IS LENGTH CONTRACTION MERELY A GEOMETRICAL PROJECTION?

On Aug 26, 3:39 pm, Tom Roberts wrote in
sci.physics.relativity:

http://groups.google.com/group/sci.p...7d548d1bf664b4

If you are thinking of "length contraction" in SR, then you are
confused. That does not affect any object, it is merely a
geometrical projection between relatively moving frames.

Tom Roberts

Then explain this, Honest Roberts (the quotations below act like the
face of Medusa the Gorgon - on seeing them, Roberts gets petrified and
never replies):

http://math.ucr.edu/home/baez/physic...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://www.quebecscience.qc.ca/Revolutions
Stéphane Durand: "Pour mieux comprendre le phénomène de ralentissement
du temps, il est préférable d'aborder un autre phénomène tout aussi
paradoxal: la contraction des longueurs. Car la vitesse affecte non
seulement l'écoulement du temps, mais aussi la longueur des objets.
Ainsi, une fusée en mouvement apparaît plus courte que lorsqu'elle est
au repos. Là aussi, plus la vitesse est grande, plus la contraction
est importante. Et, comme pour le temps, les effets ne deviennent
considérables qu'à des vitesses proches de celle de la lumière. Dans
la vie de tous les jours, cette contraction est imperceptible.
Cependant, si une fusée de 100 m passait devant nous à une vitesse
proche de celle de la lumière, elle pourrait sembler ne mesurer que 50
m, ou même moins. Bien sûr, la question qui vient tout de suite à
l'esprit est: «Cette contraction n'est-elle qu'une illusion?» Il
semble tout à fait incroyable que le simple mouvement puisse comprimer
un objet aussi rigide qu'une fusée. Et pourtant, la contraction est
réelle... mais SANS COMPRESSION physique de l'objet! Ainsi, une fusée
de 100 m passant à toute vitesse dans un tunnel de 60 m pourrait être
entièrement contenue dans ce tunnel pendant une fraction de seconde,
durant laquelle il serait possible de fermer des portes aux deux
bouts! La fusée est donc réellement plus courte. Pourtant, il n'y a
PAS DE COMPRESSION matérielle ou physique de l'engin."

http://www.parabola.unsw.edu.au/vol3...ol35_no1_2.pdf
Parabola Volume 35, Issue 1 (1999)
LENGTH AND RELATIVITY by John Steele
"The Pole in the Barn Paradox. Now we know about length contraction,
we can invent some amusing uses of it. Suppose you want to fit a 20m
pole into a 10m barn. If the pole were moving fast enough, then length
contraction means it would be short enough. (...) Now comes the
paradox. According to your friend who is going to slam the barn doors
shut just as the end of the pole goes in, the pole is 10m long, and
therefore it fits. However as far as you are concerned, the pole is
still 20m long but the barn is now only 5m long: length contraction
must work both ways by the first postulate. How can you fit this 20m
pole into a 5m barn? This paradox is apparently due to Wolfgang
Rindler of the University of Texas at Dallas. Of course the key to
this is relativity of simultaneity. Your friend sees the front end of
the pole hit the back wall of the barn at the same time as the doors
are closed, but you (and the pole) do not see things this way. You are
standing still and see a 5m long barn coming towards you at some
shockingly high speed. When the back of the barn hits the front of the
pole (and takes the front of the pole with it), the back end of the
pole must still be at rest. It cannot 'know' about the crash at the
front, because the shock wave travelling along the pole telling it
about the crash travels at some finite speed. The front of the barn
has only 15m to go to get to the back of the pole, but the shock wave
has to travel the whole length of the pole, namely 20m. The speed of
the barn is such that even if this shock wave travelled at the speed
of light, it would not get to the back of the pole before the front of
the barn did. Hence in both frames of reference, the pole fits inside
the barn (and will presumably shatter when the doors are closed)."

Pentcho Valev

Honest Roberts, do you really believe that the lengthy red herring you
have devised camouflages the fact that YOU AVOID COMMENTING ON THE
CASE WHERE THE DOORS REMAIN PERMANENTLY CLOSED and the long object
permanently trapped inside the short container? Let me refer you again
to the texts that act like the face of Medusa the Gorgon:

http://math.ucr.edu/home/baez/physic...barn_pole.html
"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://www.parabola.unsw.edu.au/vol3...ol35_no1_2.pdf
Parabola Volume 35, Issue 1 (1999)
LENGTH AND RELATIVITY by John Steele
"Hence in both frames of reference, the pole fits inside the barn (and
will presumably shatter when the doors are closed)."

Pentcho Valev


On Aug 27, 5:39 am, Tom Roberts wrote in
sci.physics.relativity:
Pentcho Valev wrote:
Then explain this, Honest Roberts (the quotations below act like the
face of Medusa the Gorgon - on seeing them, Roberts gets petrified and
never replies):

Wow! You sure have delusions of grandeur!

I generally don't respond to you, not because I am "petrified", but because
there's no point -- you have never shown any understanding of relativity, nor
any desire or ability to learn, so why should I bother trying to teach you when
you have demonstrated a complete inability to learn anything?

"Stupid is as stupid does", and that's how you act around here.

http://math.ucr.edu/home/baez/physic...barn_pole.html
[... 40 meter barn, 80 meter pole, gamma factor 2]

That is a more complicated situation than necessary, so let me simplify it,
because this physical situation is better and the essence of the paradox is
retained (even sharpened, IMHO). We assume the doors can open or close
instantaneously (unrealistic, but this is just a gedanken).

The pole has a proper length of 80 meters, and the barn has a proper length of
40 meters; their relative motion has a gamma greater than 2 (4 is used in the
drawings below). Let the downstream (DS) door of the barn start closed and the
upstream (US) door start open. The pole enters the (open) US door which closes
as soon as the back end of the pole passes by. The (closed) DS door opens just
before the front end of the pole hits it. Because the gamma factor is greater
than 2, both doors are closed for a brief time period WHEN OBSERVED
SIMULTANEOUSLY IN THE BARN FRAME.

In the barn frame, the moving pole is measured to be less than 40 meters long,
which means when both ends are observed SIMULTANEOUSLY IN THE BARN FRAME the
distance between the observed points is less than 40 meters. That means that
while moving it can briefly fit inside the barn with both doors closed (i.e.
both are closed SIMULTANEOUSLY IN THE BARN FRAME). After the DS door opens the
pole just sails away. In the barn frame the US door closes before the DS door opens.

In the pole frame things look considerably different. The barn is measured to be
less than 20 meters long, which means that when both ends are observed
SIMULTANEOUSLY IN THE POLE FRAME the distance between observations is less than
20 meters. As the barn approaches the pole, the US door is open and the DS door
is closed. The barn surrounds the front of the pole, and just before the front
end hits the DS door, that door opens. At this instant in the pole frame (i.e.
observed SIMULTANEOUSLY IN THE POLE FRAME) the US door is still open, and is
less than 1/2 of the way along the pole. Now the barn passes along the pole with
both doors open. When the US door has passed the back end of the pole, the US
door closes. At this instant in the pole frame, the DS door is less than 1/2 of
the length of the pole from the back end of the pole (i.e. observed
SIMULTANEOUSLY IN THE POLE FRAME). After the US door closes the barn just sails
away. In the pole frame the DS door opens before the US door closes.

ASCII art (use fixed-width font). pole is ..., barn is --- for walls and | for
closed doors, open doors are blanks (as is empty space). Scale is 4 columns = 20
meters; gamma = 4; "-" indicates motion at start and end.

BARN FRAME start:

--------
.... - |
--------

BARN FRAME US door closes:

--------
|.... |
--------

BARN FRAME pole center and barn center coincide:

--------
| .... |
--------

BARN FRAME DS door opens:

--------
| ....
--------

BARN FRAME End:

--------
| .... -
--------

POLE FRAME Start:

----
................ - |
----

POLE FRAME DS door opens:

----
................
----

POLE FRAME pole center and barn center coincide:

----
................
----

POLE FRAME US door closes:

----
|................
----

POLE FRAME End:

----
- | ................
----

So there is no contradiction, and both frame agree the pole will get through the
barn, even though both doors of the barn were closed for a brief time period
SIMULTANEOUSLY IN THE BARN FRAME. But both doors are never closed SIMULTANEOUSLY
IN THE POLE FRAME.

As you can see, the difference in simultaneity between the frames is an
essential aspect of this. "Length contraction" is NOT sufficient to describe
this. The relativity of simultaneity resolves the paradox, because the order of
doors opening and closing are DIFFERENT in the two frames.

Yes, "length contraction" IS geometrical projection. Observing the endpoints of
the pole simultaneously in the barn frame PROJECTS the ends of the pole onto the
x coordinate of the barn frame (motion is along x). It should be clear that to
measure the length of a moving object you must mark both ends simultaneously in
your frame and measure the distance between the marks -- nothing else could be
called a measurement of the moving object's length in this frame (some aspect of
its motion would be included in the measurement).

Tom Roberts

On Aug 27, 11:37 pm, Tom Roberts wrote in
sci.physics.relativity:
Pentcho Valev wrote:
Roberts, do you really believe that the lengthy red herring you
have devised camouflages the fact that YOU AVOID COMMENTING ON THE
CASE WHERE THE DOORS REMAIN PERMANENTLY CLOSED and the long object
permanently trapped inside the short container?

I avoid that because nobody knows what would happen -- it requires knowledge of
material properties in a regime that is OUTRAGEOUSLY far removed from any
experience we have. The simplified version I described captures the essence of
the pole and barn paradox without introducing the red herring you concentrate
on: material properties of doors and pole.

It is QUITE clear to me that it is utterly impossible to stop a macroscopic
object moving ~0.9c within a few meters -- the energy density required is TRULY
ENORMOUS [#], and VASTLY beyond what any known material could withstand. And
it's silly to assume this, even in a gedanken.

[#] the kinetic energy of a 10 kilogram pole moving with gamma=4
FAR exceeds all of the hydrogen bombs ever detonated. And you
want to contain all that energy in the doors of a barn.

Yes, it is also impossible to construct doors that open and close
instantaneously, but that is not really essential to the paradox, because one
could omit the doors completely and just observe the locations of the pole ends.

Dishonest Valev, it is necessary to have some knowledge of the subject, so you
can distinguish what is essential from what is not. The material properties of
pole and barn are not. The instantaneous doors are not. The impossibility of
getting a macroscopic object to move so fast is not. But the relationships
between frames and the relativity of simultaneity are essential.

Tom Roberts

Correct, Honest Roberts:

Conditional 1: If Einstein's 1905 constant-speed-of-light postulate is
true, arbitrarily long objects can, IN PRINCIPLE, be trapped inside
arbitrarily short containers and therefore length contraction is NOT
merely a geometrical projection.

Additional unessential assumptions concerning the form and the
properties of object and container allows us to elaborate:

Conditional 2: If Einstein's 1905 constant-speed-of-light postulate is
true, the volume of the long object can, IN PRINCIPLE, be reduced
arbitrarily.

I hope you accept the above conditionals, Honest Roberts. It is up to
any reader to judge the consequent absurd and reject the antecedent,
or to judge the consequent extremely reasonable and sing, with
abandon, "Divine Einstein" and "Yes we all believe in relativity,
relativity, relativity".

Pentcho Valev

On Aug 28, 4:14 pm, Tom Roberts wrote in
sci.physics.relativity:
Pentcho Valev wrote:
Conditional 1: If Einstein's 1905 constant-speed-of-light postulate is
true, arbitrarily long objects can, IN PRINCIPLE, be trapped inside
arbitrarily short containers and therefore length contraction is NOT
merely a geometrical projection.

You need to learn logic, and geometry, and relativity. Your conclusion is false.
Geometrical projection can explain fast-moving long objects trapped briefly
inside a short container, just as it explains carrying a long ladder through a
narrow doorway.

But cannot explain long objects trapped PERMANENTLY inside a short
container, and according to Einsteinians cleverer than you, this
PERMANENT trapping is a valid consequence of Einstein's 1905 constant-
speed-of-light postulate:

http://math.ucr.edu/home/baez/physic...barn_pole.html
"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://www.parabola.unsw.edu.au/vol3...ol35_no1_2.pdf
Parabola Volume 35, Issue 1 (1999)
LENGTH AND RELATIVITY by John Steele
"Hence in both frames of reference, the pole fits inside the barn (and
will presumably shatter when the doors are closed)."

Therefore, Honest Roberts, according to special relativity, length
contraction is NOT merely a geometrical projection.

Pentcho Valev

On Aug 29, 7:54 pm, Tom Roberts wrote in
sci.physics.relativity:
On 8/28/11 8/28/11 - 11:04 AM, Pentcho Valev wrote:

But cannot explain long objects trapped PERMANENTLY inside a short
container,[...]

NOTHING can "explain" that, because it will not and can not happen. As I pointed
out before, the energy densities required are trillions of times larger than
anything remotely feasible.

As I said several times, this is IRRELEVANT to the issues of SR brought up by
the pole and barn paradox. The fact that you obsess over the irrelevancies
indicates how little you understand about SR.

Tom Roberts

Here we go again. Honest Roberts, yesterday I called your attention to
the fact that "long objects trapped PERMANENTLY inside a short
container" is an example taught by Einsteiniana's priests:

http://math.ucr.edu/home/baez/physic...barn_pole.html
"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://www.parabola.unsw.edu.au/vol3...ol35_no1_2.pdf
Parabola Volume 35, Issue 1 (1999)
LENGTH AND RELATIVITY by John Steele
"Hence in both frames of reference, the pole fits inside the barn (and
will presumably shatter when the doors are closed)."

Your brothers Einsteinians also teach that, if Einstein's 1905
constant-speed-of-light postulate is true, a bug can be both dead
(according to one observer) and alive (according to the other):

http://hyperphysics.phy-astr.gsu.edu.../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 far as I remember, you hate this example but, again, don't blame me
- just send a protesting letter to Georgia State University.

Pentcho Valev