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Re: non-inertial frames



On Wed, 1 May 1996, Mark Sylvester wrote:
...
The article called attention to the surprising and nonintuitive directions
of acceleration that would be found at and inside the event horizons of a
black hole. The author's terminology was sometime's confusing, but in no
case did his arguments depend on introducing nonexistent forces.

I'm willing to believe that the arguments do not *depend* on
"non-existent" forces, but Abramovicz uses them pretty freely:
"...the centrifugal force, the outward push away from the centre
of the curve"
"...the total force, which is the sum of the centrifugal and
gravitational forces..."
All your worst nightmares!
In answering a critic in a letter to Sci.Am. he says "...the
introduction of those fictitious forces makes the problem much
easier. My discussion could have been in terms of free-falling
frames and centripetal forces, but that would have obscured the
subject."
...

I think if he had simply expressed himself in terms of the real
accelerations that would be detected relative to any frame he
wanted to use, he would have been much clearer. The nonintuitive
nature of the directions of such accelerations at and inside the
surface of a black hole (bending of light, Etc.) was his point.
But you're right -- looking back at the article I see his terminology
was deplorable. You have to reverse the direction of practically every
notion he uses to see what he's talking about. He keeps using dynamical
terms for simple kinematical concepts. (I think he thought it would
catch the public's fancy more -- someone must have told him to be
dynamical.)

...
I found myself across the dinner table from him (the institute
where he spends some of his time is down the road from me) and
brought up the subject. In the course of the conversation he
said "...I wish people would not call them fictitious forces. In
the non-inertial frame they are perfectly real." - a statement
which I found pretty shocking at the time.
...

You were right to be shocked -- I think I would have had to bite my
tongue or leave the table!


...
As for the work done by a fictional force, why is this a
crucial objection? Work done by the accelerating force, and hence
kinetic energy, are frame-dependent even when we are comparing
inertial frames.
...
We are using "frame-dependent" here in two different senses. Kinetic
energy is a relative concept in the sense that the work you would
do or the energy you would transfer in colliding with me depends on
the relative speed between us as determined in any inertial frame
you wish to use. The Newtonian formula (or for that matter, the
relativistic formula) for such KE is only valid relative to
inertial frames, but then you may transform your expression to any
frame you wish -- you will just get non-Newtonian formulas for
expressing this same real kinetic energy if you transform to
noninertial frames. The relative nature of KE is often stated with
a tacit understanding of something like "frame in which you are at
rest vs. frame in which I am at rest," and in that sense it can
be said to be "frame-dependent" -- change the frame in which you
are at rest (i. e., speed up relative to me) and the kinetic energy
changes, but that same KE will be (invariantly) computed using kinematic
data relative to any frame I want.

By the way, when investigating the centrifugal force as naively
experienced inside a rotating space station
^^^^^^^^^^^

This of course has been a major bone of contention in this thread --
I would claim that we don't (even naively) "experience" a centrifugal
force in such a space station. We experience only the centripetal force
of the wall of the space station pressing in on us, and we naively
misreport it as somehow directed in exactly the opposite direction.

In other words, we report the force we are exerting on the wall of the
spacecraft (what the spacecraft is "feeling") as if it were the force we
are experiencing. Someone in another post had what I thought was an
interesting explanation of why we might make this strange transposition.

Nowadays most people have had the actual experience of a carnival
centrifuge, so I find in physics or introductory astronomy courses
that it is a useful example to bring up. Once it is pointed out
that if they accurately report only what they actually feel (the
inward pressure of the wall on their backs), things work out much
better, they have no problem from then on.


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