Frequently Asked Questions
About
Paradox #1
Series #7
by:
Paul
Marmet
Many
people know the "Twin Paradox". It shows that, if one of the twins
travels at large velocities, his age appears younger than the other
twin, who did not travel. This application of relativity is well known,
but of course such experiment has never been done and cannot be
verified experimentally. It is more challenging to consider a
paradox
that has already been verified experimentally. Let us examine the
"Earth Paradox".
------------------------------------------------------
Earth Paradox
Let us use a very accurate method of measuring the size of the Earth.
From a location on the equator, let us use the international primary
standard of length to measure a distance of about 300 meters along the
equator. In fact, the exact distance is really 299.792458 meters so
that this distance is exactly one microsecond-light. At
that
distance, we draw a line on the ground. Then we repeat the same
measurement along the Earth equator for another similar distance of 300
meters, and we draw another line. This procedure is repeated thousands
of times until the full circle around the Earth is completed and the
experimenter arrives again at the point of departure. This is
illustrated below on figure 1. We find that the number of
lines drawn
on the Earth equator is about 133 425.
In the second part of the experiment, we send a beam of light around
the Earth equator. We can anticipate that at each microsecond, the beam
of light passes each line drawn on the ground, because they have been
spaced by one microsecond-light (by definition). When we send the
beam
eastward, light goes across 133425 lines, and therefore take 133425
microseconds to go around the world, passing each line every
microsecond. Also, when we send the beam westward, the beam of
light
also passes one line every micro-second, so that light takes 133425 to
complete the trip around the world. Of course, the experiment is well
done and light is traveling inside a vacuum pipe in which air has been
completely pumped out.
However,
following the Sagnac effect published in 1914 it has been shown
experimentally that light takes a longer time to go around the world
Eastward than Westward. The Sagnac effect is well known. It has been
added in the Global Positioning System (GPS) to determine time and
coordinates on Earth. The Sagnac effect is also used in optical
gyroscopes. It is very well extablished.
----------------------------------
How can the experiment above with light moving across each of the
133425 lines every microsecond be compatible with the observed Sagnac
effect? How can the time taken, to go around the world be longer when
going Eastward then Westward, since there are the same number of lines
(133425)? Light takes exactly one microsecond to go between lines
(by
definition).
===================
The answer to this problem will be given (and explained) here as soon
as I have time to write it down, probably during the first part of
2000. Make a bookmark if you
want to remember the Web address.
Explanation now published at "The GPS and the Constant Velocity of
Light"
Of
course, it is not a real paradox. It is physical reality. The
answer
is logical and uses conventional logic (I mean without the magic
space-time distortion).
Note: Don't tell me that it is because the Earth
is rotating. So what?
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llustration of the
Paradox
Figure 1
Paradox #1 December, 1999
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