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General Relativity and the concept of curved spacetime replacing the "force" of gravitation is really beautiful, and I thought one could probably find similar descriptions of other forces like electromagnetism.

But then I read that all the other known forces have some sort of "force-carrier" particle, which seem to make this idea less sensible... but honestly I have no clue about these topics.

If the graviton is found, does the concept of curved spacetime become just a really useful and beautiful analogy? Does the existence of force-carrier particles make any concepts/properties of higher dimensions like curvature in spacetime explaining the force not "real"?

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The graviton is only a good approximation of these phenomena of space-time curvature and dynamics. The force carrier interpretation does not spoil the underlaying geometrical interpretation.

Other force carriers are similarly related to geometrical objects that describe spaces less easy (maybe in some cases even impossible) to be interpreted in a straightforwardly physical, tangible way (as extra dimensions let's say), but that can be easily seen as mathematical spaces whose points are the possible values of some parameters that enter our description of nature.

The change of these parameters in such spaces do not alter the results of our predictions, which means that their transformations are symmetries of our theories.

When these transformations are done in a different way at every space-time point they can be described by a field which corresponds to the graviton. These fields are the other force carriers.

For instance in the case of electromagnetism, the mathematical space is a circonference, the parameter that "lives" in this space is related to the electric charge and the photons are the force carriers that arise by the invariance under transformations of this parameter made in a different way at every spacetime point. The maxwell equations derive from geometrical principles similar to those of general relativity, but now the curvature involved is related to both the spacetime and the new mathematical space.

Gravity turns out in the same way with the difference that now the transfornations are changes of coordinates which depend on the position in the spacetime.

These are very complex topics and introducing them in less loose terms would be difficult for me here. However if anybody has any other remarks please do comment or edit.

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  • $\begingroup$ thank you, that's great, but how is the mathematical space of electromagnetism a circumference? $\endgroup$ – ctsmd May 10 at 20:13
  • $\begingroup$ because in quantum field theory you can change the definition of the electric charge of all the fields by multiplying it times a factor $e^{i\theta}=cos\theta+i sin\theta$ and this parameter $\theta$ can represent an angle and therefore a point on a circumference. To motivate it further you would need to understand some quantum field theory.. $\endgroup$ – AoZora May 10 at 20:29
  • $\begingroup$ oh ok... so it's like a phasefactor, but yeah im still far from understanding quantum field theory i only somewhat recently started learning maths and physics, thanks anyway $\endgroup$ – ctsmd May 10 at 20:35
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From the point of view of modern physics and the standard model we describe the three forces of Electromagnetism, Weak, and Strong nuclear forces using the exchange of force field quanta. This is where the idea of a "force-carrier" particle comes in. The Photon, Weak Boson, and Gluon. In a quantum theory of gravity thus would be the graviton.

However, your idea about using geometry to describe other forces is not off the mark. This was the path pursued by theorists before the formalization of quantum theory in the 1920s. Kaluza-Klein theory adds extra dimensions to space-time and manages to derive a description of EM fields using the extra pieces of the metric tensor. There are other extensions of gravity that use the torsion field and with this you get more degrees of freedom to play with (even without extra dimensions). Einstein himself started research in both of these areas, add torsion to his final edition of relativity before his death.

Modern particle physics is very successful in describing everything but gravity. The paradigm there is that the force fields arise from local symmetry of the matter fields. This is called gauge theory and uses group theory, symmetries and Lie algebra to describe the pattern we see in particle data. GR uses differential geometry to describe the nature of gravity. Now there is symmetry in gravity, group theory does come into play, and there is an underlying differential geometry for gauge group manifolds. However, they mean different things in each paradigm and are somewhat at odds with each other. Most QF theorists and particle physicists I learned from in graduate school vehemently opposed unification that didn't respect the standard model, thinking GR was an "ugly" theory. I went the other way. I think there is a lot of uncharted territory in the extensions of differential geometry that have not been ruled out. Then of course there is string theory.

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  • $\begingroup$ QFT people seeing GR as ugly! Beauty really is in the eye of the beholder... $\endgroup$ – Stéphane Rollandin May 12 at 12:51
  • $\begingroup$ I agree. It's all beautiful and getting more interesting by the day. $\endgroup$ – ggcg May 12 at 13:23

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