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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

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questionauthority

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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

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εllipse

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

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

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 requiredquestionauthority said:Does magnetism bend space?

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EnumaElish

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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.)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.

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ohwilleke

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Phobos

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questionauthority said: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)

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George Jones

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εllipse said: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

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ahrkron

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George Jones said: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?

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George Jones

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ahrkron said: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

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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.

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Antiphon

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εllipse said: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

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