Spinning disk and the speed of light

[MeJennifer]

There is certainly a circumference for the disk in a non-rotating Minkowskian frame. However, there isn't really any such thing as the circumference in a "rotating frame".

But there is!
If you stand on the edge of a disk and I stand right next to you and you start to rotate on it and I stay inertial we will meet again.
Needless to say that we would not agree at all on both the duration and distance of the trip but nevertheless we would both agree our wordlines formed a closed loop!

And the helix example shows why. Or rather it should show why. You seem not to get the point I'm trying to make, and I don't understand the difficulty. And I don't seem to be able to think of a way to explain it better than I already have.

The helix example shows something else, it shows that if we insist on splitting space-time in 3+1 for an observer on the disk we will have many troubles ahead to put it mildly.

You seem not to get the point I'm trying to make, and I don't understand the difficulty.

Actually I think do get your point but I am lost as to why your point has anything to do with: "...the "circumference" of the helix in the above article isn't really well defined, because it just isn't a geometrically closed object."

It seems that your point is that there is no proper plane of simultaneity describing the complete ring (let alone the disk) for an accelerating observer on the ring, and thus one cannot calculate the circumference in terms of space only. And I do not disagree with that! I am fully aware of that.
But that does not mean that there is no circumference!

 

[Demystifier]

Sometimes I'm a little slow. Are you actually claiming to *be* H Nikolic? If so, a hearty welcome to PF, and many cyber kow-tows.

https://www.physicsforums.com/showpost.php?p=1196920&postcount=11

makes me think this is in fact the case. Of course, if you're just, to use the idiomatic expression, yanking our chains, I take it all back...

Well, I cannot prove this, but yes, I am H. Nikolic.
By the way, I am not a native english speaker, so plese explain me the expressions "kow-tows" and "yanking our chains, I take it all back"! Thanks!

 

[pervect]

Hi, and welcome to Physics forums!

A kow-tow is a gesture of respect, literally a deep bow - a detailed description is in the wikipedia article http://en.wikipedia.org/wiki/Kowtow

To yank someone's chain is to decieve or manipulate somoene. A google search turns up http://www.thefreedictionary.com/yank+chain

 

[Chris Hillman]

Clarification needed?

Oh dear! In trying to walk the fine line between avoiding the kind of "discussion" which drove me out of sci.physics.* and then out of WP, while not entirely ducking my responsibility to try to correct serious errors should I spot them, I may have once again stepped on several toes.

For the good order Chris, my questions were simply made from a perspective of clarification and improving my understanding not from a position of trying to contradict you.
I am here to learn and in the best of my ability, which is not that great, to help others.

Jennifer, don't worry, I have enjoyed your questions and I do think you are trying to learn, which I much appreciate!

Be aware that some of the same individuals who played a role in driving me out of sci.physics.* and later out of WP have PF accounts, and naturally I wish to avoid encouraging them to try to drive me out of PF too! (To avoid confusion: at the moment of my post, I don't think any of them have shown up in this thread, but I wish to duck out before that happens. And I certainly with to avoid naming names or to encourage guessing, but the only way to do that appears to be for me to quit this thread, or even PF.)

I do see now how much time and effort Chris has devoted to write all these
articles. Don't let this get you down Chris!

Thanks! I really appreciate that! My hope is that those who see them and are not yet familiar with frame fields, the kinematical decomposition of a timelike congruence (acceleration vector, expansion tensor, vorticity tensor) will be motivated to learn these concepts/techniques so that they can read the articles with full appreciation.

I like them only partially. Since I was not completely satisfied with the existing resolutions of the Ehrenfest paradox, I made my own resolution:
http://arxiv.org/abs/gr-qc/9904078
See also
http://arxiv.org/abs/gr-qc/0307011

Which I studied, along with many dozens of other papers or arxiv eprints, when I was writing "my" versions of the WP articles I cited. (Again, these were at least somewhat collaborative, with User:Pjacobi making important contribs to at least one article.) I made a conscious decision not to cite all the research papers I studied (dating back to the original papers) because I believe that general encyclopedia articles should simply cite a review paper in preference to repeating the citations in such a review. (It is safe to assume I read all the arXiv eprints and all the papers cited by Gron, for example.)

Well, I cannot prove this, but yes, I am H. Nikolic.

Well, you guess correctly that I consider some of your papers correct and others somewhat misleading, but I plead exhaustion. That whole experience was so horrific that I doubt I'll ever to seriously discuss this topic again--- in my initial comments I was simply trying to point some members toward my own previous attempt to summarize some of the best previous contributions. While in happier times I would have been eager to learn from knowledgeable and insightful comments on my own writings, I think I'll have to let the cited versions of these articles speak for themselves, and to avoid any further discussions, especially in fora filled with pseudonymous "personas".

Like pervect, I was not aware until you spoke up that you are Nikolic, but thanks for clarifying this. For what it is worth, I was not thinking of you when I mentioned the large number of awful papers/eprints in this subject: I was thinking of authors whose papers I consider entirely without any redeeming features whatsoever, the kind of author who ignores the vast pre-existing literature, either out of laziness or out of the assumption that their own "brilliant insights" render all prior efforts moot. Paraphrasing the late Lloyd Bentsen (an American politician), all I have to say to those people is "You, sir, are no Einstein!". I don't think they are here yet but (having said what I just said) I should leave before they turn up!

Shucks - here I thought we could have an argument and maybe I could learn something.

As could I! And in happier times there would have been nothing I would have enjoyed more. Since you cited the RfC in which my comment rather obviously reflects my distress over my bitter disillusionment with WP (a volunteer project I joined with perhaps overly idealistic enthusiasm, because its stated goal, of bringing good information, understanding and appreciation to the masses, is so dear to my heart) and my anger over the way in which leadership failures (in regard to policy and procedure) fostered an environment so hostile to scholars that one stubborn ignoramus succeeded in destroying, apparently permanently, my former enjoyment of writing about math/physics, I hope and expect that you realize that my inability to continue to participate in this thread has nothing to do with you. Utopian social experiments have a long history of destruction, and apparently WP is no exception to this rule.

I will also agree with Chris's remarks that there are unfortunately a lot of confused papers out there on the topic, so that the student who picks a paper at random on the rotating disk, seeking enlightenment, risks being further confused.

Thanks for that!

I think our current disagreement is a judgement of degree regarding how much effort one should expect to expend in learning this subject well enough to make well-informed and thoughtful comments.

My position is that this area is extraordinarly subtle, full of conceptual pitfalls. In fact, one could say (paraphrasing Misner) that this topic may be a universal mindtrap offering ample scope for every conceptual error it is possible to make in relativistic physics.

(A predatory philosopher could go on a most satisfying rampage here. I find it frustrating to observe that young philosophers of physics seem to invariably be guided into revisiting the same tired ground endlessly contested by their elders, when there is so much fertile territory for ripping careless argumention to shreds in the very next feedlot, as it were.)

I have two suggestions for a compromise:

1. A related and very interesting topic (analyzing "fishing" in Rindler or Schwarzschild models) has recently been discussed at length by Greg Egan http://gregegan.customer.netspace.net.au/SCIENCE/Rindler/RindlerHorizon.html where one can begin to see some of the subtlety of trying to treat deformed materials relativistically, even if one tries to avoid developing a fully fledged general theory of elasticity. In my experience, those who haven't attempted a detailed analysis of an idealized model (and who haven't critically examined about their results) tend to vastly underappreciate this subtlety.

2. Give me some time (months? years?) to get a bit less depressed over this topic and PM me to arrange a one-one discussion--- maybe bye and bye I will find this topic somewhat less distressing. My only request would be that you get some experience using frame fields and kinematic decomposion first, since my analysis was based on these techniques and I worked hard to make that analysis clear to anyone with this background knowledge, and in invading unknown territory it is best to avoid splitting up the expeditionary force, as it were. (C.f. Stanley's notorious mission to "rescue" Emin Pasha--- which I see is quite inadequately explained in his WP wikibio.)

 

[pervect]

2. Give me some time (months? years?) to get a bit less depressed over this topic and PM me to arrange a one-one discussion--- maybe bye and bye I will find this topic somewhat less distressing. My only request would be that you get some experience using frame fields and kinematic decomposion first, since my analysis was based on these techniques and I worked hard to make that analysis clear to anyone with this background knowledge, and in invading unknown territory it is best to avoid splitting up the expeditionary force, as it were. (C.f. Stanley's notorious mission to "rescue" Emin Pasha--- which I see is quite inadequately explained in his WP wikibio.)

I'm also sorry if I have stepped on any toes - I think PF badly needs more knowledgeable people, especially in the relativity forums, and I'd like to recruit as many as possible - and definitely I don't want to drive any away, or contribute to driving any away.

I'm reasonably familiar with frame fields. However, I'm not as familiar with the vorticity tensor, the expansion tensor, or the Raychahurdi equation as I would really like, though I've at least heard of them. (I gather that the Raychahurdi equation is what you are referring to as a "kinematic decomposition"?). Also, I have not yet had a chance to read Gron - it's on my list to grab the next time I make it to a library with access. But if it will take you years to feel like talking about it again, I guess I have plenty of time to fetch it :-). (I should also add that I'm not particularly fond of E-mail, but of course that's not your problem, it's a personal quirk of mine, one of many, and I'm not opposed to it enough to miss a good physics discussion).

I'd really like your opinion on the spinning buckytube wire analysis I posted. (I have the depressing thought that your reply will show that it's not as clearly written as I could hope for, though I've tried to clarify a few points and I've made minor edits to it for hopefully improved clarity).

I'll expand on the analysis with a little conceptual overview. First off, one can view the wire as a swarm of atoms. And one can regard the atoms as connected to each other by springs, which are an abstract representation of the electromagnetic fields.

My first point is that in physically known materials like the buckycable, the amount of energy in the "springs", i.e. the fields holding the atoms together, is basically negligible. I go through some calculations to hopefully demonstrate this, using Hooke's law (which I feel is applied well within its bounds of applicability) - and to come up with a number for the magnitude of the energy stored in this form. I point out that this has an elementary interpretation in terms of non-relativistic mechanics, that the energy stored in these interatomic fields is just the work done in stretching the wire.

My next point is that because the energy in the fields is neglgible, we can basically justify the approximation of the wire as n atoms, each of which has a velocity v. Because the velocity is so low, we can use the Newtonian formula for kinetic energy. Because the energy in the fields is so small we are justified in ignoring the amount of energy it takes to set these fields in motion (it will be present, but small). We then have a complete reasonably accurate accounting for the total energy of the spinning wire. This is just the number of atoms in the wire (which is a relativistic invariant), multipled by the energy (rest mass*c^2) of each atom, multiplied by the gamma factor. In this case the velocity is so low that one can equally well use the Newtonian formula mc^2 + .5 m v^2 instead of multiplying by gamma. The energy in the mechanical stretching of the wire is also present, but it's basically so small in magnitude as to be irrelevant.

I could try to make the presentation a bit more formal, by actually writing down the stress-energy tensor that I expect in the non-rotating frame explicitly. But to do this I would need Poisson's ratio for the bucky material or equivalent information - i.e. information on how much the width of the wire changes when we stretch it under tension. I think it is simpler to talk about the total energy of the wire, instead and avoid the issue. It's simplest to focus on the number of atoms (which does not change) - which we can do, since the contribution to the stress-energy tensor of the fields holding the atoms together is so small.

 

[pervect]

I've been reading "Relataivisitc contraction and related effects" in non-inertial frames, http://arxiv.org/abs/gr-qc/9904078, and I have a few comments

The way that the "generally accepted line element" is determined is to integrate the Lorentz interval along a joining line of constant time. "Constant time" is defined by the coordinate system used.

This seems to be pretty much universal - for instance, this is how the cosmologists arrive at what they call, variously, proper distance or sometimes comoving distance - by integratng the Lorentz interval along a line joining the two points of constant cosmological time.

This then gives the formula quoted in the paper as the "conventional formula" - because t is constant, all the terms with dt in them are zero in the line element for distance.

The proposal to replace the line element seems to me to be equivalent to integrating the Lorentz interval over some other curve to define a distance measure, i.e. some curve other than a curve of constant coordinate time. I haven't quite worked out the details of exactly what curve this corresponds to, though I have some suspicions which I won't write down at this point.

 

[Chris Hillman]

We're cool, man, we're cool!

Hi, pervect,

I'm also sorry if I have stepped on any toes - I think PF badly needs more knowledgeable people, especially in the relativity forums, and I'd like to recruit as many as possible - and definitely I don't want to drive any away, or contribute to driving any away.

I wasn't worrying about Jennifer driving me away, or H. Nikolic driving me away, or in fact about anyone who has yet participated in this thread. And
I certainly am not worrying about you driving me away! You're one of the main reasons why I bother to turn up here at all! (That's a convoluted compliment.) I'll take the unusual step of explaining a bit of background by PM.

I'm reasonably familiar with frame fields. However, I'm not as familiar with the vorticity tensor, the expansion tensor, or the Raychahurdi equation as I would really like, though I've at least heard of them. (I gather that the Raychahurdi equation is what you are referring to as a "kinematic decomposition"?).

Actually, it is what you start with to derive the Raychaudhuri equation. Namely, the invariant decomposition of any timelike vector field into acceleration vector, expansion tensor, and vorticity tensor. The expansion tensor is designed exactly to answer questions like "is this thing rigid", so recoiling in fear of the unfamiliar is like me telling someone who wants to compute volume "futzing with complicated and confusing sequence of simplicial approximations is all fine and well, but there's this thing called integral calculus which you really outta learn forthwith". Once you become familiar with this stuff I am confident you will agree with my little analogy! This is an absolutely fundamental concept, useful for a gazillion things, many having nothing to do with gtr or even physics.

(For example, the Hopf fibration is a lovely thing: as an exercise, you should compute the expansion and vorticity tensor of the Clifford congruence on S^3, which consists of a family of great circles which fills up the sphere; each pair is linked but they maintain constant distance while twisting around one another in the sense of vorticity; this is possible because the geodesic convergence due to positive curvature exactly compensates for the increase in distance from the "twisting"; compare a pair of Clifford circles with a pair of skew lines in euclidean three-space.)

Incidently, gr-qc/??12140 (oh no, a bit error, I've been zapped by a cosmic ray or something) by Costa and Herdeiro, has a nice remark about the so-called Raychaudhuri scalar, which in terms of the electrogravitic or tidal tensor is analogous to Gauss's law with a pressure term added to the mass density; see Baez and Bunn's well known expository eprint, "The Meaning of the EFE".