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Re: non-inertial frames

From: "A. R. Marlow" <<marlow@beta.loyno.edu>>
On Thu, 25 Apr 1996, Mark Sylvester wrote:
Just as much as my computer monitor is in equilibrium
on the table, with the "fictitious" gravitational force counter-
balancing the thrust of the table.
........
I have become a lot less
centripetally dogmatic since starting to include the Equivalence
Principle in the course that I teach (by adopting the Cosmology
option in the IB Higher Level course).

The equivalence principle of course has nothing to say about what
forces your monitor experiences. It simply says that in a small enough
region of spacetime, you may substitute flat spacetime for curved spacetime
if your accuracy requirements are not too great.

I've been mulling over this for a while, and Rick Tarara brought
up the question again. Dr Marlow's reply confirms my thought
that the E.P. puts the F=mg gravitational force acting downwards
in the same "fictional" category as the centrifugal demon.

There was an article a few
years ago in Scientific American by Mark Abramovich on the unexpected
effects one experiences when orbiting a black hole, which sparked
a similar "fugal vs petal" debate. I must have another look at that
article.


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 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.

(The article is in the March 93 Sci. Am. and the letters in the
July 93 issue. There was also a more technical, i.e. with
equations, article in AJP)


Date: Mon, 29 Apr 1996 23:08:52 +0000 (GMT)
From: "A. R. Marlow" <<marlow@beta.loyno.edu>>

Once again, standard mechanics says that Newton's laws simply do not
apply in noninertial frames and there is no attempt to make them apply in
such frames. You do not get correct answers: for example, you calculate
nonzero work done by "centrifugal force" in the examples discussed
previously, I calculate zero work done by such a "force." Both answers
obviously cannot be correct.

Now what is this?
So I'm in my spaceship accelerating at 9.8ms^-2, doing
experiments in mechanics or whatever. Newton's laws do not
apply? Easy. Introduce "g"=9.8ms^-2. No objection yet from Dr
Marlow, as long as we don't write F=mg acting backwards. But we
do this all the time with "gravity". Yes I know we've been
through all this - I just want to state the situation as a
student raised on almost any one of the textbooks I've met would
see it.

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.

By the way, when investigating the centrifugal force as naively
experienced inside a rotating space station, we would also find
a requirement for a "local" field if "tidal" forces are to be
negligible. A typical point that a student would raise, against
my best efforts to explain why gravity is really different from
kinematic effects.

I'm following this discussion with rapt attention.

Mark.

Mark Sylvester, UWCAd, Duino, Trieste, Italy.