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Re: The fallacy of affirming the consequent



Kevin beat me to the punch, a reference where this is worked out in detail
is:

"A First Course in General Relativity", pp 10-15, Cambridge UP, Bernard
Schutz. (ISBN 0-521-2770-0)

Joel Rauber

Does anyone have a reference or arguement for relaxing the linear
transformation assumption??

-----Original Message-----
From: Ken Caviness [mailto:caviness@SOUTHERN.EDU]
Sent: Wednesday, April 09, 2003 10:38 AM
To: PHYS-L@lists.nau.edu
Subject: Re: The fallacy of affirming the consequent


Pentcho Valev wrote:

However Einstein needs something different:

B -> A, A, therefore B /4/

He proceeds in accordance with /4/ - builds Lorentz
equations on B and
so creates the sequence (A therefore B therefore Lorentz
equations) -
the illusion is that
Lorentz equations ultimately stem from A. In fact, A CAN be
a corollary
of B or Lorentz equations, in accordance with /3/, but
Lorentz equations
can BY NO MEANS be
deduced from A.

I vividly remember an assignment in my freshman year
Engineering Physics class
where we were asked to _derive_ the Lorentz transformation
equations from
Einstein's postulates that the laws of physics and the speed
of light are the
same for all inertial observers. I have since used this in
my classes or as a
homework assignment. The only additional assumption needed
is that the
transformations be linear in all the variables
(x,y,z,t,x',y',z',t'). That
was handled by the statement that we would _first_ seek a set of
transformation equations which was linear, but if necessary
we could back off
from that requirement.

Briefly, if you let

x = A x' + B y' + C z' + D t', y = E x' + ..., etc., the
unknown constants can
be identified by symmetry arguments and the requirement that
the speed of
light be measured by both primed and unprimed observers as c.
The Lorentz
transformation falls out in your lap, i.e., the Lorentz
equations can indeed
"be deduced from A" + the additional requirement that the
dependence be
linear.

For what it's worth,

Ken Caviness
Physics Department
Southern Adventist University
http://physics.southern.edu/