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Re: Newton's 3rd law? was Re: inertial forces (definition)



Hi Bob-
In response to:
*********************************************************
Hi Jack,
Out of curiosity, can you indicate any mathematical statements in Physics
where " = " does not mean a numerical (or perhaps vector or tensor)
equality?
************************
At the risk of flagellating a moribund equine, yes:
VxB = |V||B|sine(theta) where "theta" is the angle between
the two vectors V and B.
This statement is a mathematical identity (definition of the cross
product) and has no physical content.
Contrast that use of the equal sign with:
F = VxB
which does have physical content. It relates the numerical values of the
6 independently measurable components of V and B with the three independently
measurable values of the components of F.
The equal sign in the first equation stands for "is", in the second
equation it predicts the result of an experiment.
John expanded on this theme in his post following your question.
Regards,
Jack




"I scored the next great triumph for science myself,
to wit, how the milk gets into the cow. Both of us
had marveled over that mystery a long time. We had
followed the cows around for years - that is, in the
daytime - but had never caught them drinking fluid of
that color."
Mark Twain, Extract from Eve's
Autobiography