# What is the nature of gravity?

1. Jun 2, 2014

### jryp998

Hi, I'm trying to understand what the nature of gravity is. I know it is a force, and I know that heavy objects tend to attract other object, but why? It seems that this is because spacetime is bent. I don't really know what that means because my knowledge about spacetime is limited.

Everywhere I see, people explain this with the analogy of having a bowling ball sitting on a stretched sheet (representing spacetime), bending it, so a golf ball would tend to fall towards the bowling ball. But that explanation doesn't satisfy me, because the bowling ball makes a lower point on the sheet, and the golf ball is only attracted towards the bowling ball because of gravity. So that explanation basically only says that gravity occurs because of gravity.

Could anyone give me a better explanation as to why heavy objects bend spacetime and why would other objects get attracted to the bigger one in that case?

Thank you.

2. Jun 2, 2014

### Staff: Mentor

Actually, no, it isn't. In General Relativity, gravity is spacetime curvature. More precisely, *tidal* gravity is spacetime curvature. But all of the other aspects of gravity also arise because of spacetime curvature.

Why is gravity not a force in GR? Because you can't feel it; an object moving solely under the influence of gravity is in free fall, weightless, feeling no force. In GR, a force has to be a *felt* force. Our common way of speaking about gravity obscures this, because when we stand on the surface of the Earth, feeling our own weight, we say it's because gravity is "pulling" us downward. But actually, the reason we feel weight is that the Earth's surface is *pushing* us upward; if the Earth's surface were not there (if, say, we were falling into a very deep hole), we would not feel weight, just as objects in orbit about the Earth do not feel weight. It was this insight--that if a person falls freely, he will not feel his own weight--that first started Einstein on the road to GR.

The presence of mass causes spacetime to be curved, yes; and that spacetime curvature changes the paths of other objects so that they tend to fall towards the mass.

Yes, you're right; this "explanation" doesn't really explain anything. Aside from the circularity which you mention, there is another problem: the "rubber sheet" analogy only deals with *spatial* curvature, not *spacetime* curvature. It's *spacetime* curvature that's important. See further comments below.

Unfortunately, the plain fact is that nobody knows *why* the presence of mass causes spacetime to curve. We just know that it does. There are various speculations about this: for example, some people think spacetime is indeed sort of like an elastic medium, a "rubber sheet" (but a more complicated kind of elastic medium than the "rubber sheet" analogy you mention assumes), that is distorted by the presence of mass. Perhaps when we have a theory of quantum gravity, it will be clearer how spacetime curvature emerges from lower-level processes. But right now, it's just something we have to accept, because the theory of GR works.

Because a freely falling object follows a "straight line" in spacetime, but the curvature of spacetime makes the line appear "curved" towards the mass when we look at a projection of it into 3 spatial dimensions, which is how we're used to visualizing things. For a better visualization of the curvature of spacetime around a gravitating mass, which includes the time dimension, try here:

http://www.relativitet.se/spacetime1.html

3. Jun 3, 2014

### jryp998

Thank you very much for this detailed explanation. I'm still a little confused though. I'm still trying to digest the information in the link you gave me.

I get confused with the term "freely falling" because, again, I relate that to gravity, which is my initial question to begin with. I understand that the straight line gets curved towards the big mass, but what I don't understand is why does the small mass has to go in that direction towards the big mass. What prevents it from going the opposite way. I probably have to read more on the subject of spacetime to understand this though.

4. Jun 3, 2014

### Staff: Mentor

It's a line in space-time, not space - and you can only move forward in time so you can only follow that line in one direction.

Suppose you and I were to stand on the equator, 100 meters apart, and then both start walking due north. We'll become aware that some force seems to be shoving us towards one another so that by the time we reach the north pole we're bumping elbows. We'd have to start at the north pole and walk south for curvature to send us farther apart.

5. Jun 3, 2014

### Staff: Mentor

To the extent there's a relationship, it goes the other way: "freely falling" is the more fundamental thing, because we can directly measure it: just test for weightlessness. The behavior of freely falling objects around the Earth, as opposed to their behavior way out in space far away from all other bodies, is what tells us about the Earth's gravity; but freely falling objects, weightless objects, can be present anywhere, whether there is gravity or not.

It can go the opposite way--but if it does, it won't be freely falling. It will need some real force, some force that can be felt, to push it. The straight line in spacetime is the path in spacetime that freely falling objects follow. A better way of saying this is, by looking at the paths in spacetime that freely falling objects follow, we *find out* what the straight lines are in spacetime. The spacetime paths of freely falling bodies are like rulers in ordinary geometry; they mark out the straight lines.

6. Jun 3, 2014

### Maxila

I've always been uncomfortable with this type of explanation because of energy, if you free fall you gain kinetic energy, stand on the surface you have potential energy (weight), in orbit you have kinetic energy, all of which imply a "counter force"... and depicting gravity with a rubber mat and a bowling ball, a 2 dimensional representation of a four dimensional effect (3 dimensions and the dimension of space-time), is not a good way to try and visualize it either.

Last edited: Jun 3, 2014
7. Jun 3, 2014

### Staff: Mentor

Relative to a person who is not free-falling, yes. But relative to you, they are the ones gaining kinetic energy. Energy is frame-dependent.

No, these are not the same. Weight is a force; in the case where you are standing on the surface of the Earth, your weight is the force of the Earth pushing up on you, keeping you from freely falling. As such, weight is directly observable.

Potential energy, OTOH, is, like all other kinds of energy, frame-dependent. It depends on your position, and "position" is frame-dependent. In fact, in general in GR, potential energy isn't even well-defined; it's only in special cases, like isolated gravitating bodies, that it can even be defined at all.

But as I pointed out earlier in this thread, this "force" is one you can't feel; an object in orbit is weightless and feels no force. That's why, in GR, gravity is not a "force", and an object in orbit is following a straight line in curved spacetime.

Which is why I agreed with the OP, in post #2 of this thread, that that "explanation" of gravity doesn't really explain anything. But the "rubber mat and bowling ball" depiction is not a depiction of spacetime curvature; it's a depiction of *space* curvature only. The two are not the same. I linked to a better visualization of spacetime curvature a few posts back.

8. Jun 4, 2014

### pervect

Staff Emeritus
First things first - the notion of the "nature" of gravity is probably philosophical, rather than scientific, in that knowing any/all experimental results of experiments about gravity won't necessarily give you definite knowledge of what gravity is - it will, however give you knowledge of how it acts. That's all you can really expect from science. So don't expect from science what it can't give.

Thus I'd recommend keeping in mind that what GR has to say about gravity may not be any sort of "ultimate" answer. However, it is probably the best answer we have at the current time and is interesting in its own right.

That said, lets go onto your next question - what is space-time. I think a lot of the discussion has skipped over some of the really basic points.

So we can start out with the question of "what is time". We don't really need a very sophisticated answer to this complex question for our purposes. All we really need to know is that we can represent time with a timeline, and that marks on the timeline have a 1:1 correspondence with what we call time. If we want to be more precise, it might be useful to mention that we're talking about the notion that's usually called "coordinate time" here.

We can also represent space graphically with a similar line, which represents how far away things are.

When you combine the representation of time with a line, with the representation of space as another line, you can see that space-time in 1+1 dimensions can be represented by a 2-dimensional surface . Space-time has the property that there is a 1:1 correspondence between points on the diagram, and "events" in reality, though with only 1+1 dimensions we only represent a small subset of "reality" with our diagram.

Representing more dimensions of space along with the dimension of time would be useful, but it's harder to visualize (especially when we get to the next part, curvature) and not needed here.

Hopefully you've seen or heard of space-time diagrams, which can also be thought of as graphs of position vs time. You've probably heard or seen these graphs drawing on flat surfaces.

If you imagine drawing these same space-time diagrams on something curved (like the surface of a sphere) rather than on something flat (like a plane), you'll have a representation of curved space-time.

If you look at some of the references posted previously, you will see how drawing your 1-space + 1-time diagrams on curved surfaces generates effects which are equivalent to gravity. In case you missed them, I'll repost the reference I think makes the most sense.

9. Jun 4, 2014

### jryp998

Thanks to everyone for the great answers. Although I still can't understand it very well, I'm on the right path now. I actually have more questions than before now, but that's a good thing.

Thanks.

10. Jun 6, 2014

### Mueiz

although the model of the rubber sheet and the ball is very widespread it is very misleading for those who want to understand what space-time curvature means for the for the first time because they can not differentiate between what is common in the unimagineabe reality and the model used to explain this reality thus many misconception about this reality (which are true conception of the model ) is transmited to mind of the reader ..Although i do not think this model is the best one i can mention some remarks that can make it less harmful
1) the model is imagineabe and the reality is unimagineabe
2) the space in the model is two-dimensional and is four-dimensional for the reality (space-time)
3) the cause of the curvature in the model is the wight of the ball but the cause of the curvature in spacetime is the existence of matter
4) the cause of the cuved motion of an object near the ball toward it the curvature and gravity while the cause of this motion in reality is the curvature .
5) the balll in the model is found out the space and the matter in reality is foudnd inside the space-time.
6) the ball and the space (the sheet) have different number of dimension and the exicistence of matter in space-time and the space-time have the same number of dimension.
7) the can not be a straight line in both the model and reality.
I think there is a better way to explain the cuvature of space-time than this by using a model of a closed book and pen inside it is better regarding the remarks 3,4,5,6.

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11. Jun 9, 2014

### jobermark

You could think of it as the force that results from the fact that when matter aggregates densely, time slows down.

We usually derive time dilation from gravity, but I think it is just as reasonable to say that the dilation itself causes the gravity. If time is moving slower at one end of a rigid object from the point of view of its other end, then that rigid object is going to be drawn toward its retarded end.

Any motion in any other direction that the free end wishes to take will not be matched by the slowed end, and the overall motion will be curved toward the slowed end. So the side of every particle nearest a greater aggregation of mass causes a force pulling that particle in the direction of the aggregation...

We focus on the dilation of length, and think of "curvature", because messing with time is confusing. But the two things are really the same -- 'some space slows time' and 'some space acts bigger than other space' are both different ways of saying 'some space resists velocity more than other space', because Geodesics are not really about space or time, they are about the path that allows constant velocity.

Last edited: Jun 9, 2014
12. Jun 10, 2014

### Staff: Mentor

That's only reasonable if you can show us the math. If, starting from the assumption that "when matter aggregates densely time slows down" you can derive the equations of motion for objects moving under the influence of gravity, then you might be on to something. If not, you're just kidding yourself (and violating the forum rule about personal theories).

13. Jun 10, 2014

### WannabeNewton

I'm going to indulge you, only because there is a very limited sense in which time dilation can be used to calculate "gravity" (a term I will need to qualify more carefully) but the rest of your post is completely nonsensical.

If we are in a space-time $(M,g_{\mu\nu})$ that possesses a time-like Killing field $\xi^{\mu}$ then we can define an extended rigid stationary frame given by the orbits of $\xi^{\mu}$. If $M$ is asymptotically flat then this rigid frame is characterized by its non-rotation relative to spatial infinity. It is easy to show that the observers following the orbits of $\xi^{\mu}$ have an acceleration $a^{\mu} = \nabla^{\mu} \ln (-\xi^{\mu}\xi_{\mu})^{1/2}$. Defining $\varphi := \ln (-\xi^{\mu}\xi_{\mu})^{1/2}$ we then see that $a^{\mu} = \nabla^{\mu} \varphi$ so in the rigid frame defined above, a freely falling observer will have an acceleration $a^i = -\partial^i \varphi$ which is what we usually call "the acceleration due to gravity" in Newtonian gravity; the freely falling observer will also be subject to other forces in this rigid frame, such as the inertial forces arising from $\vec{\nabla}\times \vec{\xi} \neq 0$ in local inertial frames.

At the same time, $\varphi$ is of course also the gravitational time dilation factor in $M$. So acceleration due to gravity can, in this limited sense, be seen as arising from the gravitational time dilation factor. But acceleration due to gravity is not a gauge-invariant quantity and can always be transformed away by boosting to a local inertial frame from the above rigid frame at any given event. The gauge-invariant quantities associated with "gravity" are obtained from space-time curvature which, unlike the acceleration due to gravity, cannot be obtained from $\varphi$. Indeed the physical content of GR is that gravity really only manifests itself in a gauge-invariant way due to the gravitational tidal forces arising from space-time curvature, and that acceleration due to gravity is simply the byproduct of separating the geodesic equation $u^{\mu}\nabla_{\mu}u^{\nu} = 0$ into an "inertial" part ("inertial" in the sense of $F = ma$, not "inertial" in the sense of fictitious) and a "gravitational" part relative to a rigid reference frame.

14. Jun 10, 2014

### jobermark

That "limited sense" is all that matters to me. At any given scale, I can say the acceleration of gravity is caused by time dilation, but overall I don't get to. Since we cannot actually experimentally test 'overall', that is OK with me.

The curvature of space is an entirely within-theory construct, after all. Only the deviation of motion is observable. So insisting upon which causes which is merely a matter of convention.

The point is that there are a lot of equivalent ways of looking at these effects, and saying things like "gravity is not a force" are just poisoning the well. As experienced or measured experimentally, gravity is a force, and curved space-time is a nice way of describing why that force arises where it does. There are others.

To Nugatory -- the math is the same math, just do it backward.

15. Jun 10, 2014

### Staff: Mentor

That depends on your definition of "force". Since an object moving purely under the influence of gravity is weightless, in free fall, feeling no acceleration, it seems odd, to say the least, to say that a "force" is causing its motion, since this "force" is not felt.

The force we actually measure (as in, we measure weight, proper acceleration, etc.) is not the force of gravity; it's the force of whatever is pushing on the measuring device to keep it from freely falling. For example, the weight you feel standing on the surface of the Earth is due to that surface pushing up on you; that's the force you're actually experiencing or measuring. The "force" of gravity in this situation is a "fictitious" force or "pseudo-force" that is only necessary to introduce because you're using a non-inertial frame in which you, standing on Earth, are at rest; the pseudo-force "explains" why you remain at rest in this non-inertial frame even though there is a force pushing you upward. But this pseudo-force can't be measured directly; it's an artifact of using a non-inertial frame.

16. Jun 11, 2014

### Staff: Mentor

I don't see how that works. We can start with the Einstein field equations describing the relationship between spacetime curvature and the distribution of matter; find the Schwarzchild solution to the field equations for static spherically symmetric distributions of matter; then calculate gravitational time dilation from the Schwarzchild solution. But how would we do it in reverse? The Schwarzchild solution implies gravitational time dilation, but not the other way around; and the EFE implies the Schwarzchild solution but not the other way around.

17. Jun 11, 2014

### pervect

Staff Emeritus
I suspect that this idea is inspired by some variant of Newton-Cartan theory. It appears to involve modelling gravity as some sort of scalar field (one number, your "time dilation"). Skipping over the issue of whether or not this sort of "time dilation" is actually compatible with technical issues such as Lorentz covariance, this scalar theory doesn't enough degrees of freedom to be equivalent to GR, which is a tensor theory. So, in short, the full behavior of GR can't be modeled in such a simple theory,.

The reasons we think of curvature in regard with gravity are not as you describe, and don't involve "resisting velocity" at all.

For example, consider the procedure in figure 1 below, taken from Taylor's "Exploring Black Holes", downloadable from http://www.eftaylor.com/general.html, a procedure that allows one to get the "shape" of a 2d surface embedded in a 3d space.

Using idealized "strings" that minimize distance , and carying out this procedure on the "shape" of the equatorial plane of a static massive body (using rockets that hover in place rather than "nails") does not give results for this 2d surface that are consistent with a plane, but rather that of the 3d surface sketched below.

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