Talk:Ehrenfest paradox/Archive 1

Resolution of the paradox?=

So what happens to the disk? Does it shrink from the Lorentz contraction? Does the circumference change? Tzarius 11:00, 22 March 2006 (UTC)

Rotation is not compatible with rigidity, see Born rigidity. What will happen depends on the elastic properties of the disk. --Pjacobi 18:10, 12 April 2006 (UTC)

The details of what happens to a real disk depend upon the material properties of the disk, but the basic ideas are summarized in the last section of the new version (see below). ---CH 01:33, 28 May 2006 (UTC)

New version

I have replaced the stub with a completely new version which parallels the discussion in Born coordinates, as promised.

In my view, the citations presently given are more than adequate, since this is an encyclopedia article, not a review article in Reviews of Modern Physics. It is very likely that sooner or later cranks will want to add citations to their own incorrect web "paper" (or even a cranky recent arXiv eprint or two or three or five). Such edits should be reverted with a pointer to the FAQ article or the 1977 and 2002 Grøn papers. Be aware that several of the papers in the 2002 book are mostly incorrect. In fact, most papers in this area are frankly not of sufficient quality to even be worth reading, much less citing.---CH 01:27, 28 May 2006 (UTC)

I deprecate red links for non-notable figures. However, Weyssenhoff is probably notable and the philosopher Adolph Grünbaum certainly is notable as a well known 20th century philosopher wrote wrote extensively about the philosophy of space and time. Janis is the Janis of the Janis-Newman-Winacour solution. Don't red link any of those unless you have already improved the wikibiography of Newman. ---CH 01:58, 28 May 2006 (UTC)

I'm impressed by the work you put into this article. Still, as it is now, the paradox isn't clearly stated and even difficult to find (there is a definite need for a plain English summary intro). It's also worth elaborating on what happens to the disc, while stressing that that question is very different from that about the geometry of rotating frames. Harald88 10:51, 28 May 2006 (UTC)

I was aware of this when I declared the new version substantially complete (when I removed the inuse flag). I have kept this possible objection in mind and if an idea occurs to me for ameliorating the problem (which is not outweighed by other considerations), I will try it out. For the moment, here is my explanation of the origin of this flaw in the current version:

It would be awkward to try give complete statements of "the" paradox because as I tried to briefly explain in the article, the "paradox" was mis-stated by Ehrenfest in 1909: he thought the circumference would be shorter as measured by disk-riding observers, whereas Einstein showed in 1916 that it will be longer. Since (due to the inadequacy of both existing articles dealing with the so-called "Lorentz contraction") I needed to pause to describe (without pretending to really discuss or explain) the relevant trigonometry, it would have been impossible to avoid a very lengthy "introduction" had I not tried to oversimplify. Incidently, I did consider quoting Ehrenfest's original formulation in a later section, following Grøn, but since the original text is confusing even as a statement of Ehrenfest's incorrect version, I then would have needed to explain what Ehrenfest was trying to say, which would have been more distracting that enlightening, and would have unbalanced the structure even further.

In any case, since I needed to functionally separate the introduction or executive summary from the section summarizing various mostly positive contributions, I was forced to try to extract what is common to Ehrenfest and Einstein for the statment in the introduction, and to shove the difference between their version into the "history" section. But I thought (and still think) this is actually beneficial since it hopefully draws in and helps to guide the reader.

Another problem: it is a bit difficult to find clear statements of what individual researchers found so "paradoxical" at various times during the long (and irritating/comical) history of this topic, particularly since many authors, even most, do not bother to try to explain precisely what is troubling them! To some extent, this complaint is unfair since of course an author who can clearly explain what is troubling him can usually clearly explain a satisficatory resolution of the problem.

In the "history" section, I tried to avoid mentioning the many papers (including almost all recent eprints) which are mostly or entirely incorrect, for various reasons:

1. Explaining mistakes would greatly increase the length of the article,
2. Many papers actually repeat much earlier mistakes and fail to take any account of previous advances in understanding; established this in particular cases would again greatly increase the length of the article,
3. This is not a historical survey in Archive for the History of Exact Sciences or a review article in Review of Modern Physics,
4. I find the history in no way edifying, except for the one point I mention which might be of interest to historians of science (second-tier literature which ignores previous work by leaders in the field, possibly because the authors simply haven't grasped this earlier work),
5. I hope to avoid arguing with kooks over incorrect arguments in various recent eprints, which would only confuse everyone who hasn't mastered the literature and appropriate techniques.

This partially explains why I wound up saying very little about what would happen to a real disk, since (as I did say) one of the major sources of error in most of these papers is that authors tried to apply an ill-considered idealization which confuses rather than clarifies the situation. I do think that the summary, while short, does summarize the essence of the problems noted by various authors including Grøn. However, I expected and still expect to say a bit more about the question of what happens to a real disk when more background articles are in place. In particular, once adequate articles are in place on Kleinian geometry, I expect that existing articles on so-called "Lorentz contraction" can be merged with material from the first section on the trigonometric way to understand this effect, which should enable me to shorten that section.---CH 15:57, 29 May 2006 (UTC)

Thanks for the largely expanded new version! This effort is by no means diminished by some nitpicking, I have to do:

• I'm still a little missing my old stub [1], as I fear the new version will leave non-expert readers clueless. Perhaps the summary in Section 0 can be expanded a bit.
• And, as some of your other contributions, you use a narrative discouraged by our manual of style ("We", etc). I hope some of our busy copy-editors will give this a look. I, not being a native speaker, prefer to abstain from most of copy editing, in fear of introducing new errors.

Pjacobi 16:18, 29 May 2006 (UTC)

I liked some aspects of the stub, and just experimented with trying to incorporate it (suitably rewritten) into a new section right after the executive summary, but the result was pretty dreadful. I consider the manual of style to offer general guidelines, not iron-clad rules. In particular, "we" is a common convention in mathematical exposition, as you probably know. There is a nice book (with contributions of Halmos and other noted expositors) on mathematical writing which I could cite if anyone would be willing to read it. In fact there are two or three books I could cite, plus the Chauvenet prize volumes. To make a long story short, use of "we" evokes great passion pro and con. But so does every alternative. ---CH 16:33, 29 May 2006 (UTC)

Peter and Harald: I hope it is clear that I acknowledge your concerns, in fact these same concerns had already occurred to me! I felt that the solution to multiple concerns I came up with was the best available in lieu of further neccessary background articles. I just revisited this and what I did still seems like the best solution to me overall, taking everything into account. I'm not entirely happy with this state of affairs either, but I'd prefer to wait until I have a better idea (or someone suggests an idea I haven't already tried and rejected myself). ---CH 16:36, 29 May 2006 (UTC)

"Correct" statement of the "paradox"?

I think that Peter's stub is in fact a great summary.

1. Out of concern for the general reader, something like that needs to be in the intro.

2. However, his version seems to subtly disagree with the version by Chris.

By chance, only last week I discussed and explained the rotating disc issue to a friend, happily leaning on the draft overview on http://freeweb.supereva.com/solciclos/gron_d.pdf (the first page is blank). At that time I didn't pay attention to Ehrenfest, instead I used the citations to explain to him how differently stating the problem results in seemingly contradictory answers. Thus I will have to read it again, and compare it with this article. To remove all confusion, this article must first of all conform in essence with the paradox as Eherenfest stated it. Harald88 22:29, 29 May 2006 (UTC)

No, no, my version wasn't in disagreement, it was only significantly more modest. It only goes to what is seen by the inertial observer, leaving comoving, corotating observes as an exercise for the reader. --Pjacobi 18:57, 30 May 2006 (UTC)

Well, that is exactly how I understand Ehrenfest's description of his paradox. But in that case the presentation of the paradox as presented now is erroneous, and also the phrase that Albert Einstein notices something overlooked for seven years: the disk-riding observers measure a longer circumference, C′ = 2 π r √(1-v^2)-1, not a shorter one, not C′ = 2 π r √(1-v^2), as Ehrenfest had claimed.

Where did Ehrenfest make such a claim? Harald88 20:08, 30 May 2006 (UTC)

Harald, since the historical review by Grøn is readily available on-line, why don't you take some time to study that? As you will see, you have somehow misunderstood the order of events.

I think I confused you when I spoke of "two versions". I probably should have referred to "the original incorrect statement and the later correct statement of the so-called paradox". Particularly since in later versions I might discuss related but distinct "paradoxes" involving rotating charged cylinders and suchlike.

With primed quantities denoting the result of measurements by disk-riding observers and unprimed quantities the result of measurements by static observers, here are the two versions: in Ehrenfest's 1909 statement of the paradox, he concluded that while r = r', C' = C √ (1-v^2) < C. Much later, in 1916, Einstein noticed that Ehrenfest goofed; he should have said r = r', C' = C (√ (1-v^2))^-1 > C. IIRC, Ehrenfest gracefully accepted this correction. In any case (see Grøn 2002) there is a clear consensus that there is only one correct statement of the original "paradox" and that is Einstein's statement. Whew! I hope that is clear now! If not, read Grøn 2002.

BTW, Ehrenfest, published three or four papers discussing his version between 1909 and 1916. See Grøn's historical survey. ---CH 21:23, 30 May 2006 (UTC)

I discussed Ehrenfest's description of 1909 as first cited in that draft paper by Gron - hey it was me who provided that link! His first version looks fine to me; I didn't spot C' = C √ (1-v^2) < C but only C' < C; and he seems to describe exactly what Pjacobi presented but not what Einstein presented, which as Planck had pointed out, is something entirely different. I'll read it again tomorrow to see if I can also read it in such a way that it is wrong. Harald88 21:58, 30 May 2006 (UTC)

OK, I think you'll see that my description completely agrees with Grøn. Note that Pjacobi agrees with me on this point. ---CH 02:29, 31 May 2006 (UTC)

I'm far from convinced that it agrees with Grøn's rendering of Ehrenfest or, (and that is essential), with Ehrenfest himself.

The citated parts of Ehrenfest in Grøn appear to be about dynamics as viewed from the stationary frame only. Does anyone have Ehrenfest's paper? It is probable that the full paper is clearer than the few cited passages.

Meanwhile, as a reminder, here is again the old intro which according to you agrees with you and not with me, but which really looks excellent to me:

The Ehrenfest paradox, first presented by Paul Ehrenfest 1909 in the Physikalische Zeitschrift, is an apparent paradox in relativity.

In its original formulation it discusses the rotation of a rigid disc. The radius R as seen in the laboratory frame will be equal to its value for the stationary disc. But the perimeter p will be Lorentz-contracted to smaller value than at rest, by the usual factor γ.

At the most basic level, the paradox stems from the fact that rigid bodies are not compatible with relativity, and even a carefully chosen setup of forces to mimick rigid bodies is possible only for selected cases, not including a rigid rotating disc.

But after clarifying the situation for the inertial observer, discussions about the situation as seen by co-moving observers continue to the present day. In fact, the Ehrenfest paradox may be the most basic phenomenon in relativity that still gets different interpretations published in peer-reviewed journals.

Harald88 20:51, 1 June 2006 (UTC)

Have you studied the paper by Grøn as I suggested, or have you not? I don't see why you are having such difficulty seeing that the quoted text is saying exactly the same thing I did, only at much greater length. ---CH 02:17, 2 June 2006 (UTC)

Sure I studied the internet version one week before this discussion. I also studied the Ehrenfest article now, it turned out that I already had it.

A bit misleading in Grøn is that in his summary it looks as if Ehrenfest used both the stationary frame formulation and the co-moving frame formulation.

Instead, Ehrenfest explicitly stated that in his analysis he only used the stationary frame definition of "relativistically rigid".

But I found that Grøn's page 19 is particularly clarifying, and that Eddington sketched Ehrenfest's paradox correctly. Ehrenfest showed with a dynamic example that a rotating rigid cylinder is self-contradictory, while Einstein didn't consider that problem at all.

Max Planck had already pointed out in 1910 that one shouldn't confuse such analyses. In order not to similarly confuse the readers, it's necessary to similarly split up the article between the Ehrenfest paradox and the Einstein rotating disc analysis. In fact, that analysis is unrelated, and thus arguably off-topic. At most a small part of this article should be devoted to it. Harald88 09:15, 3 June 2006 (UTC)

I take it that after seeing PJacobi's figure below you have come around to his/my POV regarding the Ehrenfest paradox in Einstein 1916 versus Ehernfest 1909? ---CH 09:38, 3 June 2006 (UTC)

I take it that after reading Ehrenfest's article, he will support a correct rendering of it in Wikipedia. Have you actually read Ehrenfest's paper? If you know German, I can send it to you. Harald88 10:01, 3 June 2006 (UTC)

I can read German if I must but don't worry, I can get the paper elsewhere. Are you willing to let me improve the article? I take it you do realize that PJacobi agrees that he, myself, and Grøn are all in agreement here? I think the problem is that the current version is confusing you, but if you are willing to walk through it with me (er.. tomorrow?), I hope that by explaining whatever is confusing you I can improve the article myself. Does that sound good to you? ---CH 10:37, 3 June 2006 (UTC)

Not really: Wikipedia articles are supposed to be group efforts by a number of editors, and editors are requested to "be bold". IMO anyone who does not know Ehrenfest's paper should not edit a discussion of it. The problem is that you didn't base yourself on the original text and probably Grøn's paper confused you; moreover the article now smells of WP:OR. But there is no hurry, we all have our lives. Harald88 14:39, 3 June 2006 (UTC)

BTW, this is how http://www2.corepower.com:8080/~relfaq/rigid_disk.html summarizes Ehrenfest's paper: Ehrenfest noted that a disk cannot be brought from rest into a state of rotation without violating Born's condition. Integrating tau out of Born's condition, we see that infinitesimally close particles must keep the same proper distance. So in the original rest frame, they suffer Lorentz contraction in the transverse direction but none in the radial direction. The circumference contracts but the radius doesn't. But in the original rest frame, the circumference is a circle, sitting in a spatial slice (t=constant) of ordinary flat Minkowski spacetime. In other words, we would have a "non_Euclidean circle" sitting in ordinary Euclidean space. This is a contradiction. Regards, Harald88 14:48, 3 June 2006 (UTC)

Suggestion for improvement

It seems to me that the section "Statement of the 'paradox'" doesn't get around to stating the issue until the last paragraph. Before that is very technical overview of special relativity that I suspect will be a major turn-off to most readers. I suggest that this overview be removed. It would help the article tremendously if it would "cut to the chase" and deal directly with the "paradox" first. Then it can bring up the issues created in resolving the paradox. --EMS | Talk 13:58, 2 June 2006 (UTC)

Exactly! - that's what Pjacobi and I stressed above. What do you think of his version as intro? Harald88 08:35, 3 June 2006 (UTC)

EMS and Harald: frame fields and coordinate charts are a fundamental tool in working with Lorentzian manifolds. I'd be happy to walk step by step through any computations.

I trust I have made it clear that once background articles are in place, I expect to improve this article. However, I think it is best if you (Harald) let me do that myself. ---CH 09:40, 3 June 2006 (UTC)

Wikipedia is a common effort by the world community which helps to smoothly eliminate errors by individuals. In the long run, this may allow Wikipedia to become better than for example Brittannica. Harald88 09:58, 3 June 2006 (UTC)

Er... I'll take that as "yes". ---CH 10:38, 3 June 2006 (UTC)

Hmm... lookit those timestamps... Carl Hewitt strikes again! --CH 10:40, 3 June 2006 (UTC)

Ehrenfest train

After day's work I've decided to try my creative side and aimed for an illustration which may appeal to readers not interested in mathematics.

As most modern authors, I'd suggest to leave the question of expansion of the disk by centrifugal forces aside and take the setup of an (elastic) ring in fixed gearing. IMHO it's gets even more illustrative, when dividing the elastic ring in rigid and and elastic sections.

At rest

At 0.6c

Voila! The Ehrenfest train, consisting of 40" boxcars alternating with elastic joiners, at rest also 40" long.

In the example pictures 12 boxcars are choosen. In the left picture you see the situation at rest. On board (light red) and platform-side (light blue) yard sticks agree, that

• a boxcars measures 40"
• a joint measures 40"
• the complete train measures 960"

In the right pictures the trains moves with 0.6c. Now the platform-side (light blue) yard sticks give, that

• a boxcars measures 32"
• a joint measures 48"
• the complete train measures 960"

Whereas the on board (light red) yard sticks give, that:

• a boxcars measures 40"
• a joint measures 60"
• the complete train measures 1200"

BTW, the Ehrenfest train can also do double duty as Bell's spaceship paradox on rails.

Pjacobi 00:46, 3 June 2006 (UTC)

That's great! Your example does provide a simpler variant of Einstein's rotating disc analysis, and is thus neat as introduction for that. But Ehrenfest showed the impossibility of rotating an otherwise unelastic cylinder, and I don't think that this example makes that clear.

IMHO it's better to separate these analyses in two distinct articles: One about the Ehrenfest paradox, and a more general one about the rotating disc in relativity. Harald88 09:31, 3 June 2006 (UTC)

Good work, Peter! I will incorporate these figures somehow tommorrow. ---CH 09:34, 3 June 2006 (UTC)

Harald, please let me revise the article myself

Harald, I have not denied that my version has shortcomings. Ed and Peter have made good suggestions which I am considering how to implement. I thought you were going to let me revise it myself?

About Ehrenfest: you are somehow confused. I did not mischaracterize Ehrenfest's statement; you simply misunderstood what I wrote. If you will just give me a chance to revise the article myself, this might become moot since the problem is that you have misunderstood the current version. OK? ---CH 22:14, 3 June 2006 (UTC)

Please be aware that "let people revise articles themselves" doesn't fit with Wikipedia philosophy. The current version doesn't present the facts right, and I follow Wikipedia's policy to "be bold". But I can be patient a few more days; hopefully you'll read and understand Ehrenfest 1909 on Tuesday (a casual reading won't do), and correct some parts accordingly. As this is now a true disagreement about factual accuracy, I'll put up an appropriate banner. Harald88 11:11, 4 June 2006 (UTC)

Harald - I must admit that you are proving to be quite a character here, to the point where it is tempting to remove that tag for no other reason than that you are the one who placed it there. Simply put, you have once again put forward an incorrect interpretation of the facts. Chris' version is in fact the correct explanation of the paradox, and of Ehrenfest's article.

Here is the issue: Let there be a disk which is of radius r but of a circumference of r < 2πr. What we have in that case is a simple non-Euclidean geometry. There is nothing wrong with that. For example, create a circle a mile in radius along the surface of the Earth and measure its circumference, and you will find that the circumference is less than 2πr miles, albeit not by much. What is going on is that the curvature of the Earth has dimished the circumference. In three dimensions, that circle would be seen as having its "real" center insider the Earth, and being of a radius of slight less than 1 mile.

So the "inconsistency" of the radius and the circumference is not the issue. Instead, Ehrenfest concluded that the "static" observer would see the circumference of the disk as still being C = 2πr, which is a Euclidean geometry, while at the same time the disk riding observers would find the circumference of the disk to be C < 2πr, which is non-Euclidean. The contradiction is that the disk cannot physically be both Euclidean and non-Euclidean at the same time. BTW - Do recall that Einstein showed in 1916 that Ehrenfest mistated the paradox (as the disk-riding observer sees C > 2πr and the static observer C = 2πr instead), but this does not undo the assertion of there being a paradox (as C > 2πr is just a diferent type of non-Euclidean geometry).

I kindly request that you study this posting, and then carefully reread the Ehrenfest article yourself. I hope that you will be able to remove the {{disputed}} tag in good faith after that. --EMS | Talk 00:26, 5 June 2006 (UTC)

EMS, instead I have once again put forward a correct presentation of facts; and this time the issue is not open for interpretation, there is no ambiguity. Of course there is no inconsistency of the radius and the circumference but in R'. I kindly request you to study Ehrenfest's paper (it's not much longer than your posting!) and cite the exact phrases where Ehrenfest:

1. claimed that in the "static" frame the circumference of the disk is "still 2πr"

2. stated that "disk riding observers" would find the circumference of the disk to be < 2πr.

It's not Ehrenfest who misstated his own paradox but you. As a matter of fact, he even didn't discuss a disc! Please don't pretend to understand what you haven't even read.

Harald88 09:55, 5 June 2006 (UTC)

Ouch - I'm being sloppy here. Yes - According to Ehrenfest the disk (or whatever) appears OK to the rotating observer and the edge Lorentz contracted to the laboratory observer, while Einstein showed that the disk is OK for the laboratory observer but is expanded for the moving observers. I have correct my statements above, and still stand by my assertion that the crux of the "paradox" is an apparent topology conflict. --EMS | Talk 19:45, 5 June 2006 (UTC)

Addendum - CH is claiming that my edits in response to Harald88 introduce an error instead of removing one. At this point, if I have to choose a side blindly, I would side with CH given the level of experience and history of both. For now, I will seek to find some time for doing a library search. --EMS | Talk 01:24, 6 June 2006 (UTC)

Bingo! - Found what I needed in a Google Scholar search. See below. --EMS | Talk 01:45, 6 June 2006 (UTC)

BTW, Pjacobi's presentation does not have these errors ("disc" instead of "cylinder "(of height H) is a minor glitch):

The radius R as seen in the laboratory frame will be equal to its value for the stationary disc. But the perimeter p will be Lorentz-contracted to smaller value than at rest, by the usual factor γ

I trust that after comparing Ehrenfest's paper with Pjacobi's summary vs. that of CH, you will all see that the presentation of CH is erroneous while that of Pjacobi is quite correct. But to prevent a misunderstanding as EMS suggests here above, it's better to either stick to Ehrenfest's notation as follows;

The radius R' as seen in the laboratory frame should be equal to its value for the stationary disc. But the perimeter 2 π R' should be Lorentz-contracted to a smaller value than at rest, by the usual factor γ. This leads to the contradiction that R'=R and R'<R.

or, preferably, to adopt a more modern standard notation as follows:

The radius R as seen in the laboratory frame should be equal to the value R₀ of the stationary disc. But the circumference 2 π R should be Lorentz-contracted to a smaller value than at rest, by the usual factor γ. This leads to the contradiction that R=R₀ and R<R₀.

Harald88 12:19, 5 June 2006 (UTC)

Harald, it is obvious to myself, Peter, and Ed that you are confused, and I am having a hard time understanding why. For this reason and others, of the four of us, I consider you are by a long margin the least qualified to contemplate any major revisions of the article. I, OTH, wrote almost all of the current version, have recently studied many relevant papers, and am familiar with the relevent mathematics and background.

Leaving aside the issue of whether my own characterization of the essence of what Ehrenfest said is the same as what you quoted:

1. On the one hand, I think you believe that the article should focus on a complete history fully and fairly characterizing the complex views of each participant. I feel that proposal would really call for a book because the history is long and complex, because the views of some participants evolved over time (in particular, I am still not sure whether you appreciate that Ehrenfest wrote several papers and also personal letters discussing this topic), and most of all because all of this would have to be placed in a broader historical context in the history of ideas in physics.
2. On the other hand, I myself believe that the focus of the article should be on clearly explaining the essence of the confusions which have surrounded the long and sometimes contentious history of the "paradox". Peter, Ed, and I all agree that the current version (due almost entirely to myself) has serious shortcomings in that regard. Peter very helpfully produced some fine figures which I want to use in the revision, and Ed has also offered some constructive suggestions. You quite frankly have not offered any constructive suggestions along those lines, probably because you are somehow so confused that you don't even recognize that neither I nor Grøn mischaracterized the essence of what Ehrenfest said.
3. I don't know how much experience you have in expository writing, but one major goal is to avoid unneccessarily distracting the reader by indundating him with a flood of irrelevant detail. In particular, in the case of a cylindrical symmetry, the axial coordinate is inessential, and for our purposes there is no essential distinction between discussing rotating disks and rotating cylinders. Indeed, I did not even bother to mention that the cylindrical chart is adapted to cylindrical symmetry, not to a disk (oblate spheroidal coordinates might be better adapted to a disk, if one really is studying some problem in which the axial coordinate is not inessential, e.g. in studying the gravitational field produced by a massive thin disk).

Harald, you are frankly not being helpful at all. I wish you would be quiet now, let me rewrite the article (you should recognize that this will entail a lot of work), study the result, and then ask any questions, or raise any concerns, in the talk page. OK?---CH 14:32, 5 June 2006 (UTC)

I was a bit slow getting started because wikiservice was a bit slow. This seems to have ameliorated. I just inserted the first section into length contraction and am about to start revising the article. ---CH 15:11, 5 June 2006 (UTC)

So far I fully agree with Pjacobi's version, and apart of the fact that I insist on presenting the paradox as he did, basically he and WMS made the same same suggestions for improvement as I made - just read this page again! Thus you are building up a consistent history of misrepresentation of people's contributions, both in literature and on the Talk pages. After all these insults of you I kindly suggest you to shut up with your unbased criticisms. Although the article as it has been until today, exactly corresponds to "irrelevant detail", I will look at the article after you had a chance to read Ehrenfest's paper in which he stated what now is called "Ehrenfest paradox". Also, I wait with interest for Pjacobi's comments after he has found time to study that paper of Ehrenfest. Harald88 17:41, 5 June 2006 (UTC)

WMS? Do you mean EMS (Ed Schaefer)? Could you please take the time to study the new version, study Grøn's 2002 review, and then to try to explain the nature of your objection clearly and concisely? TIA---CH 18:13, 5 June 2006 (UTC)

BTW, regarding the nature of the dispute between Harald and the rest of us, Harald changed the flag, which I reverted. As I have tried to explain, I think there are good reasons to avoid trying to give a complete description of the enormous literature on this topic (like lack of space). I never claimed to give a complete account (with all the neccessary historical context) of the early papers by Ehrenfest, Planck, Einstein, etc., which deal with this topic. Considerable oversimplification is not only neccessary (lack of space/time) but desirable (service to our readers).

The dispute seems to about about whether my oversimplified summary of Ehrenfest's views is so somehow so terribly unfair to Ehrenfest as to be unacceptable even in this encyclopedia article. Or maybe about which is worse: oversimplifying the history (which I am comfortable with, and Harald apparently not) or oversimplifying the discussion of the resolution (which I am less confortable with, and where Harald apparently wants less detail, not more.) ---CH 18:25, 5 June 2006 (UTC)

My edit line was munged (looks like the servers are badly stressed right now), but I was trying to say that since Harald and I can't even agree on what the dispute is about, I have changed the {{Disputeabout|whatever}} flag back to a {{disputed}} flag. I hope this will be acceptable to Harald. ---CH 18:50, 5 June 2006 (UTC)

According to Gron, the Ehrenfest paradox is named after the contradiction as presented in Ehrenfest 1909. Nothing more is needed in this article, and that would enormously simplify matters. In fact, Ehrenfest's presentation there is just as Pjacobi's stub stated (see also here above) before you removed it (instead of building on it, as is the Wikipedia way). You claim that you and he agree while I agree with his version. Thus in theory we have consensus, and he and I requested it to be reinserted.

Then why do you refuse to reinsert it and instead insist on a rendering that is disputed and which is clearly your own WP:POV and WP:OR? Harald88 18:41, 5 June 2006 (UTC)

Harald, it looks like Peter is too busy to check in right now, but as far as I know, he is not in disagreement with me or Ed over anything. Why don't we all just wait for him to reappear and comment? OK? TIA ---CH 18:50, 5 June 2006 (UTC)

Chris that's fine to me, in fact it's what I had in mind all along. Apparently Ehrenfest wrote in his mother tongue so that any misreading from you and/or me will be best spotted by him.

Still I'll clarify some more below.

Regards, Harald88 22:30, 6 June 2006 (UTC)

The "disputed" tag

My advice at this time is to leave that tag alone. IMO, Harald88 "owns" it, and it gets removed either by him or with the approval of a consensus of the editors. I don't see that the dust has settled on this article anyway, although the Harald does not appreciate the fact the the "paradox" as presented in the stub wasn't even paradoxical.

In any case, I advise that we continue to refine this article, and then if Harald is still standing his ground after we are happy with it (with "we" including Peter and anyone else interested in this topic) then we can do a poll and (given a consensus to do so) remove the tag. I don't see any good reason not to respect the tag for now or not to listen to Harald and see if we can come to an agreement with him without exeerting an undue amount of effort. (I don't expect such an agreement, but a consideration of his objection may lead to better article anyway.) --EMS | Talk 20:01, 5 June 2006 (UTC)

New first section

OK, I think Peter's figures pretty much solved the problem. All I had to do was to cram the distracting trigonometry into another article :-/ and provide a verbal description of the figures to make an entirely new first section. The other sections are almost untouched.

I removed the fact flag from the history section because that section clearly points the reader to the 2002 paper by Grøn which is available on line, quotes (in translation) from Ehrenfest's 1909 paper, and gives complete bibliographic citations to all of Ehrenfest's papers which deal with this topic.

Comments? ---CH 16:26, 5 June 2006 (UTC)

This is a definite improvement. There is still too much jargon in the other sections, but at least that is the issue now. Already people can read this article and get some idea as to what the fuss is all about. --EMS | Talk 17:07, 5 June 2006 (UTC)

I now see a new problem: We have lost the statement of the topology conflict between the two observers, which is the crux of the claim of a paradox. --EMS | Talk 20:17, 5 June 2006 (UTC)

Ehrenfest's original argument

From gr-qc/0309020 "The Relative Space: Space Measurements on a Rotating Platform" by Matteo Luca Ruggiero, published Eur.J.Phys. 24 (2003) 563-573:

"According to Ehrenfest[1], the formulation of the paradox is the following one:
"Let R,R′ be the radii of the rotating disk, as measured, respectively, by the inertial and rotating observer; ω is the constant angular velocity of the disk, as measured in the inertial frame. The paradox arises when the following contradictory statements are taken into account:
"(a) The circumference of the disk must show a contraction relative to its rest state, 2πR < 2πR′, since each element of the circumference moves in its own direction with instantaneous speed ωR.
"(b) If one considers an element of a radius, its instantaneous velocity is perpendicular to its length; thus, an element of the radius cannot show a contraction with respect to the rest state. Therefore R = R′."

So CH is right: Ehrenfest called for the circumference to be contracted, and my orginal posting that Harald88 contested was the correct one.

Harald - The ball is now in your court. If you still believe that I was originally wrong, then kindly produce evidence from the literature that this is not what Ehrenfest was claiming. --EMS | Talk 01:55, 6 June 2006 (UTC)

Specifically, if unprimed = static and primed = disk-riding, then R′ = R but C′ = C (1-v²)^1/2 < C according to Ehrenfest, vice R′ = R but C′ = C (1-v²)^-1/2 > C according to Einstein and all subsequent authors (except Becquerel). ---CH 22:08, 6 June 2006 (UTC)

EMS and CH, that's a piece of cake. I already provided above two English formulations that disagree with the intro of the above English version. Nevertheless, EMS did show that CH didn't originate this misunderstanding himself, and that's a good thing.

It's not hard to spot the inconsistency in the above rendering but the facts are easily verified by checking Ehrenfest's own paper. Ehrenfest states that he will give an example based on the "first mentioned" definition, which is "based on the measurement system of a resting observer" as follows:

Ein Körper verhält sich relativ-starr, heißt: er deformiert sich bei einer beliebigen Bewegung fortlaufend so, daß jedes seiner infinitesimalen Elemente in jedem Moment für einen ruhenden Beobachter gerade diejenige Lorentz-Kontraktion (gegenüber dem Ruhezustand) aufweist, welche der Momentan-Geschwindigkeit des Element-Mittelpunktes entspricht. (emphasis mine)

Next he presents the example roughly as Pjacobi (and the two sources) already summarized. R is the radius before the cylinder is made to rotate, and R' the radius when made to rotate, as seen by an observer in rest.

-> please notice the error made by your reference: there is only a rest frame, no rotating frame here!

Ehrenfest next concludes that according to the above definition, in the rest frame:

(a) The circumference of the disk must show a contraction relative to its rest state, 2πR' < 2πR, since each element of the circumference moves in its own direction with instantaneous speed ωR.

(b) If one considers an element of a radius, its instantaneous velocity is perpendicular to its length; thus, an element of the radius cannot show a contraction with respect to the rest state. Therefore R' = R.

That is a clear contradiction.

His analysis is crystal clear and correct; it's a fable that he should have written that 2 pi R' > 2 pi R.

Thus I repeat my recommandation to render it as follows in this article, avoiding such confusions:

The radius R as seen in the laboratory frame should be equal to the value R₀ of the stationary disc. But the circumference 2 π R should be Lorentz-contracted to a smaller value than at rest, by the usual factor γ. This leads to the contradiction that R=R₀ and R<R₀.

(And to EMS: yes this paradox is a real contradiction - see paradox)

Regards, Harald88 23:05, 6 June 2006 (UTC)

Harald, it is not "Ehrenfest's paper", singular, but "Ehrenfest's papers discussing the "paradox", plural; see Grøn, see Grøn, please see Grøn. Ehrenfest's thought developed over time and in the end I am pretty sure that he accepted Einstein 1916, although evidence for this might be found only in his personal letters. ---CH 23:12, 7 June 2006 (UTC)

If CH and the reference are mistaken in the effect of the contraction as described by Ehrenfest, that is all well and good IMO. Indeed, that is what I had visualized at first and meant to write with respect to above. However, I am not going to re-correct that posting again! [Actually, the reference may have meant what you have shown, but that is not obvious.  :-( . The trouble is that the references leave out the "in the rest frame" part, creating the ambiguity]. BTW - I hope that the german that you bolded meant "in the rest frame".

Beyond that, let's get down to brass tacks, because either way Ehrenfest mistated the paradox. The circumference cannot contract, but the individual molecules do. That is what Einstein found, and that is the basis on which almost all researchets on the paradox since (with one natable and early exception) have analyzed it. So while I support the presentation of Ehrenfest's paradox in it's original form for historical reasons (as done in the article currently), I also support the basic statement of the paradox being that the disk-riding observers find the circumference increased while the "stationary" observers do not.

Also, what do you mean by "a real contradiction"? As stated, there is a paradox here, and I have said as much. However, the paradox itself is not real. The volume of spacetime is not both Euclidean and non-Euclidean at the same time as Ehrenfest thought. Instead, Einstein's research showed that the volume stays constant for the labroatory observer, and instead the disk/cylinder must shatter. Showing that the contradiction does not exist given the current formulation is actually harder, but has been done on a number of bases anyway. --EMS | Talk 04:07, 7 June 2006 (UTC)

Ehrenfest attacked the notion of rigid motion in special relativity and showed that it's impossible for the length dL of each unit on the cylinder to Lorentz contract without a corresponding contraction of dR. Thus he simply sticks to the rest frame and doesn't suggest any non-Euclidean geometry; there is no need for such complications. His paradox corresponds not to Einstein's discussion of what disk-riding observers would see, but to Einstein's remark that an absolutely rigid disk would shatter. There is concensus that real rotating disks undergo a relativistic shrinking effect that slightly counteracts the expansion due to inertial forces. Harald88 07:03, 7 June 2006 (UTC)

Harald - In that model, you have a disk which is under tension in the tangential direcetion and under compression in the radial direction (and as a mechanical issue I see nothing wrong with that). However, do note that you are not dealing with ideally rigid materials in that case. If the disk material cannot expand/contract substantially, then the radius stays constant and the rim material can no longer cover the expanded locally-measured circumference. Hence the rigid rotating disk must shatter.

BTW - You have also missed the point on the issue of topology. Ehrenfest concluded that the disk must act as if R' = R and R' < R at the same time. This being a paradox in relativity is very must best couched as an issue of topology. Otherwise you can just hide beind the Lorentz contraction and brush off the apparent contradiction. Instead, this is a much complex situation to deal with. --EMS | Talk 15:46, 7 June 2006 (UTC)

EMS, your first point: exactly, that's the whole point! The kind of "Rigid" rotational motion as was proposed is not possible in relativity. And your second point: Ehrenfest did not conclude that the cylinder must act like that, instead he showed the premise of rigid motion wrong. Harald88 08:06, 8 June 2006 (UTC)

Reading the very short (less than one page) Ehrenfest 1909 note, Harald88 provided me with, I try to state the claims in short:

1. rigid motion, observed from a lab system is equivalent to each infinitesimal volume element being Lorentz-contracted in its direction of motion
2. only a very limited set of movements fulfills this criterion
3. the criterion is equivalent to Born's criterion published just months before, that each comoving observer see its infinitesimal environment undeformed. (If one tries reading between the lines, it may be the case that Ehrenfest had planned to publish more extensively about rigid movements in relativity, but Born's earlier publication stopped him in the tracks)
4. a simple counterexample is the disc put in rotating motion: for it to be rigid in tangential direction, the circumference must contract to 2πR'<2πR, but rigidity in radial direction implies 2πR'=2πR
5. it follows a somewhat unclear note, about the possibility of an additional length contraction term depending on rotation or acceleration

That's all. The paradoxical in this stage, is the incompatibility of SR and accelerated motion. IMHO the Ehrenfest train example picture and its underlying calculation is fitting illustration of this. Another possible illustration would be the Ehrenfest bowl, giving a mesh of ideally rigid elemnts which are allowed to bend at the joints, the disc would bend out of the z=0 into a bowl-like shape. Pjacobi 08:35, 7 June 2006 (UTC)

Hi Peter. Acutually, SR is compatible with accelerated motion, and it has been so from the beginning. But so-called "rigid" acceleration is only possible in special (and idealised) cases.

There is a problem with your train as illustration for the Ehrenfest paradox: It is essentially different from the original example in that the rails are not co-moving and forcing the train to be expanded in the instantaneous frames of the carriages. Without the rails (and ignoring inertial forces) the whole train will nearly exactly Lorentz contract. And an "Ehrenfest bowl" is similarly non-paradoxical when all elements are allowed to fully Lorentz contract.

IMHO, more helpful would be an illustration that is very close to Ehrenfest's rotating cylinder but more visual, for example a bicycle wheel with spokes: it is impossible for the rim to Lorentz contract without deforming the spokes. I would volunteer making such a sketch if I knew how to make illustrations for Wikipedia.

On second thought: I agree that a disc turned into a bowl is visually more impressive than a cylinder of slightly reduced dimensions. If - as you seem to suggest - you volunteer to draw an Ehrenfest bowl example, that could be neatly used to illustrate the Ehrenfest paradox as follows: After presenting the relativistic deformation of the (thin) disc/bowl, we can next explain:

A high cylinder can of course not bend like a bowl. Ehrenfest pointed out that a cylinder's volume elements can't Lorentz contract without laterally contracting as well. That disproved the premise of "rigid" acceleration for the case of a rotating cylinder. Harald88 11:55, 8 June 2006 (UTC)

Peter, just to clarify: are you aware that Grøn cites several papers by Ehrenfest discussing this stuff? Grøn quotes extensively from Ehrenfest's first paper on Born rigidity, but also summarizes his later papers. Regarding "Ehrenfest bowl", again see Grøn for important later contribs from other authors. I hope you have a chance to read Grøn's 2002 review paper, since this is an extremely concise survey of a vast literature! If you feel inspired to make a figure illustrating this and put it here, I will incorporate that into the article.---CH 23:09, 7 June 2006 (UTC)

@Harald:

• Yes, I'm speaking about the incompatibility of "rigid" accelelerations in SR.
• The rails are only replacing ideally rigid spokes. It is a setting often employed to discuss the problem.
  • Assuming rigid spokes the rim, will tear, assuming rigid rim the spokes will crumble, assuming rigid spokes and rim but bendable joint, it will fold up into the z-direction. Rigid spokes *and* rigid rim isn't possible and this is already in the oroginal Ehrenfest paper.

@CH: I'm done with a first reading of Grøn's paper and learnt a number of points:

• The train illustration is fortunately not original reasearch and Grøn gives A. Metz, Les Problèmes Relatifs a la Rotation Dans la Théorie de la Relativité, Le Journal de Physique et le Radium, 13, 224 (1952) as first occurence.
• The bowl case is even older and seems to date back to 1910: [50] G. Stead and H. Donaldson, The Problem of Uniform Rotation treated on the Principle of Relativity, Phil.Mag. 20, 92 (1910).
• There are still many disagreeing papers published, even in semi-reputable journals like, e.g. [58] F. Winterberg, Resolution of the Ehrenfest Paradox in the Dynamic Interpretation of Lorentz Invariance, Z. Naturforsch. 53a, 751 (1998). In summary the EP seems to be quite a failure of the scientific method (or of the rational thinking of some scientists), in not reaching consensus in nearly 100 years on a not that difficult problem. This phenomenon may be of significant interest to our readers and would deserve an adequate treatment in the article, even if it shed a negative light on the scientific community. Wikipedia is not censored for the self-esteem of physicists.
• I consider the intuitive argument on page 33 (originally at Ø. Grøn, Relativistic description of a rotating disk, Am. J. Phys. 43, 869 (1975).) a good point, as it relates the impossibility to set up a conspiracy of forces to achieve rigid motion to the impossibilitry of global Einstein synchronisation along the rim.

But I also have some nitpicking with Grøn's text

• I cannot understand, that he tries to make a central difference between Ehrenfest's and Einstein's papers. Ehrenfest doesn't intended to state a paradox, he only wanted to give a simple example for the impossibility of Born rigid motion in the general case. His mode of presentation was reductio ad absurdum -- and that may have confused a number of readers.
• At least in this review paper, he doesn't come over as a pedagogical genius. The stuff looks more difficult that it has to be, the separation in chapters is somewhat artifically, and arguments are repeated.

Pjacobi 14:24, 8 June 2006 (UTC)

I already referred EMS to the article "paradox", it's worth to have a look. As many people misunderstand the meaning of "paradox", it may be better to expand: "Such a contradictory presentation is called a paradox; this paradox disproved the premise of so-called "rigid" acceleration for rotating objects."

Apart of that, I wasn't aware that Einstein discussed a paradox in his writings about rotating reference frames. What is his paradox do you think, where did he write it, and why do you call it "Ehrenfest's paradox"? So far I see no reason to combine them in one article - instead I agree with Max Planck that the two subjects should not be confused. Harald88 05:51, 9 June 2006 (UTC)

No I don't think, there is more than accidental overlap between paradox and reductio ad absurdum. Ehrenfect IMHO never thought of presenting a paradox, but an arguable obvious implicition of SR. Neither, I believe, has Einstein seen a paradox. But the problem of the rotating has become wellknown under the name Ehrenfest paradox, by the century-long stream of dissenters and confusing discussion of it. One faction of the dissenters, took the possibility of rigid motion to be more important than SR and argued for modification (or abandoment) of SR (and this is in a sense linked somewhat to the original Ehrenfest paper via its last paragraph). Another important faction of dissenters tried (and tries today, hello Modern Galilean relativity) to accumulate discrepances between SR and "common sense" and named them "paradox" to disprove SR. --Pjacobi 08:11, 9 June 2006 (UTC)

Peter, he obviously didn't critisize SRT but "Born rigidity"; and presentation of such criticism as a contradiction is called a "paradox". If you disagree with calling a contradiction that results from an erroneous premise a "paradox", please discuss that matter in the article paradox and cite the literature that supports your disagreement.

In any case, a problem is not called a paradox. For that one needs a suggestion of error, such as a clear contradiction or a conflict with common sense. If you're right that a significant number of articles confuses Ehrenfeld's paradox (an accepted true contradiction) with either a calculation problem or with a conflict with common sense, then that must of course be mentioned in this article. But so far I don't recall to have seen evidence of that; for example Grøn's text contains some confusions that he copied from others, but he rapidly distinguishes between the Ehrenfest paradox and Einstein's analysis of rotating frames (indeed, his subject is not limited to the Ehrenfest paradox). - Harald88 11:49, 9 June 2006 (UTC)

If this is not a misunderstanding on my side what you mean, then it's a serious misunderstanding on your side of the Ehrenfest 1909 paper. Ehrenfest in no way criticizes Born rigidity. He may have been a little upset that Born achieved priority and he lost the chance it going being to be known as Ehrenfest rigidity. The phrase führt zu Widersprüchen isn't meant in the sense that it's a bad definition, he explicitely states that is equivalent to Ehrenfest's earlier (!) definition and praises it for being more in the spirit of SR. In my not so humble opinion führt zu Widersprüchen is meant to say, that quite a number (almost all, so to say) movements of extended bodies cannot be Born rigid. --Pjacobi 12:01, 9 June 2006 (UTC)

That's exactly what I meant, sorry if somehow that was not clear. He criticized the idea that such a rigidity could be generally applicable.

BTW, it's not clear to me that the rest frame definition was his own definition - to me it looks like he presents an existing definition, but in fact he doesn't say either ("man" is rather vague!). Harald88 12:20, 9 June 2006 (UTC)

I think there are two issues here:

1. We all agree that my version oversimplifies the history, and in particular Ehrenfest's views. I feel this is acceptable and even neccessary in a short general encyclopedia article, and that the cite of Grøn's review will lead a serious scholar directly to the original papers. However, Harald seems to strongly feel that I went too far in oversimplyfing the historical record in the article and wants to drastically expand the discussion of Ehrenfest's views, or even to discuss only Ehrenfest 1909. I feel that would be absurd, and I think Peter and Ed would agree that the interesting thing here from a historical point of view is the existence of a long controversy, which may suggest some general lessons.
2. We call agree, I think, that this topic has engendered almost 100 years of controversy. I feel that this controversy has been largely unnecessary (at least after 1935 or so, by which time all the ingredients were in place for the resolution), and has been maintained only because really bad physicists who are poor scholars (who haven't read the prior literature and who apparently lack the ability to distinguish between the issues involved, much less to offer valuable new insights) feel free to write one more really bad paper on this topic. It seems Peter's judgement might not be quite so harsh.

Re the first topic, I wish that Harald would acknowledge that Ehrenfest published several papers dealing with this topic, and that his views evolved, as did the views of some other participants; a "true history" would require discussion of both the full context of the early writings plus discussion of how the views of Ehrenfest and others evolved, not neglecting private correspondence as sources. Bu this is really a task for historians, not Wikipedians.

I have created a new section below to try to discuss the second topic. ---CH 15:27, 10 June 2006 (UTC)

Chris, there are indeed two issues, but you entirely misunderstand what Peter and I have been telling you and what Ed also understands.

1. Contrary to what you wrote, in 1909 Ehrenfest did not conclude anything about what disk-riding observers will measure; and thus he also can't have made a corresponding error at that time. The article now makes completely erroneous claims.

2. I am not against simplifying, but IMHO you instead enormously complicate matters by mixing up Ehrenfest's paradox with Einstein's rotating disk geometry. That historically those subjects may have been confused doesn't oblige us to similarly confuse the readers - quite to the contrary! And IMO (apparently shared by Grøn) the contraversy has been unnecessary since 1910, when Planck distinguished and published the source of confusion. Of course, the Ehrenfest paradox is only a small part of Grøn's subject and so he doesn't linger on it. Harald88 20:55, 10 June 2006 (UTC)

Ehrenfest's error

Harald - You don't quite "get it" with what myself and Chris are saying about Ehrenfest's error (although I am with you on what Ehrenfest said). Ehrenfest claimed that the laboratory observer would find the circumference of the rotating disk/cylinder to be Lorentz contracted. Now a ring could contract, but for a cylinder the radius of the object is kept constant by its own material. So whereas Ehrenfest thought that circumference itself would be contracted (so that the disk-riding observers still measure an overall circumference of C = 2π r), Einstein instead found that the circumference is not contracted in the laboratory frame. That means that the disk riding observers measure a circumference of C > 2π r.

So I do agree with Chris that Ehrenfest made an error, but disagree on the form of that error. Obviously we need to iron out these kinks so that we can focus on how to create an article that is as accurate, concise, complete, and readable/understandable as possible. (I set those parameters knowing that "complete" call for a bigger article and "readable/understandable" calls for a smaller article. Also "accurate" calls for the article to be more technical, while readability is aided by its being less technical. So we have an interesting balancing act ahead of in workingthis article.) --EMS | Talk 00:42, 11 June 2006 (UTC)

EMS, Peter and I already explained several times what Ehrenfest stated so I won't repeat it again. Suffices to point out that:

1. Ehrenfest did not claim that that the laboratory observer would find the circumference of the rotating disk/cylinder to be Lorentz contracted; and

2. you are mistaken (according to all authorities on this subject) by suggesting that although a ring would Lorentz contract, the circumference of a cylinder would be "kept constant by its own material" when brought into rotation, also CH understands that (see higher on this Talk page and below in the article). Einstein discussed something completely different in the passage that you refer to, please try to understand Planck's disambiguation of 1910.

In view of this continued confusion which is completely unneccessary since 1910, it would be good to elaborate on Planck's disambiguation in this article.

When all editors here understand the cause of the confusion and how easy - in principle - each subject is when treated on its own, I expect that everyone will agree that it's beneficial to have one article about the Ehrenfest paradox, and a more general article about rotating reference frames in relativity that links to it. Not mixing them up will be decisive for making these subjects readable and understandable. Harald88 09:55, 11 June 2006 (UTC)

@EMS: There is no "Error" in the Ehrenfest 1909 paper. It presented a simple, uncontroversial "reductio ad absurdu" proof that a cyclinder cannot set in rotating motion while remaining born rigid. Ehrenfest claimed that the laboratory observer would find the circumference of the rotating disk/cylinder to be Lorentz contracted. - NOT! - He claimed that one of the conclusions of Born-rigidity would be, that the circumference has to Lorentz contract. It's formal logic: Claiming "A => B" isn't the same as claiming "B".

The Ehrenfest paper has the following logical structure

1. A => B
2. A => C
3. not (B and C)
4. not A

You are actually confirming the argument as I came to understand it's essense, but have put it into a most useful context. Given the assumption of Born rigidity, the overall argument makes a certain sense, and as a "reductio ad absurdu" actually dovetails well with Einstein's view. This leaves behind a bunch of interesting questions about what the views of Ehrenfest's argument are in the literature and when and how they came to be. I guess that I need to reread Grøn's article in light of this description. --EMS | Talk 23:07, 11 June 2006 (UTC)

@Harald: What you are getting wrong, is that "Ehrenfest paradox" has to be congruent with "Content of 1909 Ehrenfest". Obviously Ehrenfest himself named his presention not "paradox" let alone "Ehrenfest paradox". Whether perfectly fitting or not, in later literature the discussion starting with the Ehrenfest 1909 paper has been named "Ehrenfest paradox", whether or not the arguments are from Ehrenfest.

Pjacobi 10:29, 11 June 2006 (UTC)

Peter, thanks for your exposé, let's hope that your mathematical explication succeeds where our English was unsuccesful.

Note that I did not claim that the term "Ehrenfest paradox" should only refer to the 1909 paper, you misunderstood me on that point. According to Gron the term primarily refers to that paper, but he could be wrong of course. In discussions I try to logically discuss the issues point by point, and already we are discussing two points at a time. Due to the nature of paradoxes it is quite common that their meaning changes over time and this article should of course mention in what way the literature misunderstood and/or changed the sense of the term "Ehrenfest paradox". What examples do you have? Harald88 11:01, 11 June 2006 (UTC)

How much to stress the controversy?

Peter, thanks for your comments. I agree that Grøn's paper is not perfectly organized nor everywhere as clear as one might wish, but clearly despite some flaws it is an invaluable, even essential, starting point for reading. As I assume you realize, my own reading includes many of the papers he cites, plus eprints too recent to be mentioned by Grøn.

As you know, I think I have very clearly explained why this "controversy" is mainly manufactured by persons who wrote a large number of foolish, ignorant, and mostly incorrect papers, often ignoring most of the earlier literature, and thus often repeating earlier mistakes which have long since been corrected. I think I have clearly and concisely explained this while avoiding any temptation to try to write a book or even to shame the guilty parties by mentioning names of the doofuses.

Just be clear, in the history section I didn't mention every paper containing valid insights either, even ones which are not re-expressing earlier notions. But the majority of the papers discussed by Grøn were obviously wrong at the time they were submitted (even more obviously wrong today) and in an ideal world would never have been published. So I think we agree that the dismal history of publications in this area does suggest that the traditional model of scientific progress is a bit naive; in particular, essentially all the arXiv eprints since 2002 are not only wrong but repeating errors which have already been corrected by previous authors, and thus represent attempts to take a giant step backwards. My own feeling is that competent physicists quickly recognize this and warn their students as needed, but for reasons of collegiality, avoid public criticisms even though in private they may offer devastating critiques of these badly thought out papers.

Peter, you wrote "Wikipedia is not censored for the self-esteem of physicists". I emphastically agree that in all discussions like this, the interests of our readers trumps the tender egos of persons discussed in articles, much less of WP editors. However, what I had in mind in suggesting that we avoid naming names was a practical concern: I don't want to drag out of the woodwork dozens of living physicists whose papers on this topic I could criticize at length while rendering a rather harsh judgement. Arguing with dozens of aggrieved researchers about specific flaws in their work would not be a good use of my time (or yours). (You may have noticed that I am already arguing with Haisch and Ibison about their papers, and even this is taking too much of my time.) ---CH 15:27, 10 June 2006 (UTC)

arXiv eprints are in general excluded from consideration, except for those that correspond to peer reviewed articles; thus that shouldn't be an issue. And so far it has not shown here that (apart of some confusion) there really is a significant controversy about the Ehrenfest paradox in the literature. A significant and clear example would be helpful here. Harald88 10:14, 11 June 2006 (UTC)

Harald, I have no idea what you are trying to say. I was addressing Peter. If Peter is ready to let this go, I think you should too. ---CH 20:36, 11 June 2006 (UTC)

I asked you or Peter to provide an example (not from an eprint!) of the controversy that according to you exists about "the Ehrenfest paradox". Harald88 21:15, 11 June 2006 (UTC)

Harald, I think this getting ridiculous. And quite frankly a waste of my time. Are you now saying that you feel that Grøn's paper is somehow not an acceptable source? If so, I think that is absurd. In any case, you should obtain and study at least some of the papers cited in that paper. I haven't counted but there must be a hundred or more. I have read many of them, and they discuss many issues not considered by Ehrenfest, as one imagine since the great majority have been published after Ehrenfest's death in 1933. ---CH 22:12, 11 June 2006 (UTC)

No Chris, I have no clue how you can interpret my question as such a claim, especially since I agree with Planck's analysis of the confusion at that time as put forward by Grøn. And please don't overlook that his paper isn't about the Ehrenfest paradox in particular; many issues related to rotating discs are an entirely other subject. Similarly, Time dilation has not been merged inside Twin paradox - and rightly so! Harald88 22:28, 11 June 2006 (UTC)

I wish you would decide what your problem is. Are you asking that the article be renamed to Rotating relativistic disk? Will this be your last request concerning this article? ---CH 22:33, 11 June 2006 (UTC)

I have already stated it above:

1. Please correct the errors about Ehrenfest 1909.

2. I proposed and still propose for the benefit of the readers, to split this article up in one article about the Ehrenfest paradox (which is basically straightforward and non-controversial) and another about Rotating relativistic frames which may be a somewhat controversial subject about which you appear to be particularly knowledgable. There is no better disambiguation than to treat them separately, and interlink. Harald88 23:05, 11 June 2006 (UTC)

I feel I have sufficiently addressed your 1. I don't agree with your 2 either: you imply that the Ehrenfest paradox has a standard meaning "which is basically straightforward and non-controversial" (both wrong) and you want to split up the article (a really really bad idea). Could you please give this a rest now? ---CH 23:12, 11 June 2006 (UTC)

Of course point 1 needs to be understood in order to be able to judge point 2, and I'm afraid that by now Peter and I have exhausted the possibilities to try to explain point 1 to you - except if you somehow overlooked our last explanation attempts above on this page! Harald88 23:22, 11 June 2006 (UTC)

What sentence(s) in this article are you objecting to now? ---CH 01:12, 12 June 2006 (UTC)

You completely started off on a wrong leg, as you refused to acknowledge the fundamental difference between your intro and that of Peter that you deleted. All of the following erroneously represents Ehrenfest 1909 and disagrees with Planck 1910 and others who pointed out the mistake that you propagate in this article:

... the Ehrenfest paradox concerns the kinematics ... Albert Einstein noticed (in 1916) that it had been misstated! ...

the way the "paradox" was stated by Ehrenfest himself. ... one concludes that a rotating disk, as surveyed by a disk-riding observer, should have a circumference C′ = 2 π  r  (1−v²)^−1/2, i.e. larger than C = 2π r. This inconsistency with familiar euclidean geometry was what initially troubled Ehrenfest. ...

Ehrenfest was trying to argue by reductio ad absurdum that Born's notion of rigidity is in fact incompatible with special relativity. He claimed that according to Born rigidity, one should the "Lorentz contraction factor" to the circumference itself (rather than to the boxcars), whence a disk riding observer would measure a circumference of C ′   = 2 π  r (1−v²)^1/2, i.e. smaller than C = 2π r. But his argument is incorrect.

*1909: While studying Born's notion of rigidity, Paul Ehrenfest obtains (as he believes) two inconsistent notions for the "geometry of a rotating disk". He concludes that both static and disk-riding observers will measure radius r, but concludes that disk-riding observers will measure the circumference to be C′ = 2π r √(1−v²) rather than C = 2π r.

Harald88 06:17, 12 June 2006 (UTC)

@Harald88: I'm not getting your point here. The (sad) fact of the EP is, that literature is full of false papers (and, fortunately, in most cases response papers putting it right). Some authors even considered space-time to be non-flat for rotating observer: B. Kurşunoğlu, Spacetime on The Rotating Disk, Proc. Cambr. Phil. Soc. 47, 177 (1951). --Pjacobi 04:07, 12 June 2006 (UTC)

I notice that the title doesn't refer to the Ehrenfest paradox; do they claim in the article that they refer to that paradox? And probably "rotating observer" is their jargon for "rotating frame", so that they agree with Einstein.

Thus, what controversy do you think to exist? So far I only see much confusion of people in literature and on talk pages about different things, but I have found no real controversy. We should try to write the articles in such a way that no such confusion is thrown at the readers! Harald88 06:17, 12 June 2006 (UTC)