Chronology | Current Month | Current Thread | Current Date |
[Year List] [Month List (current year)] | [Date Index] [Thread Index] | [Thread Prev] [Thread Next] | [Date Prev] [Date Next] |
On Nov 19, 2006, at 10:49 PM, Jack Uretsky wrote:
Hi all-
This "accident" is not really an accident. The so-called
equivalence principle is a definition. We define Newton's
constant G so that the inertial mass for some element equals
the gravitational mass. The "accident" is that when you do the
definition for one element (or substance - however you want
to define it) it holds true for all substances, as demonstrated
by the Eotvos experiments. It is the ratio of gravitational to
inertial mass that is constant for all substance (see Weinberg,
Gravitation, Sec. I.2), and this ratio can be made unity by a
suitable definition of G (big G).
This point seems to be missed in the discussion in Halliday &
Resnick (3d Ed.) and, perhaps, in other elementary texts.
Feynman doesn't stress the point in his Lectures, although,
characteristically, he sort of sneaks up on it.
Jack,
I don't think it's right to call the equivalence principle a
definition. It is true that one might, in Newtonian mechanics, have
measured "gravitational" and "inertial" mass in different units and
then noticed that the ratio of gravitational to inertial mass appears
to be the same for all substances. But the equivalence principle
doesn't tell us merely that we should measure these two different
quantities in the same units, it says that there is only one
quantity--mass--and that gravitational forces ARE inertial forces.