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

"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.

"Androcles" wrote in message k...

[snip usual rant]

All in all he was attempting to show off his prowess as a mathematician
by confusing coordinates with distances

You mean like this?
http://users.telenet.be/vdmoortel/di...eDistance.html
http://users.telenet.be/vdmoortel/di...s/Distors.html


and including differentiation

You mean like this?
http://users.telenet.be/vdmoortel/di...DiffConst.html
?

in his derivation, but he was certainly NOT a mathematician.

Or do you mean like this?
http://users.telenet.be/vdmoortel/di...SetSolve2.html
http://users.telenet.be/vdmoortel/di...ersuasive.html
http://users.telenet.be/vdmoortel/di...droDistri.html
http://users.telenet.be/vdmoortel/di...ythagoras.html
http://users.telenet.be/vdmoortel/di...hlessBite.html
http://users.telenet.be/vdmoortel/di...Competent.html
http://users.telenet.be/vdmoortel/di.../UseTrans.html
http://users.telenet.be/vdmoortel/di...es/Sheesh.html
http://users.telenet.be/vdmoortel/di.../SetSolve.html

Dirk Vdm

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?

"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

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?

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'.

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.