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Do forces change their behavior due to the relativity?

For example if a charged particle deflects through an electric field, would the pattern and amount of deflection differ in speeds near speed of the light from the classic physics? would such fast moving particle interact differently with nuclear forces?

The paradox to me is I think if clocks run slower for a fast object then everything else should do the same to keep the physics the same in the eyes of that object. For example I think object should “feel” less outside forces to keep the power exerted in the same range. Would that be true? Any answer highly appreciated.

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    $\begingroup$ Yes; in fact, the particle moving in the electric field partly experiences it as a magnetic field. $\endgroup$
    – Alex K
    Commented Jan 28, 2023 at 1:33
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    $\begingroup$ To be precise, clocks don't "run slower" for a fast object. The object experiences normal time. Other stationary people looking at the object see it moving through time more slowly. $\endgroup$
    – RC_23
    Commented Jan 28, 2023 at 1:34

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A particle traveling at relativistic speeds behaves (to us, in the laboratory frame) as if it were heavier than when moving slowly, even though its true mass is the same in both cases. So if we apply a force to it as it zooms by it will accelerate less in response, the faster it is moving.

(That "extra mass" used to be called relativistic mass, a once-common concept which has since fallen out of use.)

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    $\begingroup$ Great explanation. You mean that relativistic mass causes need for more force for the same amount of acceleration ? Although mass really doesn’t change. $\endgroup$
    – Aug
    Commented Jan 28, 2023 at 16:20
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    $\begingroup$ rest mass is invariant. the fast- moving particle's energy content makes it heavier. $\endgroup$
    – niels nielsen
    Commented Jan 28, 2023 at 23:47
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Force, like all straightforward vector quantities (velocity, displacement, electric field etc.) is not a relativistic invariant. Transformations must be applied to calculate the magnitude and direction of a force as judged in another frame of reference.

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