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)
In the first place, if an observer measures the velocity of light,
he must always get the same result, no matter how fast he and his
apparatus are moving, or in what direction (so long as the motion is
uniform and rectilinear). This sounds harmless; but let us go back to
the Michelson-Morley experiment where the light came back in exactly
the same time from the two mirrors. If the observer supposes himself
to be at rest, he will say that the distances $O M$ and $O N$ were
equal. But if he fancies that the whole universe is moving in the
direction $O M$, he will conclude that $M$ is nearer to $O$ than $N$
is--for if they were equidistant, the round-trip would take longer in
the first case, as we have proved. If once more he fancies that the
universe is moving in the direction $O N$, he will conclude that N is
nearer to $O$ than $M$ is. His answer to the question which of the
two distances, $O M$ or $O N$, is the greater will therefore depend
on his assumption about the motion of the universe as a whole.
Similar complications arise in the measurement of time. Suppose that
we have two observers, $A$ and $B$, provided with clocks which run
with perfect uniformity, and mirrors to reflect light signals to one
another. At noon exactly by his clock, $A$ sends a flash of light
towards $B$. $B$ sees it come in at 12:01 by his clock. The flash
reflected from $B$'s mirror reaches $A$ at 12:02 by $A$'s clock. They
communicate these observations to one another.
If $A$ and $B$ regard themselves as being at rest, they will agree that
the light took as long to go out as it did to come back, and therefore
that it reached $B$ at just 12:01 by $A$'s clock, and that the two
clocks are synchronized. But they may, if they please, suppose that
they (and the whole universe) are moving in the direction from $A$
towards $B$, with half the speed of light. They will then say that
the light had a "stern chase" to reach $B$, and took three times as
long to go out as to come back. This means that it got to $B$ at 1
1/2 minutes past noon by $A$'s clock, and that $B$'s clock is slow
compared with $A$'s. If they should assume that they were moving with
the same speed in the opposite direction, they would conclude that
$B$'s clock is half a minute fast.
Hence their answer to the question whether two events at different
places happen at the same time, or at different times, will depend
on their assumption about the motion of the universe as a whole.
Public-domain text, read in full here on John Shaqi.
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