Re: The Rotating Disk

Tom Roberts wrote:

e_erpelding@xxxxxxxxx wrote:

The question is, Are there certain non-inertial reference frames such
that a bounded region of space is physically larger than as seen from
an inertial (at rest) frame.

I think that question is not well formed. For instance, on the surface
of the rotating disk you seem to want to apply length contraction to the
rotating circumference, and then claim that "the circumference is larger
to the rotating observer than to the inertial observer for which the
center of rotation is at rest."

I give an operational definition of something he might like to claim
below.

That claim is inappropriate, because to
the rotating observer that circumference is not a constant-time slice of
spacetime, and "size" really only applies to a constant-time region.

An analogy to illustrate this: consider a circle in Euclidean 3-d space.
What is the area inside it? The simple answer is "pi r^2", because that
is the area of a circle in a plane. But this is 3-d space, and one could
have any 2-d surface whose edge is that circle but which does not remain
in the plane of the circle; obviously the area of such a surface can be
anything larger than pi r^2.

The way you stated your original question implies you are thinking of a
constant-time spatial volume of spacetime. But different observers have
different notions of "time", and can obtain different results. As soon
as you open the door to non-inertial coordinates, you allow the
possibility that the 3-d spatial surface can be convoluted (as in the
analogy).

There may be something in what you say, Dr. Roberts.

However, rather than dwelling on this, I would claim that an observer
inside a mechanically stable Ehrenfest Disk (with "The Tardis"
stenciled on the hull), marking a particular spot on some circumference
with a piece of tape, then stepping out the entire circumference with
one of those mechanical measuring wheels on a stick, would indeed find
the circumference longer than 2piR, where "R" was the distance
similarly paced off to the center of the ship. I claim this
measurement is reproducible, insensitive to whether he runs or walks
around the ship, and to any subtleties at all about time: he only has
to return to the tape where he started, keeping the wheel in contact
with the deck along the circumference.

If our observer wants to confirm his measurement by sending a light
pulse along a circumferential array of mirrors he may find some
peculiarities, it is true: but that's a different experiment!

.

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  • Re: The Rotating Disk
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