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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 |
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IS LENGTH CONTRACTION MERELY A GEOMETRICAL PROJECTION?
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 |
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IS LENGTH CONTRACTION MERELY A GEOMETRICAL PROJECTION?
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 |
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IS LENGTH CONTRACTION MERELY A GEOMETRICAL PROJECTION?
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 |
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