Mathematical Inconsistencies in Einstein's Derivation of the Lorentz Transformation
in [Relativity]
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From: Dirk Van de moortel on 3 Sep 2005 16:53 "Thomas Smid" <thomas.smid(a)gmail.com> wrote in message news:1125771403.451459.272490(a)g43g2000cwa.googlegroups.com... > Todd wrote: > > "Thomas Smid" <thomas.smid(a)gmail.com> wrote in message > > news:1125762269.196256.173470(a)z14g2000cwz.googlegroups.com... > > > Daryl McCullough wrote: > > > > >>There is some parameters > > >> A,B,D,E that are functions of the relative velocity between > > >> the two frames such that for all events e > > >> > > >> x'(e) = A x(e) + B ct(e) > > >> ct'(e) = D x(e) + E ct(e) > > > > > OK, with x'(e1) = ct'(e1) your original equations > > > x'(e1) = A x(e1) + B ct(e1) > > > ct'(e1) = D x(e1) + E ct(e1) > > > result therefore in > > > A x(e1) + B ct(e1) = D x(e1) + E ct(e1) > > > > Yes, as long as you're considering events where x'(e1) = ct'(e1). > > > > > and since this must for all times t > > > D=A > > > E=B > > > > No, this is an incorrect conclusion. > > Yes, I noticed this already and I had already deleted my post before > you posted it. I shall be posting a revised version of this. Indeed, you will have to find another conclusion to draw from that fumble "since this must for all times t". Go ahead - entertain us some more ;-) Dirk Vdm > > Thomas >
From: Dirk Van de moortel on 3 Sep 2005 17:03 "Thomas Smid" <thomas.smid(a)gmail.com> wrote in message news:1125758423.977597.162290(a)g44g2000cwa.googlegroups.com... > Bilge 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. > > As far as I am aware Which is, as far as I have experienced, just as far as the tip of your nose. > the experimental discovery of the invariance of c > was big news at the time, and it exactly amounts to the fact that the > speed of light can not be represented vectorially in the usual sense. Of course, it needs a Thomas Smid Sense. > It is a scalar that has a fixed value in all reference frames. Voila. Someone who claims http://users.pandora.be/vdmoortel/dirk/Physics/Fumbles/MScPhD.html and doesn't know the difference between a vector and its magnitude. > Everything else is just a futile attempt to apply usual geometrical > principles where they can not be applied. As far as explaining these concepts to an imbecile like you is concerned, I fully agree that "futile" is an appropriate choice of words. Carry on now... Dirk Vdm
From: Ken S. Tucker on 3 Sep 2005 17:06 Androcles wrote: > "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? Most of original AE SR paper has been superseded by GR 11 years later once the defects were recognized, but it contains some very valuable and original insight like the light sphere I posted to Daryl. The silly transform bilge (aka potato head) quotes by rotating x relative to x' is misguided. AE states...(from Androcle's ref)... "Let us in ``stationary'' space take two systems of co-ordinates, i.e. two systems, each of three rigid material lines, perpendicular to one another, and issuing from a point. Let the axes of X of the two systems coincide, and their axes of Y and Z respectively be parallel. Let each system be provided with a rigid measuring-rod and a number of clocks, and let the two measuring-rods, and likewise all the clocks of the two systems, be in all respects alike." Specifically see, "axes of X of the two systems coincide" that means the rotation analogy is WRONG. (PERIOD). bilge and his gang of kooks often use junk science and math to confuse really interested people who have a genuine interest in relativity, many of whom paid taxes for LIGO, GR-b etc. and want to know why that's good. Relativity isn't simple, but why confuse it? Ken S. Tucker
From: Mike on 3 Sep 2005 17:19 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. Thomas Before getting into the mathematical inconsistency of Al's derivation of the LT, can you solve this problem: 2 chicken make 2 eggs in 2 days How may eggs 10 chicken in 10 days make? > > 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 The problem with Al's derivation of LT is that he postulates a linear transformation between the space time points in K and K': "A light-signal, which is proceeding along the positive axis of x, is transmitted according to the equation x = ct or x - ct = 0 (1) Since the same light-signal has to be transmitted relative to k' with the velocity c, the propagation relative to the system k' will be represented by the analogous formula x' - ct' = 0 (2) Those space-time points (events) which satisfy (1) must also satisfy (2). Obviously this will be the case when the relation (x'-ct') = lambda (x - ct) (3)" quoted from: http://www.bartleby.com/173/a1.html of course, no justification is provided for (3), except of the fact that it fits the final objective of the derivation. But in general, lambda can be any function f of x, x', t, t', where f not equal to infinity, and still (3) holds for all space time events that satisfy (1) and (2). Now, this demonstrates that in order to derive the LT, arbitrary assumption must be made about how the events are related in K and K'. Or, in a better way, the events are forced to relate according to (3). The proper way is to show that (3) must hold uniquely and lambda is a constant. Because by asserting (3), although the LT is derived, restrictions are placed on the structure of spacetime. But this cannot be done and it shows that the deduction is based on an explicit hypothesis. But Al did not fully comprehend the laws of logic and mathematical reasoning because he was a crank. In a mathematical derivation, any assumptions made must be carried through and stated along with the conclusion, to say the least. Of course, SR is corroborated by experiments but SR' is too. SR' is any compensatory theory which involves some other function in place of lambda in (3). the argument is of course, that SR is more elegant. I know of some lunatics that dress very elegantly. Mike
From: "Androcles" <Androcles@ on 3 Sep 2005 17:37
"Ken S. Tucker" <dynamics(a)vianet.on.ca> wrote in message news:1125778182.667429.232500(a)g47g2000cwa.googlegroups.com... | | Daryl McCullough wrote: | > 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 | | >From Androcles post...quote AE, | | "let a spherical wave be emitted therefrom, and be propagated with the | velocity c in system K. If (x, y, z) be a point just attained by this | wave, then | | x2+y2+z2=c2t2. | | Transforming this equation with the aid of our equations of | transformation we obtain after a simple calculation"... | AE | | Why use an incorrect complex analogy if the simple | physics is sufficient. Setting x and x' in differing | directions has bugged me since HS, because it's WRONG, | it's a crumby theoretical inventions that fucks | reality. AE's spherical wave gives, | | 0 = ds^2 = (cdt)^2 - dr^2 | | and then generalized to, | | 0 = g_uv dx^u dx^v . | | See that, evolved from SR threw Minkowski SpaceTime | to GR, - no silly x vs x' rotations analogy's - | it's the Lorentz Transform in a nutshell. | | Regards | Ken S. Tucker | | PS: Androcles, thanks for the link. You are welcome, and thanks for the laugh. There is no cuckoo transform, though. When Einstein makes x' infinitesimally small to differentiate his equation ý[tau(0,0,0,t)+tau(0,0,0,t+x'/(c-v)+x'/(c+v))] = tau(x',0,0,t+x'/(c-v)) he is also making c = v Androcles |