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Different conceptual origins of inertial and gravitational masses
are clear to me. But not the nuance according to which one
should also recognize two kinds of gravitational masses: active
and passive. (Perhaps it is time that I should attempt to read the
classic WMT text "Gravitation."). If Newton's third law is
valid, for two mutually attractive bodies, then how do we
decide which object is active and which is passive? Thanks
for a clear summary.
Peter Vajk wrote:
Several recent messages have talked about distinctions
between inertial mass and gravitational mass, etc.
For an excellent discussion of these issues, see Wheeler, Misner,
and Thorne's massive and classic text "Gravitation."
There are three conceptually different masses used in physics"
Inertial mass -- this is the coefficient in F = ma.
Active gravitational mass -- this is that property of an object which
DOES the attractING in Newton's Law of Universal Gravitation, or which
acts as the source term in Einstein's Gravitational Field Equations.
Passive gravitational mass -- this is that property of an object which
IS attractED in Newton's Law of Universal Gravitation.
A priori, there is no logical NECESSITY for these three to be the
same. Galileo's virtual Leaning Tower experiment, however, shows (or
could show, with the metrology available to Galileo) that the RATIO of
Passive to Inertial mass is the same for bodies of different sizes or of
different compositions within 1 part in 100 or so. The Eotvos
Experiment (circa 1900) showed an accuracy of a few parts in 10,000 or
so. The higher accuracy results from modern measurements on motions
of satellites in orbit -- don't have a handy reference on this, but
Fairbanks's group at Stanford University was pursuing this some 20 or
so We can then use Newton's Third Law (if it is valid) to show that the
ratio of Active to Passive gravitational masses is the same for
different sizes and compositions of objects to similar accuracies.
If these three masses are really the same, or are inherently
proportional to each other regardless of composition, size, density,
etc., etc., then the uniformity of acceleration in a given
gravitational field follows at once, and Einstein's representation of
gravitation by a purely geometric theory is possible, with the motion
of particles in a gravitational field represented by geodesics in the
warped four-geometry of space-time. (The Principle of Equivalence.)
But WHY these three should be equivalent to one another, and WHY these
are related to the chemistry concept of mass ("a measure of the total
amount of material") is as yet an unsolved question.