# Einstein

Relativity: The Special and General Theory

Albert Einstein: Relativity

Part I: The Special Theory of Relativity

The Behaviour of Measuring−Rods and Clocks in Motion

Place a metre−rod in the x1−axis of K1 in such a manner that one end (the beginning) coincides

with the point x1=0 whilst the other end (the end of the rod) coincides with the point x1=I. What is

the length of the metre−rod relatively to the system K? In order to learn this, we need only ask

where the beginning of the rod and the end of the rod lie with respect to K at a particular time t of

the system K. By means of the first equation of the Lorentz transformation the values of these two

points at the time t = 0 can be shown to be

the distance between the points being

.

But the metre−rod is moving with the velocity v relative to K. It therefore follows that the length of a

rigid metre−rod moving in the direction of its length with a velocity v is

of a metre.

The rigid rod is thus shorter when in motion than when at rest, and the more quickly it is moving,

the shorter is the rod. For the velocity v=c we should have

,

and for stiII greater velocities the square−root becomes imaginary. From this we conclude that in

the theory of relativity the velocity c plays the part of a limiting velocity, which can neither be

reached nor exceeded by any real body.

Of course this feature of the velocity c as a limiting velocity also clearly follows from the equations

of the Lorentz transformation, for these became meaningless if we choose values of v greater than

c.

If, on the contrary, we had considered a metre−rod at rest in the x−axis with respect to K, then we

should have found that the length of the rod as judged from K1 would have been

;

this is quite in accordance with the principle of relativity which forms the basis of our

considerations.

A Priori it is quite clear that we must be able to learn something about the physical behaviour of

measuring−rods and clocks from the equations of transformation, for the magnitudes z, y, x, t, are

nothing more nor less than the results of measurements obtainable by means of measuring−rods

and clocks. If we had based our considerations on the Galileian transformation we should not have

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