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From: John Jones on 4 Mar 2010 19:17
Pentcho Valev wrote:
> For a century human rationality has been procrusteanized into
> conformity with Einstein's idea that, for a non-rotating observer, the
> periphery of a rotating disk is LONGER than the periphery of a non-
> rotating disk:
>
> 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
>
> http://www.pitt.edu/~jdnorton/teaching/HPS_0410/chapters/general_relativity_pathway/index.html
> John Norton: "If one has a circular disk at rest in some inertial
> reference system in special relativity, the geometry of its surface is
> Euclidean. That is quite obvious, but it will be useful to spell out
> what that means in terms of the outcomes of measuring operations. If
> the disk is ten feet in diameter, then it means that we can lay 10
> foot long rulers across a diameter. Euclidean geometry tells us that
> the circumference is pi x 10 feet, which is about 31 feet. That means
> that we can traverse the full circumference of the disk by laying 31
> rulers round the outer rim of the disk. What if we have a disk of the
> same diameter of 10 feet but in rapid uniform rotation with respect to
> the first disk? Things will go rather differently. Assume that this
> rotating disk is covered with foot long rulers that move with it.
> These rulers are just like the ones that were used to survey the non-
> rotating disk. (That means that an observer moving with the rod on the
> rotating disk would find it to be identical to one of the rulers used
> to survey the non-rotating disk.) What will be the outcome of
> surveying the geometry of this rotating disk with those rods? An
> observer who is not rotating with the disk would judge all these
> rulers to have shrunk in the direction of their motion. That means
> that, according to this new observer, the surveying of the disk would
> proceed differently. Ten rulers would still be needed to span the
> diameter of the disk. Since the motion of the disk is perpendicular to
> the rulers laid out along a diameter, the length of these rulers would
> be unaffected by the rotation. 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. Thus we measure the circumference of the
> rotating disk to be greater than 31 feet, the Euclidean value. In
> other words, we find that the geometry of the disk is not Euclidean.
> The circumference of the disk is more than the Euclidean value of pi
> times its diameter."
>
> In fact this is a second procrusteanization. Initially human
> rationality is forced to believe (Paul Ehrenfest was a believer who
> did not undergo the second procrusteanization) that, for a non-
> rotating observer, the periphery of the rotating disk should be
> SHORTER than the periphery of a non-rotating disk, as Einstein's
> special relativity predicts:
>
> http://en.wikipedia.org/wiki/Ehrenfest_paradox
> "The Ehrenfest paradox concerns the rotation of a "rigid" disc in the
> theory of relativity. In its original formulation as presented by Paul
> Ehrenfest 1909 in the Physikalische Zeitschrift, it discusses an
> ideally rigid cylinder that is made to rotate about its axis of
> symmetry. The radius R as seen in the laboratory frame is always
> perpendicular to its motion and should therefore be equal to its value
> R0 when stationary. However, the circumference (2*pi*R) should appear
> Lorentz-contracted to a smaller value than at rest, by the usual
> factor gamma. This leads to the contradiction that R=R0 and R<R0."
>
> Recently John Norton informed believers that two different disks
> should be compared, one of them melted, set into rotation and then
> solidified, as Einstein found it suitable to explain in a letter to a
> friend (not elsewhere):
>
> http://www.pitt.edu/~jdnorton/teaching/HPS_0410/chapters/general_relativity_pathway/index.html
> John Norton: "Note what was not said in this account. It did not say
> that we take the first disk and set it into rotation. The reason is
> that it is impossible in relativity theory to take a disk made out of
> stiff material and set it into rotation. If one were to try to do
> this, the disk would contract in the circumferential direction but not
> in the radial direction. As a result, a disk made of stiff material
> would break apart. If we want a rotating disk made of stiff material,
> we need to create it already rotating. Once in a letter on the
> subject, Einstein remarked that a way to get a disk of stiff material
> into rotation is first to melt it, set the molten material into
> rotation and then allow it harden. The rotating disk problem has
> created a rather large and fruitless literature that suggests some
> sort of paradox is at hand. Most of it derives from a failure to
> recognize that a stiff disk cannot be set into uniform rotation
> without destroying it."
>
> Now John Norton will be able to explain to believers how an 80m long
> pole can be trapped inside a 40m long barn (the barn is melted and
> then solidified?) and how a bug can be both dead and alive:
>
> http://math.ucr.edu/home/baez/physics/Relativity/SR/barn_pole.html
> "These are the props. You own a barn, 40m long, with automatic doors
> at either end, that can be opened and closed simultaneously by a
> switch. You also have a pole, 80m long, which of course won't fit in
> the barn. Now someone takes the pole and tries to run (at nearly the
> speed of light) through the barn with the pole horizontal. Special
> Relativity (SR) says that a moving object is contracted in the
> direction of motion: this is called the Lorentz Contraction. So, if
> the pole is set in motion lengthwise, then it will contract in the
> reference frame of a stationary observer.....So, as the pole passes
> through the barn, there is an instant when it is completely within the
> barn. At that instant, you close both doors simultaneously, with your
> switch. Of course, you open them again pretty quickly, but at least
> momentarily you had the contracted pole shut up in your barn. The
> runner emerges from the far door unscathed.....If the doors are kept
> shut the rod will obviously smash into the barn door at one end. If
> the door withstands this the leading end of the rod will come to rest
> in the frame of reference of the stationary observer. There can be no
> such thing as a rigid rod in relativity so the trailing end will not
> stop immediately and the rod will be compressed beyond the amount it
> was Lorentz contracted. If it does not explode under the strain and it
> is sufficiently elastic it will come to rest and start to spring back
> to its natural shape but since it is too big for the barn the other
> end is now going to crash into the back door and the rod will be
> trapped in a compressed state inside the barn."
>
> http://hyperphysics.phy-astr.gsu.edu/Hbase/Relativ/bugrivet.html
> "The bug-rivet paradox is a variation on the twin paradox and is
> similar to the pole-barn paradox.....The end of the rivet hits the
> bottom of the hole before the head of the rivet hits the wall. So it
> looks like the bug is squashed.....All this is nonsense from the bug's
> point of view. The rivet head hits the wall when the rivet end is just
> 0.35 cm down in the hole! The rivet doesn't get close to the
> bug....The paradox is not resolved."
>
> Pentcho Valev
> pvalev(a)yahoo.com
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