I EM Force vs. Gravity: Modeling Spatio-Temporal Curvature

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The electromagnetic (EM) force cannot be modeled on spatio-temporal curvature like gravity because it does not adhere to the equivalence principle. In a scenario with charged objects, their differing charge-to-mass ratios cause them to behave differently in an EM field, unlike gravitational interactions where all masses remain together due to the equivalence of inertial and gravitational mass. Gravity's adherence to the equivalence principle allows it to be modeled effectively in terms of curvature in spacetime. While Kaluza-Klein theory attempts to incorporate electromagnetism into a higher-dimensional framework, it does not address the spatio-temporal curvature relevant to the original question. The discussion highlights the fundamental differences in how gravity and electromagnetism interact with mass and charge.
Ontophobe
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Why is it that the EM force can't be modeled on spatio-temporal curvature the way gravity can be?
 
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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.
 
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Thank you, thank, thank you. That made perfect sense to me. I'm scared to ask questions on this forum because 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.
 
Ontophobe said:
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.
 
haael said:
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.
 

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