# How is gravity created?

1. Aug 15, 2014

### Cyber Space

How is gravity created? If you have any theories or new facts discovered please share. If u have your own theory please share your reasoning along with it.

Thanks!

PS. its my first first time using this so sorry for any thing I did wrong.

2. Aug 15, 2014

### phinds

This forum does not allow personal theories, just mainstream science, so please read the rules as there are likely other ones you are not aware of and should be.

3. Aug 15, 2014

### Staff: Mentor

4. Aug 15, 2014

### Cyber Space

I have already looked into articles like that a lot. but my question is if gravity is created by matter bending space time then what causes the matter to bend space time.

5. Aug 15, 2014

### Staff: Mentor

As we seek to understand something deeper and deeper, we eventually run into a wall. In this case, your question is really good but its at the wall. General Relativity showed that there is a connection between matter and spacetime but not what causes it to act this way. Perhaps some future theory of quantum gravity will be able to answer your question but of course it will invariably leave something new unanswered.

Just remember until we know for certain the answer is: Turtles all the way down...

http://en.wikipedia.org/wiki/Turtles_all_the_way_down

6. Aug 16, 2014

### PhysicistMike

I'm going to explain this in terms of a cross between Newtonian gravity and the weak field approximation since you don't appear to know tensor analysis and differential geometry.

If someone told you that gravity is created my matter bending spacetime then they were incorrect. It's gravitational gradients that curves spacetime, not the other way around. I.e. gravity is the cause, curved spacetime is the result. Also, according to Einstein, the presence of a gravitational field is not determined by the presence of spacetime curvature but (in simple terms which aren't exactly accurate) by the non-vanishing of the gravitational gradient of the gravitational potential. So you can have a gravitational field without spacetime curvature but you can't have spacetime curvature without a gravitational field. A good example is a uniform gravitational field. The gravitational potential of a weak uniform gravitational field is of the form Phi = mgz

$$\Phi = mgz$$

The gravitational force is the gradient of this, i.e.

$$F = -\nabla \Phi = -mg$$

At this point it's important to know that spacetime curvature is a fancy way of talking about gravitational tidal forces. The Newtonian version of the tidal force tij tensor can be expressed in terms of the second derivatives of the gravitational potential, i.e.

$$t_{ij} = \frac{\partial^2\Phi}{\partial^i\partial^j}$$

If you know a little about calculus then you'd notice that the tidal force tensor is now zero and therefore spacetime curvature in a uniform gravitational field is zero.

As to why one particle exerts a force on another one - nobody knows.

7. Aug 16, 2014

### Staff: Mentor

Its turtles... ;-)

8. Aug 16, 2014

### WannabeNewton

Actually you're mistaken. There is no distinction between gravity, in the tidal sense, and space-time curvature. Gravity doesn't cause space-time curvature because well it can't cause itself. It is exactly energy-momentum that causes space-time curvature. Space-time curvature and gravity are not separate notions in GR, they are one and the same.

9. Aug 16, 2014

### ShayanJ

What about the way Feynman derived Einstein Field Equations? He didn't consider space-time curvature. How is it explained in that formulation?

10. Aug 16, 2014

### PhysicistMike

That is incorrect in the sense that I didn't say different. In fact spacetime curvature and tidal gradients are merely two different descriptions of the same exact thing.

All I said was It's gravitational gradients that curves spacetime, not the other way around. I.e. gravity is the cause, curved spacetime is the result. It wasn't the best way to describe it but it's difficult to describe. That's why I used the math, i.e. to state explicity as close as I could using Newtonian gravity to explain GR and curved spacetime. I meant that tidal gradients are caused by the varying of the force of gravity from one place to another. If the term "cause" displeases you then toss it away and replace it with a term that you like.

Only in the sense that the source causes a field which can vary from place to place if the distribution of matter dictates it. That's a bad way to say it though. It's like saying that charge causes an electric field. The correct way to say that is that charge "creates" an electric field. In the case of gravity the stress-energy-momentum tensor "creates" spacetime curvature.

That is incorrect for the reasons I stated in my post and as illustratedby the counter example I gave. I.e. Space-time curvature and gravity are not the same thing since you can have a gravitational field without spacetime curvature. In fact that was the first kind of gravitational field that Einstein used in his work on GR. He said that
The uniformly accelerating frame of reference is in a flat spacetime. You cannot introduce spacetime curvature by transforming to an accelerating frame since a vanising curvature tensor in one frame is a vanishing curvature tesor in all frames. A uniform gravitational field is therefore a perfect example of a gravitational field with zero spacetime curvature. Therefore your assertion that they're the same thing is wrong.

11. Aug 16, 2014

### Staff: Mentor

It takes a bit of stretching to get from "equivalent to" to "is", especially because the equivalence is only local.

12. Aug 16, 2014

### Markus Hanke

Wouldn't it be more accurate to say that energy-momentum is equivalent to a certain aspect of ( local ) space-time curvature, as opposed to being the cause of it ? After all, what the field equations are telling us is that - up to a proportionality constant - the components of the energy-momentum tensor are equal to a certain combination of components of the Riemann tensor, being the Einstein tensor ( which is just the double dual of Riemann ).

Granted, the distinction between equivalency and causation is a subtle one, but I think in this particular instance it might be warranted. Or am I seeing this wrong ?

13. Aug 16, 2014

### PhysicistMike

Local means "within a neighborhood" which doesn't apply to what I said. A uniform gravitational field can be very larger in fact. E.g. one way to create such a field to a high degree of accuracy is to find an asteroid whose mass density is uniform. Then you chop out parts of the surface so that it's a sphere. Then you hollow out a spherical cavity inside. Inside the cavity the field will be uniform. The distance the center of the hollow cavity is from the center of the sphere is proportional to the strength of the gravitational field inside the cavity. Therefore as expected the field inside the sphere will become zero when the cavity is concentric with the sphere. The important part here is that the field isn't local. Please note that this is an approximation to a uniform field just as the Schwarzschild metric is an approximation to any planet in the solar system since none of these are exactly spherical.

However it's most definitely true that the metrics are the same and that it's impossible to tell the difference from one to the other so that there is no possible way to say whether one "is" a uniform field or whether its uniformly accelerating. I suspect that it's called "equivalent" because in reality if you were to look at your environment then you'd see that you were in one situation or the other.

To end this off let me quote the definition of local. From Differential Geometry by Erwin Kreyzig. From page 2
This definition of local does not fit the way you used it.

14. Aug 16, 2014

### A.T.

That is a general issue in physics. You often hear stuff like "forces accelerate mass", but in fact F=ma just states a quantitative relation, not a causation one way, or the other.

15. Aug 16, 2014

### Jilang

If you take that argument to the logical conclusion you would be forced to say that spacetime curvature = energy= spacetime curvature.

16. Aug 16, 2014

### A.T.

What physics says is: Space time geometry is related to mass/energy distribution in a certain way. It doesn't say: Mass/energy causes something.

17. Aug 16, 2014

### Jilang

Yep, that was my point. There is no chicken or egg.

18. Aug 16, 2014

### Cyber Space

Thanks all for your answers. I have one more question on this topic. Do u know of any body or any organistaion that is focusing on solving the unanswered questions about gravity yet?

19. Aug 17, 2014

### Chronos

Yes, they are called physicists.

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