http://www.pitt.edu/~jdnorton/teaching/HPS_0410/chapters/general_relativity/index.html
John Norton (the cleverest Einsteinian): "If one has a disk in special relativity, the geometry of its surface is Euclidean. Say it is ten feet in diameter. That means that we can lay 10 foot long rulers across a diameter. The circumference is pi x 10 feet, which is about 31 feet. That means that we traverse the full circumference by laying 31 rulers round the outer rim of the disk. What if this disk is in rapid uniform rotation and we repeat the measurements? The same ten rulers will measure the diameter. The motion of the disk is always perpendicular to the rulers, so their length is unaffected. That is not so for the rulers laid along the circumference. They lie in the direction of rapid motion. As a result, they shorten and more are needed to cover the full circumference of the disk. The upshot is that we measure the circumference of the disk to be greater than 31 feet, the Euclidean value. In other words, we find that the geometry of is not Euclidean. The circumference of the disk is more than 2pi times its radius. The significance of this thought experiment was great. Through his principle of equivalence, Einstein had found that linear acceleration produces a gravitational field. Now he found that another sort of acceleration, rotation, produces geometry that is not Euclidean."

In 1902, in "La Science et l'hypothèse", Henri Poincaré, in order to justify non-Euclidean geometries, presented a parabole. Bidimensional creatures live on a disk. The disk is heated under its center so that the temperature is high at the center and decreases towards the periphery. The creatures use rigid measuring rods in order to determine the geometry of their world. They know nothing about the heater and accordingly discover that the ratio of the circumference and the diameter is greater than pi. The creatures conclude that Euclidean geometry cannot be true on the disk.

Albert the Plagiarist and John Norton, the cleverest Einsteinian, are forced to distort the concept of Divine Albert's Divine Length Contraction (rulers do undergo length contraction but parts of the disk covered by them do not) in order to appropriate Poincaré's result.

Pentcho Valev
pvalev@yahoo.com

John Norton, the cleverest Einsteinan, and his sillier brothers Einsteinians could solve the famous twin paradox by using the rotating disk:

http://www.amazon.com/Relativity-Its-Roots-Banesh-Hoffmann/dp/0486406768
"Relativity and Its Roots" by Banesh Hoffmann, Chapter 5.
(I do not have the text in English so I am giving it in French)
Banesh Hoffmann, "La relativite, histoire d'une grande idee", Pour la Science, Paris, 1999, p. 126:
"Dans un cas, je compare votre horloge a deux des miennes; dans l'autre, vous comparez la mienne a deux des votres; ceci permet a chacun de nous d'observer, sans absurdite, que l'horloge de l'autre est plus lente que la sienne."
Translation from French: "In one case, I compare your clock with two of mine; in the other case, you compare my clock with two of yours: this allows each of us to observe, without absurdity, that the clock of the other is slower than his own."

The observer referred to by Einstein in the following quotation has two clocks placed on the periphery of a rotating disc, and is going to compare them with a single non-rotating clock (at rest):

http://www.bartleby.com/173/23.html
Albert Einstein (1879-1955). Relativity: The Special and General Theory. 1920. XXIII. Behaviour of Clocks and Measuring Rods on a Rotating Body of Reference:
"An observer who is sitting eccentrically on the disc K' is sensible of a force which acts outwards in a radial direction..."

The only difficulty comes from the fact that the two rotating clocks are not inertial. However, by increasing the diameter of the disc while keeping the linear speed of the periphery constant, one can make them virtually inertial. That is, John Norton, the cleverest Einsteinan, and his sillier brothers Einsteinians will make two simple modifications in Einstein's rotating-disc experiment:

1. The non-rotating clock (at rest in K) is no longer placed at the center of the disc; rather, it is outside the disc but close to the rotating periphery where it can be directly compared with passing rotating clocks fixed on the periphery.

2. John Norton, the cleverest Einsteinan, and his sillier brothers Einsteinians will increase the diameter of the disc while keeping the linear speed of the periphery constant. So clocks fixed on the rotating periphery will become virtually inertial.

The two modifications will allow John Norton, the cleverest Einsteinan, and his sillier brothers Einsteinians to prove, in accordance with Einstein's 1905 light postulate, both:

1. that rotating clocks run slower than non-rotating clocks.

2. that non-rotating clocks run slower than rotating clocks.

Finally, John Norton, the cleverest Einsteinan, and his sillier brothers Einsteinians will see in the dictionary what REDUCTIO AS ABSURDUM means. They may even discover that time dilation is just as absurd as length contraction:

http://hyperphysics.phy-astr.gsu.edu/Hbase/Relativ/bugrivet.html

Pentcho Valev
pvalev@yahoo.com

Slowly but surely the world will realize that the glorious "paradoxes" that converted Albert the Plagiarist into Divine Albert are in fact absurdities and even idiocies:

http://www.personal.leeds.ac.uk/~phl4pv/Topic%20of%20Meeting.htm
"Is Frisch right in saying that `theories do not have a tight deductive structure`?.....Are these scientific conflicts and paradoxes cases of inconsistency as logicians understand the term?"

Pentcho Valev
pvalev@yahoo.com

Don Howard and John Stachel are old members of Einstein criminal cult and know how to lie but Walter Isaacson is still a naive new member who "repeats the common mistake of claiming that the circumference of the disk contracts, while the diameter does not":

http://journals.ucfv.ca/jhb/Volume_3/Volume_3_Howard.pdf
Don Howard: "In his discussion of Einstein’s “rotating disk” thought experiment, an important step on the road to general relativity’s implication of spatio-temporal curvature, Isaacson repeats the common mistake of claiming that the circumference of the disk contracts, while the diameter does not, yielding a ratio of circumference to diameter less than π (p. 192). In fact, it is the yardstick used to measure the circumference that contracts, yielding a circumference seemingly larger than for the stationary disk and thus a ratio of circumference to diameter greater than π. For a careful discussion, see John Stachel, “The Rigidly Rotating Disk as the ‘Missing Link’ in the History of General Relativity,” in Einstein and the History of General Relativity, Don Howard and John Stachel, eds. (Boston: Birkhäuser, 1989), 48-62."

In fact, naive new member Walter Isaacson has just made a valid conclusion based on Einstein's 1905 false light postulate, just like Ehrenfest did long time ago:

http://en.wikipedia.org/wiki/Ehrenfest_paradox

Pentcho Valev
pvalev@yahoo.com