Einstein's Theories of Relativity and Gravitation: A selection of material from the essays submitted in the competition for the Eugene Higgins prize of $5,000Bird, J. Malcolm (James Malcolm)
Philosophy
Einstein's Theories of Relativity and Gravitation: A selection of material from the essays submitted in the competition for the Eugene Higgins prize of $5,000
Bird, J. Malcolm (James Malcolm)
Relativity (Physics)
This every-day experience is a good illustration of the much discussed
Principle of Relativity, in its simplest form. If there were no
jolting, the motion of the train, straight ahead at a uniform speed,
would have no effect at all upon the relative motions of objects
inside it, nor on the forces required to produce or change these
motions. Indeed, the motion of the earth in its orbit, which is free
from all jar, but a thousand times faster, does not influence even
the most delicate apparatus. We are quite unconscious of it, and
would not know that the earth was moving, if we could not see other
bodies outside it. This sort of relativity has been recognized for
more than two centuries and lies at the bottom of all our ordinary
dynamical reasoning, upon which both science and engineering are based.
But there are other things in nature besides moving bodies,--above
all, light, which is intimately related to electricity and magnetism,
and can travel through empty space, between the stars. It moves at
the enormous speed of 186,000 miles per second, and behaves exactly
like a series of vibrations or "waves." We naturally think of it as
travelling through some medium, and call this thing, which carries
the light, the "ether."
Can we tell whether we are moving through this ether, even though all
parts of our apparatus move together, and at the same rate? Suppose
that we have two mirrors, $M$ and $N$, at equal distances, $d$, from a
point $O$, but in directions at right angles to one another, and send
out a flash of light from $O$. If everything is at rest, the reflected
flashes will evidently come back to $O$ at the same instant, and the
elapsed time will be $2d/c$ seconds if $c$ is the velocity of light.
But suppose that $O$, $M$, and $N$ are fastened to a rigid frame work,
and all moving in the direction $O M$, with velocity $V$. The light
which goes from $O$ toward $M$, at the speed $c$, will overtake it
with the difference of their speeds, $c-v$, taking $d/(c-v)$ seconds to
reach $M$. On the way back, $O$ will be advancing to meet it, and the
return trip will occupy $d/(c+v)$ seconds. The elapsed time for the
round trip comes out $2cd/(c^2-v^2)$ seconds, which is longer than
when the system was at rest--the loss of time in the "stern chase"
exceeding the saving on the return.
The light which is reflected from N has a different history. When
it starts, $O$ and $N$ have certain positions in the ether, $O_1$
and $N_1$. By the time it reaches the mirror, this is at $N_2$, and
$O$ is at $O_2$, and when it returns, it finds $O$ at $O_3$. The
distances for the outward and inward journeys are now equal, but
(as is obvious from the figure), each of them is greater than $d$,
or $O_2N_2$, and the time for the round trip will be correspondingly
increased. A simple calculation shows that it is $2d/\sqrt{c^2-v^2}$.
Public-domain text, read in full here on John Shaqi.
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