what do you mean by "light rod" (acoustic rod?). do tou see a relationship with "wavelenghth"? thanks sine ira et studio
Hi, Bernhard, You don't by any chance mean "optical black hole" and "acoustic black hole", do you? http://relativity.livingreviews.org/Articles/lrr-2005-12/index.html Chris Hillman
light rod Hi Chris Thanks. Such concepts are far from my grasp! I suppose that the term I have found in the literature "light rod" means a rod generated by a light signal during its propagation along a given direction. Is that definition in accordance with what we find in the literature of the subject? In a given reference frame it is r=ct if the propagation starts at t=0 from the origins. For the same reason r=ut represents the length of an "acoustic rod". In another inertial reference frame we have r'=ct' and r'=u't'. The Lorentz-Einstein transformations enable us to find out a relationship between r and r'. In a wave (optic or acoustic) we can consider a rod of proper lenght Lo that moves with u relative to I and with u' relative to I' its lengths being L and L' respectively. Considering that L and L' represent "wavelengths" we can establish a relationship between them obtaining the transformation equations for wavelengths. Revisiting Moller's approach I have some problems deriving the transformation equations for the physical quantities introduced in order to characterize the wave without using the invariance of the phase The interesting fact is that r(r') transform like frequencies do and not as wavelengths do. Thanks in advance for answers sine ira et studio
Perhaps a light rod is a massless and perfectly rigid rod? Such constructs are sometimes used in the context of filling space with some coordinate grid. Since they are massless and perfectly rigid they do not interact or move, which is useful for a thought experiment. If you had such a rod which was the same length as a particular wavelength of some wave then you could use it to measure how length contraction would affect that wavelength. Whereas if it was neither massless nor perfectly rigid, then such a measurement would acquire an error from the stresses/strains on the material and the gravitational effects. Not sure if that is what your literature is trying to convey, but it seems to fit your description.
Hi, Bernhard, Actually, now I am beginning to wonder whether you might mean "light ray" and "sound wave". Is the language you usually use by any chance German or another language other than English? Literal translations of physics terms in German into English via babelfish can sometimes be misleading. Moller, eh? So http://www.arxiv.org/find/physics/1/au:+Rothenstein_B/0/1/0/all/0/1 must be you, right? I have seen old papers by Moller, but not the term "light rod" or "acoustic rod". Most likely all of my guesses to date about what this term might mean are incorrect. Should I assume that Moller uses this terms in one of his papers? If so, is this a direct translation from a term used by him in another language? Can you give a citation? (Preferably on-line?) Hmm... OK, that sounds like a better guess than mine. Two terms which are often used in the English language gtr literature which might be similar to what you have in mind is "strut" or "pipe". For "strut" see for example p. 558 and 560 of the review paper on exact solutions by Bonnor where he discusses "struts" in the Bach-Weyl vacuum solution (two "Chazy-Curzon particles" held apart by an almost certainly nonphysical singularity in the geometry. I feel that Bonnor is far too lax in suggesting that such struts might be physically acceptable however, since this "strut" in the Bach-Weyl vacuum has no active gravitational mass, yet it is sufficiently strong to hold apart two gravitating objects. This solution, incidently, can be modified by adding a massive infinite uniform density line, which can replace this "massless strut" with two "wires from infinity". However, upon closer examination, these alleged "wires" might also appear to be something other than reasonable idealizations of ordinary wires. The citation is: Bonnor, "Physical Interpretation of Vacuum Solutions of Einstein's Equations. Part I. Time-independent solutions", Gen. Rel. Grav. 24 (1992): 551-573. For "pipe" see papers discussing the Robinson-Trautman solutions, which possess unphysical features answering to this description (were this not so, they would be more useful as exact solutions of astrophysical interest). Chris Hillman