Re: Rotation is absolute motion!
- From: sal <pragmatist@xxxxxxxxxx>
- Date: Wed, 22 Mar 2006 13:41:31 -0500
Unfortunately, I don't have time to dig into this in any detail just
now, but I did notice one thing which is worth pointing out.
On Tue, 21 Mar 2006 13:35:56 -0800, Gerald L. O'Barr wrote:
Rotation is absolute motion![ ... ]
Now I know that rotating plates, in the direction of their absolute
motions, do deform. Their diameter, in the direction of the motion,
is shortened relative to the diameter that is perpendicular to the
motion. But if I remember correctly, and what has to be made clear,
is that straight lines in these plates remain straight if they are
in a non-stressed condition. As long as the lines in these plates
remain straight, then they will cross each other in an absolutely
instantaneous way.
This is incorrect.
Straight lines in 3-space which are in uniform linear motion transform
to straight lines in 3-space under the Lorentz transform; that is
correct. However, straight lines in 3-space which are rotating about
a central point do not necessarily transform to straight lines in
3-space.
Here's how to see that this must be true:
Put a whole line of holes in each of your counter-rotating plates,
along a single radius. Each time a hole-pair lines up, that's an
event. In the frame at which the center of masses of the plates are
at rest, the "line-up events" all happen simultaneously. Call that
FoR the "stationary" frame.
Orient things so that the holes all line up on the X axis (the line of
lined-up holes defines the X axis, if you will).
Now, switch to a frame which is in uniform linear motion
along the X axis relative to the "stationary" frame. Call this the
"moving" frame.
Events strung out along the X axis which are simultaneous in the
stationary frame will most certainly _not_ be simultaneous in the
moving frame, due to the -v*g*x term in the Lorentz transform for
time.
So, in the moving frame, the holes all line up at different moments; a
"wave" of lined-up holes will move along the radius with one pair of
holes lined up at each instant (in the moving frame).
This can only happen if the "lines" of holes appear curved in
the moving frame. (Try to draw a picture of it if that's not
obvious, and remember that the two lines must always intersect at the
point at the center of the plate, in every frame of reference.)
Some presentations of rotating plates do show that the radius lines
do curve. But these curves are out of plane curves, to allow the
outer circumference to be reduced at a greater rate than those parts
of the plate that are at a smaller radius. The lines are straight
in the direction being used.
In that case "the direction being used" must be _perpendicular_ to the
line of motion of the observer. That's the only case in which
simultaneity along a line is shared by two frames of reference in
relative motion.
If the holes all line up on the X axis, then an observer in linear
motion along the Y axis will also see them line up simultaneously and
will also see the lines as "straight" at that instant. But any
observer moving in any other direction won't see it that way.
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