# Is there really no answer to what gravity is?

1. May 14, 2013

### slibbfalusken

Now every video on YouTube and every article on the subject, all of them says in great headlines: Gravity explained!... Every time I watch they give the same example every time. The blanked, the big ball and the small ball. The blanket represent two-dimensional space. The big ball a planet and the small ball a satellite. Then they place the heavy ball on the blanket so it bends and the small ball is put into orbit. Now I don't have any problems with visualizing this in three dimensions but I have two big problems.

1: Why is the object bending space time at all?

2: Why does that create a force between objects?

I would really like a answer to this. I have waited just for too long for this question. Now I would like if you don't post some equations, that only a professor in physics can understand, to explain. Now don't hesitate to give examples of a two-dimensional universe since that seems to be the only way to explain it visually.

2. May 14, 2013

### Ibix

1 Nobody knows. Maybe when we figure out quantum gravity. General Relativity only describes the deformation, not the mechanism.

2 It doesn't. General Relativity models gravity as a change in the structure of spacetime. Near a mass, objects move along curves because the rules of geometry aren't the same as the ones you learned in school. The curved path is a geodesic, which is the path that objects follow if no forces act. In flat spacetime that's a straight line. In curved spacetime, it's a curve.

3. May 14, 2013

### VantagePoint72

I think something you have to accept is that there is a limit to how much advanced physics can be explained without the help of the appropriate mathematics. I know it's frustrating when you can't find the understanding you're looking for, but please consider that the physicists you've spoken to do understand themselves what gravity—according to General Relativity (GR)—is. It is likely they are just struggling to explain it in an accessible way to someone who has a limited foundation in physics.

I agree the rubber sheet analogy does not do a good job of illustrating how GR works. I don't know that there is really a good illustration of it, outside of the actual mathematics of GR. Perhaps some of the educators here will have a better idea. In the meantime, I will give it a shot.

The answer to (2) is that curved spacetime essentially changes the notion of a straight line. Newton's understanding of inertia was that an object in motion that is not subject to any forces will continue to travel in a straight line. A straight line is defined as the shortest path between two points. Now, this continues to be true in Special Relativity (SR), with some caveats due to the fact that the geometry of spacetime is not quite the same as the geometry of space by itself. However, the basic idea is still true. An important point is that since we experience the passage of time, we are always moving through spacetime. We do so in the spacetime version of straight lines.

When something is curved, we may not be able to picture straight lines in the usual sense; but, we can still use the idea of the shortest distance between two points. For instance, on the surface of a globe, the shortest distance between two points is the segment of the great circle (that is, a full circumference of the sphere, like the lines of longitude or the equator; not the other lines of latitude since they are smaller circles) that connects the two points. You might find it helpful to play around with a globe to see how this works. Hence, great circles of a sphere are the generalization of the straight lines on flat paper. This is why if you plot the courses airplanes take on flat maps, the paths look curved: "straight" on a sphere and "straight" on a flat page are not the same thing.

Hence, we have the generalized law of inertia: in the absence of external forces, objects travel between two points according to the shortest path. Actual, the real requirement is that the path just be "extremal" but that's a mathematical detail that isn't really important for the main idea. So, by this principle, we would expect an object stuck onto a sphere but able to move freely (free, that is, of all forces besides whatever is required to keep it confined to the sphere) to move along great circles. Suppose we have a bug wandering around the surface of the globe (with no external gravitational field or any other forces like that), perhaps stuck on with little suction cups on its feet.

Now, as I said, we are always moving through spacetime. When spacetime is curved, the shortest paths taken by objects can make them behave in ways they wouldn't in flat space. Back to the globe picture, imagine two bugs wandering on surface. They stand on the equator some distance apart and both start walking north. That is, each bug walks up along a line of latitude toward the North Pole. As far as each bug is concerned, it's walking in a straight line, and these straight lines start out parallel to each other. In flat space, parallel lines stay parallel forever. For the bugs, though, they will eventually meet at the north pole. This is like the attractive "force" (though it is really, as you can see, not a force at all) in GR. If, instead, the two bugs want to stay the same distance apart as they wander around the globe, then one (or both) of them needs to apply a real force (according to the law of inertia) like a little bug-rocket in order to deviate away from great circles. So too, for you to stay where you are a fixed distance away from the centre of the earth, the earth's surface must apply an upward force on you to keep you where you are. You feel a force (just like the bug) because you are being pushed away from your natural inertial motion, which would tend to pull you towards the earth's centre. That "natural inertial motion" in curved space-time is what we call gravity.

As for your (1), why mass makes space-time curve: that is just a postulate of GR. Matter makes space-time curve according to a set of equations called the "Einstein field equations"; these have experimentally testable predictions. So far, GR has passed all these tests with flying colours. That fundamentally is why we believe matter causes space-time to curve. There are some theoretical arguments—like what I outlined above for (2)—that can be put forward to support it; however, I don't know how to describe them in an accessible away because they are very technical and mathematical. As Ibix said, a full understanding will probably require a proper quantum theory of gravity, which we do not currently have. It is best, I think, to just accept that it is a postulate of GR.

Last edited: May 14, 2013
4. May 14, 2013

### Fredrik

Staff Emeritus
Different theories will give you different answers to the question of what gravity is. There are no theory-independent answers. There's simply nothing better than an answer given by a good theory.

The two most important theories of gravity are Newton's and Einstein's.

1. In Newton's theory, gravity is just the fact that massive objects will be drawn to each other as described by Newton's law of gravity (i.e. the inverse square law). Since this formula says that the force depends only on the masses and the distance, and not e.g. on when the objects were put in their current positions, this raises a big question: How is this "instantaneous action at a distance" possible?

2. In Einstein's theory, gravity is just the geometry of spacetime. There's an equation (Einstein's equation) that describes a relationship between the geometric properties of spacetime and its matter content. This answers the big question raised by Newton's theory: There is no instantaneous action at a distance, just a relationship between matter and geometry that in some situations can be adequately described by Newton's law of gravity. However, it raises other big questions: Why is there a finite invariant speed? Why does this relationship between matter and geometry hold? Why is spacetime four-dimensional?

The only thing that can answer those questions is another theory. It would have to be a better theory of gravity than general relativity. Such a theory would of course raise some new questions that can only be answered by yet another theory.

The "heavy ball on a blanket" analogy that you have seen is often referred to as the "bowling ball analogy" or "rubber sheet analogy" here. If you search the relativity forum for words like "bowling" and "rubber sheet", you will find many posts where people complain about how bad it is. It is pretty bad, but I'm not sure that this subject can be taught at all using analogies. You will have to study differential geometry to really understand GR.

Note however that one thing you won't find in GR is the answer to the question of why matter and spacetime satisfy Einstein's equations. To ask why, is to ask why GR is a good theory, and the only thing that can answer that is a better theory.

Last edited: May 14, 2013
5. May 14, 2013

### pervect

Staff Emeritus
I don't think this has an answer in terms of anything more fundamental. One can ALWAYS ask why. Even after a very long explanation, one can ask "But why does.....". If one does not stop asking why at some point, it becomes an infinite regress of "but why, but why".

This question does have an answer, though it's rather involved.

First one has to realize that GR is not just curved space, but space-time. A space-time diagram is drawn in space - in the examples we'll use, a flat piece of paper. But one of the spatial axes on this piece of paper represent time (just as one might do in drawing a timeline, another graphical techniue for representing time with a diagram).

The other thing one needs to understand is the concepts of geodesics. This is the idea that objects move along the "straightest possible" paths. I need to add more words here, but I'm afraid I'm running out of time.

After one realizes both of these points, explanation such as the one in https://www.physicsforums.com/showpost.php?p=4281670&postcount=20 will make sense.

The name of the phenomenon is "Geodesic Deviation". The point is that geodesics on the curved surface of space-time naturally separate and accelerate away from each other, as time advances.

This is just what a force does.

The fundamental point is this. The same "force" that makes bodies have inertia, the "force" that you feel in an accelerating elevator, is gravity. Gravity is not separate from inertia. Gravity is a consequence of inertia. This is hinted at by the equivalence of gravitational and inertial masses, and formalized by the principle of equivalence. GR posits that gravity and inertia are fundamentally the same thing.

Last edited: May 15, 2013
6. May 14, 2013

### Staff: Mentor

At the bottom of every stack of "why" questions is another "why" question. They never end. This is true for everything, not just gravity.

7. May 14, 2013

### 49ers2013Champ

I like this thread. Good question, OP.

LastOneStanding, thanks for writing all that. Well put.

8. May 18, 2013

### slibbfalusken

To begin with I'd like to thank you for your good answer. I now understand that gravity is even more complex then I first thought and that I might have to wait until I go to a university before I can understand it more.

I have some questions though. I do belive I understand your ant example made sence. However it was completly different than how I thought it worked. In your example the ants are moving through time in the north direction. Space is the direction along the equator. Now I do know that we are moving through space in 3 dimensions and through time in a fourth. In your example however space it self is shrinking inwards since the distanse between everything is shrinking when the ants are closing in on the north pole. And even more confusing is the fact that it is shrinking in the 3rd dimension which in your example must represent the 5th dimension since time was the seckond in your example. I have a feeling I either must have completely misunderstood it or your example is limited due to the nature of the 3rd dimention. (What I mean is that maby it can't be explained in an accurate way when seing the universe as 2 or 1 dimensional.)

Since you seem to know alot about the subject I thought I might tell you how I thought the universe behaved and then you could tell me what things are wrong with it. After listening to alot of science shows I came to the conclusion that the universe is a 4-dimensional sphere. We are living on the surface (volyme to be technical) of the sphere. The sphere is growing and the direction outwards is the direciton of time. So that when we travel in time, the radius of the sphere grows and thus the spheres' surface grows. Now I thought that in this conclusion I could find the answer to gravity but after hearing your example I feel like I haven't understood it right.

9. May 18, 2013

### VantagePoint72

It's not so much that you've misunderstood the analogy, as you're just pushing it too far. The moral of the ant picture is: inertial motion in curved spacetime looks like motion subject to forces in flat spacetime. The actual geometry of four dimensional spacetime is not the same as the surface of a sphere; it is much more complicated. In fact, the geometry of flat 4D spacetime is the not the same as flat space—as I mentioned, time is not quite the same thing is another space dimension, unlike my ant world. However, the same moral applies.

Another important point: while the only way we can picture 2D objects like the surface of a sphere is by embedding them in 3D space (as you pointed out), it isn't necessary to do so to understand their geometry. This is an idea called "intrinsic curvature", and basically means that if there were ant physicists in my curved 2D world (1 space dimension, 1 time dimension), they would be able to describe the physics of their world using only 2D mathematics. They wouldn't need to use a third dimension to understand the motion of ants, and we don't need to use five.

The important thing to keep in mind is that, like the rubber sheet picture, my ant world just an analogy (though, in my humble opinion, a much better one). It's an imperfect analogy at that. It's not meant to explain exactly, and in detail, how gravity works—so don't push it too far—but to give you a basic sense of what's going on. The "moral" above is the important part. That, I'm afraid, is the best I can do without wading into some pretty advanced mathematics.

10. May 18, 2013

### Fredrik

Staff Emeritus
This is one of three possibilities that pops out of the equations when we assume that space is homogeneous and isotropic. Those spheres are supposed to be 3-dimensional though, not 4-dimensional. (An ordinary sphere is 2-dimensional). You can understand the expansion of the universe this way, but probably not any other aspects of gravity.

11. May 18, 2013

### Staff: Mentor

Yes. The example of a sphere is just an easy-to-visualize example to help you understand how the curvature of spacetime works with respect to geodesics.

In the example there is no 3rd dimension for the ants, there are only 2 dimensions on the ant's sphere, lattitude and longitude. The radial direction is not observable to the ants.

The surface of a sphere is a 2D surface. In this example the universe is represented as a 2D universe, 1 dimension of time and 1 dimension of space.

Any curved space can be embedded in a flat space which is a higher number of dimensions. In this case, the 2D curved space of the sphere can be embedded in a 3D flat space. The extra dimensions for embedding are not physical in any way, merely a "visualization aid". There is no reason to believe that there is actually a higher dimensional flat space in which the universe is embedded.

I think a 4D "trumpet" shape is probably more of the current conclusion. It appears that the universe will keep on getting bigger, not crunch back in on itself like a sphere.

If you think of it as a trumpet then the direction along the trumpet is time and the direction around the trumpet is space.

Yes, that is correct. Therefore we say that the universe is expanding.

12. May 20, 2013

### slibbfalusken

Wow thanks to all of you for your incredible answers! I have gotten a much better hang of it now but of course I realise that I can't understand it in much more detail than what you have explained until I have read physics at university level, which I look forward to doing.

Looks like a nice forum so I think I'm going to stay here for a while. Might learn more interesting things :)