Mathematical Inconsistencies in Einstein's Derivation of the Lorentz Transformation
in [Relativity]
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From: Dirk Van de moortel on 2 Sep 2005 12:43 "Harry" <harald.vanlintel(a)epfl.ch> wrote in message news:4318782c$1(a)epflnews.epfl.ch... > > "Dirk Van de moortel" <dirkvandemoortel(a)ThankS-NO-SperM.hotmail.com> wrote > in message news:G8_Re.184333$ZE2.10260569(a)phobos.telenet-ops.be... > SNIP > > > which shows again, that the moderators have stopped doing > > the job they used to do: > [...]> > http://groups.google.com/group/sci.physics.research/msg/3d6e51f30ecf1d6e > [...]. > > Dirk Vdm > > Thanks for pointing that one out - I look forward to see rebuttals. Can you > back up your implicit claim that that message is wrong? I doubt that you > were there... My explicit claim was that moderators have stopped doing the job they used to do. The responsibility for what you might dream about possible implicit claims of mine is entirely yours. Moderators of a research group who - don't know that Eugene Shubert is a troll who posted his tripe hundreds of time allover Usenet, and - allow Shubert to reply to himself with the name "Perspicacious", and - allow a message by anyone with - the title "That Scoundrel of Relativity, Hermann Minkowski", - the phrase "Poincarý was purposely excluded from the meeting" obviously have stopped doing the job they used to do. That is not an opinion or even a judgement. It is a fact. Dirk Vdm
From: Dirk Van de moortel on 2 Sep 2005 12:47 "Daryl McCullough" <stevendaryl3016(a)yahoo.com> wrote in message news:df9tmd0nd6(a)drn.newsguy.com... > Dirk Van de moortel says... > > >The problem is that Thomas seems to be highly allergic to > >just about everything that could possibly help him understand > >that paper. I think he has adopted as his life motto the phrase > > "I Cannot And Will Not Understand That Paper" > > Which is exactly Androcles' attitude. I'm wondering if they > might be the same person? You're the one with that kind of > psychic power... I have briefly been looking into this. If he carefully prepared this performance during a rather long time, it could be that they are one and the same. But I doubt it - and in this case it doesn't matter of course :-) Dirk Vdm
From: Thomas Smid on 2 Sep 2005 13:06 Daryl McCullough wrote: > Thomas Smid says... > > > >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. > > Yes, I blame you for it. Einstein didn't subtract > > x = ct > > from > > x = -ct > > To get > > 0 = 2ct > > You did. If you didn't understand Einstein's derivation, > you can ask about it, but don't make up your *own* derivation > and then blame its mistakes on *Einstein*. Either stand up > for your own derivation (take the blame if it is wrong), or > else use Einstein's derivation. > > Einstein's equations were these > > (3) x' - ct' = lambda (x-ct) > (4) x' + ct' = mu (x+ct) So how did he get then to (4) in your opinion? (Hint: he got to (3) using his equations (1) and (2)) Thomas
From: Igor on 2 Sep 2005 13:36 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.
From: Todd on 2 Sep 2005 14:22
Einstein's equations (1) and (2) refer specifically to a light pulse that left the origin of both frames at t = t' = 0 and travels in the positive x direction. Thus, (1) and (2) hold only for those events that are illuminated by this particular light pulse. But, note that Einstein assumes that his equation (3) holds for _all_ space-time points (events); even for events in which (1) and (2) are not true. He assumes (3) is 'fulfilled in general'. So, if x and t are the coordinates in the unprimed frame of _any_ event, and if x' and t' are the coordinates of the same event in the primed frame then Einstein is saying that these coordinates will be related by (3). In a sense, Einstein is using (1) and (2) to motivate the general equation (3). Note that (1) and (2) by themselves do not imply (3). For example (1) and (2) would be satisfied if (3) were replaced by (x' - ct')^4 = lambda*(x - ct)^2. By adding the additional assumption that space and time are homogeneous, then the transformation equations must be linear. With this additional assumption, the restricted equations (1) and (2) imply the general equation (3). Repeating this for a light pulse traveling in the negative x direction you get (4) which also is assumed to hold for _all_ space-time events. So, you can apply (3) and (4) to the _same_ event. Thus, you may add and subtract (3) and (4) to get (5). The equations (1) and (2) apply only to events illuminated by the light pulse traveling in the positive x direction. The corresponding equations with a plus sign in front of ct apply only to events illuminated by a different light pulse traveling in the negative x-direction. So the equations with the plus sign apply to a different set of events than (1) and (2), except for the single event where x = x' = t = t' = 0. So, it is not proper to add and subtract these equations to eliminate x or t. Todd |