# EM Force not Spatial Curvature?

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## Main Question or Discussion Point

Why is it that the EM force can't be modeled on spatio-temporal curvature the way gravity can be?

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PeterDonis
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2019 Award
Because the EM force does not obey the equivalence principle. For example, suppose you have three objects, one with a charge of +1, one with a charge of zero, and one with a charge of -1. You start them all off at rest relative to each other at the same point in space in the same EM field. Because of their different charges--or more precisely, their different charge to mass ratios--they will not stay together.

In the case of gravity, by contrast, all three objects would stay together (we start them at the same point in space so tidal gravity won't separate them). Heuristically, this is because gravity acts on the "mass to mass ratio", not the charge to mass ratio, and the mass to mass ratio is the same for all objects. (Usually this is described as inertial mass being the same as gravitational mass.) But observationally, the key fact is that gravity obeys the equivalence principle, whereas the EM force does not.

Thank you, thank, thank you. That made perfect sense to me. I'm scared to ask questions on this forum cuz people can be so mean. I really appreciate that you took the time to break it down for me. This encourages me to ask more questions in the future.

PeterDonis
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2019 Award
berkeman
Why is it that the EM force can't be modeled on spatio-temporal curvature the way gravity can be?
Yes, it can! See Kaluza-Klein theory.

PeterDonis
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2019 Award
See Kaluza-Klein theory.
The curvature that models electromagnetism in Kaluza-Klein theory is not spatio-temporal; it's in a dimension other than the 4 spacetime dimensions. So it's not relevant to the OP's question.