# Einstein

Relativity: The Special and General Theory

Albert Einstein: Relativity

Part I: The Special Theory of Relativity

Theorem of the Addition of Velocities.

The Experiment of Fizeau

Now in practice we can move clocks and measuring−rods only with velocities that are small

compared with the velocity of light; hence we shall hardly be able to compare the results of the

previous section directly with the reality. But, on the other hand, these results must strike you as

being very singular, and for that reason I shall now draw another conclusion from the theory, one

which can easily be derived from the foregoing considerations, and which has been most elegantly

confirmed by experiment.

In Section 6 we derived the theorem of the addition of velocities in one direction in the form which

also results from the hypotheses of classical mechanics− This theorem can also be deduced

readily horn the Galilei transformation (Section 11). In place of the man walking inside the carriage,

we introduce a point moving relatively to the co−ordinate system K1 in accordance with the

equation

x1 = wt1

By means of the first and fourth equations of the Galilei transformation we can express x1 and t1 in

terms of x and t, and we then obtain

x = (v + w)t

This equation expresses nothing else than the law of motion of the point with reference to the

system K (of the man with reference to the embankment). We denote this velocity by the symbol W,

and we then obtain, as in Section 6,

W=v+w A)

But we can carry out this consideration just as well on the basis of the theory of relativity. In the

equation

x1 = wt1 B)

we must then express x1and t1 in terms of x and t, making use of the first and fourth equations of

the Lorentz transformation. Instead of the equation (A) we then obtain the equation

which corresponds to the theorem of addition for velocities in one direction according to the theory

of relativity. The question now arises as to which of these two theorems is the better in accord with

experience. On this point we axe enlightened by a most important experiment which the brilliant

physicist Fizeau performed more than half a century ago, and which has been repeated since then

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