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On Nov 20, 2006, at 2:34 AM, John Mallinckrodt wrote:
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.
Another thing that is not an accident is worth mentioning. It is the
fact that no arbitrary constant appears in the F=m*a.
But this is true
only when F is expressed in newtons. Suppose the unit of force is
independently defined lb. In that case the N2 law would be F=k*m*a,
where k would be a dimensional constant whose magnitude would have to
be determined experimentally, by measuring F, m and a. And the unit of
k would be (lb*s^2)/(kg*m). In other words, k would be like 1/epsilon
in Coulomb Law. Once the unit of F is established we have no way of
eliminating the 1/epsilon from the Coulomb's law (unless mechanical and
electrical forces are considered to be different things with different
units). Who was the first to eliminate k by inventing a new unit of
force, newton? Was it Georgi? That unit appeared when his MKSA system
was introduced. That was the origin of our present SI.
P.S.
No one would say that m/s^2 is the same as lb/kg. Or that cm/s^2 is the
same as dyne/gram (dyne was the unit of force in the CGS system
introduced in 19th century by Maxwell). Note that force per unit mass
would also be NUMERICALLY DIFFERENT from acceleration, on our planet.
Ludwik Kowalski
Let the perfect not be the enemy of the good.
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