Why is gravity described as bending space instead of just an attractive force?

[questionauthority]

Hello,

I've always wondered why gravity was described as "bending space". Why isn't gravity simply thought of as an attractive force? Does magnetism bend space?

Eli

 

[εllipse]

I've always wondered why gravity was described as "bending space". Why isn't gravity simply thought of as an attractive force?

The answer to this question is rather complicated. There are a number of books out on special relativity and general relativity for laymen; the best layman explanation I've read is in Kip Thorne's Black Holes and Time Warps, which you can probably get at your local library. If you don't want to read the whole thing, just read the first two chapters. The first chapter explains special relativity and the second explains general relativity in simple terms. If you're interested in learning more about black holes, the rest of the book is rather fascinating as well.

To give you a general answer, in 1905, Einstein published the special theory of relativity, which explains how light can always move at the same speed for any inertial observer (see this thread). An inertial observer is someone or something that keeps a constant velocity. However, Einstein's special theory of relativity only explained a universe in which gravity doesn't exist. Obviously there is gravity in our universe, so this troubled Einstein. Then, in 1907, Einstein realized that if you're falling toward the Earth, you won't feel your own weight. Also, the Earth doesn't "feel" its own weight as it goes around the sun, and the moon doesn't feel its weight as it moves around the Earth. This led Einstein to postulate that as you fall freely through a gravitational field, you can be thought of as an inertial observer moving through curved spacetime, and by 1915 he finally had a successful, self-consistent theory of gravity, which explains our world to great detail.

That doesn't mean gravity can't be thought of as a normal-old attractive force (carried by particles), much like the other forces are (and there are, in fact, theories trying to find a way to do this, but so far with questionable success), but right now the best model we have, by far, is Einstein's general theory of relativity, and I personally hope that when it's all said and done gravity will always be best explained by curvatures in spacetime.

Does magnetism bend space?

Shortly after Einstein published his general theory of relativity, he received a paper from Theodor Kaluza who proposed that electromagnetism could also be thought of in terms of curvatures in spacetime, but in order to accomplish this Kaluza's theory required five, not four, dimensions. Einstein swayed back and forth between being enthusiastic and being skeptical of Kaluza's idea, and although he finally approved of Kaluza's paper for publishing two years after receiving it, he eventually decided Kaluza's approach wasn't the correct one. However, in Brian Greene's The Elegant Universe, he points out that one of the reasons Kaluza's theory had so many problems could have been because physicists weren't aware of the weak and strong nuclear forces at the time. I have asked in two of the subforums here (the Quantum Mechanics forum and the Strings and LQG forum) whether or not it could be possible to think of the other forces as curvatures in spacetime, but have not yet received much of a reply. Modern physicists think of electromagnetism, the strong force, and the weak force as forces being carried by particles (called quanta) rather than curvatures in spacetime. edit: And they have been very successful in doing so.

 

[EnumaElish]

Modern physicists think of electromagnetism, the strong force, and the weak force as forces being carried by particles (called quanta) rather than curvatures in spacetime.

Hasn't this been confirmed by experiments, though? The particles carrying these 3 forces have been empirically detected, have they not? (Unlike the elusive graviton.)

 

[ohwilleke]

We have a particle model that works. But, we observe the strong force by its effects, not by "observing" a particle. The strong force confines quarks to composite structures. Also, the W and Z which are strongly hypothesized to carry the weak force are very short lived. What we do is try to come up with a theory that can explain the particle tracks in accellerator experiments. We look at what comes out and how it got there and try to fill in the gaps with what the predecessors must have looked like.

 

[Phobos]

I've always wondered why gravity was described as "bending space". Why isn't gravity simply thought of as an attractive force?

ok, gravity is an attractive force. Now what causes it?

Newton vs. Einstein.
Law vs. Theory. (description vs. explanation)

 

[George Jones]

Modern physicists think of electromagnetism, the strong force, and the weak force as forces being carried by particles (called quanta) rather than curvatures in spacetime.

Interestingly, these forces are also described in terms of curvature, where the curvature is of abstract "internal" spaces, and not of spacetime.

Regards,
George

 

[ahrkron]

Interestingly, these forces are also described in terms of curvature, where the curvature is of abstract "internal" spaces, and not of spacetime.

Regards,
George

How is that? can you provide a reference?

 

[George Jones]

How is that? can you provide a reference?

Any standard physics text on elementary particles or quantum field theory, e.g., Griffiths, Halzen and Martin, Peskin and Schroeder etc. Unfortunately, these texts only treat the topic implicitly, i.e., they all fail to mention curvature explicitly!

The theory of gauge fields is formulated mathematically within the area of fibre bundles. A gauge field is a connection (like a connection in GR) that can be used to form a covariant derivative (minimal coupling), and the failure of covariant derivatives to commute gives rise to a field strength tensor that is actually a curvature tensor.

Regards,
George

 

[pervect]

For a specific example of how electromagnetism can be explained by the mathematical formalism of curvature, take a look at Kaluza-Klein theory

http://en.wikipedia.org/wiki/Kaluza-Klein_theory

The wikipedia also mentions that this theory can be extended to cover other forces. It's usually caled a Yang-Mills theory in this case. People usually don't mention that Yang-Mills theories could be regarded as being due to curvature explicitly, though, at this point it is assumed that one has a much more sophisticated mathematical vocabulary.

I'm not quite sure of the experimental falsification status of KK theory. Note that M-theory (aka string theory) follows a very similar bent to KK theory, however, and for the purposes of illustrating how forces can be explained by curvature, M-theory would also serve as an example.

But there is more to be said about why we model gravitation, specifically, with curvature. The reason is that gravity affects _everything_.

This makes it very difficult to model gravity with the "field" approach. If we have an electric field at a point, we can put a charged particle particle and an uncharged particle at that point, and observe their motions. The electric force will cause the charged particle to move differently, and we ascribe this motion to a force generated by the electric field.

But we cannot do this with a gravitational field, as everything interacts with gravity. Thus it's not really "natural" to model gravity with a field, because we cannot actually measure the field directly.

There are other reasons too, for saying that space-time must be curved (in at least a very lose sense) due to gravity. This is the phenomenon of gravitational red shift. Gravitational red shift cannot be explained without varying metric coefficients (this can be llosely defined as "curvature") - the existence of gravitational red-shift naturally leads one to propose that space-time has a varying metric, and a detailed analysis of this idea along with the requirement that gravity act like Newtonian gravity for weak fields leads to General Relativity.

 

[Antiphon]

I have asked in two of the subforums here (the Quantum Mechanics forum and the Strings and LQG forum) whether or not it could be possible to think of the other forces as curvatures in spacetime, but have not yet received much of a reply.

I had started a post in the now defunct Theory Development forum.
Exactly this was done about 50 years ago.

See the links for the Heim theory. https://www.physicsforums.com/showthread.php?t=81824