Bug and rivet paradox
in [Relativity]
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From: paparios on 14 Jun 2010 22:08 On 14 jun, 21:02, Edward Green <spamspamsp...(a)netzero.com> wrote: > On Jun 14, 3:40 pm, Tom Roberts <tjroberts...(a)sbcglobal.net> wrote: > > > > They are a natural consequence of the relativity of simultaneity. In the plate > > frame the head hits first, and in the rivet frame the foot hits first. > > > The whole point of such paradoxes is to teach the student about the > > non-intuitive aspects of relativity. The difference in simultaneity between > > inertial frames is a major departure from Newtonian mechanics and our everyday > > experience. It is, however, an essential aspect of SR. > > Yes. Got all that. The devil is in the details. > > Still, thinking about it a little more: assume the rivet is initially > unstressed. In the rest frame of the rivet, the initially undeformed > foot of the rivet strikes the bottom of the hole, and a compressional > wave starts toward the head at a speed bounded by c. In the rest frame > of the plate, the initially undeformed head hits first, and a > dilational wave starts towards the foot of the rivet at a speed > bounded by c. (The "bounded by c" obviously applies to either frame in > both cases). The ordering of these events varies, but they both must > be observed in either frame, and hence the two waves meet at an event > somewhere in the middle of the rivet. After that all bets are off. :) This is purely an academic discussion. In the real situation, a 10 gram rivet moving at v=0.6c=180000 km/sec, has a lot of kinetic energy, which means both the bug, the rivet, the hole and the wall where the hole is, will all be destroyed in the subsequent explosion (being the equivalent of about 55 kg of TNT). Miguel Rios
From: Androcles on 14 Jun 2010 22:22 <paparios(a)gmail.com> wrote in message news:e87fcd35-a702-4538-ac2a-33520447f8ed(a)c10g2000yqi.googlegroups.com... On 14 jun, 21:02, Edward Green <spamspamsp...(a)netzero.com> wrote: > On Jun 14, 3:40 pm, Tom Roberts <tjroberts...(a)sbcglobal.net> wrote: > > > > They are a natural consequence of the relativity of simultaneity. In the > > plate > > frame the head hits first, and in the rivet frame the foot hits first. > > > The whole point of such paradoxes is to teach the student about the > > non-intuitive aspects of relativity. The difference in simultaneity > > between > > inertial frames is a major departure from Newtonian mechanics and our > > everyday > > experience. It is, however, an essential aspect of SR. > > Yes. Got all that. The devil is in the details. > > Still, thinking about it a little more: assume the rivet is initially > unstressed. In the rest frame of the rivet, the initially undeformed > foot of the rivet strikes the bottom of the hole, and a compressional > wave starts toward the head at a speed bounded by c. In the rest frame > of the plate, the initially undeformed head hits first, and a > dilational wave starts towards the foot of the rivet at a speed > bounded by c. (The "bounded by c" obviously applies to either frame in > both cases). The ordering of these events varies, but they both must > be observed in either frame, and hence the two waves meet at an event > somewhere in the middle of the rivet. After that all bets are off. :) This is purely an academic discussion. In the real situation, a 10 gram rivet moving at v=0.6c=180000 km/sec, =========================================== Bwahahahahahahahahaha! "Real" situation, a 10 gram rivet moving at v=0.6c=180000 km/sec!!!!!
From: Tom Roberts on 15 Jun 2010 10:06 Edward Green wrote: > Still, thinking about it a little more: assume the rivet is initially > unstressed. In the rest frame of the rivet, the initially undeformed > foot of the rivet strikes the bottom of the hole, and a compressional > wave starts toward the head at a speed bounded by c. In the rest frame > of the plate, the initially undeformed head hits first, and a > dilational wave starts towards the foot of the rivet at a speed > bounded by c. (The "bounded by c" obviously applies to either frame in > both cases). The ordering of these events varies, but they both must > be observed in either frame, and hence the two waves meet at an event > somewhere in the middle of the rivet. After that all bets are off. :) No. You must pick one frame and describe the situation entirely in that frame. Then, if you wish, you can select another frame and describe the situation entirely in that frame. The "dilational" and "compressional" waves are in different frames, and attempting to combine them in one description is wrong. Remember that a "dilational wave" merely describes the location and motion of atoms over time. Ditto for a "compressional wave". Since the times are different in the two frames, especially in the way they map onto spatially-separated events, it's no surprise that the locations and motions of atoms are different for the two interpretations of time. This is a non-problem -- it is wholly explained by the difference in simultaneity in the two frames. There is a sound wave inside the rivet in every frame; its direction and nature ("dilational"/"compressional") depends on which frame one uses to describe it. I use a directional horn to send a sound wave to the east. Relative to an eastward-moving supersonic jet that same sound wave moves to the west. Such motions are frame dependent. Tom Roberts
From: kenseto on 15 Jun 2010 10:22 On Jun 12, 7:14 pm, Edward Green <spamspamsp...(a)netzero.com> wrote: > I'm puzzled by some aspects of the bug and rivet paradox > > http://hyperphysics.phy-astr.gsu.edu/Hbase/Relativ/bugrivet.html > > Evidently the rivet definitely hits the bottom of the hole, because > this is seen in the rivet's frame, and hence must be an event > observable in any frame. > > Also, evidently, the head of the rivet hits the plate, since this is > observable in the plate's frame, and hence must be an event observable > in any frame. > > What I'm puzzled about is the intermediate descriptions: in the rivet > frame, a compressional wave travels up the shaft of the rivet until > the plate hits the head. In the plate frame, a _dilational_ wave seems > to travel down the rivet from the opposite direction until the foot of > the rivet hits the backstop. How to reconcile these descriptions? You are paintiung yourself into a corner with your bogus assumptions. Here's what SR predicts: The length of the rivet is 2' long at its rest frame. The depth of the hole is 2' at its rest frame. The bug is 0.1' tall. Gamma is 2. From the rivet point of view the hole is 2'/2=1' tall Therefore the bug is already squished to dead just before the head of the rivet hits the wall of the hole. From the hole point of view the rivet is 2'/2=1' long. Therefore the bug is still alive just before the head of the rivet hits the wall of the hole. The above contradictory claims by the hole and the rivet is the result of the interpretation that length contraction in SR is physical. The more learned SRians realized that so they invented the interpretation that length contraction is a geometric projection effect and such effect is frame dependent.....this interpretation overcomes the contradictory claims of SR. In real life there is no physical length contraction or physical length expansion of a meter stick. New physics says that the physical length of a meter stick remains the same in all frames. However, the light-path length of a meter stick moving wrt an observer is predicted to be shorter or longer than the light-path length of the observer's meter stick.and the light-path length of the observer's meter stick is assumed to be its physical length. This interpretation resolves all the paradoxes of SR. This interpretation is included in a new theory of relativity called IRT. IRT includes SRT and LET as subsets. However, unlike SRT, the equations of IRT are valid in all environments, including gravity. IRT is described in the following link: http://www.modelmechanics.org/2008irt.dtg.pdf Ken Seto
From: Inertial on 15 Jun 2010 21:46 "kenseto" <kenseto(a)erinet.com> wrote in message news:bea1cb1a-6a7b-4398-b76d-29dea89f6f7f(a)37g2000vbj.googlegroups.com... > On Jun 12, 7:14 pm, Edward Green <spamspamsp...(a)netzero.com> wrote: >> I'm puzzled by some aspects of the bug and rivet paradox >> >> http://hyperphysics.phy-astr.gsu.edu/Hbase/Relativ/bugrivet.html >> >> Evidently the rivet definitely hits the bottom of the hole, because >> this is seen in the rivet's frame, and hence must be an event >> observable in any frame. >> >> Also, evidently, the head of the rivet hits the plate, since this is >> observable in the plate's frame, and hence must be an event observable >> in any frame. >> >> What I'm puzzled about is the intermediate descriptions: in the rivet >> frame, a compressional wave travels up the shaft of the rivet until >> the plate hits the head. In the plate frame, a _dilational_ wave seems >> to travel down the rivet from the opposite direction until the foot of >> the rivet hits the backstop. How to reconcile these descriptions? > > You are paintiung yourself into a corner with your bogus assumptions. > Here's what SR predicts: > The length of the rivet is 2' long at its rest frame. > The depth of the hole is 2' at its rest frame. > The bug is 0.1' tall. > Gamma is 2. That's not what it *predicts* .. but yes .. they are some figures on which to base the prediction Lets see if you understand what SR predicts .. or conveniently leave some facts out to confuse. > From the rivet point of view the hole is 2'/2=1' tall Yeup > Therefore the bug is already squished to dead just before the head of > the rivet hits the wall of the hole. Yeup. From rivets point of view .. two key events: Bottom of rivet his bug and it dies THEN head of rivet hits wall. > From the hole point of view the rivet is 2'/2=1' long. > Therefore the bug is still alive just before the head of the rivet > hits the wall of the hole. Yeup. From rivets point of view .. two key events: Head of rivet hits wall THEN Bottom of rivet his bug and it dies > The above contradictory claims by the hole and the rivet Not contradictory .. just different. > is the result > of the interpretation that length contraction in SR is physical. It is .. as much as any length is physical > The > more learned SRians realized that so they invented the interpretation > that length contraction is a geometric projection effect and such > effect is frame dependent..... It is not an 'interpretation' it is what SR says happens. Its not a matter of interpretation. And of course it is frame dependent .. Just like clock ticking rates and momentum and velocity etc etc > this interpretation overcomes the > contradictory claims of SR. There are no contradictions .. Just different order of events. > In real life there is no physical length contraction or physical > length expansion of a meter stick. Prove it, > New physics says that the physical length of a meter stick remains > the > same in all frames. The intrinsic proper length does. But what we call 'length' (ie spatial separation between two extremes at a given time) is frame dependent > However, the light-path length [snip nonsense from non-theory IRT]
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