🚀 go-pugleaf

For a century Einsteiniana's believers have been forced to believe
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 (18791955). 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."

Believing that the periphery of a rotating disk is LONGER than the
periphery of a non-rotating disk is difficult even for extreme
fanatics since Einstein's special relativity predicts the opposite:
the periphery of the rotating disk should be SHORTER than the
periphery of a non-rotating disk, as Ehrenfest once claimed:

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 R0>R."

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."

Pentcho Valev wrote:

Einsteiniana's fundamental absurdities:

An infinitely long object can be trapped inside an infinitely short
container. So Einsteinians can gloriously obtain any decrease in the
object's volume:

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."

An Einsteinian travelling with the rivet sees the bug squashed. The
bug sees itself alive and kicking:

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."

As two Einsteinians pass each other for the first time, either sees
the other's clock running SLOW (original absurdity). If, however, one
of the Einsteinians is nostalgic and wants to return and see his
brother again, on the second meeting he finds that the other
Einsteinian's clock has in fact been running FAST (superimposed
absurdity):

http://www.fourmilab.ch/etexts/einstein/specrel/www/
ON THE ELECTRODYNAMICS OF MOVING BODIES By A. Einstein June 30, 1905:
"...light is always propagated in empty space with a definite velocity
c which is independent of the state of motion of the emitting body.
(...) 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 we assume that the result
proved for a polygonal line is also valid for a continuously curved
line, we arrive at this result: If one of two synchronous clocks at A
is moved in a closed curve with constant velocity until it returns to
A, the journey lasting t seconds, then by the clock which has remained
at rest the travelled clock on its arrival at A will be tv^2/2c^2
second slow."

Einsteinian clocks placed at different gravitational potentials run at
different rates. The effect is insensitive to the gravitational field
difference (the two clocks may experience virtually the same
gravitational field) and this makes the absurdity particularly
exciting:

http://arstechnica.com/science/news/2010/02/scientists-obtain-highly-accurate-relativity-measurements.ars
"For example, if we synchronize two clocks, take one of them to the
top of a mountain for a while, and then bring it back to where the
other clock is, the clock that sat still will be running behind the
clock that was in the mountains - it was in a more accelerated frame,
and time passed more slowly there."

http://www.people.fas.harvard.edu/~djmorin/book.html
Chapter 14: "The equivalence principle has a striking consequence
concerning the behavior of clocks in a gravitational field. It implies
that higher clocks run faster than lower clocks. If you put a watch on
top of a tower, and then stand on the ground, you will see the watch
on the tower tick faster than an identical watch on your wrist. When
you take the watch down and compare it to the one on your wrist, it
will show more time elapsed."

Pentcho Valev
pvalev@yahoo.com