I am sitting on a swivel-stool and I push myself so that I start spinning around, and I get dizzy.

[ Editor: Court Demas posted the question to sci.physics and forwarded
to rec.puzzles (March 1994) the reply he found best, from Alon Drory,
Dept. of Physics, Boston University, who did not read rec.puzzles. ]

>This is from an argument I had with my physics professor in High
>School.  I would be interested in hearing what people think:

>I am sitting on a swivel-stool and I push myself so that I start
>spinning around.  What happens?  The combination of the sight of the
>room spinning around me, the feeling of it on my face, and of the
>fluid in my ears swishing around (this was explained to me as
>generally why we get physically dizzy - I may be wrong), make me feel
>dizzy.

>Now what would happen if the *universe* was spinning around *me*
>instead?

>1) Would I get dizzy?  The question is actually whether the fluid in
>my ears would be swished around like before [I would probrably get
>dizzy from just watching everything spin around me].

>2) Would everybody else in the room (universe too) get dizzy?

>The way I see it, I would get dizzy (from fluid swishing and sight)
>and nobody else would - because essentially the same thing is
>happening as the first time.  Relatively, nothing has changed.  My
>physics prof thought the opposite - I would get dizzy just from sight
>(no fluid swishing), and everybody else would get *physically* dizzy
>from being spun around me (the center of the universe :-)).

>I guess one question is just how you would manage to get the universe
>to spin around somebody, or whether this is any different from the
>person just spinning around.

Well, since you requested personal answers, here goes.  Your query is a
modified (and slightly less clear-cut, in my opinion) version of an
argument devised by Ernst Mach and presented in his THE SCIENCE OF
MECHANICS (I don't have more references here, but I can find them).
Mach took exception to Newton's claim in his PRINCIPIA that rotation was
absolute.  Newton sought to show this by the "bucket argument" : if you
rotated a bucket full of water, the surface of the fluid would curve,
but if you held the bucket in place and rotated the surroundings, the
surface of the fluid would remain level.  Mach answered that Newton
could not claim this since (coining a now famous phrase) "The universe
is given but once".  Thus, we cannot, by definition, experimentally
answer the question what would happen if the universe was rotated
instead of the bucket.  We cannot perform the experiment, and that's
that.  This, however, is not the end of the story.  Mach correctly
pointed out that although we cannot perform the experiment, the notion
that the fluid surface would curve if the universe was rotated instead
of the bucket is not consistent with the Newtonian framework as it was
formulated at the time.  This is because in this framework, such a
state can only follow from a force that would act on the bucket if the
universe were rotating but would not if the universe were not rotating.
While the question is not experimentally decidable, it can be discussed
within physical theory on this hypothetical basis.  It then becomes a
question of whether such a force exists or not (that *would* have this
effect).  THIS question IS an experimental question, provided this force
has other effects.  As I mentioned, such a force doesn't exist in the
Newtonian theory.  However, Mach was just criticizing this theory, so
that was no answer.  Mach then used this example to discuss other
relative motions.  Since the simplest relative motion is constant
translation, and since the noneffect of this translation is the basis of
the law of inertia (via the principle of relativity), Mach conjectured
that in fact, inertia (i.e, mass) WAS just such a PHYSICAL influence of
the remaining matter in the universe (essentially the fixed stars) upon
any object.  This is called "Mach's Principle".  Once again, it is not
DIRECTLY experimentally decidable, but the presence of a physical
mechanism needed to account for the effects must be incorporated within
the structure of the relevant physical theory.

The Newtonian theory does not accommodate Mach's Principle.  Einstein
believed that General Relativity does, but later recognized that it
does not.  The state of this principle, and incidentally of your
question, lies in the realm of the future properties of the
hypothetical Theory of Everything.  If it turns out to accommodate
Mach's Principle, we could say that the (other) experimental
confirmations of the theory also confirm (albeit indirectly) that a
rotating universe would generate a curved fluid surface in a bucket.
If it doesn't accommodate the Principle, one can always claim that the
theory is incomplete.

Sorry to have been so long winded, but this exposition was needed to
explain that the following answer to your question is not trivial.  The
answer is:

 1.  We don't know
 2.  We don't even know if the question makes any sense.
 3.  Assuming it does, in the present state of knowledge it's basically
     a matter of philosophical taste concerning what a "final" theory of
     physics SHOULD incorporate.

I hope you'll find this more helpful than confusing.  If I didn't make
myself clear enough, you can always ask me for clarifications.

A good question, by the way, you should be proud of it.

-- Alon Drory <drory@buphyk.bu.edu>