Paddlewheels in a gravity well and angular momentum

[jartsa]

Not quite. As per earlier thread, considered as a tube of matter uniformly expanding axially, a local observer at some fixed radius from spin axis will be in a decreasing mass density region, and so redshift/clock-rate is changing. Locally perceived as increasing spin rate.

The picture I now have is of 'a spinning rocket accelerating in a snug guide tube', and expelled mass/gas now spins at the same rate as the rocket.

If my picture is accurate, yes to the extent relative velocity is nonrelativistic. Otherwise the situation is modulated by SR effects as per #28 - slower and continually slowing rotation for receding/broadside relative motion, speeding up within a narrowing angular range of approaching relative motion. You may find this link to other links interesting to follow: http://casa.colorado.edu/~ajsh/sr/srfs.html

How about if we consider a spinning, laser beams emitting disk, in a straight, light reflecting tube. Light that is emitted from the middle of the disk travels throuh the tube at speed of light. Light emitted from the rim of the disk travels through the tube slower than speed of light.

(the spinning axis and tube's symmetry axis are parallel, and all laser beams are parallel to tube's symmery axis when the laser sources are at rest)

The light going though the tube must carry angular momentum that's what's slowing it down.

Next thing to do here might be to replace lasers with electron guns ... then we might conclude that the electron population's spinning rate is unchanged when the electrons are accelerated by the electron guns ... But first we should agree about the laser light case.

 

[Q-reeus]

How about if we consider a spinning, laser beams emitting disk, in a straight, light reflecting tube. Light that is emitted from the middle of the disk travels throuh the tube at speed of light. Light emitted from the rim of the disk travels through the tube slower than speed of light.

(the spinning axis and tube's symmetry axis are parallel, and all laser beams are parallel to tube's symmery axis when the laser sources are at rest)

Getting better with describing a scenario - that much is good.

The light going though the tube must carry angular momentum that's what's slowing it down.

Are you sure? In the frame of one of the peripheral lasers on the spinning disk, which direction is the back-reaction force from that laser pointing? How does that force transform into the frame we see it from? Try here for some clues: http://en.wikipedia.org/wiki/Special_relativity#Force So do you find the disk to be changing angular momentum? Then what does conservation of angular momentum imply about the emitted light going down the tube? How about emitted frequency (and any frequency spreading going on)?
[EDIT: But as yourself, and yuiop in #38 describe, there is spiral motion. So absence of torque is not the only factor to consider - here there is dispersal of angular momentum generated prior to emission.]

Next thing to do here might be to replace lasers with electron guns ... then we might conclude that the electron population's spinning rate is unchanged when the electrons are accelerated by the electron guns ... But first we should agree about the laser light case.

No doubt fun to keep bringing up new scenarios, but maybe best to get some good grounding in the basics and then you will be able to answer all this kind of thing yourself jartsa. Sorry to disappoint but apart from being no expert myself, can't really keep this thing up too long.

 

[yuiop]

How about if we consider a spinning, laser beams emitting disk, in a straight, light reflecting tube. Light that is emitted from the middle of the disk travels through the tube at speed of light. Light emitted from the rim of the disk travels through the tube slower than speed of light.

The light from the rim of the disk only appears to be traveling slower than the speed of light relative to the tube, because it bouncing of the side of the tube walls in a spiral fashion. I guess you know that, as that is presumably why you specified a light reflecting tube. I guess you also know that if the light coming of the back of the disc forms a cylinder shape parallel to the tube when the disc is not spinning, that it will form shape when the disc is spinning.

(the spinning axis and tube's symmetry axis are parallel, and all laser beams are parallel to tube's symmery axis when the laser sources are at rest)

But not when the disc is spinning.

The light going though the tube must carry angular momentum that's what's slowing it down.

Again, only slow going down the tube in a broad sense, because of the spiral path taken by the peripheral light beams. In between reflections of the side of the tube, each photon is traveling in a straight line and traveling at the speed of light. Agree?

 

[jartsa]

The light from the rim of the disk only appears to be traveling slower than the speed of light relative to the tube, because it bouncing of the side of the tube walls in a spiral fashion. I guess you know that, as that is presumably why you specified a light reflecting tube. I guess you also know that if the light coming of the back of the disc forms a cylinder shape parallel to the tube when the disc is not spinning, that it will form shape when the disc is spinning.
But not when the disc is spinning.
Again, only slow going down the tube in a broad sense, because of the spiral path taken by the peripheral light beams. In between reflections of the side of the tube, each photon is traveling in a straight line and traveling at the speed of light. Agree?

Yeah.

And when the light is spiralling ahead, it makes one round in same time as the disk made one round, when the light left the disk. I'm talking about peripheral light beam here, which has no room to expand sideways. The spiral formed by the beam has no room to expand, I mean.

 

[jartsa]

Let us consider a very simple scenario: Beings living on a spinning planet can't use the spinning of the planet as an energy source. I guess we are all familiar with this.

So we know that bouncing up and down on the pole of a spinning planet does not cause any frictional heating, that would be caused by the planet and the bouncing object having different spinning rates.

So therefore: spinning motion is immune to gravitational time dilation and velocity time dilation.

 

[ZapperZ]

Locked, pending moderation.

Zz.