An apology to Androcles
in [Relativity]
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From: Inertial on 31 Jul 2010 18:56 "Androcles" wrote in message news:CUV4o.15279$hz1.3631(a)hurricane... >Ie we see the moving rod as LONGER than it is measured in THE rest frame. >End of fuckin' story, no further mental masturbation needed. The length of the rod measured by a ruler AT REST in the moving frame (where the rod is also AT REST) will indeed be longer than the length of the moving rod as measured in the 'rest' FRAME (which is MOVING relative to the rod). That just what SR says .. the length of a rod in its own frame will be LONGER than what a 'rest' frame will measure a 'moving' rod to be. The measurement of a 'moving' rod from the 'rest' frame is shorter that the rods length in its rest frame.
From: blackhead on 31 Jul 2010 19:06 On 31 July, 17:02, Uncle Ben <b...(a)greenba.com> wrote: > On Jul 31, 10:50 am, blackhead <larryhar...(a)softhome.net> wrote: > > > On 31 July, 03:49, Uncle Ben <b...(a)greenba.com> wrote: > > >........... > > You may be right, but I don't think so. > > I've spent enough time on Androcles for a while. He is fun to tease, > but he is hopeless to teach. If you want to take over, have at him! > > Hint: He reads the section on length of rods of Einstein 1905, > relativity, up to the critical paragraphs (a) and (b) but does not > then read (a) and (b). > > The introductory paragraph introduces a rod to be measured and > establishes that its rest length is L. > > Paragraph (a) then sets the rod in motion with a comoving observer > repeating the same measurement, and, by the principles of relativity, > getting the same answer (the critical part Andy doesn't read) that > results in xi=L. Operations (a) and (b) are in section 1 Definition of Simultaneity. Here he introduces the idea of measurements of length being frame dependent because of the relativity of simultaneity, deriving the result in section 4. > Only then in (b) does E. approach the measurement of the now-moving > rod, resulting in the value of x'. (For a long time A. thought that > x' was the result of an unmentioned LT, instead of a moving point (x) > in K at the far end of the moving rod relative to the moving near end > at the origin (vt) of system k, yielding the desired (constant) length > x-vt in K of the rod.) I don't see x' mentioned in (a), (b) or $4. On the other hand, I understand what you and Androcles are doing now which seems very direct compared to how the transformations are usually used. You start with: xi = x'/sqrt( 1 - v^2/c^2)---(1) where x' = x - vt Each end of the rod is stationary at the origin and at xi = L in the moving frame k. In the stationary frame K at time t, one end of the rod will be at vt, the other at x(t), both moving at velocity v. So equation (1) can be used to find the value of xi = L one end is at using(x-vt) = L'. i.e: xi = L = x'/sqrt(1 - v^2/c^2) = L'/sqrt(1 - v^2/c^2). Which looks OK to me. > Uncle Ben
From: ben6993 on 31 Jul 2010 19:22 On Jul 31, 11:42 pm, "Inertial" <relativ...(a)rest.com> wrote: > "ben6993" wrote in message > > news:04c03713-3840-4dd5-b9bd-0a32c3298392(a)w12g2000yqj.googlegroups.com... > > On Jul 31, 3:49 am, Uncle Ben <b...(a)greenba.com> wrote: > > > > > > > On Jul 30, 9:39 pm, blackhead <larryhar...(a)softhome.net> wrote: > > > > On 31 July, 01:46, Uncle Ben <b...(a)greenba.com> wrote: > > > > > On Jul 30, 8:34 pm, mpc755 <mpc...(a)gmail.com> wrote: > > > > > > On Jul 30, 3:10 pm, Uncle Ben <b...(a)greenba.com> wrote: > > > > > > > An apology to Androcles > > > > > > > I had thought that the Einstein Expansion, proclaimed by Androcles > > > > > > in > > > > > > sci.physics.relativity, was an error of confusing frames of > > > > > > reference. But I was wrong. > > > > > > > In his 1905 relativity paper, Einstein showed that x' = xi/gamma, > > > > > > where x' is the length of a moving rod with respect to a > > > > > > stationary > > > > > > frame of reference K and xi is the length of the moving rod with > > > > > > respect to a frame k comoving with it. My difference with > > > > > > Androcles > > > > > > was that I claimed that xi is the proper length L of the rod and > > > > > > the > > > > > > shorter x' is a contracted length L/gamma. > > > > > > > I thought that Androcles had these two backward. But no, he has > > > > > > persuaded me otherwise; He agrees that x' is shorter than xi, but > > > > > > he > > > > > > insists that x' is L and xi is an expanded length Lgamma. The > > > > > > proper > > > > > > length of the rod in k increases because of the existence of > > > > > > another > > > > > > frame of reference K moving with respect to it. (This other frame > > > > > > K is > > > > > > called the "stationary" frame in Einstein's paper, but it can be > > > > > > considered moving the other way with respect to the rest frame k > > > > > > of > > > > > > the rod.) > > > > > > > This startling fresh idea would never have occurred to me without > > > > > > Androcles's guidance. > > > > > > > It seems strange that a nearby frame of reference K, by its > > > > > > relative > > > > > > motion, can expand a rod with respect to the rod's own proper > > > > > > frame k, > > > > > > while the rod maintains a constant length with respect to K > > > > > > itself. > > > > > > > Imagine me in a Concorde (k) flying over you on the ground (K) > > > > > > sucking > > > > > > on my cigar that had length L when I bought it. It seems strange > > > > > > that > > > > > > to you the cigar has length L, but because I am flying within > > > > > > your > > > > > > frame of reference, my cigar is Lgamma long. In fact, because of > > > > > > your > > > > > > frame of reference, the Concord is stretched by gamma for me but > > > > > > not > > > > > > for you. I have no idea why my cigar is now longer, because I have > > > > > > no > > > > > > idea that you are down there. > > > > > > > It seems odd, doesn't it. Perhaps Androcles will explain it to > > > > > > us. > > > > > > > Uncle Ben > > > > > > In this rare instance of someone abandoning their constant > > > > > delusional > > > > > denial state of existence, any chance you can take it a step further > > > > > and answer the following? > > > > > > Will the ripple eventually reach the Earth? If not then why not? > > > > > > 'Hubble Finds Ghostly Ring of Dark > > > > > Matter'http://www.nasa.gov/mission_pages/hubble/news/dark_matter_ring_featur... > > > > > > "Astronomers using NASAs Hubble Space Telescope got a first-hand > > > > > view > > > > > of how dark matter behaves during a titanic collision between two > > > > > galaxy clusters. The wreck created a ripple of dark matter, which is > > > > > somewhat similar to a ripple formed in a pond when a rock hits the > > > > > water." > > > > > > The ripple will eventually reach the Earth and this is evidence dark > > > > > matter exists from the galaxy cluster to the Earth. This is evidence > > > > > dark matter is the medium of space in which light waves propagate.. > > > > > > Pressure exerted towards matter by dark matter displaced by the > > > > > matter > > > > > is gravity.- Hide quoted text - > > > > > > - Show quoted text - > > > > > I have no idea, and this thread is abought the Einstein Expansion.- > > > > Hide quoted text - > > > > > - Show quoted text - > > > > Androcles rechristened the space LT as "Einstein's expansion" formula: > > > > xi = x'/sqrt(1 - v^2/c^2) with x' = x-vt > > > 1905 paper. > > > Used correctly, it transforms x coordinates of the same event between > > > different frames, not lengths directly. Androcles plugs in lengths for > > > xi, x' without considering what's involved in measuring a length. For > > > a start, it involves measuring space coordinates at the *same* time > > > and subtracting them from one another to get a length, if it's moving > > > in that frame. If the end points remain at the same locations for all > > > time, then simultaneity doesn't matter.- Hide quoted text - > > > > - Show quoted text - > > > Some ng history, Blackhead: > > > This subject has been discussed often, and in some discussions > > Androcles ha progressed all the way to a length comparison, following > > Einstein's 1905 paper. I now believe he has got it all right except > > for the final step, which is assigning values to x' and xi. He agrees > > in the meaning of the variables x' and xi, including correctly that > > x' < xi. Where he goes off the track is to insist that x'=L, and > > therefore xi= Lgamma. The correct path is to assign xi=L and conclude > > that x' = L/gamma. > > > The absurdity of this error is the point of this thread. > > > Uncle Ben- Hide quoted text - > > > - Show quoted text - > >I have been led through all this a few months ago, line at a time of > >the relevant section of the 1905 paper, by Androcles. Thank you > >Androcles. But my memory of the details have faded. > > You poor thing .. falling for androcles lies > > >OK, so Androcles is finding that Einstein's beta is 2 for v = 0.866c. > >In other words, the length of a rod measured in frame k (using xi and > >tau) is twice as big as it would be if measured in frame K (using x > >and t). That's fine isn't it? > > Yeup .. it is measured shorter from the moving frame. > > >The rod is stationary withinin frame k > > So k is the rest frame, and the rod is twice the length that it is measured > to be in the moving frame K > > >so its length is easily > >measured as L within frame k. (Einstein's paper uses x' instead of L.) > >So xi=L gives the rod length in frame k. > >Now what is the rod length in frame K? Since xi=2x, then x=0.5L. Ie > >we see the moving rod as shorter than it is measured in its rest frame. > > You just got it backwards .. the same as Ancy .. he can't do simple math and > things the x/2 is twice as big as x- Hide quoted text - > > - Show quoted text - >so its length is easily >measured as L within frame k. (Einstein's paper uses x' instead of L.) >So xi=L gives the rod length in frame k. >Now what is the rod length in frame K? Since xi=2x, then x=0.5L. Ie >we see the moving rod as shorter than it is measured in its rest frame. "You just got it backwards .. the same as Ancy .. he can't do simple math and things the x/2 is twice as big as x " Length is xi=L as measured with a ruler in the rod's own rest frame k. Ie rest length=L Apparent length is x= L/2 as calculated in the observer's frame K. That means I see the rod shortened as it moves past me. Have I really got it backwards?
From: Inertial on 31 Jul 2010 19:31 "ben6993" wrote in message news:60b7087f-eb8e-4dd1-b0c5-9f56c03d8f41(a)j8g2000yqd.googlegroups.com... > Have I really got it backwards? Sorry. . I misread your post. No .. you have it correct. If the moving length is half the rest length, then the rest length is double the moving length.
From: ben6993 on 31 Jul 2010 19:36
On Aug 1, 12:31 am, "Inertial" <relativ...(a)rest.com> wrote: > "ben6993" wrote in message > > news:60b7087f-eb8e-4dd1-b0c5-9f56c03d8f41(a)j8g2000yqd.googlegroups.com... > > > Have I really got it backwards? > > Sorry. . I misread your post. No .. you have it correct. If the moving > length is half the rest length, then the rest length is double the moving > length. Thanks. I am glad I don't have to re-think that one through again. |