Richard Feynman writes about Newton’s Second Law of Motion in his work “Lectures on Physics” (Chapter 15):

For over 200 years the equations of motion enunciated by Newton were believed to describe nature correctly, and the first time that an error in these laws was discovered, the way to correct it was also discovered. Both the error and its correction were discovered by Einstein in 1905.

Newton’s Second Law, which we have expressed by the equation

\[ F=d(mv)/dt \]

was stated with the tacit assumption that m is a constant, but we now know that this is not true, and that the mass of a body increases with velocity. In Einstein’s corrected formula m has the value

\[ m=\frac{m_0}{\sqrt{1-v^2⁄c^2}} \]

where the rest mass represents the mass of a body that is not moving and c is the speed of light […]”. Quote end.

In fact, if in the equation of the Second Law of Motion the mass m is replaced by the formula of the relativistic mass depending on the velocity, after having carried out the differentiation, the expression of the relativistic acceleration results (see derivation).

Richard Feynman’s text continues with the statement:

For those who want to learn just enough about it so they can solve problems, that is all there is to the theory of relativity – it just changes Newton’s laws by introducing a correction factor to the mass.” Quote end.

That is what we describe on this website (see “Sequence of relativistic proofs“).

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