EINSTEIN'S 1905 POLYGON SCENARIO

http://www.fourmilab.ch/etexts/einstein/specrel/www/
ON THE ELECTRODYNAMICS OF MOVING BODIES, by A. Einstein, June 30, 1905: "From this there ensues the following peculiar consequence. If at the points A and B of K there are stationary clocks which, viewed in the stationary system, are synchronous; and if the clock at A is moved with the velocity v along the line AB to B, then on its arrival at B the two clocks no longer synchronize, but the clock moved from A to B lags behind the other which has remained at B by tv^2/2c^2 (up to magnitudes of fourth and higher order), t being the time occupied in the journey from A to B. It is at once apparent that this result still holds good if the clock moves from A to B in any polygonal line, and also when the points A and B coincide."

That is, as the moving clock (initially at A) travels along a closed polygonal line and is consecutively checked against synchronous stationary clocks spread out on the line (the clock at B is just one of them), its reading is getting smaller and smaller than theirs.

This conclusion is correct in the sense that it validly follows from Einstein's 1905 two postulates (no matter whether the postulates are true or false). Yet in Einstein's relativity time dilation is mutual so there is another correct conclusion that Einstein somehow failed to notice in 1905: The STATIONARY clock at B lags behind MOVING clocks going round the polygon. Consider synchronous clocks (ants in the picture) travelling with constant speed along a closed polygonal line (the clock initially at A is just one of them) and passing a single stationary clock (the clock at B) located in the middle of one of the sides of the polygon:

http://www.wpclipart.com/page_frames...e_portrait.png

Einstein's relativity predicts that the single stationary clock runs more slowly than the travelling clocks it consecutively meets, in the sense that the difference between the reading of the travelling clock just being met and that of the single stationary clock increases with the number of meetings.

If clocks are replaced with ants, Einstein's relativity predicts that the single stationary ant is gradually getting younger than the travelling brothers it consecutively meets, in the sense that the difference between the age of the travelling ant just being met and that of the single stationary ant increases with the number of meetings.

Clearly the two legitimate moieties of mutual time dilation - "single moving clock lags behind multiple stationary clocks" and "single stationary clock lags behind multiple moving clocks" contradict each other in Einstein's 1905 polygon scenario. We have reductio ad absurdum, which means that at least one of Einstein's 1905 postulates is false.

Einsteinians can try to save Einstein's relativity by proving that "single stationary clock lags behind multiple moving clocks" is wrong in the closed-polygonal-line scenario (a proof that should already have been given in Einstein's 1905 article).

Pentcho Valev

http://www.amazon.com/Relativity-Its.../dp/0486406768
Relativity and Its Roots, Banesh Hoffmann, p. 105: "In one case your clock is checked against two of mine, while in the other case my clock is checked against two of yours, and this permits us each to find without contradiction that the other's clocks go more slowly than his own."

Implication: If a single clock is consecutively checked against multiple clocks spread out on a closed line, then Einstein's relativity predicts that the single clock runs more slowly than the multiple clocks, no matter whether the single clock is moving and the multiple clocks stationary or, vice versa, the single clock is stationary and the multiple clocks moving along the closed line.

This implication is inherently contradictory and fatal for Einstein's relativity but Einsteinians have managed to unsting it. Its proof is easy for "moving single clock, stationary multiple clocks" and somewhat more difficult for "stationary single clock, moving multiple clocks", for the simple reason that in the latter case the presence of noninertiality requires additional arguments. In Einstein's schizophrenic world such additional arguments would not be advanced, let alone discussed, and Einsteinians have safely sent the case "stationary single clock, moving multiple clocks" to oblivion.

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In 1920 Einstein compared a stationary clock placed at the center of a rotating disk and a clock fixed on and moving with the rim. He concluded that the moving clock runs more slowly than the stationary one:

http://www.bartleby.com/173/23.html
Albert Einstein: "...the clock at the centre of the disc has no velocity, whereas the clock at the edge of the disc is in motion relative to K in consequence of the rotation. According to a result obtained in Section XII, it follows that the latter clock goes at a rate permanently slower than that of the clock at the centre of the circular disc, i.e. as observed from K."

Einstein failed to notice that, in his inconsistent theory, the conclusion that the moving clock runs more slowly than the stationary one has an equipollent counterpart: the stationary clock runs more slowly than the moving one. Next I am going to show that the two conclusions are equally legitimate in Einstein's relativity.

Let us replace the stationary clock at the center of the disk (Clock 1 in the picture) with another clock (Clock 3 in the picture) sitting at rest outside the disk but very close to the rim so that its reading can be checked against readings of clocks fixed on and moving with the rim (the last requirement - "very close to the rim" - is not fulfilled in the picture where Clock 3 is shown to be somewhat distant from the rim):

http://www.upscale.utoronto.ca/PVB/Key/relgen1.jpg

Now we can imagine many copies of the stationary Clock 3 spread out around the disk so that the clock moving with the rim (Clock 2) is consecutively checked against them. According to Einstein's relativity, the checking will show that the moving Clock 2 runs more slowly than the stationary copies of Clock 3.

We can also imagine many copies of the moving Clock 2 spread out all over the rim so that the clock sitting at rest outside the disk (Clock 3) is consecutively checked against them. What will the checking show? Does the stationary Clock 3 run slower or faster than the moving copies of Clock 2?

Here Einsteinians utter a single phrase - "clocks moving with the rim are not inertial, you cannot synchronize them" - then stick their heads in the sand and remain so until the danger is over. The phrase is highly dishonest because Einstein has actually answered the question without caring whether or not clocks moving with the rim are inertial (that is, based entirely on special relativity), and his answer is: the stationary Clock 3 runs FASTER than the moving copies of Clock 2 (see the reference above).

Instead of sticking their heads in the sand, Einsteinians should PROVE Einstein's conclusion that the stationary Clock 3 runs FASTER than the moving copies of Clock 2. The problem is that, for the scenario in which a single stationary clock consecutively meets multiple moving clocks and is checked against them, Einstein's relativity says the opposite of what Einstein teaches in the reference above: the stationary Clock 3 runs SLOWER than the moving copies of Clock 2. By increasing the perimeter of the disc while keeping the linear speed of the rim constant, we can convert moving clocks fixed on the rim into VIRTUALLY INERTIAL clocks (the "gravitational field" they experience is reduced to zero). Now Einstein's relativity says that, as the stationary Clock 3 consecutively meets two (or more) moving copies of Clock 2 and is checked against them, the checking will show that it runs MORE SLOWLY than them:

http://www.amazon.com/Relativity-Its.../dp/0486406768
Relativity and Its Roots, Banesh Hoffmann, p. 105: "In one case your clock is checked against two of mine, while in the other case my clock is checked against two of yours, and this permits us each to find without contradiction that the other's clocks go more slowly than his own."

The absurdity is obvious - the stationary Clock 3 runs both FASTER than the moving copies of Clock 2 (Einstein's original conclusion) and SLOWER than the moving copies of Clock 2 (an equally legitimate conclusion that Einsteinians hate to think of). We just have reductio ad absurdum: the consequent (mutual time dilation) is absurd, therefore the antecedent (Einstein's 1905 constant-speed-of-light postulate) is false.

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