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

[David Bowman <David_Bowman@GEORGETOWNCOLLEGE.EDU>]

Regarding Cliff Parker's question:

> I am surprised by this statement.  Would you please expand on this idea?

Is it OK if I butt in here?

Newton's 3rd law implies and is consistent only with instantaneous
interaction at a distance.  It is inconsistent with the retarded
causation of relativity--both special and general.  The only kind of
Newton's 3rd law that can survive when relativity is taken into account
is for a zero distance contact force between particles.  Unfortunately we
don't know of any such forces in real life.  The closest to a real
contact force we can come up with is for the weak interaction whose range
is about 2 x 10^(-18) m.  All realizable forces are carried through the
intermediary of a field of some kind.  Such a field propagates changes no
faster than c.  This means that Newton's third law can't hold for any two
spatially separated objects interacting via the field because they can't
keep in instantaneous communication with each other so they can exert
their respective forces on each other in a way that can be precisely
synchronized as exactly "equal & opposiite".  Of course, this does not
mean that Newton's third law is not an excellent *approximation* in many
important instances.  In the case of gravitation it is an even better
approximation than it is for electromagnetism because gravitational
interactions tend to have the effect of their actual retarded interaction
cancel out in the near field to a higher order in 1/c^2 than they do for
electromagnetic forces.

> I have been teaching my students that they attract the earth as the earth
> attracts them.  If I am teaching wrong ideas I would at least like to know
> why the idea is incorrect.  Are you saying that field theory replaced
> Newton's gravitational force theory, just as general relativity replaces
> both?

General relativity *is* a field theory.  The field mediating the
interaction between sources is the metric of spacetime, and in GR
anything with energy, momentum, and/or stress counts as a source of
gravitation.

> I am not thoroughly versed in field theory but have thought that it
> was an alternative to the idea of a gravitational force but not necessarily
> superior.  Can you briefly tell me why field theory is superior to Newton's
> theory?

GR (and a couple of other metric field theories of gravitation) agrees
with all the most precisely measured experimental data.  Newton's theory
does not.

David Bowman
David_Bowman@georgetowncollege.edu