EINSTEIN'S 1905 POLYGON CONUNDRUM

In his 1905 paper Einstein suggests that, if a single moving clock travels along a closed polygonal line and is consecutively checked against multiple stationary clocks spread out on the line, it will show less and less time elapsed than them:

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 the single moving clock shows less and less time elapsed than the multiple stationary clocks can rigorously be deduced from Einstein's 1905 constant-speed-of-light postulate (and the principle of relativity), on the additional assumption that the acceleration experienced by the moving clock at the apexes of the polygon is immaterial.

The moving clock can then be identified with the travelling twin from the famous twin paradox scenario - one infers that the traveller gets younger and younger than stationary brothers.

The problem is that Einstein's relativity provides an opposite prediction as well, again rigorously deducible from Einstein's 1905 constant-speed-of-light postulate - moving clocks show MORE AND MORE time elapsed than stationary clocks (travellers get OLDER AND OLDER than stationary brothers). Here is a picture that can explain this:

http://www.pitt.edu/~jdnorton/teachi...ty/clocks..gif

According to Einstein's relativity, the single moving clock consecutively meeting synchronous stationary clocks runs more slowly than them, in the sense that the difference between the reading of the stationary clock just being met and that of the single moving clock gradually increases with the number of meetings (in the picture, the moving clock agrees with the reading of the leftmost clock as it passes by but when it passes the rightmost, it reads much less). Yet Einstein's relativity also predicts that, if the single clock is STATIONARY and the multiple synchronous clocks MOVING, it is again the single (stationary this time) clock that is running more slowly (in the sense defined above).

Clearly Einstein's 1905 constant-speed-of-light postulate entails absurdities and should be rejected as false. The speed of light does depend on the speed of the light source, as predicted by Newton's emission theory of light and unequivocally confirmed by the Michelson-Morley experiment in 1887:

http://www.philoscience.unibe.ch/doc...S07/Norton.pdf
John Norton: "These efforts were long misled by an exaggeration of the importance of one experiment, the Michelson-Morley experiment, even though Einstein later had trouble recalling if he even knew of the experiment prior to his 1905 paper. This one experiment, in isolation, has little force. Its null result happened to be fully compatible with Newton's own emission theory of light. Located in the context of late 19th century electrodynamics when ether-based, wave theories of light predominated, however, it presented a serious problem that exercised the greatest theoretician of the day."

http://philsci-archive.pitt.edu/1743/2/Norton.pdf
John Norton: "The Michelson-Morley experiment is fully compatible with an emission theory of light that CONTRADICTS THE LIGHT POSTULATE."

http://books.google.com/books?id=JokgnS1JtmMC
"Relativity and Its Roots" By Banesh Hoffmann, p.92: "Moreover, if light consists of particles, as Einstein had suggested in his paper submitted just thirteen weeks before this one, the second principle seems absurd: A stone thrown from a speeding train can do far more damage than one thrown from a train at rest; the speed of the particle is not independent of the motion of the object emitting it. And if we take light to consist of particles and assume that these particles obey Newton's laws, they will conform to Newtonian relativity and thus automatically account for the null result of the Michelson-Morley experiment without recourse to contracting lengths, local time, or Lorentz transformations. Yet, as we have seen, Einstein resisted the temptation to account for the null result in terms of particles of light and simple, familiar Newtonian ideas, and introduced as his second postulate something that was more or less obvious when thought of in terms of waves in an ether."

Pentcho Valev

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."

If a single clock moving along a closed polygonal line consecutively meets multiple stationary clocks spread out on the line, it lags behind them not because it is moving and they are stationary (this is a misleading explanation devised by Einstein), but because it is SINGLE and they are MULTIPLE. That is the genuine logic inherent in Einstein's relativity:

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."

This means that, according to Einstein's relativity, if the single clock is stationary and if it consecutively meets multiple clocks moving with constant speed along the closed polygonal line, then the stationary clock lags behind the moving clocks.

Clearly Einstein's 1905 constant-speed-of-light postulate entails absurdities and should be rejected as false.

Pentcho Valev