EINSTEIN IDIOCIES: THE ROTATING DISK

http://www.pitt.edu/~jdnorton/teachi...ity/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

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.../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.../bugrivet.html

Pentcho Valev

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/~phl...%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

On Jun 17, 7:22 am, Pentcho Valev wrote:
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/~phl...%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


yes

On Tue, 17 Jun 2008 04:33:48 -0700 (PDT), Pentcho Valev
wrote:


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

I'd say the solution to this paradox is to distinguish between two
kinds of length contraction as follows:

I. Suppose the bug and its hole are at rest in 3-space and that the
rivet is moving.

Then:

1) In the frame of the bug, the Lorentz transform of the length of the
rivet represents a genuine length contraction.

2) In the frame of the rivet, the Lorentz transform of the depth of
the hole represents only an apparent length contraction--necessary to
keep calculations consistent.

So the bug is safe in this case.

II. Suppose the rivet is at rest in 3-space and the bug and its hole
are moving.

In this case, the situation is reversed and the bug gets squashed.

III. Suppose the bug and rivet are both moving through 3-space.

Then:

1) In the frame of the bug, the Lorentz transform of the length of the
rivet represents a length contraction that is part genuine and part
only apparent.

2) Ditto for the Lorentz transform for the depth of the hole in the
frame of the rivet.

So in this case the outcome would depend on which is moving faster
through 3-space.

I don't see any way to resolve this paradox with the spacetime
concept.


-- Surfer








Pentcho Valev

On 17 Jun, 08:33, Pentcho Valev wrote:
http://www.pitt.edu/~jdnorton/teachi...s/general_rela...
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.

All the relativity paradoxes result in making assumptions at one point
about perfect rigidity. Relativity limits rigidity, the speed of sound
cannot exceed that of light. This is no exception. A disc moving at
relativistic speed will expand because it is elastic. The fucticious
light inextensible string must in a relativistic context have a speed
of sound = c.

In point of fact in real life (the non ideal case) odd things happen
when we exceed the speed of sound NOT light.

Odd point - a civil war bullet (slower than sound in water) travells
further in water than high velocity bullets which all disintegrate.


- Ian Parker

Ian Parker wrote:
All the relativity paradoxes result in making assumptions at one point
about perfect rigidity.

Assumptions?
perfect rigiidity is what you use to determine a straight line
for accurate measurements and without such perfect rigidity
and "physical measurements", there is no "physical proof".

You have bendy lightwave proof only in anything that uses light beams
to measure stuff that is all messed up with gravity and curving
of the light.
you have a rubber ruler
nothing more.



Relativity limits rigidity, the speed of sound
cannot exceed that of light. This is no exception. A disc moving at
relativistic speed will expand because it is elastic. The fucticious
light inextensible string must in a relativistic context have a speed
of sound = c.

Yes,
limit rigidity so the "theory" can not be wrong to itself".



In point of fact in real life (the non ideal case) odd things happen
when we exceed the speed of sound NOT light.

Very true, but not odd enough that classical stuff, when done
correctly, does show "how" it all happens like such.


Odd point - a civil war bullet (slower than sound in water) travells
further in water than high velocity bullets which all disintegrate.

slow and efficient.. wins the race..
the turtles are everywhere!
LOL

--
James M Driscoll Jr
Spaceman

On Jun 17, 12:39*pm, "Spaceman"
wrote:
Ian Parker wrote:
All the relativity paradoxes result in making assumptions at one point
about perfect rigidity.

Assumptions?
perfect rigiidity is what you use to determine a straight line
for accurate measurements and without such perfect rigidity
and "physical measurements", there is no "physical proof".

You have bendy lightwave proof only in anything that uses light beams
to measure stuff that is all messed up with gravity and curving
of the light.
you have a rubber ruler
nothing more.


Relativity limits rigidity, the speed of sound
cannot exceed that of light. This is no exception. A disc moving at
relativistic speed will expand because it is elastic. The fucticious
light inextensible string must in a relativistic context have a speed
of sound = c.

Yes,
limit rigidity so the "theory" can not be wrong to itself".


In point of fact in real life (the non ideal case) odd things happen
when we exceed the speed of sound NOT light.

Very true, but not odd enough that classical stuff, when done
correctly, does show "how" it all happens like such.


Odd point - a civil war bullet (slower than sound in water) travells
further in water than high velocity bullets which all disintegrate.

slow and efficient.. wins the race..
the turtles are everywhere!
LOL

--
James M Driscoll Jr
Spaceman

Actually, the answer is 42.

Harry C.

On Jun 17, 3:44*pm, john wrote:
On Jun 17, 7:22 am, Pentcho Valev wrote:

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/~phl...%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


yes

W. H. Newton-Smith, The rationality of science, Routledge, London,
1981, p. 229:

"A theory ought to be internally consistent. The grounds for including
this factor are a priori. For given a realist construal of theories,
our concern is with verisimilitude, and if a theory is inconsistent it
will contain every sentence of the language, as the following simple
argument shows. Let ‘q’ be an arbitrary sentence of the language and
suppose that the theory is inconsistent. This means that we can derive
the sentence ‘p and not-p’. From this ‘p’ follows. And from ‘p’ it
follows that ‘p or q’ (if ‘p’ is true then ‘p or q’ will be true no
matter whether ‘q’ is true or not). Equally, it follows from ‘p and
not-p’ that ‘not-p’. But ‘not-p’ together with ‘p or q’ entails ‘q’.
Thus once we admit an inconsistency into our theory we have to admit
everything. And no theory of verisimilitude would be acceptable that
did not give the lowest degree of verisimilitude to a theory which
contained each sentence of the theory’s language and its negation."

The deduction performed by Newton-Smith is unacceptable to a physicist
since « from ‘p’ it follows that ‘p or q’ » is not a mathematical
deductive argument (see a definition of mathematical deductive
argument in http://www.wbabin.net/philos/valev9.pdf ). Still the
central idea – that the lowest degree of verisimilitude should be
given to an inconsistency – is correct.

Pentcho Valev

wrote:
On Jun 17, 12:39 pm, "Spaceman"
wrote:
Ian Parker wrote:
All the relativity paradoxes result in making assumptions at one
point about perfect rigidity.

Assumptions?
perfect rigiidity is what you use to determine a straight line
for accurate measurements and without such perfect rigidity
and "physical measurements", there is no "physical proof".

You have bendy lightwave proof only in anything that uses light beams
to measure stuff that is all messed up with gravity and curving
of the light.
you have a rubber ruler
nothing more.


Relativity limits rigidity, the speed of sound
cannot exceed that of light. This is no exception. A disc moving at
relativistic speed will expand because it is elastic. The fucticious
light inextensible string must in a relativistic context have a
speed of sound = c.

Yes,
limit rigidity so the "theory" can not be wrong to itself".


In point of fact in real life (the non ideal case) odd things happen
when we exceed the speed of sound NOT light.

Very true, but not odd enough that classical stuff, when done
correctly, does show "how" it all happens like such.


Odd point - a civil war bullet (slower than sound in water) travells
further in water than high velocity bullets which all disintegrate.

slow and efficient.. wins the race..
the turtles are everywhere!
LOL

--
James M Driscoll Jr
Spaceman

Actually, the answer is 42.

It is!
It is always 42!
but don't think too hard about it.
Mysterious things just smack you in the head if you do.
LOL


--
James M Driscoll Jr
Spaceman