"Martin Hogbin" wrote in message
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"Pmb" wrote in message
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"Martin Hogbin" wrote in message
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I would have thought that calling them 'the Lorentz
transformations in spherical polar coordinates' would
make everyone happy.
I could only guess as to why they were named and defined that way.
However
I'm going strictly on facts - i.e. what I see defined throughout the
relativity literature. When it comes to "Lorentz Transformation" and
"Lorentz Group" that's what I find - at least in the more mathematical
treatments.
I am having some difficulty understanding your point.
Is it simply a matter of nomenclature?
I'm sorry but I don't understand where the difficulty lies. The first thing
I posted in this thread was the following
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Alas there is more misinformation being passed around. This time regarding
the precise definition of "Lorentz Transformation."
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That means that this is a question - *only* - on what the term means - i.e.
on nomenclature.
Are you merely
saying that you have never seen the transformations
of SR expressed in terms spherical polar coordinates
described as the 'Lorentz transformations'?
Sure. I guess you can say that. I guess you could also say that I've never
seen and electron refer to as a "blue duck" either. One is standard
terminology - the other isn't. And there's good reason for it. A
transformation takes the coordinates as expressed in one coordinate system
and expresses them in terms of components in another coordinate system. The
point remains the same point.
Are you familiar with orthogonal transformations? If not see -
http://www.geocities.com/physics_world/orthog_trans.htm - I use this as an
example in what follows.
For example: In Euclidean geometry a rotation of one set of Cartesian axes
into another set is an orthogonal transfromation. A point in 3-space remains
the same point - it's just labeled differently. The Euclidan metric g =
diag(1,1,1) remains unchanged. So an orthogonal transfromation relables
points. However not all coordinate transformtions are orthogonal
transformations. Changing from Cartesian to Cartesian is orthogonal but
chaning from Cartesian to spherical is not an orthogonal transfromation. But
it's just as legitimate a transformation as any other transformation. I
simply isn't an orthogonal transformation.
The Lorentz transformation is an orthogonal coordinate transformation in
spacetime in Lorentzian goemetry. However this does not mean that no other
coordinate transformations in spacetime
The details are in --
http://www.pma.caltech.edu/Courses/p...p01/0201.2.pdf
See page 27
With this in mind - The misinformation being passed around here has the
following Eucledian analogy. It's similar to claiming that a transformation
from one set of spherical coordinates to another set of spherical
coordinates is an orthogonal transformation. Is it a transformation? Yes.
Absolutley! Without question. Does it retain the Euclidean distance dL? Yes.
But it is NOT an orthogonal transformation. An orthogonal transformation
does not change the Euclidian metric g = diag(1,1,1). It is meaningless to
even ask if such a spherical to sphercial transformation keeps g =
diag(1,1,1) unchanged since it doesn't even start with it. However an
orthogonal transformation has the property that it does not change g.
Think of Lorentz transformations as being orthogonal transformations in
spacetime.
There is more on this in the University of California - Berkely notes --
http://d0lbln.lbl.gov/110bf03/110bf03-110bs97-rel.pdf
See the part called "Spacetime intervals."
I hopes this clarifys my point. If not then I'll be more than happy to
clarify further.
Pmb