# Curvatures in spacetime explained by momentum?

• michael879
In summary: If you model a spherical space in which, "the radius of the sphere is time, and its expanding", you might realize that once time is used in the model then the model cannot expand but has to be static, or frozen as movement would require another time dimension.
michael879
ok, so the way the whole "gravity is a curvature of space-time" was explained to me was with a 2d model. If anyone has read flatland (not sure about the name) imagine that world put onto a sphere, which represents the universe. The radius of the sphere is time, and its expanding. Gravity would be like taking a balloon and pushing it in with your finger. From this view it seems a lot like momentum to me though. The sum of all momentum has to be 0, since the big bang was an explosion from a point. Therefore, and point in space-time with mass would have to go slower then points with less or no mass (p = mv). Does this sound possible? or do I have gravity wrong?

I also think that the real question is what causes our abstract spacetime to curve in the first place. The problem with time expanding is that time is an abstract invariant by definition. Since time is abstract, it's physically meaningless. The real focus here is motion, not time.

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Starship said:
I also think that the real question is what causes our abstract spacetime to curve in the first place. The problem with time expanding is that time is an abstract invariant by definition. Since time is abstract, it's physically meaningless. The real focus here is motion, not time.
But time would basically be how much our universe has expanded since t=0. What I am saying is that momentum might be what causes space to curve. In the flatland case, everything is on a plane wrapped around a sphere. When something with mass slows down (expands slower) it would create a warp in space time like what I believe the "curvature" to be (not positive about what it actually is tho).

In general relativity, gravity is not a consequence of the universe expanding. The Schwarzschild solution, for instance, represents the solution for gravity in a static non-expanding space-time.

So whatever your theory is, exactly (I really didn't follow it, too many words and not enough mathematics), it can't be exactly equivalent to GR, if your theory can't predict gravity in a non-expanding universe (ala the Schwarzschild solution in GR).

pervect said:
In general relativity, gravity is not a consequence of the universe expanding. The Schwarzschild solution, for instance, represents the solution for gravity in a static non-expanding space-time.

So whatever your theory is, exactly (I really didn't follow it, too many words and not enough mathematics), it can't be exactly equivalent to GR, if your theory can't predict gravity in a non-expanding universe (ala the Schwarzschild solution in GR).
ok my "theory" (Im really just trying to understand relativities representation of gravity) is that the reason these gravity "curvatures" occur is because of momentum. In a spherical spacetime, gravity would look like "dent" or indentations in the surface of the sphere. I was thinking in an expanding universe this could be cause by momentum since everything with more mass would have to move slower then things with less, thereby distorting the space time they exist in.

Can you show me any mathematical proof that gravity exists in a nonexpanding universe? We live in an expanding one so do we rly have any good way of knowing whether gravity can exist in a nonexpanding one?

The standard solution of GR for a local static gravitational field around a spherical mass is the Schwarzschild solution. This is a 'mathematical proof' that gravity exists in a non-expanding universe as that solution is embedded in a Minkowski, flat space and static metric. It is this solution that is being verified in the solar system experiments that have verified GR.

If you model a spherical space in which, "the radius of the sphere is time, and its expanding", you might realize that once time is used in the model then the model cannot expand but has to be static, or frozen as movement would require another time dimension. This would not be an expanding balloon or soap bubble but rather an onion - with layers (like Shrek? All right I have kids!)

This model is proposed in the preprint Self Creation Cosmology - An Alternative Gravitational Theory (page 27 section 9 "A novel representation of space-time geometry").

You might then say that the expansion of the universe and the passing of time are two different observations of the same phenomena, however what that phenomenon actually is would remain a mystery.

Garth

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What Garth said. Basically, in standard GR, we can mathematically model a non-moving object (with no momentum in the standard physical sense of momentum) in a static non-moving space-time (which has no "momentum" even in a non-standard sense which you appear to be using the word). This mathematical solution still exhibits gravity, and is the Schwarzschild solution.

If your theory (whatever it is) cannot duplicate this result, it is not equivalent to standard GR.

Note that the cosmological expansion of the universe is insignificant on the scale of the solar system, and the Schwarzschild solution of GR (the gravitational field of the non-moving sun) is what we use to predict such measurements as

bending of light around the sun
the Shapiro time delay effect for radar signals which pass close to the sun

If you are sitting near a massive object (like the sun), and you are not moving, and the sun is not moving, but the sun is still attracting you to it, it is difficult for me to envision how one can explain this force of attraction (gravity) as being due to "momentum".

If you are sitting near a massive object (like the sun), and you are not moving, and the sun is not moving, but the sun is still attracting you to it, it is difficult for me to envision how one can explain this force of attraction (gravity) as being due to "momentum".

What I shall say now is not standart; but imagine two persons hanging a string, a cord; suppose that one of them do not move and and that the other is turning the cord on itself as long as it is possible: at some time the cord will be shorter and shorter... forcing the person who is turning it to come closer to the other one...

Cann't you transpose this image to the fields?

Momentum is a function of [mass x distance]/[time]. The curvature of spacetime also includes a time element in the calculation. Therefore, it is not useful to describe spacetime in terms of momentum. It is simpler to use the geometrical description [curvature].

In standard GR, momentum is part of the stress-energy tensor and hence contributes to the stress energy tensor (left-hand side of Einstein's equations), and hence to curvature (the right-hand side of Einstein's equations). However, momentum is not the sole cause of curvature. Energy density, and pressure, also contribute terms to the stress-energy tensor.

In addition, as I mentioned, I don't see how an explanation that focuses on momentum as the only cause of gravity can explain the gravity of a non-moving body and a non-moving observer (a very important case).

So my answer is that while momentum does have gravitational effects, in standard theory it's not the sole cause of gravity.

pervect said:
In standard GR, momentum is part of the stress-energy tensor and hence contributes to the stress energy tensor (left-hand side of Einstein's equations), and hence to curvature (the right-hand side of Einstein's equations). However, momentum is not the sole cause of curvature. Energy density, and pressure, also contribute terms to the stress-energy tensor.

In addition, as I mentioned, I don't see how an explanation that focuses on momentum as the only cause of gravity can explain the gravity of a non-moving body and a non-moving observer (a very important case).

So my answer is that while momentum does have gravitational effects, in standard theory it's not the sole cause of gravity.

Good point for you; absolutely ok with your intervention; and bad point for me (Once more time my bad English...) I was introducing the image of the cord, thinking to angular momentum, not momentum, and this because of my actual own investigations. Sorry for this stupid thing and thank you for the precisions. In fact I was asking me if the polarisation of a EM wave could also be a cause for introducing curvature in space-time; and the way around: if curvature in space-time can be the origin of a kind of polarisation for the EM waves? What do you think of this idea?

## 1. How does momentum cause curvatures in spacetime?

Momentum is a property of moving objects that describes their motion. In the theory of general relativity, it is described as the "flow" of energy and momentum through spacetime. When an object with momentum moves through spacetime, it causes a distortion or curvature in the fabric of spacetime, much like a heavy object placed on a trampoline.

## 2. Can momentum cause spacetime to curve in multiple directions?

Yes, momentum can cause spacetime to curve in multiple directions. The amount and direction of this curvature depends on the magnitude and direction of the momentum of the object. This is why objects with different velocities will have different effects on the curvature of spacetime.

## 3. Is momentum the only factor that causes curvatures in spacetime?

No, momentum is not the only factor that causes curvatures in spacetime. In the theory of general relativity, mass and energy also play a role in determining the curvature of spacetime. This is described by Einstein's famous equation E=mc^2, which shows the equivalence between mass and energy.

## 4. Can momentum cause time to slow down?

Yes, momentum can cause time to slow down. This is known as time dilation and is a key concept in the theory of relativity. When an object is moving at high speeds, its momentum causes it to experience time at a slower rate compared to a stationary object. This effect has been confirmed through experiments and is essential for accurate GPS navigation.

## 5. How does the curvature of spacetime affect the motion of objects?

The curvature of spacetime affects the motion of objects by causing them to follow curved paths or geodesics. This is because objects will always follow the shortest path through the curved spacetime, much like how a ball will roll along the curved surface of a hill. This explains why objects appear to be attracted towards massive objects like planets, as they are following the curvature of spacetime caused by the planet's mass.

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