I got this idea from Einstein's insight using the falling elevator. He says, that Gravity really cannot be distinguished from any other force accelerating the elevator.

A bunch of questions on here (such as Can all fundamental forces be fictitious forces?, Why do we still need to think of gravity as a force? and Why is gravity such a unique force?) concern whether gravity is like the other forces. The answers seem to suggest that really gravity and the other forces are very much alike: all four forces can be described in geometrical ways (Yang-Mills) and all are transmitted in fields with light-speed.

My question thus is, whether the other 3 forces also warp space-time somewhat in the same way that gravity does?

And, imagine we were magnetical and we were living on a big magnet pulling us down exactly like gravity does, would the magnetical force close to the magnet also "slow down" our time (as in gravity: being close to heavy objects makes time run slower in relation).


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The curvature in a Yang-Mills field is completely different from the curvature in general relativity - perhaps I should have made this more explicit in my answer to Can all fundamental forces be fictitious forces?

In a Yang-Mills field the curvature is in a mathematical object called a connection. If you are interested the Wikipedia article on the Yang-Mills equations gives a good summary of this, but I'm afraid it will be completely opaque to anyone who hasn't studied differential geometry.

The bottom line is that the EM, weak and string forces are not due to any curvature in spacetime and therefore do not directly cause anything analogous to gravitational time dilation. The reason I included the word "directly" is because all forms of energy contribute to the gravitational field, so any energy associated with the three forces will contribute to the gravitational field.

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    $\begingroup$ The curvature of YM is not really "in the connection", is it? The YM gauge group is equipped with a connection, just like in GR spacetime is equipped with a connection. The key difference is that the manifold of the YM geometry is the according Lie group, while the manifold of GR is spacetime. $\endgroup$
    – scaphys
    Jan 28, 2023 at 12:40
  • $\begingroup$ @scaphys That's how my diff geo book describes it, and I note that Wikipedia uses the same description. However this isn't intended to be a rigorous way of describing the curvature and I'm sure more precise descriptions exist. $\endgroup$ Jan 28, 2023 at 16:45
  • $\begingroup$ @JohnRennie can I assume, that the way in which "any energy associated with the three forces will contribute to the gravitational field" is by means of E=mc², that is that they add to the mass? $\endgroup$
    – John Smith
    Jan 31, 2023 at 9:25
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    $\begingroup$ @JohnSmith Yes, for example if you add up the masses of the three quarks in a proton this comes to only 1% of the proton mass. The rest of the mass comes from the strong force interaction between the quarks. So 99% of the gravitational field generated by protons (and neutrons) actually comes just from the strong force interaction! $\endgroup$ Jan 31, 2023 at 9:33

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