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Re: non-inertial frames



On Thu, 25 Apr 1996, Malcolm Davis wrote:


"al" == al clark <al@sci.nccu.edu> writes:

al> You do not feel a force pulling you out, ie. a centrifugal
al> force, What you feel is the force pushing you in. ...

Let me rewrite Al's paragraph thus

You do not feel a force pulling you down, ie. a gravitational
force, What you feel is the force pushing you up.

This statement is equally correct. However, does this mean that
gravity is a "fictitious" force? Well, maybe from a GR standpoint it
is. Nonetheless it is quite useful to work in a Newtonian reference
frame where the gravitational force on an object is quite "real",
i.e. must be accounted for in F=ma.


If you want to keep people in the dark about our best 20th century
understanding of how gravitation works, how our solar system and the
universe is constituted, then continue in the proposed vein. On the other
hand, if you want to open to them the new horizons of understanding
discovered in the early part of this century, then ask them to reflect on
the term -mg in our equations, and why it is there. This was one of the
biggest clues exploited by Einstein in feeling his way toward the theory
of gravitation as geometric curvature of spacetime: Why do we not feel
any force of gravity, but only the push of the Earth upwards on the soles
of our feet? Why do pressure sensors not reveal any force but the push
upward by the surface of the Earth? Why do pressure sensors register
zero force on all sides when we are falling with an acceleration of
g = 32.2 ft/s*s relative to the surface of the Earth? (I.e., when
we are in freefall?) Einstein finally answered these questions in
1916 -- The only force acting on us when we are standing on the
surface of the Earth is the electromagnetic push of the Earth on the
bottom of our feet. This causes an acceleration of 32.2 ft/s*s
relative to an unaccelerated (i.e., inertial) frame of reference. We
incorporate therefore an extra acceleration of -32.2 ft/s*s in all
our acceleration terms when working relative to the Earth's surface
simply to compensate (as Coriolis taught us to do) for the fact that
Earth is not a true inertial frame. Once this was cleared up, Einstein
was able to go on to show that gravitation was the very real grip that
curved spacetime holds on matter, dictating how matter should move
in freefall, and defining what an inertial frame is. Forces, such as the
electromagnetic, then cause matter to accelerate away from inertial
trajectories. A good start toward understanding all this is to recognize
clearly the nature force in other situations, and not get in the habit of
confusing it with accelerations.

The same is true for the other "fictitious" forces. For example, it
is much simpler to handle the problem of the ballistics of a long
range artillery piece using a non-inertial frame at rest with the gun
and include the Corriolis force, than to work in the frame where the
rotation of the earth must be accounted for explicitly.

Why not just include the Coriolis acceleration above, and omit the
confusion of calling it a "force." This is even simpler -- it
allows you to work freely in the noninertial frame, and you don't
even have to go the extra step of performing the mental gymnastics
of renaming something to call it something it's not. This is as
simple as asking people to call a comet a comet and not a meteor.

general connotations associated with "fictitious". So while students
need to come to see how the forces simplify (every force has a source)
when we view the situation from an inertial frame, exorbitant efforts
to "prove" the fictitious-ness of these forces I believe merely
"prove" that physics is not related to the students' reality.


We prove that physics is not related to the student's reality every time
we introduce a force that neither the student's nor anyone else can
feel!

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