Understanding Einstein's simple derivation of the LorentzTransformation

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.

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

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.

Marvin the Martian wrote:
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.

Please READ what is quoted above. Read it more carefully. Your "no" was
responding to "Lorentz obtained the transform equation via an ansatz, without
justification or explanation.", which is manifestly true. My stating that your
"no" was wrong was in response to that, and carried no implication that "they
don't hold Maxwell's equations invariant".


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

SO?

So Lorentz did not derive the Lorentz transformations, in the usual sense of the
word, contrary to your claim (to which I was responding, even though you seem
unable to follow threads very well).


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.

This is just plain not true, in the context of 1905. What we today call
"Maxwell's equations" are not at all Maxwell's theory (1865). In the context of
Maxwell's theory, Einstein's 1905 paper is quite remarkable, and is inconsistent
with Maxwell's derivation.

You have the history backward -- it was Einstein's 1905 paper (among
others) that showed what you claim to be in the Maxwell's equations
already. You could not have made that claim before those papers.

IOW: it is not appropriate to use TODAY'S understanding of electrodynamics to
claim that Einstein's paper was "trivial and stupid", because his paper was
INSTRUMENTAL in forming that modern understanding.


Postulates are not needed if they can be derived.

That's an excessively narrow-minded viewpoint. It is often enlightening to
derive a given theory from a different set of postulates, as that can help
display limitations or generalities in the theory that are not obvious from the
original/initial derivation.

For instance, you are clearly quite ignorant of Maxwell's
original derivation of his theory, which included what have
become known as "Maxwell's equations". In particular, his
derivation is inconsistent with the PoR, and is rejected
by the physics community today. Since the advent of SR,
electrodynamics has been completely re-conceptualized,
incorporating SR and _SOME_ of Maxwell's ideas, plus ideas
from several others (most especially Lorentz), yielding a
theory known as Classical Electrodynamics. The Maxwell's
equations are part of this theory, but with different
meanings for the symbols therein.

For instance, from Einstein's derivation (and also from the standpoint of
Lorentz and Poincaré), SR should strictly apply only to electrodynamics. We know
now that it is MUCH more general, and also applies to the strong, weak, and
gravitational interactions (locally). A different set of postulates can easily
show that it is more general than any of them thought, and is independent of
light or electrodynamics. Such as:
1. Einstein's statement of the PoR.
2. There is a finite upper bound on the speed of information transfer.

Indeed, a given theory's set of equations can be derived from any sufficient set
of its theorems. The choice of which are theorems and which are postulates
(axioms) is arbitrary, and subject to one's sense of propriety and elegance.

And finally, as I said before, Einstein's postulates can NOT be derived from
Maxwell's theory. Nor from his equations alone without implicitly accepting what
Einstein (and others) showed back in 1900-1906.


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

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

You are wrong. Go _READ_ Maxwell's treatise of 1865.

Swearing at others because of your own personal ignorance is not helpful.


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?

I am not "getting" this anywhere, but MAXWELL "got it" in his 1865 treatise. His
theory included an aether and a field related to motion relative to the aether
frame -- things which have not survived the test of time. But you are clearly
ignorant of this, and attempt to blame me.

I repeat: Swearing at others because of your own personal ignorance is not helpful.


That's simply NOT SO. It isn't there.

Yes, it is. You need to learn to distinguish Maxwell's theory (1865) from modern
re-formulations of electrodynamics. Our modern formulation includes "Maxwell's
equations" to honor the man, but it does not include most aspects of his
original theory (in particular, its aether frame, the molecular/vortex
discussions thereof, nor the field related to motion relative to the aether
frame). While a subset of his equations is present in our modern formulation,
the meanings of the symbols in those equations are DIFFERENT from what Maxwell used.


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

It is not "the math" that matters here, it is the MEANINGS OF THE SYMBOLS THAT
APPEAR IN THE EQUATIONS.

I remind you that a physical theory consists of:
* a set of equations
* a description of the meanings of the symbols therein
* a description of how to relate at least some of the symbols to
measurements in the real world.

In Maxwell's theory, the coordinates and field components are relative to the
aether frame. In the ostensibly similar equations of Classical Electrodynamics
the symbols have morphed into being relative to any inertial frame.

There is more subtlety and beauty here than you can see, because you are blind
to important distinctions in the historical development of electrodynamics.
Don't blame me for your personal limitations.


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.

I repeat: Swearing at others because of your own personal ignorance is not helpful.


Geeze louise, you don't know basic physics!

The problem is not mine.

I repeat: There is more subtlety and beauty here than you can see, because you
are blind to important distinctions in the historical development of
electrodynamics. Don't blame me for your personal limitations.


and classical
mechanics (which includes the PoR)

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

You have to read what I wrote, not how you sliced it up. Go back and do so.

But yes, classical mechanics is indeed not consistent with Einstein's postulates
(not that they are "silly", of course). You seem particularly unable to grasp
the essential aspects of various physical theories, and too willing to project
your own failures onto others.

Hint 1: classical mechanics is consistent with Galilean relativity.
Hint 2: SR is not.
Hint 3: Today we use relativistic mechanics, not classical mechanics,
except when the latter is a suitable approximation to the former
(which it is in very many cases, including our everyday lives, but
not at particle accelerators).

Exercise for advanced readers: discuss what this inconsistency
means to Einstein's use of "coordinates in which the equations
of Newtonian mechanics hold good". Note that Perrett and Jeffery's
translation touches on this in a footnote that is not part of
the original text.


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

I repeat: Swearing at others because of your own personal ignorance is not helpful.

History often seems absurd to those who weren't there and/or don't understand
the issues.


Tom Roberts

On Jul 25, 1:39*am, 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 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

"Apparently Poincaré was unaware of Larmor's contributions, because he
only mentioned Lorentz and therefore used for the first time the name
"Lorentz transformation"."

http://en.wikipedia.org/wiki/History...ransformations

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 Jul 24, 8:38*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. He did not even display them in the form we use
today until after 1905. Einstein derived them from his two postulates, and
displayed them in the form used today. I believe Einstein was instrumental in
christening them "Lorentz transformations". The earlier paper by Voigt that
displayed an equivalent transform was not (re-)discovered until the name
"Lorentz transform" was well established.

Tom Roberts

Poincare christened it the Lorentz transformation before 1950. It was
not in it final form then. Poincare christened the "relativity
principle" before 1905, so he, in effect, christened the theory of
realtivity. But Einstein published the final form of the Lorentz
Transformation first, and he dispensed with aether. Poincare was
close to showing that aether could be a undetectible convention in
print by mid 1905 but a bit too late, and he never rejected it because
he thought light needed a medium.

On Jul 24, 8:38*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. He did not even display them in the form we use
today until after 1905. Einstein derived them from his two postulates, and
displayed them in the form used today. I believe Einstein was instrumental in
christening them "Lorentz transformations". The earlier paper by Voigt that
displayed an equivalent transform was not (re-)discovered until the name
"Lorentz transform" was well established.

Tom Roberts

The wiki says the Voigt tranform is not equivalent, that it has a
different value for time dialation:

http://en.wikipedia.org/wiki/Woldemar_Voigt

Poincare christened the Lorentz Transform (when it was not quite in
its final form)

On Jul 25, 2:42*pm, Tom Adams wrote:
On Jul 24, 8:38*pm, Tom Roberts wrote:

[..]

The wiki says the Voigt tranform is not equivalent,
that it has a different value for time dialation: [..]

Indeed it's not equivalent. The confusion is partly due to Lorentz,
who wrongly acknowledged Voigt for having found the transformations
earlier. In fact, Voigt's transformations even have a different
application.

Poincare christened the Lorentz Transform (when it was
not quite in its final form)

The difference with the usual version of textbooks is minor; the main
difference is that S and S' are exchanged.
He put c=1 so that epsilon=v/c also equals v and v/c^2, which reduces
the number of symbols; this has become quite popular. And note that l
can immediately be dropped, as it is equal to 1.

http://en.wikisource.org/wiki/On_the...ron_%28June%29

Harald

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/