Mathematical Inconsistencies in Einstein's Derivation of the Lorentz Transformation
in [Relativity]
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From: Thomas Smid on 2 Sep 2005 09:38 Dirk Van de moortel wrote: > Combining the equations like he did (algebraicly "solving a system > of two equations with two unknowns") is the analytic geometry > equivalent of finding the interesection between the light paths: > { x - c t = 0 > { x + c t = 0 > ==> > { 2 c t = 0 > { x - c t = 0 > ==> > { t = 0 > { x = 0 > So the intersection of the signals happens at time t = 0 at > distance x = 0. Dirk, I am sorry to say you have a flawed understanding of maths. These two equations are *only* valid at x=0 and t=0, so they can not possibly describe light paths. According to your 'method' you might as well conclude from the two equations (1) x=1 (2) x=0 and by inserting (1) into (2) that (3) 1=0 Thomas
From: Thomas Smid on 2 Sep 2005 09:42 Daryl McCullough wrote: > You can't subtract (1) from (3), since x in (1) refers > to a *different* event than the x in (3). It's not the > same value of x, and it's not the same value of t. > Think about it in terms of a *car* driving down a > road that runs East-West at 10 meters/second. Don't blame me for it. I am merely reproducing Einstein's derivation at http://www.bartleby.com/173/a1.html here. Thomas
From: russell on 2 Sep 2005 09:46 Thomas Smid wrote: > Daryl McCullough wrote: > > > You can't subtract (1) from (3), since x in (1) refers > > to a *different* event than the x in (3). It's not the > > same value of x, and it's not the same value of t. > > Think about it in terms of a *car* driving down a > > road that runs East-West at 10 meters/second. > > Don't blame me for it. I am merely reproducing Einstein's derivation at > http://www.bartleby.com/173/a1.html here. Huh? You told us that equation 3 was not "explicitly" in Einstein's paper. (I wonder why that was?) So, you are not telling the truth here, are you? > > Thomas
From: Thomas Smid on 2 Sep 2005 09:54 russ...(a)mdli.com wrote: > Thomas Smid wrote: > > Daryl McCullough wrote: > > > > > You can't subtract (1) from (3), since x in (1) refers > > > to a *different* event than the x in (3). It's not the > > > same value of x, and it's not the same value of t. > > > Think about it in terms of a *car* driving down a > > > road that runs East-West at 10 meters/second. > > > > Don't blame me for it. I am merely reproducing Einstein's derivation at > > http://www.bartleby.com/173/a1.html here. > > Huh? You told us that equation 3 was not "explicitly" > in Einstein's paper. (I wonder why that was?) So, you > are not telling the truth here, are you? You should wonder why Einstein was not explicitly writing down my equations (3) and (4) but merely stated 'If we apply quite similar considerations to light rays which are being transmitted along the negative x-axis...' and then went on straight to the combined equation. Maybe it was because he did not want the mathematical inconsistency to be that obvious? Thomas
From: russell on 2 Sep 2005 10:04
Thomas Smid wrote: > russ...(a)mdli.com wrote: > > Thomas Smid wrote: > > > Daryl McCullough wrote: > > > > > > > You can't subtract (1) from (3), since x in (1) refers > > > > to a *different* event than the x in (3). It's not the > > > > same value of x, and it's not the same value of t. > > > > Think about it in terms of a *car* driving down a > > > > road that runs East-West at 10 meters/second. > > > > > > Don't blame me for it. I am merely reproducing Einstein's derivation at > > > http://www.bartleby.com/173/a1.html here. > > > > Huh? You told us that equation 3 was not "explicitly" > > in Einstein's paper. (I wonder why that was?) So, you > > are not telling the truth here, are you? > > You should wonder why Einstein was not explicitly writing down my > equations (3) and (4) but merely stated 'If we apply quite similar > considerations to light rays which are being transmitted along the > negative x-axis...' and then went on straight to the combined equation. > Maybe it was because he did not want the mathematical inconsistency to > be that obvious? The reason is that he would have had to use different notation (to distinguish the different x's and t's) making the presentation unnecessarily awkward. Though actually it is something of an abuse of notation to use "x" at all to mean a specific value of x. (Daryl's use of "L", for example, is better.) It's quite a customary abuse, but unfortunately it seems to confuse the hell out of cranks who read Einstein's paper. You are not the first. |