Date: 1999 - 2000
What is rotation that it is found everywhere at all size
scales in the universe? It exists in spin in fundamental particles, as
rotation of planets about suns, of suns in galaxies, of galaxies in clusters, etc.
The person who asked me this question said they
had tried to deal with things like conservation of angular momentum, but
that doesn't really say why rotation itself is
such a common thing at all scales of physical reality. Can you help?
Two facts imply rotation. (1) we have more than one spacial
dimension, that is, it takes more than one number to say where in the
world you are. Why there are 3 dimensions, and not 1 or 5 billion is
something no one, I think, knows. (2) empty space looks the same in
all directions. That is, if you go straight forward 10 miles in empty
space, or turn immediately left and go 10 miles in that direction, you
see no different, by which I mean any physics experiment your perform
comes out the same in both locations. Why this is true is not really
questioned, because it's the simplest thing you could imagine, and
you'd really need a reason for it to be other than this.
Because of (1) and especially (2), in the absence of any other
matter, it costs no energy at all for a body to turn to face another
direction. Why? Well, if it DID cost energy, then you could tell
what direction you were facing, or going toward, and (2) would not be
Because it costs no energy for bodies not near other bodies to
rotate, they usually do. Or more precisely, if even once they are set
rotating, then there is usually nothing to stop them doing so forever.
So we see a lot of rotating things.
A further, very important fact, is that when other bodies ARE near,
they usually cause orbital motion, which is another form of rotation.
This is true because of the interesting fact that (3) gravitational
forces between extended spherically symmetric bodies act as if all the
mass of each body were concentrated at its center.
Because of (3), if we see two spherical bodies near one another, we
can immediately reconsider this system as ONE extended body consisting
of two blobs on the ends of a long, massless, invisible, springy
stick. The two bodies may approach or recede from one another, which
we just consider the springy stick getting longer or shorter. When we
consider the whole stick-with-blobs system, we see that the
stick-with-blobs will in general rotate, because it is an isolated
object, and there is no energy cost for it to do so. Stepping back
and looking at the system as two bodies again, we see that the spin of
the stick-with-blobs object is equivalent to rotation of the two
bodies about their common center of mass. In the case of two
equal-mass bodies, like a binary star, that would be about a point
equidistant from each. In the case of a heavy and very light body,
like the Sun and the Earth, the point of rotation is barely away from
the center of the Sun towards the Earth, so we might as well say the
Earth rotates around the Sun.
Spin of atomic particles is completely different.
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Update: June 2012