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Natural Science Forum / Physics / Relativity / December 2005Understanding the Lorentz transformations
Hi , everybody in this group Let's consider light propagation along the x-axis to left and to right from a given point in 2 relatively moving IRS. At any time ,in any of the considered IRS, light travels equal distances to left and to right. Now, in the 2 IRS the law of light propagation is x=ct and x'=ct' respectively. The relation between x and x' is given by the Lorentz transformation. Now, my question is :Does the Lorentz transformation give the equal left and right distances as it should? It seems to me ,at first sight, that it does not. Am I wrong? All the bests for you guys in the coming year ! Happy New Year! LL xray4abc write: > Let's consider light propagation along the x-axis > to left and to right from a given point in 2 relatively moving IRS. But these are already three... > xray4abc write: > [quoted text clipped - 3 lines] > But these are already three... > -- Well,let's count -----------------------------<c-------O-------c>------------------------------- ------------------------------------<c---------O'-v>-----c>------------------------------- I can see 4,............ without glasses.... but 3......? LL xray4abc write: >> xray4abc write: >> [quoted text clipped - 11 lines] > > I can see 4,............ without glasses.... but 3......? Ok O'and v, but what where has O been left? I don't know what O' is. Anyway. > The relation between x and x' is given by the Lorentz transformation. So v> is O? > Now, my question is: Does the Lorentz transformation > give the equal left and right distances as it should? I don't know what you mean. > xray4abc write: > >> xray4abc write: [quoted text clipped - 25 lines] > I don't know what you mean. > -- OK: O- origin of x axis in IRS nr 1 O'- origin of x' axis in IRS nr 2 x=x'=0 when t=t'=0 that is when the light is emitted in both directions v -is the relative speed of the 2 IRS i.e. of the O and O' origins ox and 0'x' should be understood as overlaping lines, though they are shown as separate for a clearer view On the other hand : !!! The posting was not meant as an introduction to the subject ! It was intended for clarifying a relatively subtle aspect of the Lorentz transformations, rarely mentioned in discussions in this group or elsewhere. LL xray4abc write: >> xray4abc write: >> >> xray4abc write: [quoted text clipped - 39 lines] > the Lorentz transformations, rarely mentioned in discussions in this > group or elsewhere. Your diagram is wrong either way, because light propagation is absolute, once light was emitted in O it stays "in place", i.e. their wavefront in all directions, including <c and c>, is invariant to any arbitrary observer, including O'. Secondly, which distances (plural) are you referring to: > > Now, my question is: Does the Lorentz transformation > > give the equal left and right distances as it should? > Hi , everybody in this group > Let's consider light propagation along the x-axis [quoted text clipped - 6 lines] > Now, my question is :Does the Lorentz transformation give the > equal left and right distances as it should? No... Minkowski space-time is anisotropic. << Thus, space-time has a non-isotropic nature which is quite unlike Euclidian space with its positive definite metric.>> http://farside.ph.utexas.edu/teaching/jk1/lectures/node13.html > It seems to me ,at first sight, that it does not. > Am I wrong? You are correct. > All the bests for you guys in the coming year ! > Happy New Year! > > LL http://farside.ph.utexas.edu/teaching/jk1/lectures/node13.html http://arxiv.org/abs/physics/0204034 http://web.mit.edu/8.02t/www/802TEAL3D/teal_tour.htm << Time-independent Maxwell equations Introduction Coulomb's law The electric scalar potential Gauss' law Poisson's equation Ampère's experiments The Lorentz force Ampère's law Magnetic monopoles? Ampère's circuital law Helmholtz's theorem The magnetic vector potential The Biot-Savart law Electrostatics and magnetostatics Time-dependent Maxwell's equations Introduction Faraday's law Electric scalar potential? Gauge transformations The displacement current Potential formulation Electromagnetic waves Green's functions Retarded potentials Advanced potentials? Retarded fields Summary >> http://farside.ph.utexas.edu/teaching/em/lectures/lectures.html Sue... > Hi , everybody in this group > Let's consider light propagation along the x-axis [quoted text clipped - 8 lines] > It seems to me ,at first sight, that it does not. > Am I wrong? If the IRTs have relative speed v and their origins coincide when their clocks are set to 0, the Lorentz transformation is { x' = g ( x - v t ) { t' = g ( t - v x/c^2 ) where g = 1/sqrt(1-v^2/c^2) These equations are valid for all events (x,t), that have coordinates (x',t') in the other frame. Your equation x = c t is only valid for "events on a right ray", so if you want to know whether this is correct, just put the 3 equations together { x = c t { x' = g ( x - v t ) { t' = g ( t - v x/c^2 ) , and anything you find should be valid for all events taking place on that light ray. You find: { x = c t { x' = g ( c t - v t ) = g ( c - v ) t = c g (1-v/c) t { t' = g ( t - v c t /c^2 ) = g (1-v/c) t So you see that indeed x' = c t' Note that, still for the light ray, the 3rd equation gives t' = g (1-v/c) t = sqrt[(c-v)/(c+v)] t which gives with the definition of frequency: f' = sqrt[(c+v)/(c-v)] f for the observed frequencies of the light. The coordinates of the events on the light ray in the other direction satisfy the equation x = -c t and you can easily verify that this gives x' = -c t' In fact, the two transformation equations can be derived by demanding that x = c t transforms to x' = c t' and x = -c t to x' = -c t' > All the bests for you guys in the coming year ! > Happy New Year! Likewise, cheers, Dirk Vdm > > Hi , everybody in this group > > Let's consider light propagation along the x-axis [quoted text clipped - 38 lines] > f' = sqrt[(c+v)/(c-v)] f > for the observed frequencies of the light. Oops... due to sloppy editing, I forgot the most important part of your question - sorry :-) Note that, for the event on the light ray, the 2nd equation gives x' = c g (1-v/c) t = g (1-v/c) x = sqrt[(c-v)/(c+v)] x which tells you that x' <> x meaning that, supposing that the light ray would trigger an event (e.g. an explosion) somewhere, the two observers don't agree on the distance of this explosion. This is not strange, since they also don't agree on the times of this event, as you noticed from the third equation. They only agree on the speed of the light ray that caused the event. Dirk Vdm > Hi , everybody in this group > Let's consider light propagation along the x-axis [quoted text clipped - 13 lines] > > LL tau = (t-vx/c²)/sqrt(1-v²/c²) tau = (t-uy/c²)/sqrt(1-u²/c²) tau = (t-wz/c²)/sqrt(1-w²/c²) xi = (x-vt)/sqrt(1-v²/c²) eta = (y-ut)/sqrt(1-u²/c²) zeta= (z-wt)/sqrt(1-w²/c²) If one is right they all are, if one is wrong they all are. Carry three watches or do not move sideways or ride an elevator. Der alte Hexenmeister. > > Hi , everybody in this group > > Let's consider light propagation along the x-axis [quoted text clipped - 24 lines] > > Der alte Hexenmeister. It seemed so quaint to you that even when its idiocy was pointed out to you, you can't help repeating it? PD Der alte Hexenmeister wrote: > > Hi , everybody in this group > > Let's consider light propagation along the x-axis [quoted text clipped - 24 lines] > > Der alte Hexenmeister. It seemed so quaint to you that even when its idiocy was pointed out to you, you can't help repeating it? PD Carry three watches or do not move sideways or ride an elevator, hypocrite. Der alte Hexenmeister. > > Hi , everybody in this group > > Let's consider light propagation along the x-axis [quoted text clipped - 22 lines] > If one is right they all are, if one is wrong they all are. > Carry three watches or do not move sideways or ride an elevator. Drop the watch and move however you please. *** " as judged from K " *** http://www.bartleby.com/173/12.html Androclese, You are doing a "heck of a job" http://www.google.com/search?hl=en&q=%22heck+of+a+job%22&btnG=Google+Search :-) Sue... Sue... > Der alte Hexenmeister. Der alte Hexenmeister wrote: > > Hi , everybody in this group > > Let's consider light propagation along the x-axis [quoted text clipped - 22 lines] > If one is right they all are, if one is wrong they all are. > Carry three watches or do not move sideways or ride an elevator. Drop the watch and move however you please. *** " as judged from K " *** http://www.bartleby.com/173/12.html I PLACE three metre-rods in the x'-axis of k', the y'axis of k', the z'axis of k' in such a manner that one end (the beginning) coincides with the point x' = 0,0,0, whilst the other end (the end of the rod) coincides with the point x' = 1,0,0, another rod end (the beginning) coincides with the point y' = 0,0,0, whilst the other end (the end of the second rod) coincides with the point y' = 0,1,0, a third rod end (the beginning) coincides with the point x' = 0,0,0, whilst the other end (the end of the third rod) coincides with the point z' = 0,0,1. What is the length of the three by one metre-rods relatively to the system K? In order to learn this, we need only ask where the beginning of the rods and the end of the rods lie with respect to K at a particular time t of the system K. By means of the first equation of the cuckoo transformation the values of these six points at the time t = 0 can be shown to be x(beginning of rod) = 0.sqrt(1-v²/c²) x(end of rod = 1.sqrt(1-v²/c²) y(beginning of rod) = 0.sqrt(1-u²/c²) y(end of rod = 1.sqrt(1-u²/c²) z(beginning of rod) = 0.sqrt(1-w²/c²) z(end of rod = 1.sqrt(1-w²/c²) ---- yada yada yada. Little witch, visit Diagon Alley for new text books, the necromancer Einstein is boiling and bubbling in my cauldron. I'm serving him up for Eye of Newt stew. Androclese, You are doing a "heck of a job" http://www.google.com/search?hl=en&q=%22heck+of+a+job%22&btnG=Google+Search The correct title and name is Professor Androcles Dumbledore, please address to "Headmaster of sci.physics.hogwarts". I receive all email via OWLS. Der alte Hexenmeister. :-) Sue... Sue... > Der alte Hexenmeister. > Der alte Hexenmeister wrote: > > > Hi , everybody in this group [quoted text clipped - 51 lines] > z(beginning of rod) = 0.sqrt(1-w²/c²) > z(end of rod = 1.sqrt(1-w²/c²) Hello Sailor! Nice set of exponents ya got... but you are wearing out the keyboard. Use the pointing device: http://farside.ph.utexas.edu/teaching/jk1/lectures/node13.html ...and save the keyboard for more important things like text adventure games. :o) Sue... > ---- yada yada yada. > Little witch, visit Diagon Alley for new text books, the [quoted text clipped - 17 lines] > > > > Der alte Hexenmeister. |
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