Green's Paradox
in [Relativity]
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From: Androcles on 5 Aug 2010 21:42 http://www.androcles01.pwp.blueyonder.co.uk/GreensParadox.htm
From: Uncle Ben on 5 Aug 2010 23:59 On Aug 5, 9:42 pm, "Androcles" <Headmas...(a)Hogwarts.physics_z> wrote: > http://www.androcles01.pwp.blueyonder.co.uk/GreensParadox.htm For my version (which agrees with Einstein), see www.greenba.com, "Relativity" link, article entitled "Androcles and the Einstein Expansion" Uncle Ben
From: harald on 7 Aug 2010 07:58 On Aug 6, 5:59 am, Uncle Ben <b...(a)greenba.com> wrote: > On Aug 5, 9:42 pm, "Androcles" <Headmas...(a)Hogwarts.physics_z> wrote: > > > http://www.androcles01.pwp.blueyonder.co.uk/GreensParadox.htm > > For my version (which agrees with Einstein), see > > www.greenba.com, > "Relativity" link, > article entitled "Androcles and the Einstein Expansion" > > Uncle Ben "The requested URL /www.greenba.com was not found on this server. " Harald
From: Uncle Ben on 7 Aug 2010 10:03 On Aug 7, 7:58 am, harald <h...(a)swissonline.ch> wrote: > > For my version (which agrees with Einstein), see > > > www.greenba.com, > > "Relativity" link, > > article entitled "Androcles and the Einstein Expansion" > > > Uncle Ben > > "The requested URL /www.greenba.comwas not found on this server. " > > Harald Androcles and the "Einstein Expansion" In the newsgroup sci.physics.relativity (s.p.r) there is often found among the cranks and trolls who populate it, to the extent of perhaps 80%, one particularly obnoxious character who calls himself Androcles, a name from Greek mythology. Androcles published in 2009 a new interpretation of Einstein's derivation of the Lorentz Contraction, claiming that by virtue of a simple confusion, Einstein actually proved that a moving rod is longer, not shorter, than the same rod at rest. Androcles tells us that Einstein was insane. The old-timers in s.p.r. advise one not to respond to Androcles's rantings, but I enjoy the verbal jousting that goes on there, and I think that unless one confronts him from time to time, the occasional newcomer to the newsgroup will be gulled into taking hm seriously for a while. I also believe that when an opponent refuses to admit an error, one should make the error so clear to everyone else, that his obstinacy can be seen to be a character flaw, not a defense of his position. The reader will find in these pages a link to Einstein's first paper on relativity. His discussion of the length of moving objects can be found in Section 4, just after he derives the Lorentz Transformation. In that section Einstein's demonstration of the contraction caused by speed is done in three dimensions in a few lines so clearly that no one can be misled. Earlier however in Section 3, he has to derive the Lorentz Transformation and concludes with the four equations of the LT, three for space and one for time. The equation corresponding to the x axis of coordinates is xi = beta(x - vt) which Androcles seizes upon. (The meaning of the variables is described in the following:). Einstein's argument In his setup for Section 3, Einstein considers two inertial frames of reference. (The term "inertial" had not been invented at that time, so he describes them as "frames in which Newton's laws of motion hold."). Let K be a system of coordinates x,y,z,t which he calls the "stationary" system. Let k be a system that coincides with K at t=0 but is moving towards the +x direction and has coordinates designated by greek letters xi, eta, zeta, and tau. Let a measuring rod lie on the x axis of K (and the xi axis of k). It is at rest in k (and therefore moving in K). In k, the ends of the rod are at xi=0 and xi=L0 although Einstein does not use the notation L0.. The question is posed, how long is the rod when measured in K, given its rest length L0 in k. Einstein describes the relation of the two systems of coordinates: the origin of k is moving in K as x=vt, where v is the relative speed and t is the time in system K. That is where one end (say, the left end) of the rod lies. The right end of the rod is at some farther point, say x', (measured in K from the origin of k), on the x axis. Thus x' is a constant we may also call L, the desired unknown. Thus the rod lies in K between x=vt and x= vt + L. (Einstein uses x' instead of L. He writes the equation as x' = x - vt, where x is set fixed as the K coordinate of the right end of the rod). In k, the rod lies at rest on the xi axis between xi=0 and, say, xi = L0 (which Einstein writes as simply xi.). Deriving the Lorentz Transformation equations, Einstein finds that xi = beta * x', or using our terminology, in which Einstein's "beta" is now universally called "gamma", L0 = gamma * L So L = L0/gamma This is the Lorentz Contraction. Enter Androcles Androcles agrees that xi = gamma*x', but he mixes up x' and xi and concludes that L = L0*gamma, which he describes as the Einstein Expansion. When confronted with this, Androcles starts dodging. He says he will discuss this if others will discuss something else first (the difference between closing speed and relative speed, which are identical pre-relativity). I complied, whereupon he proposed another challenge before he would face his error. I drew the line and called him a coward for not being able to acknowledge his error. Hence this article. UB 7/13/2009 ..
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