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EINSTEIN 1905 DERIVATION OF LORENTZ TRANSFORMS
Crucial for the derivation is the equation:
http://www.fourmilab.ch/etexts/einstein/specrel/www/ § 3. Theory of the Transformation of Co-ordinates and Times from a Stationary System to another System in Uniform Motion of Translation Relatively to the Former (1/2)[tau(0,0,0,t) + tau(0,0,0, t + x'/(c-v) + x'/(c+v))] = tau(x', 0,0, t + x'/(c-v)) The notation is confusing but essentially Einstein uses an expression for the differential of a function of two variables Z=f(X,Y) which nowadays is used only in chemical thermodynamics: dZ = (dZ/dX)dX + (dZ/dY)dY where (dZ/dX) and (dZ/dY) are partial derivarives. The postulates are four, not two. The two additional postulates are given he http://isites.harvard.edu/fs/docs/ic...les/chap11.pdf "11.4 The Lorentz transformations 11.4.1 The derivation Remarks: 1. We have assumed in eq. (11.16) that Dx and Dt are linear functions of Dx' and Dt'. And we have also assumed that A, B, C, and D are constants, that is, they dependent at most on v, and not on x,t,x',t'." Pentcho Valev |
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EINSTEIN 1905 DERIVATION OF LORENTZ TRANSFORMS
"Pentcho Valev" wrote in message oups.com... Crucial for the derivation is the equation: http://www.fourmilab.ch/etexts/einstein/specrel/www/ § 3. Theory of the Transformation of Co-ordinates and Times from a Stationary System to another System in Uniform Motion of Translation Relatively to the Former (1/2)[tau(0,0,0,t) + tau(0,0,0, t + x'/(c-v) + x'/(c+v))] = tau(x', 0,0, t + x'/(c-v)) The notation is confusing but essentially Einstein uses an expression for the differential of a function of two variables Z=f(X,Y) which nowadays is used only in chemical thermodynamics: dZ = (dZ/dX)dX + (dZ/dY)dY where (dZ/dX) and (dZ/dY) are partial derivarives. The postulates are four, not two. The two additional postulates are given he http://isites.harvard.edu/fs/docs/ic...les/chap11.pdf "11.4 The Lorentz transformations 11.4.1 The derivation Remarks: 1. We have assumed in eq. (11.16) that Dx and Dt are linear functions of Dx' and Dt'. And we have also assumed that A, B, C, and D are constants, that is, they dependent at most on v, and not on x,t,x',t'." Pentcho Valev There are a few blunders/quirks in the equation worth noting. (1/2)[tau(0,0,0,t) + tau(0,0,0, t + x'/(c-v) + x'/(c+v))] = tau(x',0,0, t + x'/(c-v)) The first is the strange mixture of the coordinate x' (which appears on the RHS) and the distance x' which is divided by c+v one way and c-v the other on the LHS. In the case of Sagnac the distance x is the circumference, rendering the coordinate x' = 0. The second is the distance travelled, x in the stationary frame but x+vt one way and x-vt back again, giving t = x'/(c-v) but NOT t = (x+vt)/(c+v) on the return. Again we refer to Sagnac, where the blunder is repeated by others: http://www.androcles01.pwp.blueyonde...gnacIdiocy.htm where alpha takes the place of vt. vt = alpha.R. The third blunder is the RHS, because for equality we should have tau(x',0,0, t + x'/(c-v)) = tau(0,0,0, t + x'/(c+v)) which I've highlighted he http://www.androcles01.pwp.blueyonde...ket/eq22.A.GIF The fourth is the (1/2), it's the only non-algebraic term used and should be [t1-t0]/[t2-t0], thereby correctly matching the term on the RHS with the LHS. The fifth is the inclusion of the spatial coordinates in a function which can only return a single value, there being no function xi(x',0,0, t+x'/(c-v)). The sixth is the confusion between frames, for if we have t in the stationary frame we should have x in the stationary frame also. The seventh is the inclusion of the redundant terms y=0, z=0, t=0. Einstein attempted to make his so-called "definition" (actually a false postulate) 'we establish by definition that the "time" required by light to travel from A to B equals the "time" it requires to travel from B to A' valid in both the moving and stationary frames. http://www.androcles01.pwp.blueyonde...rt/tAB=tBA.gif All in all he was attempting to show off his prowess as a mathematician by confusing coordinates with distances and including differentiation in his derivation, but he was certainly NOT a mathematician. |
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EINSTEIN 1905 DERIVATION OF LORENTZ TRANSFORMS
On Sep 29, 5:04 am, Pentcho Valev babbled:
The notation is confusing but essentially Einstein uses an expression for the differential of a function of two variables Z=f(X,Y) which nowadays is used only in chemical thermodynamics: You don't do much theoretical research, do you? |
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EINSTEIN 1905 DERIVATION OF LORENTZ TRANSFORMS
"Igor" wrote in message ups.com... On Sep 29, 5:04 am, Pentcho Valev babbled: The notation is confusing but essentially Einstein uses an expression for the differential of a function of two variables Z=f(X,Y) which nowadays is used only in chemical thermodynamics: You don't do much theoretical research, do you? He does a lot of anal research. Dirk Vdm |
#6
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EINSTEIN 1905 DERIVATION OF LORENTZ TRANSFORMS
On Sep 29, 8:10 pm, "Dirk Van de moortel" dirkvandemoor...@ThankS-NO-
SperM.hotmail.com wrote: "Igor" wrote in oglegroups.com... On Sep 29, 5:04 am, Pentcho Valev babbled: The notation is confusing but essentially Einstein uses an expression for the differential of a function of two variables Z=f(X,Y) which nowadays is used only in chemical thermodynamics: You don't do much theoretical research, do you? He does a lot of anal research. Dirk Vdm so what, doctors always do anal, are you a doctor? |
#7
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EINSTEIN 1905 DERIVATION OF LORENTZ TRANSFORMS
On Sep 29, 2:04 am, Pentcho Valev wrote:
Crucial for the derivation is the equation: http://www.fourmilab.ch/etexts/einstein/specrel/www/ § 3. Theory of the Transformation of Co-ordinates and Times from a Stationary System to another System in Uniform Motion of Translation Relatively to the Former (1/2)[tau(0,0,0,t) + tau(0,0,0, t + x'/(c-v) + x'/(c+v))] = tau(x', 0,0, t + x'/(c-v)) The notation is confusing but essentially Einstein uses an expression for the differential of a function of two variables Z=f(X,Y) which nowadays is used only in chemical thermodynamics: dZ = (dZ/dX)dX + (dZ/dY)dY where (dZ/dX) and (dZ/dY) are partial derivarives. It is not even that. Einstein, or whoever the actual author was, was totally hand-waving. 15 years later, Einstein would re-derive the Lorentz transform from two equations equating zero with zero. The dim- witted Einstein Dingleberries would be so awe-struck by that mathemaGic trick. However, some true scholars would call that bullsh*t and rightfully toss Einstein into the trashcan labeled 'NITWIT'. |
#8
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EINSTEIN 1905 DERIVATION OF LORENTZ TRANSFORMS
On Sep 30, 12:45 am, Koobee Wublee wrote:
On Sep 29, 2:04 am, Pentcho Valev wrote: Crucial for the derivation is the equation: http://www.fourmilab.ch/etexts/einstein/specrel/www/ § 3. Theory of the Transformation of Co-ordinates and Times from a Stationary System to another System in Uniform Motion of Translation Relatively to the Former (1/2)[tau(0,0,0,t) + tau(0,0,0, t + x'/(c-v) + x'/(c+v))] = tau(x', 0,0, t + x'/(c-v)) The notation is confusing but essentially Einstein uses an expression for the differential of a function of two variables Z=f(X,Y) which nowadays is used only in chemical thermodynamics: dZ = (dZ/dX)dX + (dZ/dY)dY where (dZ/dX) and (dZ/dY) are partial derivarives. It is not even that. Einstein, or whoever the actual author was, was totally hand-waving. 15 years later, Einstein would re-derive the Lorentz transform from two equations equating zero with zero. The dim- witted Einstein Dingleberries would be so awe-struck by that mathemaGic trick. However, some true scholars would call that bullsh*t and rightfully toss Einstein into the trashcan labeled 'NITWIT' At least the so-called Einstein Dingleberries knew how to perform simple algebraic tasks, such as tranforming domains, before indulging in the calculus. |
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