special relativity

The equation explained

\varphi(v) = 1 ,

In wordsThe factor is one, whatever the speed.OverviewPutting the last two conditions together fixes the factor: its square is 1, and the factor itself is 1.Full explanationThe product of the factor for

v

and for

-v

is 1, and the two factors are equal. So the factor times itself is 1. A number whose square is 1 is 1 or

-1

, and the paper writes

\varphi(v) = 1

without further comment. The other root would reverse the sign of every force component even for

v = 0

, when

k

and

K

coincide and must measure the same forces. With the factor gone, the relations of p. 908 become the transformation of the next display.Every step

\varphi(v) \cdot \varphi(-v) = 1

From inverting the relations, two displays back.

\varphi(v) \cdot \varphi(v) = 1

Replace

\varphi(-v)

\varphi(v)

, which symmetry allows.

\varphi(v) = 1

A number whose square is 1 is 1 or

-1

. The paper takes 1;

-1

would reverse every component even at

v = 0

, where the two systems coincide.AlsoOverviewFull explanationEvery step

Read it in the paper