because that's what they do in curved spacetime. The trampoline analogy doesn't really express this very well. But it's really not possible for a simple analogy to cover all the details.

That's quite alright! :) Anyway, so does this mean that curved spacetime is the ultimate reason for gravity? Can I say, "Curved spacetime is the cause of gravity" and be entirely correct?

 

[Ibix]

That's quite alright! :) Anyway, so does this mean that curved spacetime is the ultimate reason for gravity? Can I say, "Curved spacetime is the cause of gravity" and be entirely correct?

Curved spacetime is gravity is closer.

 

[ProfuselyQuarky]

The trampoline analogies tend to be a bit conceptually confused. I'm rather fond of the "Parable of the Apple", which explains gravity as geodesic deviation. I haven't seen any good popularizations of it though. The textbook original can be found by googling for ""Once upon a time a student lay in a garden under an apple tree reflecting on the difference between Einstein's and Newton's views". You should get a hit from "Gravitation, part 3 page 3" in the google books result.

The first thing that is needed to appreciate the analogy is to understand what a geodesic is. The ants are assumed to follow the most economical path on the apple, i.e. the curve of shortest distance lying entirely on the surface of the apple, i.e. a geodesic.

The second necessary mental leap is to understand that the apple does not represent space, but a space-time diagram. To appreciate this, it is very helpful to know the principle of extremal aging, often simplified as the principle of maximal aging. Matter moving through space takes a path through space-time that maximizes the proper time. It gets a bit confusing regarding the path of maximal aging as the "most efficient". It seems more like the least efficient. But it turns out that the details of the sign do not really matter, the point is that the path is an extremal path.

It's this second mental leap that's the hardest to convey. One might think of drawing space-time diagrams on the apple. Of course, one has to know what a space-time diagram is to appreciate this. Unfortunately it seems that the concept of a space-time diagram is abstract enough that it's just not appreciated, it seems to be (for instance) very difficult to get an interested poster to draw one.

If things go well, and both points are appreciated, then the result is this. The geodesic paths on the surface of the apple diverge due to the curvature of the apple. The geodesic paths through space-time diverge due to the curvature of space-time. We can regard this deviation as a tidal force. If we ignore time dilation as an apprxomation (it turns out to be not a very good approximation, unfortunately), we can regard the tidal forces as changes in an underlying force, called gravity.

Thanks! The "Parable of the Apple" analogy is much more understandable and, I suppose, more accurate. So the apple represents the curved spacetime that Ibix was talking about? I think I got it. Thanks a lot, guys!

 

[ProfuselyQuarky]

Curved spacetime is gravity is closer.

Sorry, what do you mean by that?

 

[Ibix]

Sorry, what do you mean by that?

A series of compressions and rarefactions in the atmosphere doesn't cause sound - it is sound. In the same way, curvature of spacetime doesn't cause gravity, it is gravity.

 

[phinds]

So it's a facade? They only "look curved", but not really?

I have no idea what you mean. Do you understand that there are different geometries? Riemann Geometry is one way of describing things. Einstein found that geodesics in space-time follow Riemann Geometry, not Euclidean. From the point of view of Riemann Geometry, lines that are defined as straight in Euclidean Geometry are curved and in Euclidean Geometry, lines that are straight in Riemann Geometry are curved. We humans evolved living in a world where Euclidean Geometry prevails as a description of reality so we tend to use its terms rather that the terms of Riemann Geometry. So we say space-time is curved, but that's just a reference in one framework. One that, as it turns out, is not the best one to describe some aspects of reality.

 

[ProfuselyQuarky]

A series of compressions and rarefactions in the atmosphere doesn't cause sound - it is sound. In the same way, curvature of spacetime doesn't cause gravity, it is gravity.

Got it. Thank you so much! Everything is clear now.

 

[Aman Trivedi]

We recently touched base with gravity in regards to general relativity and I'm a bit perplexed. So apparently (and correct me if I'm wrong) gravity is created when the mass of the universe warps, or bends, space-time. I've read all those analogies about a trampoline curving due to an object of mass, but (here's where I'm confused) doesn't a trampoline or blanket anything bend because of the presence of gravity? How can the warping of space-time cause gravity if gravity is the one causing the warping?

Thanks for asking this question! I too have often wondered about this. Cheers!