*Reference: **Einstein’s 1920 Book*

*This paper presents Part 1, Chapter 7 from the book **RELATIVITY: THE SPECIAL AND GENERAL
THEORY by A. EINSTEIN.
The contents are from the original publication of this book by Henry
Holt and Company, New York (1920).*

*The paragraphs of the original
material (in black) are accompanied by brief comments (in color) based on the present
understanding. Feedback on these comments is appreciated.*

*The heading below is linked to
the original materials.*

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## The Apparent Incompatibility of the Law of Propagation of Light with the Principle of Relativity

There
is hardly a simpler law in physics than that according to which light is
propagated in empty space. Every child at school knows, or believes he knows,
that this propagation takes place in straight lines with a velocity ** c**
= 300,000 km./sec. At all events we know with great exactness that this
velocity is the same for all colours, because if this were not the case, the
minimum of emission would not be observed simultaneously for different colours
during the eclipse of a fixed star by its dark neighbour. By means of similar
considerations based on observations of double stars, the Dutch astronomer De
Sitter was also able to show that the velocity of propagation of light cannot
depend on the velocity of motion of the body emitting the light. The assumption
that this velocity of propagation is dependent on the direction “in space” is
in itself improbable.

*The free
velocity of any object in space is fixed by its inertia. This is the case not unique
to light. Light has a very small amount of inertia (quantization), which fixes
its velocity to a finite value.*

In
short, let us assume that the simple law of the constancy of the velocity of
light ** c** (in vacuum) is justifiably believed by the child at school.
Who would imagine that this simple law has plunged the conscientiously
thoughtful physicist into the greatest intellectual difficulties? Let us
consider how these difficulties arise.

Of
course we must refer the process of the propagation of light (and indeed every
other process) to a rigid reference-body (co-ordinate system). As such a system
let us again choose our embankment. We shall imagine the air above it to have
been removed. If a ray of light be sent along the embankment, we see from the
above that the tip of the ray will be transmitted with the velocity ** c**
relative to the embankment. Now let us suppose that our railway carriage is
again travelling along the railway lines with the velocity

**, and that its direction is the same as that of the ray of light, but its velocity of course much less. Let us inquire about the velocity of propagation of the ray of light relative to the carriage. It is obvious that we can here apply the consideration of the previous section, since the ray of light plays the part of the man walking along relatively to the carriage. The velocity**

*v***of the man relative to the embankment is here replaced by the velocity of light relative to the embankment.**

*W***is the required velocity of light with respect to the carriage, and we have**

*w*** w = c – v**.

The
velocity of propagation of a ray of light relative to the carriage thus comes
out smaller than ** c**.

But
this result comes into conflict with the principle of relativity set forth in
Section V. For, like every other general law of nature, the law of the
transmission of light *in vacuo* must,
according to the principle of relativity, be the same for the railway carriage
as reference-body as when the rails are the body of reference. But, from our
above consideration, this would appear to be impossible. If every ray of light
is propagated relative to the embankment with the velocity ** c**, then for this reason
it would appear that another law of propagation of light must necessarily hold
with respect to the carriage—a result contradictory to the principle of
relativity.

*We have a better assessment of this situation when we replace the carriage by Earth and the embankment by Sun. Earth and Sun have their own velocities fixed by their inertia, just like light has. Therefore, the velocity of light shall be different relative to the Earth and to the Sun. This does not conflict with the principle of relativity.*

In
view of this dilemma there appears to be nothing else for it than to abandon
either the principle of relativity or the simple law of the propagation of
light *in vacuo*. Those of you who have
carefully followed the preceding discussion are almost sure to expect that we
should retain the principle of relativity, which appeals so convincingly to the
intellect because it is so natural and simple. The law of the propagation of
light *in vacuo* would then have to be
replaced by a more complicated law conformable to the principle of relativity.
The development of theoretical physics shows, however, that we cannot pursue
this course. The epoch-making theoretical investigations of H. A. Lorentz on
the electrodynamical and optical phenomena connected with moving bodies show
that experience in this domain leads conclusively to a theory of
electromagnetic phenomena, of which the law of the constancy of the velocity of
light *in vacuo* is a necessary
consequence. Prominent theoretical physicists were therefore more inclined to
reject the principle of relativity, in spite of the fact that no empirical data
had been found which were contradictory to this principle.

*The same
law of inertia applies to the earth, the sun, and the light. There is no unique
law that applies only to the propagation of light. Einstein is using light as a
“body of reference” here. That would have been okay if light had zero inertia
(infinite velocity), but the velocity of light is finite indicating that it has
a small amount of inertia.*

*The
inertia of matter, in general, is so large compared to the inertia of light, that
the inertia of light may be ignored. Therefore, light as “body of reference” with
“zero” inertia is a good approximation for velocities in the material domain.*

At
this juncture the theory of relativity entered the arena. As a result of an
analysis of the physical conceptions of time and space, it became evident that *in reality there is not the least
incompatibility between the principle of relativity and the law of propagation
of light*, and that by systematically holding fast to both these laws a
logically rigid theory could be arrived at. This theory has been called the *special theory of relativity* to
distinguish it from the extended theory, with which we shall deal later. In the
following pages we shall present the fundamental ideas of the special theory of
relativity.

*It must be emphasized, however, that because of the assumption above, the conclusions of the special theory of relativity may not be extended to velocities greater than those found generally in the material domain. Unfortunately, Einstein himself violated this caution.*

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## FINAL COMMENTS

*The theory of relativity requires that the co-ordinate reference frames be rigid for the purpose of measurement. Inadvertently, this means that the inertia of the reference frames be constant. Fortunately, this condition is almost met in the material domain, which forms the basis of our investigation. Because of this condition we are able to apply the theorem of the addition of velocities in classical mechanics.*

*Light does not comply with this condition because its inertia is infinitesimal compared to the inertia in material domain. This large difference in inertia produces much larger difference in velocity of light and the velocities in material domain, so much so that the velocity of light is near infinite in comparison.*

*From the reference frame of light all the material velocities are infinitesimal. That is why the velocity of light appears to be constant despite the motion of inertial frames.*

*The theory of relativity is essentially using light as its reference frame of “zero inertia”. Therefore, any difference in velocity due to difference in inertia in the material domain can now be corrected by the relativity formula, which Newton’s formula was unable to do. However, light as a reference frame of “zero inertia” is not going to work in the field domain.*

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