Understanding Einstein's simple derivation of the LorentzTransformation

On Sun, 24 Jul 2011 20:44:53 -0500, Sam Wormley wrote:

On 7/24/11 4:19 PM, Marvin the Martian wrote:
Damn it!!

Einstein did NOT derive the Lorentz transformation.

Wanna bet, Marvin!

The Lorentz transformation was originally the result of attempts by
Lorentz and others to explain how the speed of light was observed to be
independent of the reference frame, and to understand the symmetries of
the laws of electromagnetism. Albert Einstein later re-derived the
transformation from his postulates of special relativity. The Lorentz
transformation supersedes the Galilean transformation of Newtonian
physics, which assumes an absolute space and time (see Galilean
relativity). See: http://www.fourmilab.ch/etexts/einstein/specrel/www/

He didn't "re-derive" ****.

He showed how his "postulates" are consistent with the Lorentz
transformation. The Lorentz transformation predates SR - Einstein's paper
on the electrodynamics of moving particles QUOTES it. The whole paper is
nothing but an application of the Lorentz transformation. (Sometimes
called the Lorentz-Fitzgerald transformation)

Since the Lorentz transformation is the mathematical transform under
which maxwell's equations are invariant, and SR is nothing more than the
Lorentz transformation itself, this his first "postulate" is stupid. The
transform has been verified by experiment and thus isn't a postulate at
all, it is a theory.

The second postulate about the speed of light being constant is also a
direct result of Maxwell's equations. The MM experiment was nothing more
than another experiment that affirmed this.

On Sun, 24 Jul 2011 19:38:57 -0500, Tom Roberts wrote:

Marvin the Martian wrote:
Einstein did NOT derive the Lorentz transformation. Lorentz derived the
Lorentz transformation.

I disagree. Lorentz obtained the transform equation via an ansatz,
without justification or explanation.

No, the Lorentz transform holds Maxwell's equations invariant.

He did not even display them in
the form we use today until after 1905.

Irrelevant if they are in the form of a matrix or not.

Einstein derived them from his
two postulates, and displayed them in the form used today.

Bull****. The Lorentz transformation was DESIGNED to hold Maxwell's
equations invariant under change of velocity. The first "postulate" is
thus circular logic. So is the second, since the velocity of all
electromagnetic radiation is a constant according to MWE.


I believe
Einstein was instrumental in christening them "Lorentz transformations".

Actually, they were called the Lorentz Fitzgerald transformation.

On Jul 24, 2:19 pm, Marvin the Martian wrote:

Damn it!!

shrug

Einstein did NOT derive the Lorentz transformation.

That is very correct. The Lorentz transform was not derived by
Einstein the nitwit, the plagiarist, and a liar. shrug

Lorentz derived the Lorentz transformation.

No, technically it was Larmor, but conceptually it was Poincare.
shrug

Marvin the Martian wrote:
On Sun, 24 Jul 2011 19:38:57 -0500, Tom Roberts wrote:
Marvin the Martian wrote:
Einstein did NOT derive the Lorentz transformation. Lorentz derived the
Lorentz transformation.
I disagree. Lorentz obtained the transform equation via an ansatz,
without justification or explanation.

No, the Lorentz transform holds Maxwell's equations invariant.

Your "no" is just plain wrong -- go read his 1904 paper. He pulled his "change
of variables" out of the air with no explanation or justification, as I said.

Yes, the Lorentz transforms do hold the ME invariant, but that was first shown
by Poincaré, not Lorentz. Indeed, Lorentz made a mistake in his 1904 paper, and
the equations he presented are not invariant (his error relates to the
transformation of charge density, not the transformation of coordinates). That
paper is the basic reason they carry his name (1904 preceding 1905).

(Einstein only discussed the vacuum Maxwell-Hertz equations, and
thus did not have this issue.)


He did not even display them in
the form we use today until after 1905.

Irrelevant if they are in the form of a matrix or not.

None of the early papers display them as a matrix. That came much later as group
theory was applied. Matrix notation is almost essential to display them in their
full 4-d splendor.

But yes, this is more a side comment, not a major point.


Einstein derived them from his
two postulates, and displayed them in the form used today.

Bull****. The Lorentz transformation was DESIGNED to hold Maxwell's
equations invariant under change of velocity. The first "postulate" is
thus circular logic. So is the second, since the velocity of all
electromagnetic radiation is a constant according to MWE.

Strong words from someone who clearly does not understand either the issues or
the history.

Einstein's contribution was showing that Maxwell's equations and the PoR are not
inconsistent. The PoR is NOT AT ALL "circular logic", because Maxwell's theory
has a unique aether frame, and the PoR does not apply -- in Maxwell's theory the
speed of light is c only in the aether frame, and is most definitely NOT the
same in all frames. The inconsistency between Maxwell's theory (which violates
the PoR) and classical mechanics (which includes the PoR) was the central
conundrum of theoretical physics just before 1905. Especially because
experiments showed that electrical, optical, and magnetic phenomena did obey
some sort of relativity, but Maxwell's theory did not. Note that today's
non-quantum theory of electromagnetism is called "Classical Electrodynamics" and
not "Maxwell's theory" -- it merely retains Maxwell's equations as a part of the
theory, in a way completely unanticipated by Maxwell.

IOW: you are applying today's understanding of electrodynamics, not the context
of 1905. The Maxwell's equations of Classical Electrodynamics are most
definitely NOT Maxwell's theory; Classical Electrodynamics was developed
specifically with SR in mind, and a subset of equations from Maxwell's theory
was rescued from oblivion and carry his name.

Einstein, of course, made many other major contributions to
theoretical physics....


You don't seem to understand that before 1905 the coordinate transformations
between Cartesian coordinates of relatively moving frames were strictly the
province of MECHANICS, not electrodynamics. Einstein was breaking new ground
when he melded them together in his 1905 paper. For instance, that's why his
entire first part does not discuss electrodynamics at all, just coordinate and
velocity relationships, i.e. MECHANICS.


Tom Roberts

"Marvin the Martian" wrote in message
...
On Sun, 24 Jul 2011 20:44:53 -0500, Sam Wormley wrote:

On 7/24/11 4:19 PM, Marvin the Martian wrote:
Damn it!!

Einstein did NOT derive the Lorentz transformation.

Wanna bet, Marvin!

The Lorentz transformation was originally the result of attempts by
Lorentz and others to explain how the speed of light was observed to be
independent of the reference frame, and to understand the symmetries of
the laws of electromagnetism. Albert Einstein later re-derived the
transformation from his postulates of special relativity. The Lorentz
transformation supersedes the Galilean transformation of Newtonian
physics, which assumes an absolute space and time (see Galilean
relativity). See: http://www.fourmilab.ch/etexts/einstein/specrel/www/

He didn't "re-derive" ****.

Einstein derived the equations (called the Lorentz transformations) from the two
postulates of special relativity. Historically, though, he was not the first to
write down those transformations.


He showed how his "postulates" are consistent with the Lorentz
transformation. The Lorentz transformation predates SR - Einstein's paper

Einstein showed that the Lorentz transformations are a consequence of the two
postulates. All physical laws are the same in all reference frames and that
includes Maxwell's laws.

Since the Lorentz transformation is the mathematical transform under
which maxwell's equations are invariant, and SR is nothing more than the
Lorentz transformation itself, this his first "postulate" is stupid. The

There is nothing stupid about it and relativity is more than just one set of
transformations. Relativistic invariance applies to gobs of other things beyond
Maxwell's equations ... e.g. the uncertainty principle, matter waves, the color
force, gravity waves, and so on.

transform has been verified by experiment and thus isn't a postulate at
all, it is a theory.

Correct, the theory of relativity has been experimentally proven beyond a
reasonable doubt. The term "postulate" is just a linguistic remnant; a way of
speaking now and no longer a reference to a speculative idea.


The second postulate about the speed of light being constant is also a
direct result of Maxwell's equations.

It is a trivial result of relativity but not a direct result of Maxwell's
equations. If Maxwell's equations are used with the Galilean transformations
then, in many reference frames, the speed of light is not the same in all
directions.

*

"K_h" wrote in message
...
| Einstein derived the equations (called the Lorentz transformations) from
the two
| postulates of special relativity.

No he didn't, you are bull****ting. Einstein "derived"
xi = (x-vt) DIVIDED by sqrt(1-v^2/c^2), which is NOT a Lorentz
transformation.

On Jul 24, 5:38 pm, Tom Roberts wrote:
Marvin the Martian wrote:

Einstein did NOT derive the Lorentz transformation.
Lorentz derived the Lorentz transformation.

I disagree. Lorentz obtained the transform equation via an ansatz, without
justification or explanation.

On the contrary, Einstein the nitwit was the one who derived the
Lorentz transform based total gibberish. Einstein the plagiarist was
the one who knew about the Lorentz transform beforehand. Einstein the
liar lied about all that in his 1905 papers as well as his 1920 book
on relativity. shrug

He did not even display them in the form we use
today until after 1905.

It does not matter how you write down the particular presentation of
the Lorentz transform. As long as it is mathematical the same as the
modern accepted form all is fine. That is unless you are algebra
illiterate. shrug

Einstein derived them from his two postulates, and
displayed them in the form used today.

These two assumptions were reverse-engineered from the Lorentz
transform. shrug

I believe Einstein was instrumental in
christening them "Lorentz transformations".

Your belief is totally wrong. The reason why Poincare called it the
Lorentz transform was because Lorentz was the first person to
realization there are actually an infinite such transforms that will
satisfy the null results of the MMX as well as the classical Maxwell’s
equations. shrug

The earlier paper by Voigt that
displayed an equivalent transform was not (re-)discovered until the name
"Lorentz transform" was well established.

Your understanding is not even close. Here are the Voigt, Larmor’s,
and Lorentz’s transforms.

**** The Voigt Transform

** dt0 = dt + v0 dx / c^2
** dx0 = dx + v0 dt
** dy0 = dy sqrt(1 – v0^2 / c^2)
** dz0 = dz sqrt(1 – v0^2 / c^2)

**** Larmor’s Transform

** dt0 = (dt + v0 dx / c^2) / sqrt(1 – v0^2 / c^2)
** dx0 = (dx + v0 dt) / sqrt(1 – v0^2 / c^2)
** dy0 = dy
** dz0 = dz

**** Lorentz’s Transforms

** dt0 = (dt + v0 dx / c^2) / (1 – v0^2 / c^2)^n
** dx0 = (dx + v0 dt) / (1 – v0^2 / c^2)^n
** dy0 = dy (1 – v0^2 / c^2)^(n – 1/2)
** dz0 = dz (1 – v0^2 / c^2)^(n – 1/2)

Where

** dt0, dx0, dy0, dz0 = Parameters of the absolute frame of reference
** sqrt(v0^2) = Absolute speed of the oberver
** n = Any real number

Given another observer using primed coordinate system, of course,
Larmor’s transform can be written as follows.

** dt0 = (dt’ + v0’ dx’ / c^2) / sqrt(1 – v0’^2 / c^2)
** dx0 = (dx’ + v0’ dt’) / sqrt(1 – v0’^2 / c^2)
** dy0 = dy’
** dz0 = dz’

If the vectors [v0] and [v0’] are in parallel, Larmor’s transform for
both the primed and the unprimed observer nullifies the absolute frame
of reference which is the Lorentz transform:

** dt’ = (dt + v dx / c^2) / sqrt(1 – v^2 / c^2)
** dx’ = (dx + v dt) / sqrt(1 – v^2 / c^2)
** dy’ = dy
** dz’ = dz

Where

** [v] = Velocity of dt as observed by dt’
** [v0] * [v0’] = sqrt(v0^2) sqrt(v0’^2)

And that was how Poincare wrote down the Lorentz transform above.
Notice if the vectors [v0] and [v0’] are not in parallel, the Lorentz
transform should not be valid. shrug

On Sun, 24 Jul 2011 23:07:33 -0700, K_h wrote:

"Marvin the Martian" wrote in message
...
On Sun, 24 Jul 2011 20:44:53 -0500, Sam Wormley wrote:

On 7/24/11 4:19 PM, Marvin the Martian wrote:
Damn it!!

Einstein did NOT derive the Lorentz transformation.

Wanna bet, Marvin!

The Lorentz transformation was originally the result of attempts by
Lorentz and others to explain how the speed of light was observed to
be independent of the reference frame, and to understand the
symmetries of the laws of electromagnetism. Albert Einstein later
re-derived the transformation from his postulates of special
relativity. The Lorentz transformation supersedes the Galilean
transformation of Newtonian physics, which assumes an absolute space
and time (see Galilean relativity). See:
http://www.fourmilab.ch/etexts/einstein/specrel/www/

He didn't "re-derive" ****.

Einstein derived the equations (called the Lorentz transformations) from
the two postulates of special relativity. Historically, though, he was
not the first to write down those transformations.


He showed how his "postulates" are consistent with the Lorentz
transformation. The Lorentz transformation predates SR - Einstein's
paper

Einstein showed that the Lorentz transformations are a consequence of
the two postulates. All physical laws are the same in all reference
frames and that includes Maxwell's laws.

No. The two "postulates" are a direct result of Maxwell's equations
(which are NOT laws, btw) and the Lorentz transformation. Einstein was
confused.

Since the Lorentz transformation is the mathematical transform under
which maxwell's equations are invariant, and SR is nothing more than
the Lorentz transformation itself, this his first "postulate" is
stupid. The

There is nothing stupid about it and relativity is more than just one
set of transformations. Relativistic invariance applies to gobs of
other things beyond Maxwell's equations ... e.g. the uncertainty
principle, matter waves, the color force, gravity waves, and so on.

The math IS the theory. All the rest is non-science and subjective.

You're impressed that a transformation that was designed to keep
Maxwell's equations invariant... keeps Maxwell's equations invariant.
That, I find amusing.

There is nothing at all about SR that has any relevance at all the
Heisenberg Uncertainty Principle or quantum mechanics. Where the hell did
THAT come from? Einstein didn't even believe or understand QM, he had an
irrational belief and a stupid preconceived bias AGAINST Quantum
mechanics (and a few other things, like Lemaitre's Big Bang Theory).

transform has been verified by experiment and thus isn't a postulate at
all, it is a theory.

Correct, the theory of relativity has been experimentally proven beyond
a reasonable doubt. The term "postulate" is just a linguistic remnant;
a way of speaking now and no longer a reference to a speculative idea.

Actually, length contraction has never been shown experimentally. Don't
overstate the case. The consistency of the speed of light and time
dilation has been shown experimentally.

I guess you don't know what a postulate is. It has nothing to do with a
speculative idea.

The second postulate about the speed of light being constant is also a
direct result of Maxwell's equations.

It is a trivial result of relativity but not a direct result of
Maxwell's equations.

The hell it isn't. Once you solve Maxwell's equations for the wave
equation, the speed of the wave, c, falls right out.


If Maxwell's equations are used with the Galilean
transformations then, in many reference frames, the speed of light is
not the same in all directions.

Maxwell's equations are not invariant under a Galilean transformation,
which leads to the conclusion that the physics of electromagnetism would
have to be dependent upon the frame of the observer, which is an absurd
result.

Once you solve for the correct transformation, you see that the speed of
light is a constant wrt all observers.

Einstein's contributed three things:

* He used circular logic to claim that the laws of physics under the
proper invariant transformation are invariant.

* That the speed of light is constant, which he took to be a postulate
instead of looking at Maxwell's equations, which show that the speed of
the electromagnetic wave is a constant.

* He wrote a paper that said "Hey!! What Lorentz and Fitzgerald Said!"

Of his three contributions to SR, the first two are silly and the last
one useful, as even Lorentz didn't understand the significance of the
Lorentz-Fitzgerald transformation. Einstein showed the significance of
the Lorentz-Fitzgerald transformation - THAT was his contribution.

On Jul 24, 5:19*pm, Marvin the Martian wrote:
Damn it!!

Einstein did NOT derive the Lorentz transformation.

Lorentz derived the Lorentz transformation.

The wiki on the history of the Lorentz tranformation indicates that
Einstein was the first to publish a paper with the Lorentz
transformation in its final from. Poincare had a draft of a paper
with the final form mid 1905.

Poincare named an number of similar equations "Lorentz Tranformation"
starting around 1901, but Einstein was the first to publish the final
form.

Poincare was close to a theory that made it impossible to detect the
aether wind, but he still thought light needed a medium. The unique
thing Einstein did in 1905 was to be the first to completely reject
the existence of aether.

On Mon, 25 Jul 2011 00:39:40 -0500, Tom Roberts wrote:

Marvin the Martian wrote:
On Sun, 24 Jul 2011 19:38:57 -0500, Tom Roberts wrote:
Marvin the Martian wrote:
Einstein did NOT derive the Lorentz transformation. Lorentz derived
the Lorentz transformation.
I disagree. Lorentz obtained the transform equation via an ansatz,
without justification or explanation.

No, the Lorentz transform holds Maxwell's equations invariant.

Your "no" is just plain wrong

Go ahead and show they don't hold Maxwell's equations invariant then.

-- go read his 1904 paper. He pulled his
"change of variables" out of the air with no explanation or
justification, as I said.

SO?

Yes, the Lorentz transforms do hold the ME invariant,

Oh, so admit I'm right. Amusing.

but that was first
shown by Poincaré, not Lorentz.

Not the issue.

True enough, Lorentz was trying to explain the MMX with time dilation and
Fitzgerald's contribution was length contraction, but Maxwell's equations
are invariant under a Lorentz-Fitzgerald transformation.

Indeed, Lorentz made a mistake in his
1904 paper, and the equations he presented are not invariant (his error
relates to the transformation of charge density, not the transformation
of coordinates). That paper is the basic reason they carry his name
(1904 preceding 1905).

Even if, so what? The fact remains, it is true that the Lorentz
transformation holds Maxwell's equations invariant.



(Einstein only discussed the vacuum Maxwell-Hertz equations, and
thus did not have this issue.)

That was Einstein's usual excuse for plagiarism. "oh! I didn't know it
was done before!" In the real world, utter failure to do a literature
search is no excuse for plagiarism.

He did not even display them in
the form we use today until after 1905.

Irrelevant if they are in the form of a matrix or not.

None of the early papers display them as a matrix. That came much later
as group theory was applied. Matrix notation is almost essential to
display them in their full 4-d splendor.

But yes, this is more a side comment, not a major point.

Then what are you gibbering about?

Einstein derived them from his
two postulates, and displayed them in the form used today.

Bull****. The Lorentz transformation was DESIGNED to hold Maxwell's
equations invariant under change of velocity. The first "postulate" is
thus circular logic. So is the second, since the velocity of all
electromagnetic radiation is a constant according to MWE.

Strong words from someone who clearly does not understand either the
issues or the history.

Einstein's contribution was showing that Maxwell's equations and the PoR
are not inconsistent.

As I said, that was a trivial and stupid exercise, as Einstein's
postulates are a direct result of Maxwell's equations and the Lorentz
transformation. Postulates are not needed if they can be derived.

The PoR is NOT AT ALL "circular logic", because
Maxwell's theory has a unique aether frame,

No it doesn't. That's bull****.

and the PoR does not apply
-- in Maxwell's theory the speed of light is c only in the aether frame,

Given Maxwell's equations and the transformation that holds them to be
invariant, where the hell are you getting that an aether frame is
required or indicated? That's simply NOT SO. It isn't there.

No aether frame is in the equations NOW, and an aether frame wasn't there
in 1904 when they had the same exact math.

and is most definitely NOT the same in all frames. The inconsistency
between Maxwell's theory (which violates the PoR)

Holy **** that was a dumb thing to say. Maxwell's equations do NOT say
that the speed of light is not constant or that the laws of physics are
different for different observers.

The whole moving magnetic field thing was one of the issues that bothered
physicist back then.

Geeze louise, you don't know basic physics!

and classical
mechanics (which includes the PoR)

What?! Classical mechanics are not consistent with Einstein's silly
postulates!!

This is absurd. You're clearly talking out of your ass.