Re: Coriolis, etc.

["A. R. Marlow" <marlow@beta.loyno.edu>]

On Thu, 25 Apr 1996, Ari Epstein wrote:
> As an oceanographer, I feel some sort of duty to interject something
> here.
>
> A. R. Marlow <marlow@beta.loyno.edu> feels strongly that the word
> "force" is improper to use when referring to phenomena, such as the
> Coriolis effect (clever sidestepping, eh?), that are observed only in
> non-inertial reference frames. It seems to me, though, that one
> important consequence of general relativity is that there are *no*
> preferred reference frames for doing physics  ...

This is simply not true of general relativity, although it seems to be
a widespread belief among nonspecialists in general relativity.  See,
for example Misner, Thorne & Wheeler, GRAVITATION (Freeman,1973), pp. 18,
ff. for the GR analog of Newtonian inertial frames (local Lorentz frames
= local inertial frames) and their very special properties.

: non-inertial frames are
> just as valid as inertial frames, as long as we're explicit about
> precisely what kind of reference frame we're dealing with.

This statement, of course, is equally true in Newtonian physics as in
Einsteinian physics.  Non-inertial frames are just as valid as inertial
frames, as long as we do not say they have the same properties.


> ...  General
> relativity tells us that a man in a falling elevator is correct when
> he says that there is no gravitational force (except the tiny forces
> due to his mass and the elevator's mass) observable *in his reference
> frame* and does his physics accordingly. 

This is another statement that is widely believed in the nonrelativistic 
community, but is simply not true in general relativity.  If your
elevator is, for example, falling in the vicinity of Earth, you will be
able to measure the tidal effects  --  objects in the half of the elevator
closer to the Earth will experience greater stress than those in the half
of the elevator farther from Earth,  and thus you will be able to detect 
both the presence of the gravitational field of Earth and measure its
strength.  
All these myths about the theory of relativity seem to have taken hold 
in the public mind, and are very difficult to shake, possibly because
Einstein himself, during the years between 1905 and 1915, when he was 
struggling to incorporate gravitation into special relativity, made 
many missteps, and published them, including papers using elevators, Etc.
For example, as late as 1912, in a paper reasoning about light rays in
falling elevators, Einstein published a calculation of the amount of 
bending of light by a gravitational field.  The value he got in 1912
was off by a factor of 2 from the later experimentally checked correct
value he got from general relativity in 1916.

> ... Likewise, a man in a
> windowless, accelerating rocket ship is perfectly correct, in a
> general-relativistic sense, if he chooses to say that *in his
> reference frame* he observes a "downward" force that acts on all
> objects,

If he reports an observed downward force acting on all objects when
what he has really observed is merely a downward acceleration, then
he is lying.  On the other hand, if he has taken the proper experimental
trouble to measure accurately the forces acting on the objects in his
ship, and finds a downward directed force, then all is well.  But it
must be strongly emphasized that the means used to measure forces are
totally different from the means used to measure accelerations, and
you cannot substitute one for the other without committing experimental
fraud.

> ... and that the strength of that force is proportional to a
> given object's mass. We (in an inertial frame) could re-write his
> equations, substituting the rocket's acceleration for his observed
> "force," but our equations are no better than his. We observe his
> spaceship to be accelerating; he observes a force on all the objects
> in it.

If we can substitute the rocket's acceleration for his "observed"
force, then he was lying about having observed a force in the first
place.  What he observed was merely an acceleration, and he jumped 
to the unwarranted conclusion that there was a force.  If he had 
taken the trouble to check for forces, he would not have found them.
I find it very hard to believe that there is such widespread willingness
to entertain the proposition that forces and accelerations are 
interchangeable, in spite of the vast differences in the definitions
of two concepts and the methods of detecting and measuring the two 
different entities.

> In that case, it should be perfectly acceptable to take the surface of
> the spinning Earth as our reference frame, and to formulate our
> equations accordingly. Hence I can say (with only a little
> trepidation) that *in this reference frame* we observe a force on any
> moving object, 

"Observe a force" in the sense of "detect a force, measure a force," 
or do you mean "observe an acceleration" and then jump to the 
unwarranted conclusion that there must be some corresponding force?
The two are totally different procedures.

> ...
> I disagree when Marlow says that the "fictitious" forces "will not do
> any of the things expected of forces in ANY reference frame." In my
> spinning reference frame (his too, by the way), Coriolis acts
> *precisely* as a force. 

Sorry, but it acts precisely as an acceleration, which is what it is,
and how it was introduced by Coriolis  --  it has none of the properties 
of force:  it's not going to set off any pressure meters, it has no
equal and opposite force anywhere else.  Please read any good modern
mechanics text on this.


> This is why all oceanographers (and meteorologists) believe so
> strongly in General Relativity. :*)

I hope they believe strongly enough in it to study it carefully.

> ...
> P.S. I agree that what we have here is primarily a linguistic
> argument; it depends what we mean when we say the word "force."

It does indeed.  It depends on whether when we say "force" we mean
what has been meant in the physics and astronomy community from at
least the time of Newton, or whether we are willing to be confused
about the difference between "force" and "acceleration."  After
all, the difference is no more than the difference between "meteor"
and "comet," clearly two interchangeable terms!

A. R. Marlow                          E-MAIL:  marlow@beta.loyno.edu
Department of Physics                 PHONE:   (504) 865 3647  (Office)  
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