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Paradox #1

Series #7      by: Paul Marmet
( Last checked 2017/01/15 - The estate of Paul Marmet )
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        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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