Mathematical Inconsistencies in Einstein's Derivation of the Lorentz Transformation
in [Relativity]
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From: Ken S. Tucker on 3 Sep 2005 01:43 Bilge (potato head) wrote: > Thomas Smid: > >Many people maintain that the Lorentz transformation is derived > >mathematically consistently and that there is therefore no way to > >challenge SR on internal consistency issues. Is this really so? > > Yes. It's really so. Lorentz boosts and spatial rotations > are obtained in the same derivation. If the lorentz transforms > are mathematically inconsistent, then so is euclidean geometry. > I trust you haven't disproved the pythagorean theorem, since > disproving the pythagoren theorem would be big news and a > ticket to fame. Do you believe the coordinate transformation, > > x' = x cos(A) - y sin(A) > y' = y cos(A) + x sin(A) > > is mathematically inconsistent? If not, then your argument against > the transformation, > > t' = t cosh(A) - x sinh(A) > x' = x cosh(A) - t sinh(A) > > is inconsistent. Ding-bat, x and x' are defined parallel, no relative rotation occurs. Read Minkowski 1908, get updated...sheesh.
From: Bilge on 3 Sep 2005 08:29 Ken S. Tucker: > >Ding-bat, x and x' are defined parallel, no >relative rotation occurs. You must still be upset about losing that game show to a mentally challenged lichen. Does pretending to know something and posting it on usenet make you appear 3lit3 up there in canada? >Read Minkowski 1908, get updated...sheesh. No matter what your neighbors say, brain death is not becoming. Try getting your fashion advice from someone who isnt out to make you look stupid as an entertnaining diversion from shoveling snow.
From: Daryl McCullough on 3 Sep 2005 09:41 Ken S. Tucker says... >Bilge (potato head) wrote: >> Do you believe the coordinate transformation, >> >> x' = x cos(A) - y sin(A) >> y' = y cos(A) + x sin(A) >> >> is mathematically inconsistent? If not, then your argument against >> the transformation, >> >> t' = t cosh(A) - x sinh(A) >> x' = x cosh(A) - t sinh(A) >> >> is inconsistent. > >Ding-bat, x and x' are defined parallel, no >relative rotation occurs. Bilge is talking about a generalized spacetime rotation, using hyperbolic trigonometric functions instead of ordinary trigonometric functions. His equations explain the analogy very well. The parameter A is defined by tanh(A) = v/c. Then cosh(A) = square-root(1/(1-tanh^2(A))) = gamma. sinh(A) = tanh(A) cosh(A) = gamma v/c. So his "rotation" equations are equivalent to the usual Lorentz transformations. -- Daryl McCullough Ithaca, NY
From: Thomas Smid on 3 Sep 2005 10:09 Igor wrote: > Thomas Smid wrote: > > Many people maintain that the Lorentz transformation is derived > > mathematically consistently and that there is therefore no way to > > challenge SR on internal consistency issues. Is this really so? Let's > > for example have a look at Einsteins own derivation (from his book > > 'Relativity: The Special and General Theory') given at > > http://www.bartleby.com/173/a1.html which seems to be a very elegant > > way of deriving the Lorentz transformation. > > > > It is only necessary here to examine the initial equations for this, > > which describe the 'equations of motion of a light signal' in the > > unprimed and primed reference frames, i.e. > > > > (1) x-ct=0 > > (2) x'-ct'=0 > > where c is the speed of light (which obviously has to be a constant >0) > > > > In the same way, the propagation of a signal in the opposite direction > > yields > > (3) x+ct=0 > > (4) x'+ct'=0 > > (note that these equations are not written explicitly in Einstein's > > derivation). > > > > >From equations (1)-(4), the Lorentz transformation is then derived by > > some algebraic manipulations. > > > > But are the above equations mathematically consistent at all? Let's > > subtract equation (1) from (3), which yields > > (5) 2ct=0 > > which means that for any time t>0 > > (6) c=0, > > in contradiction to the requirement that c>0. > > > > This shows that the equations used to derive the Lorentz transformation > > are mathematically inconsistent. The fact that the Lorentz > > transformation itself seems to be mathematically consistent only > > demonstrates that the 'length contractions' and 'time dilations' > > involved in the completion of the derivation are not ony physically > > unacceptable (as argued on my page > > http://www.physicsmyths.org.uk/lightspeed.htm ) but also mathematically > > inconsistent as they contradict the initial definitions. > > > > Thomas > > > Congratulations! You've just discovered that the average speed of two > light rays moving in opposite directions vanishes. What this has to do > with inconsistencies in the Lorentz transformation, which you didn't > even get to, I have no idea. My first reaction was that this had to be > a big joke, since no one could be that stupid. But I could be wrong. c is not an average speed here. It is the usual speed of light (which is being treated as a scalar in Einstein's derivation (in contrast to x, which is being treated as a vector). I have explained it already to Dirk above (post #12 by date) that the two equations x+ct=0 and x-ct=0 can not describe two light rays moving in opposite directions as they can only both be valid for either c=0 (i.e. the signals are not propagating at all) or t=0 (the signals did not have time to propagate) and in either case hence x=0. You effectively have therefore either the equations 0+0*t=0 and 0-0*t=0 or 0+c*0=0 and 0-c*0=0 (the same result is obtained in the primed frame). I wonder how you want to derive the Lorentz transformations from this (or reversely, just insert x=0 and t=0 (or c=0) into the usual Lorentz transformation formula and see what you are left with). Thomas
From: "Androcles" <Androcles@ on 3 Sep 2005 10:17
"Ken S. Tucker" <dynamics(a)vianet.on.ca> wrote in message news:1125726201.180219.286850(a)g49g2000cwa.googlegroups.com... | | Bilge (potato head) wrote: | > Thomas Smid: | > >Many people maintain that the Lorentz transformation is derived | > >mathematically consistently and that there is therefore no way to | > >challenge SR on internal consistency issues. Is this really so? | > | > Yes. It's really so. Lorentz boosts and spatial rotations | > are obtained in the same derivation. If the lorentz transforms | > are mathematically inconsistent, then so is euclidean geometry. | > I trust you haven't disproved the pythagorean theorem, since | > disproving the pythagoren theorem would be big news and a | > ticket to fame. Do you believe the coordinate transformation, | > | > x' = x cos(A) - y sin(A) | > y' = y cos(A) + x sin(A) | > | > is mathematically inconsistent? If not, then your argument against | > the transformation, | > | > t' = t cosh(A) - x sinh(A) | > x' = x cosh(A) - t sinh(A) | > | > is inconsistent. | | Ding-bat, x and x' are defined parallel, no | relative rotation occurs. | Read Minkowski 1908, get updated...sheesh. ROFLMAO! Well done, Ken. I'm still curious about http://www.fourmilab.ch/etexts/einstein/specrel/www/ dtau/dx' + v/(c^2-v^2).dtau/dt = 0. dtau/dx' ??? Ive heard of dx/dt, but dt/dx? Integrate that and time is a function of distance, right? Androcles. |