Alas there is more misinformation being passed around. This time regarding
the precise definition of "Lorentz Transformation." The misinformation is
that, for example, a transformation from frame S which has spherical spatial
coordinates (t,r,theta,phi) to another frame S' moving relative to S and
having coordinates (t',r',theta',phi') is a Lorentz transformation. That is
incorrect. While there most certainly exists transformations as suich and
which leave the spacetime interval ds^2 invariant they are not refered to as
"Lorentz Transformations." That term has a very specific meaning.

Let S have coordinates X = (t,x,y,z) and S' have coordinates X' =
(t',x',y',z'). These coordinates are often refered to as "Lorentz
Coordinates" or "Minkowski Coordinates." Let n = Minkowski metric =
diag(1,-1,-1,-1). The correct, precise, definition of a Lorentz
transformation is as follows

Definition: A transformation L from X to X', i.e. X' = LX, is a
transformation for which n'LL = n.

Such transformations include rotations, reflections and boosts. This
definition is found in most decent texts on relativity and tensor analysis.

Sources -
From Thorne and Blanchard's new text --
http://www.pma.caltech.edu/Courses/p...p01/0201.2.pdf - page 28

"Introducing Einstein's Relativity," D'Inverno, Oxford Univ. Press, (1992),
page 109-111
"Tensors, Differential Forms, and Variational Principles," Lovelock & Rund,
Dover Pub., (1989), page 53
"Electrodynamics and Classical Theory of Fields and Particles," Barut, Dover
Pub., (1980), Chapter 1

Pmb

Subject: Definition of "Lorentz Transformation"
From: "Pmb"
Date: 9/27/03 8:38 AM US Mountain Standard Time
Message-id:

Alas there is more misinformation being passed around. This time regarding
the precise definition of "Lorentz Transformation."

You were already MATHEMATICALLY PROVEN WRONG when I gave you the Lorentz
transformation in spherical coordinates.

"Pmb" wrote in message ...
Alas there is more misinformation being passed around. This time regarding
the precise definition of "Lorentz Transformation." The misinformation is
that, for example, a transformation from frame S which has spherical spatial
coordinates (t,r,theta,phi) to another frame S' moving relative to S and
having coordinates (t',r',theta',phi') is a Lorentz transformation. That is
incorrect. While there most certainly exists transformations as suich and
which leave the spacetime interval ds^2 invariant they are not refered to as
"Lorentz Transformations."

What are they referred to as?

Martin Hogbin

"Martin Hogbin" wrote in message
...

"Pmb" wrote in message
...
Alas there is more misinformation being passed around. This time
regarding
the precise definition of "Lorentz Transformation." The misinformation
is
that, for example, a transformation from frame S which has spherical
spatial
coordinates (t,r,theta,phi) to another frame S' moving relative to S and
having coordinates (t',r',theta',phi') is a Lorentz transformation. That
is
incorrect. While there most certainly exists transformations as suich
and
which leave the spacetime interval ds^2 invariant they are not refered
to as
"Lorentz Transformations."

What are they referred to as?

They don't have a name.

Pmb

Subject: Definition of "Lorentz Transformation"
From: "Pmb"
Date: 9/27/2003 2:43 PM US Mountain Standard Time
Message-id:


"Martin Hogbin" wrote in message
...

"Pmb" wrote in message
.. .

While there most certainly exists transformations as suich
and
which leave the spacetime interval ds^2 invariant they are not refered
to as
"Lorentz Transformations."

What are they referred to as?

They don't have a name.

Pmb



Yes they do. They are Lorentz.

"Martin Hogbin" wrote in message
...

"Pmb" wrote in message
...
Alas there is more misinformation being passed around. This time
regarding
the precise definition of "Lorentz Transformation." The misinformation
is
that, for example, a transformation from frame S which has spherical
spatial
coordinates (t,r,theta,phi) to another frame S' moving relative to S and
having coordinates (t',r',theta',phi') is a Lorentz transformation. That
is
incorrect. While there most certainly exists transformations as suich
and
which leave the spacetime interval ds^2 invariant they are not refered
to as
"Lorentz Transformations."

What are they referred to as?

Martin Hogbin

Moller wrote a general relation between the spatial vector and the time in
his text "The Theory of Relativity." This relation is found in many places
such as Goldstein's "Classical Mechanics" - But that is not exactly a
"coordinate transformation" since it has little, if nothing, to do with
coordinates. In fact you don't even need to write coordinates down in that
relation. In that view you're changing frames of reference rather changing
coordinate systems - a subtle difference

Pmb

(WaiteDavid137) wrote in message ...
Subject: Definition of "Lorentz Transformation"
From: "Pmb"
Date: 9/27/03 8:38 AM US Mountain Standard Time
Message-id:

Alas there is more misinformation being passed around. This time regarding
the precise definition of "Lorentz Transformation."

You were already MATHEMATICALLY PROVEN WRONG when I gave you the Lorentz
transformation in spherical coordinates.

You're posting garbage AND lies waite?

sigh! As USUAL your bogus claim about this pathetic "proof" of yours
is rooted in your failure to understand a simple definition - that of
"Lorentz transformation"

Your poor edcuation has failed to inform you that a Lorentz
transformation IS NOT defined as a relationship between coordinates in
one frame of referance to that in another frame moving relative to the
first.

Go learn your basic terminology and come back when you're ready to try
again.

Unless you could be a man about it and prove the the definition I gave
you is wrong - unless you're too scared?

Mr. Pmb - waite's relativity teacher

Pmb:
[...]
incorrect. While there most certainly exists transformations as suich
and which leave the spacetime interval ds^2 invariant they are not
refered to as "Lorentz Transformations." That term has a very specific
meaning.

Lorentz transforms are transforms which preserve inertial frames.

Let S have coordinates X = (t,x,y,z) and S' have coordinates X' =
(t',x',y',z'). These coordinates are often refered to as "Lorentz
Coordinates" or "Minkowski Coordinates." Let n = Minkowski metric =
diag(1,-1,-1,-1). The correct, precise, definition of a Lorentz
transformation is as follows

Definition: A transformation L from X to X', i.e. X' = LX, is a
transformation for which n'LL = n.

Thats obviously incorrect. The rotation:

[ cos(A) -sin(A) ]
X' = [ ] X
[ sin(A) cos(A) ]

Doesn't satisfy the relation you've written, since LL = L^2 != 1.
Multiply it out. You also might try actually writing the equations
out instead of trying to use notational shortcuts that only let you
shoot yourself in the foot.

Such transformations include rotations, reflections and boosts.

Unfortunately, your definition only gives reflections, since the
operator LLX only equals X for L = +/- 1.

This definition is found in most decent texts on relativity and
tensor analysis.

Sources -
From Thorne and Blanchard's new text --
http://www.pma.caltech.edu/Courses/p...p01/0201.2.pdf - page 28

Which doesn't agree with you. What they have written is:

q_uv L^u_a L^v_b = g_ab

L^u_a and L^v_b are inverses of each other. That is not what you have
written. In particular, rotations are orthogonal transformations and
an orthogonal transformation is defined by a matrix for which the
transpose is equal to the inverse. Also, note the example they give at
the top of the next page (29).

Furthermore, the relations given don't _define_ lorentz transforms.
What your reference says is that a transform which satisfies those
relations is a lorentz transform. But, that's strictly because the
transforms were derived in order to preserve the scalar product
under the assumption of the minkowski metric. To wit, your reference
defines the transforms by first defining X and X' as inertial frames.
In order to find a transform between them, the transformation has to
preserve inertial frames.

"Pmb" wrote in message ...

"Martin Hogbin" wrote in message
...

"Pmb" wrote in message
...
Alas there is more misinformation being passed around. This time
regarding
the precise definition of "Lorentz Transformation." The misinformation
is
that, for example, a transformation from frame S which has spherical
spatial
coordinates (t,r,theta,phi) to another frame S' moving relative to S and
having coordinates (t',r',theta',phi') is a Lorentz transformation. That
is
incorrect. While there most certainly exists transformations as suich
and
which leave the spacetime interval ds^2 invariant they are not refered
to as
"Lorentz Transformations."

What are they referred to as?

They don't have a name.

I would have thought that calling them 'the Lorentz
transformations in spherical polar coordinates' would
make everyone happy.

Martin Hogbin

(WaiteDavid137) wrote in message ...
Subject: Definition of "Lorentz Transformation"
From: "Pmb"
Date: 9/27/2003 2:43 PM US Mountain Standard Time
Message-id:


"Martin Hogbin" wrote in message
...

"Pmb" wrote in message
.. .

While there most certainly exists transformations as suich
and
which leave the spacetime interval ds^2 invariant they are not refered
to as
"Lorentz Transformations."

What are they referred to as?

They don't have a name.

Pmb



Yes they do. They are Lorentz.

No contect here. More unsubstantiated boguis claims

Mr. Pmb - waite's relativity teacher