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Re: The Sarma-Denker construction (Formerly: Cause and Effect)



Hi all-
I was, in a sense, being silly. JD's construction cannot
simulate a (fictitious) centrifugal force for obvious symmetry reasons.
Hint: Think of the path of an insect trying to fly radially
outward from the center of the region where John has planted his mass
distribution.
Regards,
Jack

Adam was by constitution and proclivity a scientist; I was the same, and
we loved to call ourselves by that great name...Our first memorable
scientific discovery was the law that water and like fluids run downhill,
not up.
Mark Twain, <Extract from Eve's Autobiography>

---------- Forwarded message ----------
Date: Mon, 23 Oct 2000 13:31:26 -0500 (CDT)
From: Jack Uretsky <jlu@hep.anl.gov>
To: "phys-l@lists.nau.edu: Forum for Physics Educators" <PHYS-L@lists.nau.edu>
Subject: Re: Cause and Effect

Once you bring concepts from general relativity into the argument
then JD's construction (mass distribution to mimic a rotating frame)
fails. The point is that a rotating frame has the same curvature (of
spacetime) as the same frame with rotational velocity zero. On the
other hand, the "simulating" mass distribution changes the spacetime
curvature. One says that the rotating frame and the frame with a
mass distribution have different geometries.
In other words, the GR answer to the Sarma question is, "No."
Regards,
Jack

Adam was by constitution and proclivity a scientist; I was the same, and
we loved to call ourselves by that great name...Our first memorable
scientific discovery was the law that water and like fluids run downhill,
not up.
Mark Twain, <Extract from Eve's Autobiography>

On Mon, 23 Oct 2000, D.V.N.Sarma wrote:

The reason for asking this question is this.
Some members of this list have said that noninertial
frames are the ones from which one can conclude
accelerations cause forces.

The inertial forces in noninertial frames have a label
which identifies them i.e., they are always proportional
to the masses on which they act.

The only analogy to these forces in inertial frames appears to be
gravitational force. By JD's admission it is not easy to replicate
the inertial forces in noninertial frames by suitable gravitational
configurations in inertial frames. That is these forces are a class by
themselves.

Thus any general equivalence in status of inertial frames with
gravitational fields and noninertial frames is not posiible. Even
Einstein's equivalence principle says that a uniform gravitational
field can be "locally" equivalent to a frame uniformly acelerated in
the opposite direction (or is it the other way round). This word
"locally" hides I think quite a lot i.e., that it is just a mathematical
device with out a counter part in reality.

Is it possible to make

f = ma

bidirectional with out the above equivalence?

regards,

Sarma.


At 04:59 AM 10/23/00 +0530, D.V.N.Sarma wrote:
What type of mass distribution in an inertial frame will produce
gravitational effects similar to the effects produced in the noninertial
frame of a rotating platform?

See below.

Is there a symmetry between inertial forces and gravitational
forces such that one can always be replaced by another?

Good question. The answer is "No and yes and no".
1) Rotation presumably means rigid rotation of the frame. (If it's not
rigid, you will notice the tearing immediately.) This cannot mimic a
general mass distribution.
2) Very theoretically speaking, there is a mass distribution that can
mimic the centrifugal field. If you have a "spare dimension" this may even
be semi-practical: imagine motion confined to a (nonrotating) plane. Just
below the plane you distribute a bunch of mass. The mass density increases
(rapidly) as a function of distance from some designated point. If you do
it right, the acceleration as a function of position goes like 1/r^2. OTOH
the Coriolis effects (acceleration as a function of _velocity_) are broken,
so it doesn't mimic rotation perfectly.
3) If you tried to do this in full dimensionality, you would need
cylinders of mass, and you couldn't move around without bumping into the mass.