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 […].

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. End quote.

The question that arises is, where was the error before Einstein’s correction in reality: in the law itself or in its interpretation?

The correct interpretation of the law

In my opinion, the Second Law of Motion, defined as the equivalence between the acting force and the time derivative of momentum, was correct even before Einstein. In fact, thanks to this interpretation, the law can also be used with a variable mass.

Opponents of this notion often reply that Newton thought mass was constant because acceleration, not momentum, was proportional to force.

But these people fail to realize that Newton did not invent the law, he just discovered it. What he thought about it is important for the history of physics, but it has no meaning for physics itself.

It is wrong to believe that the law can only be applied to a constant mass.

The “Lex Secunda” can be used with variable mass

In reality, the Second Law of Motion, also known as “Lex Secunda”, can also be used with the relativistic velocity-dependent mass and in interaction with the equivalence principle between energy and mass E=mc² (see the derivation of the relativistic scalar acceleration, mass, kinetic energy and vectorial acceleration).

It turns out that the “Lex Secunda” is generally valid and compatible with the theory of relativity.

Don’t you think so? Then please take a little time and see what is shown on the page "Sequence of Relativistic Proofs" of this website.