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Re: Coriolis, etc.





As an oceanographer, I feel some sort of duty to interject something
here.

A. R. Marlow <marlow@beta.loyno.edu> feels strongly that the word
"force" is improper to use when referring to phenomena, such as the
Coriolis effect (clever sidestepping, eh?), that are observed only in
non-inertial reference frames. It seems to me, though, that one
important consequence of general relativity is that there are *no*
preferred reference frames for doing physics: non-inertial frames are
just as valid as inertial frames, as long as we're explicit about
precisely what kind of reference frame we're dealing with.

As a relativity theorist, I have to inject a couple of other comments
here. The price you pay in general relativity (or even special
relativity for that matter) for a frame-independent formulation of
the laws of physics is that you give up the idea of a force.
Relativistic physics is formulated strictly in terms of fields and
energy, not forces. The fact that you do NOT get the same form for
your equations of motion when transforming Newton's laws to a
rotating frame means that they are not consistent with general
relativity and require modification or being scrapped altogether.

To put it another way: Galilean relativity tells us that a man in a
windowless carriage moving at constant velocity (relative to an
inertial frame) is perfectly correct when he says that he is
motionless, and when he does his physics accordingly. General
relativity tells us that a man in a falling elevator is correct when
he says that there is no gravitational force (except the tiny forces
due to his mass and the elevator's mass) observable *in his reference
frame* and does his physics accordingly. Likewise, a man in a
windowless, accelerating rocket ship is perfectly correct, in a
general-relativistic sense, if he chooses to say that *in his
reference frame* he observes a "downward" force that acts on all
objects, and that the strength of that force is proportional to a
given object's mass. We (in an inertial frame) could re-write his
equations, substituting the rocket's acceleration for his observed
"force," but our equations are no better than his. We observe his
spaceship to be accelerating; he observes a force on all the objects
in it.

In that case, it should be perfectly acceptable to take the surface of
the spinning Earth as our reference frame, and to formulate our
equations accordingly.

Except for one thing -- the equivalence principle only applies to
gravity. The man in the falling elevator carries a local inertial
frame with him but the man in a rotating system does not. You can
define an instantaneous inertial frame for him but it will change
from moment to moment. When you transform from one of these
instantaneous inertial frames to the next, you get relativistic
effects very like the Coriolis effect. It is the laws of physics that
are invariant in form from one frame to another and all observers
must agree on those but the exact manifestation of those laws
eventually requires a recognition of exactly what sort of reference
frame you are doing your measurements from. You don't get to
reformulate your equations of motion in different reference frames
since that would violate the principle of relativity -- everybody
agrees on the same fundamental laws. You can and indeed must make
different predictions for observations in different reference frames
but they must all be consistent with the same fundamental
relationships.

In the end, we have to recognize that what we are really dealing with
in the laws of physics are interactions between particles. If it is
impossible to identify the other particle, then we cannot be dealing
with an interaction, hence not really a force. In other words,
Newton's third law tells us that all forces are really pairs of
forces on different particles, which pair of forces constitutes an
interaction. With regard to the Coriolis "force," we cannot identify
the second object since it does not exist. Hence, to admit it as a
force would be to admit a violation of the Third Law. This is, of
course, a non-relativistic formulation.


Ari Epstein

P.S. I agree that what we have here is primarily a linguistic
argument; it depends what we mean when we say the word "force."


Paul J. Camp "The Beauty of the Universe
Assistant Professor of Physics consists not only of unity
Coastal Carolina University in variety but also of
Conway, SC 29526 variety in unity.
pjcamp@csd1.coastal.edu --Umberto Eco
(803)349-2227 The Name of the Rose
fax: (803)349-2926