## The nature of gravity and spacetime

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LTK
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### The nature of gravity and spacetime

(Inspired by xkcd#675)

I think we've all seen the image of the two-dimensional analogy to spacetime curvature. (This one.) Until recently I never really gave it any thought, but suddenly I came to the realization that it was much like a sheet of (frictionless) rubber with a ball placed on it. It made the concept of gravitation easily understandable: When you place a ball, which represents a planet, on the rubber sheet, which represents spacetime, it creates a well: spacetime distortion. When you place another, smaller object next to it, it will roll into the well that the larger ball has created, thus being pulled to the larger ball by gravitation. When you roll the smaller ball towards the larger one, its path may be curved when passing through the well, or it may start to roll in circles around it.

Okay, here comes the thought experiment that completely overturns general relativity with the 'ball on a rubber sheet' idea. It's very puzzling how an inanimate object can exert a force on something a million miles away, without changing energy levels anywhere. All it takes for gravitational force to be exerted is the existence of a body, without it actually doing anything. If I look at the rubber sheet this is explained: The balls are not the cause of the force that brings them together, but the wells are. The wells in the sheet are, ironically, created by gravity, but let's forget about that for a moment. What brings the balls together is the nature of a sheet to create wells, so the balls are only indirectly involved in their respective attraction.

So, if extrapolated to spacetime, can it be said that it's actually spacetime itself that causes gravitational force instead of the mass that inhabits it? If spacetime can be distorted in this way, it can be regarded as a substance rather than just coordinates. A substance with a density, maybe? If a body creates a distortion in spacetime, this can be regarded as a change in density, somewhat like dropping a ball into a container of fixed volume. Only the shift in density is static, and concentrated around the object rather than equated with the rest of the volume. Instead, this shift pulls other objects toward the areas of greater density.

What I was trying to say here, although probably irrelevant, is that spacetime and mass are mutually exclusive and cannot exist in the same place. Mass expels its volume in spacetime outwards of the atomic nuclei, which creates a density increase analog to the density of the mass.

Thank you for bothering to read my wannabe theoretical physicist theories. Tell me if it makes any sense at all.

*strokes goatee*

RogerMurdock
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### Re: The nature of gravity and spacetime

I'm not an expert physicist or anything, but what sort of implications would your theory have? Would your theory predict anything different from what we already observe? Or are you just asking if this is a nice way of thinking of things?

Edit: I read your idea more closely, and I think I know what you're saying now. Basically, what if mass clumping together is caused by gravity, not the other way around. This could be valid, but think about it. We know that if I have something that weights one solar mass and add it to something else that weights one solar mass, I'm going to have twice the gravitational force. What caused this? The "well" didn't change, I just manually moved them, and gravity changed. What i'm trying to say that mass -> gravity is a very cause -> effect relationship when you view it this way, and your idea doesn't mesh with reality.
Last edited by RogerMurdock on Tue Dec 15, 2009 11:55 pm UTC, edited 1 time in total.

Twistar
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### Re: The nature of gravity and spacetime

I was actually just reading about this in my book ("The Dancing Wu Li Masters") and it says that one of the theories (or maybe this is the accepted thought?) is that matter actually IS curved spacetime. It's all very very confusing to me. I have a lot to learn.

JWalker
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### Re: The nature of gravity and spacetime

LTK wrote:(Inspired by xkcd#675)
What I was trying to say here, although probably irrelevant, is that spacetime and mass are mutually exclusive and cannot exist in the same place. Mass expels its volume in spacetime outwards of the atomic nuclei, which creates a density increase analog to the density of the mass.

I was with you up until this part. I'm not sure what you're saying here, what do you mean they can't exist in the same place?

At any rate you have somewhat the right idea. Einstein's Field Equations (THE equations of gravity) simply relate curvature of a 4-d metric space (called spacetime) to components of an object called the stress energy tensor. The stress energy tensor is made out of things like energy and momentum fluxes.

Einstein's most famous equation is [imath]E=mc^2[/imath], which says energy and mass are really the same object. In General Relativity we have [imath]\mathcal{G}=8\pi\mathcal{T}[/imath] (Einstein's field equations) which relates energy/momentum to space curvature. In the same sense as with [imath]E=mc^2[/imath] telling us that energy and mass are the same thing, Einstein's field equations tell us that spacetime curvature and mass/energy/momentum are the same thing.

Klotz
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### Re: The nature of gravity and spacetime

Spacetime isn't a fluid.

doogly
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### Re: The nature of gravity and spacetime

It is very wrong to say that matter and space can't occupy the same... space? You are gonna use the word space here, right? That's a sign of how wrong you are.

You are correct that gravity can act as a source for gravity. It is like how gluons have color (the strong force charge). This isn't because gravity has a mass, but it does carry energy, in say a gravitational wave. You get nonlinear effects like this, it's p cool.
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andyisagod
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### Re: The nature of gravity and spacetime

LTK wrote:(Inspired by xkcd#675)
Okay, here comes the thought experiment that completely overturns general relativity with the 'ball on a rubber sheet' idea. It's very puzzling how an inanimate object can exert a force on something a million miles away, without changing energy levels anywhere. All it takes for gravitational force to be exerted is the existence of a body, without it actually doing anything. If I look at the rubber sheet this is explained: The balls are not the cause of the force that brings them together, but the wells are. The wells in the sheet are, ironically, created by gravity, but let's forget about that for a moment. What brings the balls together is the nature of a sheet to create wells, so the balls are only indirectly involved in their respective attraction.

How does this reconcile with electromagentism where we don't have a rubber sheet view but can have inanimate objects exerting force on something a million miles away.

The relationship between matter, energy and gravity is very close. The matter tells space-time how to curve and space-time curvature tells matter where to go. Without the energy density or matter i.e without the balls on your sheet the space time would be flat. It you have only say a very light ball (one that doesn't deform the sheet) it rolls along the sheet in a straight line. You need both the sheet deforming and the balls weighing the sheet down to get the right behaviour, and this is pretty much how gravity works as well.

LTK
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### Re: The nature of gravity and spacetime

JWalker wrote:I was with you up until this part. I'm not sure what you're saying here, what do you mean they can't exist in the same place?

At any rate you have somewhat the right idea. Einstein's Field Equations (THE equations of gravity) simply relate curvature of a 4-d metric space (called spacetime) to components of an object called the stress energy tensor. The stress energy tensor is made out of things like energy and momentum fluxes.

Einstein's most famous equation is [imath]E=mc^2[/imath], which says energy and mass are really the same object. In General Relativity we have [imath]\mathcal{G}=8\pi\mathcal{T}[/imath] (Einstein's field equations) which relates energy/momentum to space curvature. In the same sense as with [imath]E=mc^2[/imath] telling us that energy and mass are the same thing, Einstein's field equations tell us that spacetime curvature and mass/energy/momentum are the same thing.

That last bit about mass and space being mutually exclusive came from the thought that if space is not simply a place that things exist in, but something that can be distorted or tunneled through, then the place that both space and matter exist in might restrict space from being where matter is, which creates a distortion of space bending around matter. Forget about that, it adds nothing.

I knew about mass and energy basically being different manifestations of the same thing, but I didn't know about spacetime distortion and mass being just as similar. Hmm...

RogerMurdock wrote:I'm not an expert physicist or anything, but what sort of implications would your theory have? Would your theory predict anything different from what we already observe? Or are you just asking if this is a nice way of thinking of things?

Edit: I read your idea more closely, and I think I know what you're saying now. Basically, what if mass clumping together is caused by gravity, not the other way around. This could be valid, but think about it. We know that if I have something that weights one solar mass and add it to something else that weights one solar mass, I'm going to have twice the gravitational force. What caused this? The "well" didn't change, I just manually moved them, and gravity changed. What i'm trying to say that mass -> gravity is a very cause -> effect relationship when you view it this way, and your idea doesn't mesh with reality.

In the first place it was a nice way of thinking of things. But it might imply that, in case of distorted space exercising force on mass instead of mass exercising force on mass, gravity is an instataneous force rather than a speed-of-light-propelled wave-force. I see that gravity waves have only been indirectly proven to exist, but I should read more into that.

I'm not quite sure whether or not what you're thinking what I'm thinking is actually what I'm thinking. What I was saying is, while bodies are attracted to one another by gravitational force, this force may not be exercised by either of the two bodies but by spacetime itself. The cause-and-effect chain is more like mass->spacetime distortion->gravity instead of directly relating mass and gravity.

Klotz wrote:Spacetime isn't a fluid.

How do you know?

schrodingasdawg
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### Re: The nature of gravity and spacetime

JWalker wrote:Einstein's most famous equation is [imath]E=mc^2[/imath], which says energy and mass are really the same object. In General Relativity we have [imath]\mathcal{G}=8\pi\mathcal{T}[/imath] (Einstein's field equations) which relates energy/momentum to space curvature. In the same sense as with [imath]E=mc^2[/imath] telling us that energy and mass are the same thing, Einstein's field equations tell us that spacetime curvature and mass/energy/momentum are the same thing.

The one problem I have with this interpretation is that spacetime can be curved where there is no matter present, e.g. the Schwarzschild metric is an empty-space solution that is valid outside the mass responsible for the curvature. So I've always thought of energy/momentum as a source of spacetime curvature rather than the same thing.

thoughtfully
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### Re: The nature of gravity and spacetime

There's nothing special about black holes here (and the Schwarzchild metric applies to any spherically symmetric nonrotating body, btw). Any massive body is going to warp space outside of itself. Otherwise, space would be flat, and there'd be no gravitation.

Perfection is achieved, not when there is nothing more to add, but when there is nothing left to take away.
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vega12
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### Re: The nature of gravity and spacetime

andyisagod wrote:
LTK wrote:(Inspired by xkcd#675)
Okay, here comes the thought experiment that completely overturns general relativity with the 'ball on a rubber sheet' idea. It's very puzzling how an inanimate object can exert a force on something a million miles away, without changing energy levels anywhere. All it takes for gravitational force to be exerted is the existence of a body, without it actually doing anything. If I look at the rubber sheet this is explained: The balls are not the cause of the force that brings them together, but the wells are. The wells in the sheet are, ironically, created by gravity, but let's forget about that for a moment. What brings the balls together is the nature of a sheet to create wells, so the balls are only indirectly involved in their respective attraction.

How does this reconcile with electromagentism where we don't have a rubber sheet view but can have inanimate objects exerting force on something a million miles away.

The relationship between matter, energy and gravity is very close. The matter tells space-time how to curve and space-time curvature tells matter where to go. Without the energy density or matter i.e without the balls on your sheet the space time would be flat. It you have only say a very light ball (one that doesn't deform the sheet) it rolls along the sheet in a straight line. You need both the sheet deforming and the balls weighing the sheet down to get the right behaviour, and this is pretty much how gravity works as well.

Close, but a very light ball will have its path deflected by space-time curvature just as much as a massive ball. This is just like how a bowling ball and feather fall at the same speed in a vacuum. Another extreme is the case of deflected light, light being completely massless.

andyisagod
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### Re: The nature of gravity and spacetime

LTK wrote:In the first place it was a nice way of thinking of things. But it might imply that, in case of distorted space exercising force on mass instead of mass exercising force on mass, gravity is an instataneous force rather than a speed-of-light-propelled wave-force. I see that gravity waves have only been indirectly proven to exist, but I should read more into that.

I'm not quite sure whether or not what you're thinking what I'm thinking is actually what I'm thinking. What I was saying is, while bodies are attracted to one another by gravitational force, this force may not be exercised by either of the two bodies but by spacetime itself. The cause-and-effect chain is more like mass->spacetime distortion->gravity instead of directly relating mass and gravity.

The mass warping space time, objects then moving in a warped space time is the theory of general relativity. I'm not entirely sure how you think your theory is different once you strip away all the stuff about mass and space time not occupying the same space.

vega12 wrote:Close, but a very light ball will have its path deflected by space-time curvature just as much as a massive ball. This is just like how a bowling ball and feather fall at the same speed in a vacuum. Another extreme is the case of deflected light, light being completely massless.

No, if there are no other masses then any object will travel in a straight line in an otherwise flat metric. Masses are not defelected by their own gravity. Obviously even a very small mass will deform space time as it passes through it but if you had a single photon you probably wouldn't worry about the photons gravitational effects esspecially if you're considering it in isolation.

doogly
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### Re: The nature of gravity and spacetime

Light doesn't work like nearly massless particles though, because gravity couples to pressure as well as energy. Dust / single particles don't exert pressure, but light does, in fact for them [imath]\rho=p[/imath], so you have twice as much interaction as you would in the Newtonian case. This factor of two was one of the early successful predictions of GR, measured during an eclipse by Eddington.
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andyisagod
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### Re: The nature of gravity and spacetime

doogly wrote:Light doesn't work like nearly massless particles though, because gravity couples to pressure as well as energy. Dust / single particles don't exert pressure, but light does, in fact for them [imath]\rho=p[/imath], so you have twice as much interaction as you would in the Newtonian case. This factor of two was one of the early successful predictions of GR, measured during an eclipse by Eddington.

Ok but for the example (which was orginally to do with balls and sheets anyway) is it ok if we say that a single photon is not a significant source of curvature.

doogly
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### Re: The nature of gravity and spacetime

Yeah, that's fair, unless it is something like planck scale energetic.
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PM 2Ring
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### Re: The nature of gravity and spacetime

doogly wrote:Yeah, that's fair, unless it is something like planck scale energetic.

And even then, it's important to remember that the energy of a single photon is not invariant, it's frame-dependant.

doogly
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### Re: The nature of gravity and spacetime

Well, it's covariant. That's what you wanted anyway. I wind up using 'invariant' to mean 'covariant' more often than not. And I almost never specify 'contravariant,' because I am sloppy like that. I guess stress tensor is 'naturally' meant to be covariant though, so that's right.
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taby
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### Re: The nature of gravity and spacetime

doogly wrote:Light doesn't work like nearly massless particles though, because gravity couples to pressure as well as energy. Dust / single particles don't exert pressure, but light does, in fact for them [imath]\rho=p[/imath], so you have twice as much interaction as you would in the Newtonian case. This factor of two was one of the early successful predictions of GR, measured during an eclipse by Eddington.

The effect for ultrarelativistic massive particles is not 1/2 of the effect for photons. It's nearly identical.

In fact, it was Eddington himself who first wrote about this. Darned if I can find the title of the article. Maybe your prof knows.

This is also discussed in the book Gravitation by MTW. See Exercise 25.21. As v/c approaches 1 the deflection approaches twice that predicted by Newtonian gravitation. That is, the deflection is similar to Newtonian gravitation only in the limit where v/c approaches 0. This is, of course, regarding massive particles.

vega12
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### Re: The nature of gravity and spacetime

andyisagod wrote:
vega12 wrote:
andyisagod wrote:The relationship between matter, energy and gravity is very close. The matter tells space-time how to curve and space-time curvature tells matter where to go. Without the energy density or matter i.e without the balls on your sheet the space time would be flat. It you have only say a very light ball (one that doesn't deform the sheet) it rolls along the sheet in a straight line. You need both the sheet deforming and the balls weighing the sheet down to get the right behaviour, and this is pretty much how gravity works as well.

Close, but a very light ball will have its path deflected by space-time curvature just as much as a massive ball. This is just like how a bowling ball and feather fall at the same speed in a vacuum. Another extreme is the case of deflected light, light being completely massless.

No, if there are no other masses then any object will travel in a straight line in an otherwise flat metric. Masses are not defelected by their own gravity. Obviously even a very small mass will deform space time as it passes through it but if you had a single photon you probably wouldn't worry about the photons gravitational effects esspecially if you're considering it in isolation.

My apologies; I seem to have misread what you stated originally. On my first reading of what you said, I thought you meant that a very light ball will roll in a straight line (on a curved sheet). Clearly you actually meant a single particle all by itself. My bad ^^

doogly
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### Re: The nature of gravity and spacetime

To Taby: Oh hey, right on! My bad with that.
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