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- Cool derivation of Lorentz transformation for mass by Feynman seems to start with assuming mass is constant, thereby invalidating the derivation.

In section 3.8, Feynman does a derivation of the Lorentz transformation for mass starting from

$$\frac{d}{dt}E=F \cdot v \hspace{1cm}(1) $$

But is this a valid starting point if you are going to show mass changes with velocity?

He says (1) comes from chapter 13 of his Lectures which he derives by differentiating the Newtonian formula for kinetic energy

$$ \frac{d}{dt} \frac{1}{2} mv^2 = mav = Fv \hspace{1cm} (2)$$

But this assumes mass is constant. Feynman never misses, so I know I am missing some type of explanation as to why it's valid to start with (1) to prove

$$ m= \frac{m_0}{ \sqrt{1-\frac{v^2}{c^2} } } \hspace{1cm}(3)$$

$$\frac{d}{dt}E=F \cdot v \hspace{1cm}(1) $$

But is this a valid starting point if you are going to show mass changes with velocity?

He says (1) comes from chapter 13 of his Lectures which he derives by differentiating the Newtonian formula for kinetic energy

$$ \frac{d}{dt} \frac{1}{2} mv^2 = mav = Fv \hspace{1cm} (2)$$

But this assumes mass is constant. Feynman never misses, so I know I am missing some type of explanation as to why it's valid to start with (1) to prove

$$ m= \frac{m_0}{ \sqrt{1-\frac{v^2}{c^2} } } \hspace{1cm}(3)$$

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