Re: The Traditional Superficial Explanation of Relativity

Shubee wrote on Fri, 04 Apr 2008 11:28:33 -0700:

How is it that professional physicists today can't find Lorentz
invariant expressions as easily as Poincaré did in 1905?

Fail to understant that are you asking for.

Poincaré lists 8 distinct but elementary invariants in his paper. See
the equation numbers 5 and 7 in
http://www.univ-nancy2.fr/poincare/bhp/pdf/hp2007gg.pdf How many
invariants in special relativity are you aware of?

I have not done a list and it depends of the definition of special
relativiy.

Some authors define special relativity only for kinematics. Others (e.g.
Feynman) include dynamics on external electromagnetic fields.

In the latter case that definition of special relativity contains a four-
potential A^b invariant is not in in the former.

Would include thermal effects? Then you will find new invariant non-
mechanical four quantities.

How many distinct
invariants of the Poincaré group exist?

The group is defined by generators

http://en.wikipedia.org/wiki/Poincar%C3%A9_group

for the

http://mathworld.wolfram.com/PoincareTransformation.html

You can built different invariant mathematical objects. Just built one
and check its invariance to inhomogenenous transformation.

Note if object m is an Poincaré group invariant, then km will be also,
where k is a constant.

for physics applications take a look to

http://en.wikipedia.org/wiki/Wigner%27s_classification


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