There are other curious things about the velocity of light. One is,
that no material body can ever travel as fast as light, however great
may be the force to which it is exposed, and however long the force
may act. An illustration may help to make this clear. At exhibitions
one sometimes sees a series of moving platforms, going round and round
in a circle. The outside one goes at four miles an hour; the next
goes four miles an hour faster than the first; and so on. You can
step across from each to the next; until you find yourself going at a
tremendous pace. Now you might think that, if the first platform does
four miles an hour, and the second does four miles an hour relatively
to the first, then the second does eight miles an hour relatively to
the ground. This is an error; it does a little less, though so little
less that not even the most careful measurements could detect the
difference. I want to make quite clear what it is that I mean. I will
suppose that, in the morning, when the apparatus is just about to
start, three men with ideally accurate chronometers stand in a row, one
on the ground, one on the first platform, and one on the second. The
first platform moves at the rate of four miles an hour with respect
to the ground. Four miles an hour is 352 feet in a minute. The man on
the ground, after a minute by his watch, notes the place on the ground
opposite the man on the first platform, who has been standing still
while the platform carried him along. The man on the ground measures
the distance on the ground from himself to the point opposite the
man on the first platform, and finds it is 352 feet. The man on the
first platform, after a minute by his watch, notes the point on his
platform opposite to the man on the second platform. The man on the
first platform measures the distance from himself to the point opposite
the man on the second platform; it is again 352 feet. Problem: how far
will the man on the ground judge that the man on the second platform
has traveled in a minute? That is to say, if the man on the ground,
after a minute by his watch, notes the place on the ground opposite
the man on the second platform, how far will this be from the man on
the ground? You would say, twice 352 feet, that is to say, 704 feet.
But in fact it will be a little less, though so little less as to
be inappreciable. The discrepancy is owing to the fact that the two
watches do not keep perfect time, in spite of the fact that each is
accurate from its owner’s point of view. If you had a long series of
such moving platforms, each moving four miles an hour relatively to the
one before it, you would never reach a point where the last was moving
with the velocity of light relatively to the ground, not even if you
had millions of them. The discrepancy, which is very small for small
velocities, becomes greater as the velocity increases, and makes the
velocity of light an unattainable limit. How all this happens, is the
Public-domain text, read in full here on John Shaqi.
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