Re: does circumference contract with velocity?
- From: "Sorcerer" <Headmaster@xxxxxxxxxxxxxxxxxx>
- Date: Fri, 10 Nov 2006 01:45:24 GMT
"Edward Green" <spamspamspam3@xxxxxxxxxxx> wrote in message
news:1163116048.431546.50130@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
| Gerald L. O'Barr wrote:
|
| > Subject: Re: does circumference contract with
| > velocity?
|
| > Tom Roberts <tjroberts...@xxxxxxxxxxxxx> wrote:
| > > Normally when one says "the circumference of this
| > > disk", they mean a measurement made
| > > _simultaneously_ around the entire edge of the
| > > disk. For an inertial observer (e.g. of the
| > > inertial frame in which the center is at rest) this
| > > is easy; for a rotating observer on the disk itself
| > > this is impossible -- there is no single self-
| > > consistent definition of simultaneity for a
| > > rotating system.
| >
| > Gerald L. O'Barr <globarr@xxxxxxxxx> comments:
| > Sure sounds funny. Are you sure that such a
| > simple thing as a rotation is beyond a consistent
| > definition of simultaneity? LET has no problem with
| > doing any of these things. Maybe LET is superior to
| > SR?
| >
| > Tom Roberts <tjroberts...@xxxxxxxxxxxxx> wrote:
| > > So you _must_ change your notion of what
| > > "circumference" means for a rotating disk.
| >
| > O'Barr comments:
| > Again, this sure sounds funny! Does the
| > circumference disappears? Or does it change its
| > nature? And at what velocity does all this occur?
| > What I think is that you are embarrassed at what SR
| > says, so rather than give up on your favorite
| > approach, you would rather change the meaning of what
| > is is.
|
| It's interesting that you were able to come up with the correct answer
| quite easily (apparently) from "LET". I don't think that LET and SR
| are necessarily different theories -- at least not incompatible or
| operationally different theories: I would not say that "LET works here
| and SR doesn't". Rather, to unobscure the question, one needs the
| LET-like way of viewing SR: the predictions of SR _are_ the predictions
| of LET.
|
| As for a natural definition of the rotating circumferance, I can think
| of two: one is to project the disk onto a nonrotating background, and
| measure the circumference of the image, the other is to walk around the
| circumference of the rotating disk with a meter stick, laying it off
| end to end. The difference between these two circumferences will be
| just a factor of gamma -- and neither will be the rest circumference,
| in general, since as you know, the disk is stressed -- assuming it
| doesn't break up.
|
| The first definition relies on simultaneity in the lab frame to define
| one measure, the other side-steps the issue of simultaneity
| altogether, or maybe better, limits it to a local simultaneity of the
| ends of the meter stick in the instantaneous inertial frame.
|
| "Simultaneity" is something we learn to worry about to resolves seeming
| paradoxes in SR, but in the end all that matter are predictions for
| operational tests: will the disk be stressed, and by how much?
|
| > Tom Roberts <tjroberts...@xxxxxxxxxxxxx> wrote:
| > > If instead of a solid disk you imagine a "disk"
| > > made up of thin radial fibers with increasing
| > > widths such that together they make up the disk ]
| > > when not rotating, then as the set of fibers starts
| > > rotating, small gaps will appear between the
| > > fibers, getting larger as the tangential velocity
| > > increases. Of course in practice this is
| > > immeasurably small, and for practical materials the
| > > fibers will be torn apart long before either an
| > > appreciable fraction of c is achieved or the gaps
| > > are observable.
| >
| > O'Barr comments:
| > The only gaps I know about are the gaps in your
| > head. There are no gaps in materials that have
| > rotational motion, never more than what are always
| > there, just as in linear motions, except what can be
| > attributed to internal stresses.
|
| Oh... give him his due. There is nothing wrong with this fiber
| approach, if he can't get a handle on it any other way.
|
| > What Tom says about any inertial frame is correct.
| > In any inertial frame, every clock can be perfectly
| > synced, and every measurement will be SR perfect.
| > What Tom is slow in saying that in such a perfect
| > measurement system, the length of all moving rulers
| > in that frame will be measured by these perfect tools
| > to change their lengths in the direction of their
| > motions, and all clocks will be measured to slow
| > down. These things are exactly what are measured.
| > But Tom does not like to say that any of these
| > measurements are what is actually happening. He
| > really doesn't think that there are any real changes
| > at all.
|
| The edgy character is SR is due to the reciprocity of the Lorentz
| transformation -- it's impossible to say in which direction the changes
| are "really happening". Thus, many tend to think of them as "not
| really happening". We have a concept splitting: they really happen in
| the sense they have real consequences, which are brought to the fore by
| thought experiments such as this, but "unreal" in the sense of
| reciprocity. But we can always get the correct answer, in SR at least,
| by assuming there is some ideal -- if unknown -- inertial coordinate
| systems containing the "real" information. In this problem we can make
| this ideal frame the inertial lab frame, in which the disk is rotating.
|
|
| > But when you go into a rotation mode, then these
| > changes are harder to ignore. Their reality become
| > more clear. And thus Tom needs to say that other
| > things become a problem, so he can ignore these
| > impossible possibilities that real changes really do
| > occur.
| > Sorry, Tom, you simply are wrong to support SR,
| > ****as you want to understand it!****
|
| I'm glad you added that qualifier.
|
| > and you know are wrong! I am waiting for the day you
| > retire, and will be free to say what you ought to be
| > saying.
|
| I really doubt Tom has closet heretical views. I have a feeling his
| views are his views.
|
| > Yes, some changes in SR are due to other
| > things changing, but not all.
|
| That's obscure.
|
| > Some changes, under
| > some conditions, have to be real in order for it to
| > all happen the way it happens.
|
| They have to be "real" in the sense that they have real consequences
| under the appropriate circumstances. Maybe we could draw a rough
| analogy to the apparent increase in the dimensions of a cube when we
| rotate is away from a face-on view. Whether or not the change is
| "real" depends on if we want to think of the abstract cube in
| isolation, or if we are trying to fit it through a door!
|
| Actually, I think its a fairly good analogy.
Maybe we could draw an analogy that you are obscure.
I think that's a really good analogy because I thought of it.
.
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- does circumference contract with velocity?
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- Re: does circumference contract with velocity?
- From: Tom Roberts
- Re: does circumference contract with velocity?
- From: Gerald L. O'Barr
- Re: does circumference contract with velocity?
- From: Edward Green
- does circumference contract with velocity?
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