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Re: Apparent weight



On Sun, 15 Feb 1998, Leigh Palmer wrote:

... We don't live in
an inertial frame of reference, and students instinctively
know how to cope with that. Why do we insist on complicating
their lives by telling them that some things they perceive
with their senses are real, and some are fictitious ...


I had promised myself that I would abstain from this perennial debate
about real vs. fictitious forces, but certain things that have been said
make it very difficult. First of all, if students (and the rest of us)
reported only what we perceived with our senses in the situations being
discussed, there would be no problem. For example, in the case of the
experiences in a carnival centrifuge, if we simply reported what we
experienced, we would report a force on our backs exerted by the wall of
the centrifuge pushing us toward the center of the centrifuge, and we
would be perfectly accurate. This very real centripetal force can leave
bruises, do work and be perceived, three things that fictitious "forces"
cannot do. Somehow, however, people are tempted to create the
psychological fiction of an outward force pressing them against the wall;
there is no such force, and no amount of coordinate redefinition can
create one or transform away the very real effects of the centripetal
force that actually exists. (Coordinate redefinition can of course
produce accelerations relative to any wildly gyrating frame you choose,
but none of these purely kinematical tricks have anything to do with
forces.) This is why careful physicists always distinguish between real
forces and fictitious "forces."

Similarly, if we accurately report only what we experience standing on the
surface of the earth, we will report the perception of the earth pushing
upwards on the bottom of our feet. Again, we will be perfectly correct
-- that is the only force acting on us, and it is precisely preventing us
from going into freefall (or inertial) motion in the gravitational
curvature of spacetime in our local vicinity of the solar system.
However, exactly as in the case of the centrifuge, we are psychologically
tempted to create a downward force acting on us and pressing us to the
surface of the earth; it doesn't exist, can do no work and isn't
perceived by our senses, and so it is rightly said to be fictitious. In
the course of Einstein's development of general relativity (over a period
of several years), he realized this, and expressed it in the form of the
observation that such a "force" could be transformed away by a mere change
of reference frame. (This is never the case with a real force.) He then
went on to work out what gravitation is -- the effect of traveling
through curved spacetime. These real effects are as present on the space
shuttle or in a freefalling elevator as they are at the surface of the
earth. The main difference in the space shuttle is that no one is tempted
to create a fictitious downward force since they do not experience any
upward push from the earth.

In every case, if we report only what is actually perceived, and do not
invent extra unobservable "forces," confusion vanishes.

Finally, while I agree with the praise for my friend David Hestenes'
careful and rigorous work, I feel that the impression has been left that
he somehow supports the abolition of distinctions between real forces and
fictions. He does not, and is careful to state this in his treatment of
rotating frames of reference (New Foundations for Classical Mechanics, Pp.
312, ff.). After giving the equations for "effective force," including
mass times Coriolis and centrifugal accelerations relative to noninertial
frames, numbered as equations 5.27 a and b, Hestenes states:
"Equation (5.27 a) for motion in a noninertial system is as well-defined
and solvable as Newton's equation for motion in an inertial system.
However, the "fictitious forces" in (5.27 b) can in principle be
distinguished from the "real force" f by virtue of their particular
functional dependence on m, x and x(dot). In practice, omega can be
measured directly by observing rotation of the frame relative to the
"fixed stars." Ideally, fictitious forces can be measured by observing
accelerations of free particles with respect to a noninertial frame,
though this is seldom practical. Considerations of practicality aside,
the point is that a real force (field) is distinguished from a fictitious
force by the fact that it depends on the presence of material bodies to
produce it, and it cannot be "transformed away" in a finite region of
space by a change of frame. On the basis of this distinction, then, it
can be said that Equation (5.27 a) does not have the form of Newton's law
unless omega = 0 and a = 0 in (5.27 b)."

Hestenes then goes on to describe the heuristic role that Einstein's
observation that "uniform gravititional force fields" can be transformed
away played in the formation of the general theory of relativity, as
already described above.

I would only add to Hestenes' analysis that real forces can be
distinguished by the fact that they can do useful work, while anyone who
tried to market fictitious "forces" for the same purpose should be labeled
a fraud or a quack. In every case where real work is done it can always
be tracked down to the action of a real force.


A. R. Marlow E-MAIL: marlow@loyno.edu
Department of Physics, Box 124 PHONE: (504) 865 3647 (Office)
Loyola University 865 2245 (Home)
New Orleans, LA 70118 FAX: (504) 865 2453