Seems that there is some more misinformation floating around. This time on
the meaning of the term "4-tensor."

A "4-tensor" (or "four-tensor") is a quantity which behaves like a tensor
under a Lorentz transformation. A "4-tensor" is NOT a tensor of rank-four. A
4-tensor is also known as a Lorentz Tensor.

Example: The Faraday tensor is a second rank four-tensor. That means that
it's a tensor of rank 2 defined on a 4-dimensional manifold.

For details see

"Relativity: Special, General and Cosmological," Wolfgang Rindler, Oxford
Univ., Press, (2001). Page 130 chapter 7

"7 Four-tensors: Electromagnetism in a vacuum"

For online notes for details see --
http://www.wikipedia.org/wiki/Maxwell's_equations
http://farside.ph.utexas.edu/~rfitzp...es/node10.html
http://farside.ph.utexas.edu/~rfitzp...es/node13.html
http://farside.ph.utexas.edu/~rfitzp...es/node23.html
http://farside.ph.utexas.edu/teachin...relativity.pdf
http://cosmos.astroscu.unam.mx/~serg...ml/node17.html
http://www.hep.princeton.edu/~mcdona...ldmomentum.pdf

pmb

Subject: The meaning of the term "Four-Tensor"
From: "Pmb"
Date: 9/15/2003 4:18 PM US Mountain Standard Time
Message-id:

Seems that there is some more misinformation floating around.

If you don't like the misinformation, stop sending it out.

(WaiteDavid137) wrote in message ...
Subject: The meaning of the term "Four-Tensor"
From: "Pmb"
Date: 9/15/2003 4:18 PM US Mountain Standard Time
Message-id:

Seems that there is some more misinformation floating around.

If you don't like the misinformation, stop sending it out.

An unbiased observer keeping score would note that PMB
provided lecture notes backing up his usage, while in
defense of yours you provided "nyaah, nyaah, sez you".

- Randy

Subject: The meaning of the term "Four-Tensor"
From: (Randy Poe)
Date: 9/16/03 8:36 AM US Mountain Standard Time
Message-id:

(WaiteDavid137) wrote in message
...
Subject: The meaning of the term "Four-Tensor"
From: "Pmb"
Date: 9/15/2003 4:18 PM US Mountain Standard Time
Message-id:

Seems that there is some more misinformation floating around.

If you don't like the misinformation, stop sending it out.

An unbiased observer keeping score would note that PMB
provided lecture notes backing up his usage, while in
defense of yours you provided "nyaah, nyaah, sez you".

- Randy



What score. I have no intent to give reference to other authors. There is no
reference competition going on. One difference between pmb and myself is that
pmb will misconstrue what he copies whereas I will derive what I have to prove
my own way. What I write is as valid a reference as any other author.

"Pmb" wrote in message
...
Seems that there is some more misinformation floating around. This time on
the meaning of the term "4-tensor."

A "4-tensor" (or "four-tensor") is a quantity which behaves like a tensor
under a Lorentz transformation. A "4-tensor" is NOT a tensor of rank-four.
A
4-tensor is also known as a Lorentz Tensor.

Is there a different name for a general tensor defined on a four dimensional
manifold (as opposed to one defined on say a five dimensional space), ie. a
non-qualified one that transforms under all differentiable transforms?

Jon

"Jon Hurwitz" wrote in message
...

"Pmb" wrote in message
...
Seems that there is some more misinformation floating around. This time
on
the meaning of the term "4-tensor."

A "4-tensor" (or "four-tensor") is a quantity which behaves like a
tensor
under a Lorentz transformation. A "4-tensor" is NOT a tensor of
rank-four.
A
4-tensor is also known as a Lorentz Tensor.

Is there a different name for a general tensor defined on a four
dimensional
manifold (as opposed to one defined on say a five dimensional space), ie.
a
non-qualified one that transforms under all differentiable transforms?

It's just called "tensor." I suppose the term "four-tensor" caught on since
there are often two different types of tensors used at the same time. For
example: The stress-energy tensor, T^uv (u,v = 01,2,3,4) is a second rank
4-tensor. The stress-tensor, T^jk (j,k = 1,2,3) is part of the stress-energy
tensor and are quite often discussed together. So for added clarity an
author might say "stress-energy 4-tensor .... the stress 3-tensor" or
something like that.

Good point. I'll have to do some e-mailing to find out why people use this
qualifier. Thanks.

Pmb


Jon

"Pmb" wrote in message
...
Seems that there is some more misinformation floating around. This time on
the meaning of the term "4-tensor."

A "4-tensor" (or "four-tensor") is a quantity which behaves like a tensor
under a Lorentz transformation. A "4-tensor" is NOT a tensor of rank-four.
A
4-tensor is also known as a Lorentz Tensor.

Example: The Faraday tensor is a second rank four-tensor. That means that
it's a tensor of rank 2 defined on a 4-dimensional manifold.

For details see

"Relativity: Special, General and Cosmological," Wolfgang Rindler, Oxford
Univ., Press, (2001). Page 130 chapter 7

"7 Four-tensors: Electromagnetism in a vacuum"

For online notes for details see --
http://www.wikipedia.org/wiki/Maxwell's_equations
http://farside.ph.utexas.edu/~rfitzp...es/node10.html
http://farside.ph.utexas.edu/~rfitzp...es/node13.html
http://farside.ph.utexas.edu/~rfitzp...es/node23.html
http://farside.ph.utexas.edu/teachin...relativity.pdf
http://cosmos.astroscu.unam.mx/~serg...ml/node17.html
http://www.hep.princeton.edu/~mcdona...ldmomentum.pdf

pmb

There are more obvious textual examples such as Jackson's text "Classical
Electrodynamics - 2nd Ed." page 532
------------------------------------------------
From the first postulate it follows that the mathematical equations
expressing the laws of nature must be 'covariant,' that is, invariant in
form, under the transformations of the Lorentz Group. They must therefore be
relations amoung scalars, 4-vectors, 4-tensors, etc. defined by their
transformation properties under the Lorentz group in ways analogous to the
familiar specification of tensors of a given rank under three-dimensional
rotations.
------------------------------------------------
which obviously means that a 4-tensor is a tensor in 4D spacetime. 3-tensors
are, of course, tensors defined in Euclidian space.

Pmb

(WaiteDavid137) wrote in message ...
Subject: The meaning of the term "Four-Tensor"
From: (Randy Poe)
Date: 9/16/03 8:36 AM US Mountain Standard Time
Message-id:

(WaiteDavid137) wrote in message
...
Subject: The meaning of the term "Four-Tensor"
From: "Pmb"
Date: 9/15/2003 4:18 PM US Mountain Standard Time
Message-id:

Seems that there is some more misinformation floating around.

If you don't like the misinformation, stop sending it out.

An unbiased observer keeping score would note that PMB
provided lecture notes backing up his usage, while in
defense of yours you provided "nyaah, nyaah, sez you".

- Randy



What score. I have no intent to give reference to other authors. There is no
reference competition going on.

And waite provides more proof that he's a moron

One difference between pmb and myself is that
pmb will misconstrue what he copies..

You're full of **** waite

... whereas I will derive what I have to prove
my own way. What I write is as valid a reference as any other author.

That's your problem right there. I've never quoted or copied anything
unless there was question on the validity of a definition. No
derivation can prove a definition or nomenclature to be right or
wrong.

The nomenclature "4-tensor" cannot be proved to mean anything by a
derivation.

Are you so incredible stupid that you can't figure out something this
so ridiculously easy?

Mr. Pmb - waite's relativity teacher

On 16 Sep 2003 18:30:24 GMT, (WaiteDavid137)
wrote:

What score. I have no intent to give reference to other authors. There is no
reference competition going on. One difference between pmb and myself is that
pmb will misconstrue what he copies whereas I will derive what I have to prove
my own way. What I write is as valid a reference as any other author.

You're arguing as to what is common usage of the term "4-tensor".
Since you're arguing about what other people say, it would seem that
what other people say is relevant.

Unless by common usage you mean "my personal terminology".

- Randy

pmb said:
"The rest of the world also knows that a 4-vector is a vector in 4-d
spacetime."

Waite says:
This is were you go jumping to wrong conclusions. A 4 vector is a vector with
four elements. For example you don't use the term 4 vector to mean 16 element
vectors which are also defined for 4 d spacetime. Vectors above 4 elements are
always referred to by the rank. You made the mistake of thinking that an
electromagnetic field was a 4 vector because it is defined in 4 dimensional
spacetime. You were mistaken. It is not a 4 vector as you claimed. It is rank
2. According you "your" definition above it would be a 4 vector, but that is
wrong according to the definition everyone else in the world uses. I already
told you why you were wrong, but parhaps these details will help you
understand, but I doubt it.