I'm not sure where to put this post, but it has related to relativity somewhat, so I posted it here. The question I have has more to do with philosophy of science. Anyway, according to Newton's, p = mv, F =(adsbygoogle = window.adsbygoogle || []).push({}); ^{dp}/_{dt}= ma. But according to Special Relativity, p = γmv , F =^{dp}/_{dt}= γ^{3}ma_{parallel}+ γma_{perpendicular}.

The derivation of force in terms of special relativity can be seen in the special relativity wiki section.

So if I were to analyze force at very high speeds, I would use the F = γ^{3}ma_{parallel}+ γma_{perpendicular}since that takes relativistic effects into account.

So my question is that are scientific equations valid for only certain scales? Newton's force equation should be treated as only approximation and practical for problems at low speeds. It seems to me that the other force equation is ideal for high speeds. So do you think that the progress of science (physics in particular) is just trying to come up with equations for particular experiments, and modify it until new experiments cast a new light on the theoretical side?

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# Problems with scale

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