Mathematics of Physics and Engineering

98 Theory of Relativity

aether existed, then the Earth's motion around the Sun, at the speed of
about 30km/sec, would affect the speed of light depending on the direction
of the light beam. Michelson and Morley emitted a beam of light, first in
the direction of the Earth's motion and then perpendicular to it. They used
mirrors and an interferometer to measure the speed of light in each case,
and failed to detect any significant difference; see Problem 3.3 on page 424
for details. As a result, contrary to its initial intent, the Michelson-Morley
experiment provided the first evidence against the existence of the aether,
and in that respect became the most famous failed experiment in history.
The experiment certainly had a profound effect on the further development
of natural sciences, and in 1907 Michelson became the first American to
receive a Nobel prize in physics.
In 1905, Albert Einstein, who was 26 at the time, made the result of the
Michelson-Morley experiment the basis of a new theory of relative motion,
special relativity. He proposed two postulates:

(i) An observer measures the speed of light to be the same in any direction

regardless of the observer's motion relative to other bodies; this is a

consequence of the Michelson-Morley experiment,

(ii) Any two observers moving with constant relative velocity can agree on

all observed data and mathematical relations (laws) between the data;

this is the postulate of mathematical invariance.

According to Postulate (i), all observers measure the same value for the

speed of light in a vacuum: c = 3 x 10^8 meters/second. It follows that

absolute motion (in some special frame) is unobservable, hence physically

meaningless. In other words, Einstein sided with Berkeley against Newton

on the question of relative motion. The letter c in the notation for the

speed of light is for celerity (swiftness).

According to Postulate (ii), for two observers in frames O and 0\, math-

ematical relations which hold in the frame O are to be transformed into

corresponding relations in the other frame 0\ by a transformation of the

variables (x,y,z,t) to the variables (xi,yi,zi,t\); the experimental study

of light propagation suggests that this transformation should be linear.

The result, called the Lorentz transformation, is a necessary consequence

of Einstein's two postulates.