Talk:Bell's spaceship paradox/Archive 3

To do:

• copyedit (at one point we changed notation t,x,y,z -> T,X,Y,Z, and hopefully got everything changed)

• correct numerator cosh to sinh in third expression for T at the top of the article (occurs twice)

Archives
Apr 2006 – May 2006 May 2006 – May 2006

What string?

The second paragraph under "Bell's thought experiment" asks if the string breaks, but the description of the setup doesn't mention a string. It's not until the fourth paragraph that we see a varient wherein a connecting string is mentioned.

—Preceding unsigned comment added by Shaunm (talk • contribs)

Good catch; thanks, I just fixed this. During the rewrite I somehow dropped mention of the string. BTW, look above for the "four tilde" trick for signing talk page comments.---CH 16:08, 10 June 2006 (UTC)

Errors:

The expressions for T in the first equations after the first diagram contain an error. The first term of the third expression should use a sinh function rather than cosh. The error is repeated for the second observer, presumably due to copy pasting.

Also the claim that the s'ships are further apart after stopping engines is false. The s'ships do not share a line of simultaneity as your first diagram wrongly suggests. Using capitals for coordinates moving with s'ships at constant v, and lower case for coordinates measured from the launchsite:

T(A) = γ( t(A) - v.x(A) ) and T(B) = γ( t(B) - v.x(B) )

where γ = gamma, t(A) = t(B) and x(B)-x(A) = L

thus T(B) - T(A) = -γv.L

Also X(A) = γ( x(A) - v.t(A) ) and X(B) = γ( x(B) - v.t(B) )

so X(B) - X(A) = γ.L

Therefore the proper (instantaneous) distance between the s'ships is:

sqrt{ [ X(B)-X(A) ]² - [ T(B)-T(A) ]²} = sqrt{ γ²(1-v²) }.L = L

So the s'ships have NOT moved apart at all !

Rod Ball 13:18, 22 June 2006 (UTC)

Without looking at the math, for sure the ships can't move apart in the original inertial frame if they undergo simultaneous identical acceleration in that frame. This doesn't mean that the string won't break; for sure it will have a tendency to break due to length contraction (as determined in that same frame), and I thought that it was also stated like that by Bell. Matsuda et all seem to confirm that, and, as they state, this is (should!) all be very obvious indeed.

As only primary school math is needed to explain the issue, to me the article's explanation looks needlessly complicated. Harald88 13:50, 25 June 2006 (UTC)

I'm afraid you're wrong. The string doesn't break. All the simplistic explanations (including Bell's rather fatuous one ) arrive at an asymmetric result with regard to string and s'ship distance by simply treating them asymmetrically. That is, by treating one while disregarding the other, or using stationary coordinates for one and moving coordinates for the other, etc. In order to claim that the string "contracts" ( in fact, of course, it only seems to contract when measured by a relatively moving observer ) one must have a method of measurement in mind and in every case when that method of measurement is applied to the two s'ships, their distance will also be found to appear contracted. For example, in Einstein's primary train and platform Gedankenexpt. if one imagines two fast cars keeping pace with each end of the carriage(s), one can see the equivalence of moving lengths and moving spaces where apparent relativistic "contraction" is concerned. It is also argued sometimes that in the s'ship coordinates, where the string retains its proper length, that the s'ships move apart. What you have overlooked by not looking at the math is that I converted by Lorentz transformation from the original inertial frame coordinates to the moving s'ship coordinates, in which the "switch off engine" times differ, and showed that the proper distance between the s'ships had also not changed. Hence no string-breaking.

I agree that only primary school math is needed but more essential is clear, logical reasoning somewhat beyond that level and a healthy scepticism that not everything is so just because it's been published or someone famous has endorsed it. Bell was most definitely wrong.

Try considering the launch from the POV of a moving inertial observer already passing at constant velocity v. For him the s'ships are de-celerating and an initially "Lorentz contracted" string starts to "expand" back to its proper length ( when it reaches v ). The s'ships, of course, will also start at the same reduced distance so if the s'ship distance does not follow at least the same "reverse Lorentz contraction" as the string it will grow slack ! It was originally thought by E.Dewan that since the pre-moving inertial observer sees the forward s'ship start first, that this different reason might cause the string to break. Unfortunately this doesn't pan out as is most easily seen by sketching the hyperbolae of the decelerating s'ships, when it is obvious that the Lorentz "expansion" completely dominates the marginal effect of different apparent starting times. Rod Ball 11:54, 26 June 2006 (UTC)

The above arguments that you refer to overlook the relativity of simultaneity, as well as the assumed homogeneity of space. They are contained in which publication? Harald88 12:08, 28 June 2006 (UTC)

easy to understand explanation

In comparison I found the following on the web and it may be helpful to phrase it in a straightforward, easy-to-understand way. At least, I find it crystal clear; and it doesn't even contain one equation! Harald88 15:51, 25 June 2006 (UTC)

http://72.14.221.104/search?q=cache:VpK_4RvfazEJ:mataatua.mg.wiki3.info/+bell+spaceship+%22Speakable+and+unspeakable+in+quantum+mechanics%22+pdf&hl=en&ct=clnk&cd=27 Bellsches Raumschiff-Paradoxon

Das Bellsche Raumschiffparadoxon, nach der bekanntesten Darstellung durch John Stewart Bell in How to teach special relativity (1976), ist ein scheinbares Paradoxon der Relativitätstheorie. Obwohl heute meist unter diesem Namen bekannt, wird die zugrundeliegende Fragestellung bereits seit den 1920ern diskutiert. Es verdeutlicht die Auswirkungen der sogenannten Lorentzkontraktion. Die Lorentzkontraktion ergibt sich aus der speziellen Relativitätstheorie und besagt, dass bewegte Objekte von einem ruhenden Beobachter als umso verkürzter gemessen werden, je schneller sie sich ihm gegenüber bewegen. Diese Verkürzung entzieht sich unser täglichen Erfahrung, da sie erst bei Geschwindigkeiten nahe der Lichtgeschwindigkeit messbare Auswirkungen hervorrufen würde.

John Bell legte nun folgendes Gedankenexperiment vor: :Zwei Raumschiffe fliegen hintereinander. Zwischen beiden ist ein Seil gespannt, das aber sehr dünn ist, so dass keine Kräfte darüber übertragen werden können. Reißt das Seil, wenn beide Raumschiffe zur gleichen Zeit genau gleich beschleunigen? Die auf den ersten Blick logische Antwort wäre, dass das Seil nicht reißen wird, da ja beide Raumschiffe zum gleichen Zeitpunkt eine gleich große Beschleunigung erfahren. Der Abstand zwischen den Raumschiffen muss daher gleich bleiben. Diese Gleichzeitigkeit gleich langer Beschleunigungsphasen ist aber nur in einem Bezugssystem gegeben: dem, in dem die Raumschiffe ursprünglich in Ruhe waren. In diesem Bezugssystem nimmt aber auch der Effekt der Lorentzkontraktion zu, derentwegen ein ruhender Beobachter sowohl das Seil wie auch die beiden Raumschiffe nun als verkürzt wahrnimmt. Da das Seil aber keine Zugkräfte übertragen können soll, vermag es die Raumschiffe nicht näher zusammen zu ziehen - es muss also reißen!

Zum gleichen Ergebnis gelangt man, wenn man das mitbewegte Bezugssystem betrachtet: Dort ist die Länge des Seils konstant, aber der Abstand der Raumschiffe nimmt zu.

Literatur

- J. S. Bell, How to teach special relativity, Progress in Scientific Culture, Vol 1, No 2, 1976

- J. S. Bell, Speakable and unspeakable in quantum mechanics, Cambridge University Press, 1987, ISBN 0521523389 (enthält den obigen Aufsatz)

- H. Nikolic, Relativistic contraction of an accelerated rod, Am. J. Phys. 67, 1007 (1999), preprint online as physics/9810017

Weblinks

- Bell's Spaceship Paradox USENET Relativity FAQ

- A Paradox of Two Space Ships in Special Relativity Takuya Matsuda and Atsuya Kinoshita Kategorie:Spezielle Relativitätstheorie Kategorie:Paradoxon Hydrogeographie

Huh? That's a Wikipedia mirror. It shows an older version of de:Bellsches Raumschiffparadoxon. --Pjacobi 12:28, 26 June 2006 (UTC)

Good - then there is no copyright problem! :))

Who wrote the above nice summary, do you know? Harald88 22:06, 26 June 2006 (UTC)

You know the usage of the history tab? ;-)

An abysmal version was deleted, then mostly de:Benutzer:Srbauer (an astronomer) and de:Benutzer:DL5MDA (an engineer) got a decent stub done, this version. Then an absolute nerve-cracking edit-war tool place over several months, resulting in two user bans and whatsnot. Now, nobody is really motivated to expand the article.

Pjacobi 22:16, 26 June 2006 (UTC)

The history tab is only present for editors who announced themselves for that language. Anyway, I hope that we can get such clear explanations also in the English articles. I don't mind a section for mathematicians, but (just as with the Ehrenfest paradox), if something can be explained in a way that a kid can understand it, then it should be done IMO. Complicating things is counterproductive (and the controversies that are based on overly complicated explanations demonstrate it!). A good example to follow was Feynman: most of the stuff that he really understood well (and that was a lot), he also managed to explain in a clear and simple way. Harald88 22:35, 26 June 2006 (UTC)

Simple this argument may be, but it is also fatuously wrong. It is a great pity that Bell's name has become attached to this problem since he not only didn't originate it but he merely mentioned it seventeen years later with a rather sloppy "explanation" that did no justice to Dewan & Beran's original papers, where they are very aware that there are weaknesses in the argument and take a lot of care to try and argue around them. However, they were wrong and their problem would have most likely stayed in well-deserved oblivion had Bell not been gulled by it. How could Bell have been so mistaken? Because he was primarily a quantum physicist who had an archaic and long discredited view of "relativity". Bell's relativity is not Einstein's !

Bell preferred Fitzgerald's version with absolute space and an ether. What he calls "special relativity" is as he admits "the relativity of Poincare, Lorentz and Larmor". Read the remarks immediately after his mention of the s'ships in "Speakable and Unspeakable" and note how he compares the theories of Poincare, Lorentz and Larmor with that of Einstein ( ie, Special Relativity ) and endorses Poincare etc. while excluding Einstein. Note also how he consistently refers to what is normally called "Lorentz contraction" as "Fitzgerald contraction". ( Fitzgerald was also Irish and Bell had written a short biography of him.)

Also note that Bell admits he was opposed (on the 2 s'ships problem) by the whole theory division at CERN, where one may assume there was a reasonable expertise in "modern" special relativity. Also Matsuda and Kinoshita actually complain that they received widespread contradiction from physicists in japan, who possibly had a better grasp of special relativity . Matsuda & Kinoshita construct totally incorrect diagrams using a pair of hyperbolae to represent a one point trajectory and thus render their arguments nonsensical and self contradictory.

It seems that trying to use "straight-line" diagrams, with "instantaneous" changes in velocity, to represent the s'ships motion always leads to simplistically incorrect arguments. Only using smooth (hyperbolic) trajectories gives a clear representation and at least the chance of correct analysis. Rod Ball 13:26, 26 June 2006 (UTC)

"Instantaneous" is irrelevant; it's more clearly explained with identical accelerations, and just as easy. Please cite a paper that shows the error in the above explanation (I know that it's correct, not only because it agrees with mainstream, but also because I derived it myself before hearing of the paradox). Harald88 22:11, 26 June 2006 (UTC)

What do you mean "more clearly explained with identical accelerations" ? The problem supposes identical accns. and would be meaningless otherwise. Have you read the original references ? (BTW the article you inserted is also wrong in claiming the problem goes back to the 1920's - it starts with Dewan and Beran in 1959.) If "instantaneous" is irrelevant, why do M&K have to fudge their argument by using two hyperbolae for a single point trajectory ? Even Bell in "Speakable etc" clearly specifies gentle acceleration.

If you want to really understand the problem, please analyse it from the POV of a moving inertial observer already at constant v in the same direction (as the s'ships). How do you think the string is going to be break if it's getting longer ? Check with a diagram and you will find unavoidable contradiction unless both s'ship distance and string length behave identically - just as SR predicts they should. Remember the Lorentz transformations are simply coordinate transformations and apply indifferently whether spaces or solid lengths are between say X1 and X2. It was only in the early "relativity" of Fitzgerald et.al. that solid lengths were singled out for attention. For instance, the arm of Michelson's interferometer was supposed to shorten as it was rotated from a transverse to a longitudinal orientation and by just the right amount. Special relativity swept away such nonsense with a constant c for all observers, no contraction in the rest frame, and no distinction between space and solid because the LT's were universally applicable.

As for "mainstream" - what evidence do you have for that claim ? It always sounds, when people claim to be with the "mainstream" or "majority", that it's what they want to believe - to feel more secure. In fact as I indicated above there is a "balance of opinion" on this problem and not even a vague estimate as to the proportion of physicists etc. one way or the other. ( I wouldn't for instance, put forward the fact that both Bell and Matsuda/Kinoshita were heavily outnumbered by opposition, as "evidence" of the overwhelming scale of contrary opinion.). Rod Ball 09:40, 27 June 2006 (UTC)

I replied to "instantaneous" changes in velocity", as no such thing is needed - nor is it contained, as you remark yourself, in the original description which I just took from the library. Moreover I have so far not made any edits in this article, and this page isn't for editors to debate over what others have debated. Instead different viewpoints should be explained as clearly and fairly as possible. To describe fairly is policy; describing clearly looks pretty obvious to me, and that's what this discussion is about.

1. Now, what do you think is erroneous or unclear in the above description of the solution of the problem as promoted by Bell and others?

2. BTW, you are right that "mainstream" is sometimes difficult to assess. But differently from scientific articles, Wikipedia articles are supposed to take the estimated relative popularity of views in account (WP:NPOV#Undue_weight).

Harald88 11:22, 27 June 2006 (UTC)

It seems (I think) we agree about dispensing with "inst." changing v, except I go further & contradict the article that such "kicked" impulsive motion never was what the problem was about, merely a fairly recent attempt to "simplify" that instead complicates & misleads.

Bell's "explanation" is a good example of lop-sided reasoning. He starts by supposing parallel s'ship trajectories so constant distance (fair enough) then simply "assumes" that the string contracts without considering how this might be established. In the early "relativity" of Fitzgerald/Lorentz this would certainly be the case, but not in special relativity.

If one checked the string length by marking its end's positions simultaneously, so that the differing simultaneity in the moving system (forward end seems to be registered first) would produce coordinates a contracted distance apart - then exactly the same would occur for the s'ship distance. Eg. two stationary observers mark the position of the s'ships as they fly past at the same instant by their two synchronised clocks. ( Note the exact correspondance with a moving train or moving string!) Then a contracted distance is recorded, which is not surprising to the s'ship or train etc. passengers because they see the front end recorded slightly before the rear position. This is always the case that string and s'ships behave identically regarding coordinate separation in SR. It absolutely must be so because the crucial Lorentz transformations that quantify the effect (of measurements between relatively moving systems)apply simply to coordinates, be they coordinates of the ends of the string or coordinates of the s'ships.

The question "how could the s'ships move towards each other ?" simply doesn't arise because no contraction takes place in the system itself in SR - only an apparent contraction in the measurements from a standpoint in relative motion. So from s'ship POV they stay same distance apart and string stays same length, whilst the "stationary" observer, by a procedure such as that described (or other methods) will find the same measured distance for s'ship to s'hip as between string ends. It is this that should be regarded as "obvious".

The reason Bell came to the wrong conclusion is because he's using the pre-Einstein prescription of considering actual physical shrinkage in the rest system, in the direction of motion. This was originally thought due to "resistance" of the aether and therefore obviously not applicable to empty spaces (hence difference). Merely dropping the "aether picture" does not alter the wrongness of the theory and its space/body distinctions. It's all very well for Bell to suggest that a wrong approach is acceptable or even preferable if it's pedagogically easier and always leads to the same correct answers, but few would agree with him. A wrong theory is simply wrong (as Trouton-Rankine & Chase-Tomaschek showed) even if it generates the same answers, but in this case the answers are different. Archaic Fitzgerald contraction would deny the s'ship distance could show contraction, but SR predicts that any of the usual methods of measurement that exhibit apparent contraction of a moving body would show precisely the same for an equivalently moving gap or space. Surely this is clear enough ! Rod Ball 83.244.164.35 14:42, 27 June 2006 (UTC)

I won't comment on your personal research (and indeed, I should not and you should not post it here as I stressed above).

About my point 1: We certainly agree on dispensing with "inst." changing v, as well as the uselessness of such a "simplification" for the article. And I take it from your lack of further comment on the above German account, that you don't disagree with the way it portrays Bell's version. The next step is to improve the article accordingly.

Harald88 21:02, 27 June 2006 (UTC)

Goodness, do I have to explain everything to you ! What you're calling "personal research" is simply combining reference to original texts (mainly Bell's) with straightforward (and correct) application of the standard arguments used in countless textbooks over the years in deriving "length contraction", in order to show the difference between Bell's standpoint and "modern" special relativity. This is perfectly legitimate textual comparison and not "original research" in the Wikipedia sense that would apply, for instance, to most of the current article. Anyone who has actually studied SR (as opposed to just learning the equations) will recognise the procedure I described for exhibiting length contraction and will be likely to understand that the "physical effect" is on the measurement only. This is another difference between Bell's non-SR view and Einstein's SR. Eg. when A & B are in relative motion, E's SR says A will measure B's lengths as shorter and B will measure A's lengths shorter - which means that the measurements, and not the lengths themselves, are "contracted".

May I suggest that you more thoroughly aquaint yourself with the subject (SR) rather than Bell's version of Dewan & Beran, before dismissing the relevance of my remarks in an apparent effort to avoid addressing them. Rod Ball 09:15, 28 June 2006 (UTC)

It is not easy to explain a mistaken idea. I am well acquainted with this kind of subjects, and have published about such in a reputable physics journal. Obviously the other editors here also understand the subject, and we all disagree with your claim that the calculations are faulty. The analysis as first done by Dewan and Beran is not "about Bell's view". Their explanation is very compact and clear (even more compact than that of Bell), and thus perfect to base this article on.

Thus, although I'm regularly enriching myself with the subject, I would suggest that you study SR with textbooks that don't confuse interpretation with calculation. In fact, already the 1905 paper by Einstein should be sufficient. Harald88 20:24, 30 June 2006 (UTC)

Here's what Bell himself remarked about the best (simplest!) way to explain this problem (and rather different from what Rod claimed):

"The facts of physics do not oblige us to accept one philosophy rather than the other. And we need not accept Lorentz's philosophy to accept a Lorentzian pedagogy. Its special merit is to drive home the lesson that the laws of physics in any one reference frame account for all physical phenomena, including the observations of moving observers. And it is often simpler to work in a single frame, rather than to hurry after each moving object in turn."

That remark merits inclusion in this article, as this educational point was the essence of Bell's solution of the paradox. Harald88 11:59, 27 June 2006 (UTC)

Obviously I don't agree there is any educational merit in encouraging a wrong approach that leads (sometimes) to incorrect answers. Note that Bell confesses that the only modern text he can find that conforms to his approach is an obscure hungarian book published in Budapest by a certain L. Janossy. I would be tempted to add Edmund Whittaker's "History of Theories of Aether and Electricity" where (special) relativity is similarly credited to just Poincare and Lorentz and Einstein is demoted to a "Bourbaki" role of dotting i's, crossing t's and striving after formal elegance at the expense of "simplicity". Rod Ball 14:59, 27 June 2006 (UTC)

Apparently you agree that the issue about the educational merit of a certain approach is relevant for this article. About your personal, WP:OR: your claims are not only erroneous, the belief in a contrary solution of that of Bell resembles that of Dingle, who also refused to accept any solution of SRT that results in physical effects. But I won't let myself be lured into more than one sentence of editor POV -- that is not the purpose of this Talk page, as I already pointed out to you. Please abstain. Harald88 21:02, 27 June 2006 (UTC)

I write "obviously I don't agree..." and you say "apparently you agree...". I can see why with your logic you can't appreciate why it's Bell and not I, who is subverting SR. It seems you have also not checked your reference to Dingle whose position was not as you suggest, but raising inconsistencies in Einstein's transformations for duration and elapsed time between moving clocks, which varied between his 1905 paper and 1907 and 1910 papers. Your attempt to "smear" my credibility by association with Dingle only shows a preference for mudslinging over the effort of thinking and reasoning. Rod Ball 09:33, 28 June 2006 (UTC)

I referred to your above comment starting with "It seems (I think) we agree about".

As I now had to point out too many times, on this page we only discuss editing the article - this is not a Usenet discussion group, in which one's POV about the subject matter can be "smeared": here our POV's are irrelevant. Please abstain from adding personal judgments about your POV's and that of others, which next incite replies by others from which you in turn can claim that yours has been "smeared". That kind of trolling behaviour is not what this page is for - please stop acting disruptively.

Now that we have established the editing that we agree upon, about what editing do we disagree, according to you? Harald88 11:58, 28 June 2006 (UTC)

Let's get this straight. I've been sticking up for SR 'til I'm (figuratively speaking) hoarse, so I naturally object to comparison with Dingle. Also, showing that (and why) Bell's POV is at variance with fundamental SR could hardly be more pertinent to how the article should go. Informed opinion contrary to Bell/Dewan/Beran has in the current article been inappropriately dismissed as "dissident", anti-SR, isolated and cranky.

It is natural that people who find a "paradoxical" result - contrary to Newtonian expectation - should want to draw attention to it whilst those who find - no difference from Newtonian - no breaking of thread would not bother unless pushed to do so. The fact that among a handful of references the majority adhere to Bell's result is no more significant (and possibly less significant) than the opinion of CERN's Theory Division and sufficient Japanese physicists to upset Matsuda & Kinoshita. As far as the current article goes I would summarise:

1) The diff.geom. approach is absurdly over-the-top in complexity & math.sophistication and inappropriate to SR. I can find no other book or paper that uses such machinery for this or any remotely comparable SR problem. How many readers, looking up the paradox, will have any idea what to make of the formulae ? (In any case it's wrong, and I calculate zero for the expansion tensor but since ChrisH never includes workings I can't tell where we deviate.)

2) The history of the problem is wrong. Impulsively "kicking" the rockets (Bell switched to s'ships 17 years later) was never any form of the problem. Some authors have in recent years used straight lines for only the "before" and "after" trajectories, but this is not the same thing. Most such merely reiterate a too-brief type of Bell explanation without contributing any analysis of their own. ( Mat.& Kin. do but their account is flawed with contradictions.)

3) The Hrvoje Nicolic paper is irrelevant and should be dropped. ( It's rubbish anyway but that's another topic.)

4) Expressions indicating contraction should carry some explicit or implicit indication of the sort of procedure that would produce such measurements. ChrisH is fond of saying there are various notions of distance but I would say rather that there are various ways of measuring distance, and in SR they will not always give the same result. Rod Ball 13:30, 28 June 2006 (UTC)

Thanks for these constructive remarks. My take on your points:

1. We agree that readers have the right on an easier to digest presentation of the main arguments. However, I won't go as far as deleting a mathematical elaboration for the more mathematically minded, as long as it's verifiably consistent with the POV of certain authors. And perhaps it can be improved to make it less technical.

2. We also agree that the article should discuss smooth acceleration (both for historical reasons as for power of argument).

3. I have not read that paper.

4. I did not notice the current ambiguity, but your statement is correct of course.

Cheers, Harald88 22:28, 28 June 2006 (UTC)

Rod - If you wish to do a rewrite of this article, then please feel free to give it a go. My advice is to do this in a subpage of your user page at first. (For example, User:Rod Ball/Bell's spaceship paradox.) Then let us know when you feel that it is in good shape and give the rest of us a chance to look it over.

[Contentious remarks removed at request of Haraldd88 --EMS | Talk 03:21, 3 July 2006 (UTC)]

Obviously I can't follow some of the comments your exchanging about other matters but I'll pick up a few points here.

I've already reverted to a previous statement of the problem. Chris had overloaded it with Minkowski & Lorentz refs. etc. "time zero" and so on that give only an illusion of precision, whilst missing out the rather crucial fact that they're pointing in the same direction ! The problem needs a pared-down simple as possible statement that captures essentials and anyone can understand.

On the other hand, I object to an explanation based directly on Bell's version. In his own article Bell gives grounds for doubting that he is adhering strictly to SR as we know it and his account is way too simple - "arm waving" it's usually called. There is contrary opinion as to the outcome that SR predicts and this should be recognised rather than dismissed.

I cannot see any point retaining Chris's kinematic decompositions. They are not used anywhere else for this type of SR problem, parts of it seem wrong but as intermediate steps are rarely included it's even harder to check, and finally the whole diff. geom. approach is totally at variance with the common consensus that this is a simple problem.

Diagrams are essential (in almost any relativity problem) as they save thickets of confusing verbiage, but it's essential that the diagrams accurately reflect what they're supposed to. (Chris's first diagram for instance, shows only one of the two parallel lines of simultaneity and therefore misleads the viewer to think A'-B" is the distance concerned.)

I don't see why a source like Wikipedia should necessarily always have to impose a single answer based on someone's idea of "mainstream" where there is legitimate counter-opinion. Presenting both sides (when there are two sides) stimulates the reader to think a little for him/herself and perhaps explore the subject further. Nothing is more deadening than to give the impression that a topic is "old hat", "done and dusted" and no longer worthy of serious attention.

Although I firmly believe the Bell answer is wrong I'd be content to see both arguments for and against if that's possible in the same SR context. The reason I wanted some measurement methodology to accompany any claims that lengths are contracted is that it's absolutely essential, for Bell's argument to work, that any procedure for verifying that the string becomes shorter does not apply to the s'ship distance and I don't know of any way this would happen.

.Rod Ball 10:26, 29 June 2006 (UTC)

I think that it unnecessarily complicates matters if the article presents the view that the string will come onder tension as two views, especially as Bell's approach isn't significantly different from Einstein's 1905 approach of what later became the clock paradox. It's rather well put forward by the German Wikipedia as shown above, and I have no problem to put it into English. If the counter arguments can be largely presented by one counter view as well, then it would be useful (and interesting!) if you could summarize that argument in a similar clear and compact way.

Then it will be clear to all what the basic arguments are.

Harald88 12:02, 29 June 2006 (UTC)

The two views are tension and no tension.

Your "especially..." leaves me baffled. I can't see the remotest similarity between Bell's argument and Einstein's 1905 (or later) stuff on time dila(ta)tion.(!?)

I think a purely qualitative verbal argument is not really adequate. The only difficulty I see is fleshing out the (German or English) Bell version with diagrams or analysis that are both (a) honest & complete, and (b) supportive of his conclusion. As baldly as possible the two approaches are:

1)The s'ships are not connected, so will keep constant distance, whereas the string will become Lorentz contracted and snap.

2)Lorentz contraction applies to simultaneous coordinate measurements of string ends and s'ships alike, whilst the rest frame length & distance stay equal & unchanged.

The second can be easily amplified, extended (or inverted) whereas the first has limited plausibility and cannot be extended to cover deceleration for instance.

I think perhaps it would be necessary to admit there are two different "interpretations " of SR that yield the same answers in almost all "realistic" situations but which differ in unusual cases like this problem (and the Ehrenfest paradox).

.Rod Ball 83.244.164.35 13:57, 29 June 2006 (UTC)

IMO, first things first. First the article needs as a lead a general overview of this issue. Then the first thing presented is Bell's version and analysis whether you like it or not. However, this can be immediately commented on using other analyses that are more sympathetic to you view. Next there needs to be coverage of other notable treatments of this problem. Off of the top of my head (and do be aware that some this may be WP:OR even if it is correct) I can see three scenarios that are worthy of coverage:

1. Approach #2 above
2. The proper distance between the ships increases in their own frames of reference as they accelerate
3. Becuase of gravitational time dilation in their accelerated frame of reference, the forward ship appears to accelerate faster but for less time as compared to the following ship. Therefore it is always moving away from the following ship until the following ship (with its slower but longer acceleration) comes to be "at rest" with respect to the leading ship again and cuts off its engines too. This is the view that I fear is WP:OR. (Also note that this can be viewed as being due to the shifting relativity of simultaneity as the sihps accelerate.)

I think that it is very important that this article make it clear that there is not a single method of solution to this problem, and that there need not be be one. As long as they are all operationally equivalent (in that the string breaks), there is no problem. --EMS | Talk 14:32, 29 June 2006 (UTC)

Bell does not necessarily merit priority. Dewan & Beran and J.E.Romain supplied far more thorough presentations long before. Your second would be difficult as it doesn't happen ! To try and drag in gravitational t.d. with a dubious use of EP is not a good idea. I don't think the argument works anyway - plus you can't shift from "appears to" to "therefore it is". That's the kind of thing that bedevils problems like this (and Ehrenfest's especially). Finally, the whole point is that the approach I list second predicts the string won't break ! Rod Ball 15:08, 29 June 2006 (UTC)

I took "rest frame" to mean the frame in which the spaceships were before they accelerated. In the after-acceleration "rest frame" of the ships, the distance has increased. In any case, external documentation for any appraoch listed is essential. We can then discuss how to organize the material. --EMS | Talk 17:43, 29 June 2006 (UTC)

Also, my possibility #2 very much is what happens. That is the point of the current article and of the consensus of relativists. It is an odd thing in relativity, but for the string to stay unbroken, the following spaceship must use more thrust (locally) than the leading ship uses. (I was doing a reconcilliation of the time dilation formula for observers in the top and bottom of an accelerated box some years ago, and was at first shocked to discover that the proper acceleration for the observers had to be different for the results to be consistent. Only later did I learn that this is a known result of relativity theory.) Note that in this "paradox", the thrusts are locally the same. --EMS | Talk 18:20, 29 June 2006 (UTC)

New lead

It looks to me that the discussion has gone widely beyond the subject of this section. To finalize that, here's my proposal for a new lead (incl. part of the existing lead) as based on the above German Wikipedia stub, shortened and with a few improvements. As the lead should reflect the presentation of the article, it's related to the above comments anyway. From the article I get that there is no unified counter opinion; but if that's wrong, perhaps Rod can clarify that issue. Thus, allowing for Rod's disagreement that the best known solution corresponds to a clear "mainstream" opinion, for now I have as draft lead:

Bell's spaceship paradox is a thought experiment of special relativity, with as purpose to clarify the effects of the so-called length contraction. The best known example was discussed by J. S. Bell in 1976, but a previous example had earlier been discussed by E. Dewan and M. Beran in 1959.

Two identical spaceships take off one behind the other and between them a fragile rope is tied. Will the rope break after some time, if both spaceships take off simultaneously with exactly the same acceleration? According to Bell and a number of others, in the spaceship launcher's reference system the distance between the ships must remain constant while the rope is contracted, so that at a certain point in time the rope should break! The same result is obtained by using a series of instantaneously co-moving reference frames: from that viewpoint, the equilibrium length of the rope remains constant, but the distance between the spaceships increases.

Nevertheless, from time to time papers appear according to which those solutions are incorrect, so that the rope should not break.

Harald88 18:41, 29 June 2006 (UTC)

That looks good to me. It does a good job of summarizing the literature (and I will admit that knowledge of the literature is a strength of yours), and of stating the issue. So I can support it as the new lead for this article.

I still feel that this article needs to be rewritten to be less technical and to give more coverage to the history of this matter, but your proposed lead will probably be good even in the new version. --EMS | Talk 18:58, 29 June 2006 (UTC)

Yes, the lead is meant to set the stage for just such an improved article. It is nice to agree about such issues. Probably Peter will agree too; I only hope that Chris will go along as well, as then the ideas for improvement are unanimous despite the different POV's. Harald88 19:17, 29 June 2006 (UTC) Harald88 19:17, 29 June 2006 (UTC)

Chris will not go along with anything that does not document how the string breaks, and I will be loathe to do so myself. This effort may be doomed give Rod's view, but OTOH if we can work in an air of mutual respect it may be possible to achieve something good. As this may be an area that can play off of your strengths, I apologize for my "attack" above, and will do my best to work with you. Just be advised that I expect you to stay calm and patient with Rod and myself, and respectful of other views in return. --EMS | Talk 20:51, 29 June 2006 (UTC)

Thanks, please take back (=delete) that one sentence and I'll forget about it.

About the article's content, I'm not sure to understand what you mean with "not document how the string breaks". Please elaborate. Harald88 22:59, 29 June 2006 (UTC)

[below text moved by Harald88 from "mainstream or dissident" to this topic] I've rewritten the intro. accurately & succinctly, I think. It captures the various names, the fact that they are all the same problem and the priority of Dewan & Beran (5 double column pages) compared to Bell's half page precis, leading into the description...Rod Ball 10:25, 30 June 2006 (UTC)

I notice that you ignored this discussion. Thus I'll combine the two leads. Harald88 15:52, 30 June 2006 (UTC)

When combining them I found that all essential information was already contained in the above draft. IMO the journals in which they published are not essential for the lead (they go into the article space), and the same for alternative names (of which there are probably many more). I inserted the precision that both historical papers agreed on the solution of the problem. Harald88 16:16, 30 June 2006 (UTC)

"with as purpose to" doesn't make sense. Maybe you should rewrite that phrase.--Klaser 16:42, 30 June 2006 (UTC)

Oops! OK thanks. I'm also not entirely happy with my "according to the above discussions", perhaps "the above accounts" or "the above-mentioned authors", would be smoother. Harald88 18:06, 30 June 2006 (UTC)

I have done a change to the lead, also getting rid of the "so-called" business. (There is a physical reality to length contraction albeit in the frame where the ruler is moving.) --EMS | Talk 18:10, 30 June 2006 (UTC)

We were editing it at the same time, but I included your changes in my edit. Harald88 18:29, 30 June 2006 (UTC)

And Rod, about your continued argument under the wrong subject header: I had already corrected the lead into stating it's the same example. Harald88 19:34, 30 June 2006 (UTC)

mainstream or dissident

For the moment the lead doesn't suggest that one view is more popular or mainstream than another, based on Rod's disagreement. However, the references in the article support the distinction between "dissident" and "mainstream", as no recent "dissident" view in a mainstream journal is referenced. Is any such publication known that has passed peer review in a reputable publication? In principle, only such should be mentioned by name and are to be taken into account for discussion. Harald88 19:35, 29 June 2006 (UTC)

In particlar: I don't know the reputation of the AAPPS bulletin. Harald88 06:59, 30 June 2006 (UTC)

Nobody knows? Apparently Chris was quite correct in presenting the best known solution (that the rope breaks) as "mainstream". Harald88 15:56, 30 June 2006 (UTC)

I can't object to that too much as such labels are inherently POV. At this point I want to see what Rod Ball can come up with. Now that I see where he is coming from, I see why you were calling his view WP:OR, although if there is a body of work that supports his view, then it may be more non-standard than inappropriate. (Remember the Wikipedia is here to document existing knowledge. That is not necessarily the same as that which is correct. So I will attempt to educate Rod Ball about the string breaking so that we can agree on how to order a rewritten article, but at the same time we need to determine what the state of knowledge on this issue is instead of the final state of the string.)

Do be advised that I have found that it is easier to work with a well-written article that you disagree with than a poorly-written one that you do agree with. That is why I want to see what Rod can produce, although you are free to try your hand at a rewrite too. Just be ready to see it criticized by the both of us (and possibly with cotradictory suggestions for improvement). --EMS | Talk 20:42, 29 June 2006 (UTC)

in fact I wasn't calling his view about the subject matter WP:OR, as his view is apparently based on certain papers of which I hadn't checked if they are allowable source material for Wikipedia - that's what this section here is for, to establish that. Instead I commented on his unreferenced POV that made Bell's solution look suspect - as if problem solving in one frame is somehow not SRT. Einstein used the same approach for his 1905 clock calculation and Ehrenfest similarly for his rotating cylinder argument.

About what POV's to reckon with, WP:OR is very clear. That should help us to get consensus about how accepted certain views are, and which views should be mentioned at all. On a sidenote, I'm also curious to see what Rod can produce as counter arguments.

As concerns article rewrite, I would hope that it can be done as teamwork - that's anyway the way Wikipedia works, especially with subjects about which there is disagreement. It's an illusion to think in such a case that a well-written article that is written in one go by one person will survive in that state. It is more practical to ask someone with good writing skills to re-edit an article after the dust has been settled. Harald88 23:02, 29 June 2006 (UTC)

I think that we are close to being on the same page in that regard. I think that we all agree that what is needed is a less technical article. However, I have other duties and even now am putting more effort into this than I should. So I need someone else to at least do the hard work of the first draft. After that, the rest of us can either work with it or reject it, although I would rather avoid the latter if at all possible. --EMS | Talk 01:29, 30 June 2006 (UTC)

proper distance

[subject header inserted by Harald88 Harald88 14:45, 2 July 2006 (UTC)]

BTW I thought I'd heard EMS's approach 3 before and soon found - Edmond M. Dewan, Amer.J.Phys. 31, p384 (1962) "Stress effects due to Lorentz contraction" where the same idea of gravitational time dilation is used. However it's a shaky analogy as a completely uniform pseudo-field (ie. constant in the direction of free fall) is in no way equivalent to a "real" gravitational field of space-time curvature. For a good discussion see http://www.citebase.org/cgi-bin/fulltext?format=application/pdf&identifier=oai:arXiv.org:physics/0204044 .Rod Ball 11:19, 30 June 2006 (UTC)

Also, the proper distance between the s'ships in their own frame of reference does not increase as they accelerate. This is precisely what the simple L.T. calculation at the top of this page clearly shows. The engine-switch-off-to-become-inertial can be imposed at any time during acceleration and the LT's show the proper distance is invariant. Rod Ball 12:41, 30 June 2006 (UTC)

Rod - You did not compute the proper distance between the ships but instead the invariant interval between the ships at events which are simultaneous in the frame of reference of the spaceship launcher. As computed, that indeed is always L. In fact, that is an important attribute of this thought experiment. Note that part of the input into your calculation was the local time difference T(A) - T(B) = γ v L. To obtain a proper distance, you must use events such that T(A) = T(B). (I lack the time to do the correct calculation now, and may not be able to get around to it until Wednesday at the least. However I sincerely assure you that this is the source of your error.) --EMS | Talk 15:52, 30 June 2006 (UTC)

Oops. Never mind the wait. You have already computed the proper distance above (although you did not realize it for what it was). As noted, in the coordinates of the final frame of reference X(A) - X(B) = -γ L. So the correct proper distance calculation given T(A) = T(B) is

${\sqrt {\Delta X^{2}-\Delta T^{2}}}={\sqrt {(-\gamma L)^{2}-0^{2}}}=\gamma L,$

and it is therefore shown that the string will break. --EMS | Talk 16:03, 30 June 2006 (UTC)

I'm sorry, but you are quite wrong. You need look no further than http://en.wikipedia.org/wiki/Proper_length

Also I think my intro. is definitely clearer and more accurate than Harald's replacement. "With the purpose of" is not really true, Bell's is not another "example" but the same thought expt. stripped down to ~half page. It should be D&B's Problem, brought to wider attention by Bell, as I said. Let's try and be accurate when it costs no effort ! Also why include the details (omitting that they point in the same direction) when they are already more clearly described under "Thought Experiment"? "The same rsult is obtained..." cannot be just baldly asserted when there is no justification. I'm not nitpicking - it's now a messier than when I left it.Rod Ball 18:35, 30 June 2006 (UTC)

I already had corrected that it's the same example; and I agree with the sequence, no problem. -> Done.

PS please stay on-topic, this topic is discussed in the section above). Harald88 09:25, 1 July 2006 (UTC)

Rod - I know the proper length article and what it says. I wrote it. I repeat: Your calculation is correct, but you are calculating the wrong thing. You are calculating the simultaneous proper distance between the ships in the frame of reference of the launcher. That indeed is always L. However, in the frame of reference of the ships themselves, their simultaneous proper distance is γ L, and that is the operative proper distance for the string. Once again, note that ΔT is -γ v L in your calculation. So you are computing the proper distance between events that are not simultaneous in the frame of reference of the accelerated ships. That is the issue.

On the issue of the lead, I advise proposing your modification to the first paragraph here, and let's see if we can come to an agreement about it. I can support giving the 1959 article first billing, but it has to be made clear how this exercise came to be called Bell's paradox. In any case, we don't need an edit war over something that we should be able to figure out as a group. --EMS | Talk 19:02, 30 June 2006 (UTC)

Indeed, I had also commented that this must be a mistake with simultaneity. The problem is defined such that the (moving) distance between the ships (in fact between their centres of mass) in the launcher frame remains L -- and that needs to be stressed in the article. Everyone agrees that according to the LT's, in other frames that distance differs from what it is in the launcher frame. Harald88 14:45, 2 July 2006 (UTC)

To EMS: at the end of the New Lead section you say "there is a physical reality to length contraction albeit in the frame where the ruler is moving". I hope you mean "in the frame with respect to which the ruler is moving", otherwise you are at variance with SR. this is the main issue. In Fitgerald-Lorentz-Poincare-Larmor (FLPL) relativity contraction happens in the rest frame of the body but is supposed to be "imperceptable" (see next para) whereas in SR "rest lengths" are the same unchanged proper length. In short, you can explain the Michelson-Morley expt. either by having the interferometer arm contract as it rotates 90 degrees or by assuming the constancy of the velocity of light, but not both. Note that Bell writes (in same article):

"The factor [1/gamma] is accounted for by the Fitzgerald contraction of her metre sticks. But will she not see that her metre sticks are contracted when laid out in the z direction - and even decontract when turned back in the x direction ? No, because the retina of her eye will also be contracted, so that just the same cells receive the image of the metre stick as if both stick and observer were at rest.....Moreover, imagining herself to be at rest, she will not know that light overtakes her, or comes to meet her, with different relative velocities c+/-v."

Hence Bell is not arguing from the POV of SR, but an alternative "relativity" (FLPL) he considers equivalent. As Arthur I. Miller notes in his treatise on early relativity:

"Einstein's definitions served to emphasize that his length contraction differed fundamentally from Lorentz's which asserted that something happened to the rod in [the rod's frame] but compensating factors prevented the inertial observer from ascertaining changes in shape."[p.222]

I have to assume that Bell was unaware that the Dewan & Beran problem was a rare case where the predictions of the two theories markedly differ because of the unusual involvement of an empty spatial distance. In Einstein's theory this would exhibit "contraction" exactly as a solid length would under all the measurement methodology Einstein lays down in his original papers, whereas in Lorentz's (FLPL) theory it could not, because of the "mechanistic" model of such contraction in his theory. Experimental results as well as theoretical superiority [of Einstein's approach] have subsequently strongly disfavoured the Fitzgerald-Lorentz-Poincare-Larmor version.

Also, you are dead wrong on proper distance. The proper distance is the same for all relatively moving frames - that's why it's called "proper" distance. Consult any textbook. Rod Ball 19:49, 2 July 2006 (UTC)

Some comments:

- "there is a physical reality to length contraction albeit in the frame where the ruler is moving" means the same as "in the frame with respect to which the ruler is moving". And I'd put it as follows: length contraction is a perceived physical phenomenon in the frame relative to which the ruler is moving (which for all practical purposes means again the same thing).

- Rod, I'm sorry that I have to repeat (and now emphasize) that this page is not for discussions about SRT. Therefore, after this I will ignore your ideas about it.

- It is irrelevant if one refers to Bell's paper or Dewan&Beran's paper whose example he unknowingly discussed: they fully agree on the essential points. And happily so, for that allows to keep the article's presentation clear and straightforward.

- Thus, please stop cluttering this page with debates about your ideas of Bell's interpretation of SRT: even if it would make a difference (which in fact it doesn't), such a discussion is irrelevant since we can focus on the original paper by Dewan&Beran, and I already proposed to do so.

- As by now everyone incl. myself has tried to explain it to you, here a last attempt: according to SRT (see Einstein 1905), a "moving" object "is" (perceived to be) length contracted (except if it is stretched of course!). Also, a "stationary" object "is" uncontracted, thus the "proper" length (I'm afraid that the proper length article is ambiguous and overly technical, see [1] for a simpler definition). Note that we're free to choose whatever inertial frame as reference; it's similar to kinetic energy in classical mechanics, which also depends on one's choice of reference frame.

- In order to be constructive, please do attempt to briefly summarize the contrary opinion by Hsu et al. That's so far the only alternative POV to eventually take into consideration. Probably you know it well and want to advocate it. Harald88 22:05, 2 July 2006 (UTC)

I'm glad we all agree about the "with respect to which" bit, as the albeit left a little ambiguity. Harald, I wish you would stop trying to stifle discussion of matters directly relevant to the article and the problem. If you read what I last wrote with quotations, you will realise I am not "discussing SR" but pointing out that that Bell is self avowedly not using SR, and that what he is using differs significantly conceptually, but more importantly leads to different results in this particular problem.

Since you are familiar with Einstein's 1905 paper you might care to check that the measurement regime he specifies for length contraction would apply equally validly to two separate objects moving at the same velocity. This would refute Bell/Dewan/Beran's string breaking prediction. Taking the trajectories as parallel because they must be seperately the same, and therefore representing the distance between them as constant is an "indirect" measurement and not at all the kind that Einstein had in mind. Rather he considered an observer alongside the path of the s'ships as they fly past and marking positions simultaneously by his time. This would give the same result for s'ship distance as for string length. (Another point: Bell did not "unknowingly" discuss D&B - he references them in his article.)

The counter position can pick holes in the Bell/D&B view in several ways:

1) That s'ship distance should be treated the same as string length.

2) That attempted corroboration from POV of constant v observer leads instead to contradiction. (Dewan tries to deal with this in his 2nd paper of 1962 but goes astray in arguing in effect the breakage always occurs at the same instant the s'ships are launched.)

3) That a 3rd observer in a slightly less powerful rocket would not see breaking as his relative v would not be enough.

4) That the reciprocity of contraction is not preserved when the s'ships remain unlaunched and the previously static ground observer is launched opposite way instead.

5) That for accelerated motions of extended lengths the usual LT needs to be replaced by the Moller-Wu-Lee transformation.

So the last is not the only POV to be considered. Rod Ball 09:05, 3 July 2006 (UTC)

Rod, it appears that you still didn't understand what this page is meant for, and that putting it in bold also doesn't help. Nevertheless, I'll here copy a sentence of the standard short Talk page header: Please note this is not a forum for discussing the topic generally.

In particular, "The counter position can pick holes in the Bell/D&B view in several ways" is not what Wikipedia is for. What we're supposed to do here is to discuss of how we present an overview of what specific pro and contra arguments have been published - and not what one might discuss in a peer reviewed paper. After someone else (you?) manages to get such a paper published in for example the AJP, we'll be happy to include it. But for now, the only alternative POV that we know of and that we are allowed to discuss is the one paper by Hsu et al.

For example, if they claimed that "Bell is self avowedly not using SR", then that may be used in the article. Thus I'm curious to see your summary of their counter arguments. Harald88 22:39, 3 July 2006 (UTC)

PS: I think that POV's are in general best expressed by editors who support those POV's. For that reason, I hope that EMS will not convince you that Hsu's POV is in error before you have summarized it. Harald88 23:01, 3 July 2006 (UTC)

LOL! I applaud the spirit if not the plan. I think that it would be easier to get agreement if Rod understands his error, but you are right in that we need him to help document the "contra" viewpoint whether I "convert" him or not. --EMS | Talk 04:30, 4 July 2006 (UTC)

Rod - Harald is right in that we need to take this discussion off-line. Please go to my Wikipedia user page (User:ems57fcva) and use "e-mail this user". That way I can deal with your mistake in using the proper distance between events this the final rest frame of the spaceships which are not simultaneous. BTW: T(A) - T(B) = - γ v L (for the final rest frame of the spaceships) means that in that frame the lead (A) spaceship shut off its engine before the following (B) ship did. So to reverse the exercise, the B ship has to start firing its engines first and the A ship wait for γ v L before firing its engine. Otherwise, as you surmised, the distance between the ships would increase even more.

In any case Bell did use, understand, and believe in relativity. You are just missing a subtle point involving simultaneity here, and I hope to soon enough show you the mistake.

Beyond that, the issue here in Wikipedia is what is known/believed and not what is true. Do keep that in mind as we try to sort out this article. --EMS | Talk 21:34, 3 July 2006 (UTC)

So you seriously think the quote above from Bell's own article beginning "The factor [1/gamma] is accounted for..." is special relativity do you ??

Of course it is. You own math above shows how. (Δ X = γ L). --EMS | Talk 14:35, 5 July 2006 (UTC)

It most certainly is not. Try reading the whole paragraph. He is clearly asserting contraction in the rest frame, contrary to SR, and using all that "contracted eyeball" nonsense to explain its non-detectability. This is the old Lorentz-Fitzgerald ether-derived theory that I feel you have difficulty distinguishing from SR. No molecular explanation is necessary either, if no contraction happens in the rest frame. I emphasize that "in the rest frame" means w.r.t. an obsever traveling with the object - it does not mean "when the object is returned to a state of rest". Rod Ball 12:09, 18 July 2006 (UTC)

Wikipedia is also not a forum for an individual or clique to enforce their viewpoints by editorialy suppressing alternative published POV's by denigration and highly selective ad hoc criteria for acceptability.

Dewan himself introduces 2) and discusses it in his 2nd paper of 1962. Nawrocki covers 1), 3) and 4) and 1) is again quoted as significant opposition by Matsuda & Kinoshita.

JH Field's artticle is also pertinent.

Again, Wikipedia is an open resource for all to edit, not just a select few of self-appointed dictatorial thought police. If your view of the problem is as completely obviously correct as you maintain, why are you so frightened of presenting any counterview ? Nobody will be persuaded if it's "obviously" wrong, or do you just want to stop people thinking for themselves ?

If I was frightenned of the counter-view, I would not ask you to draft a rewrite. Where is it, or do myself and Harald need to do that? Beyond that, I would rather you e-mailed me and took the discussion of the mechanics of the paradox off-line. However, if you prefer I will ask you some questions about your viewpoint here. I do not at all want you to accept my viewpoint without my having shown you acceptable reason to do so, but I very much assure you that good reason exists. If nothing else, perhaps you would like to answer two questions for me? What is the physical significance of the X coordinate? What is the physical significance of the T coordinate? --EMS | Talk 14:35, 5 July 2006 (UTC)

And contra Harald, POV's are often best expressed by those who don't share them, otherwise there's a tendency for "cheerleading" & contempt for opposition. I for instance, never wished to "squash" Bell's view, rather to expand it to include more of D&B and insert a fair description of caveats etc. raised by referenced objectors. Rod Ball 08:38, 4 July 2006 (UTC)

I now expanded the article somewhat more about the arguments of D&B and Bell. Rod, you are very welcome to include a fair description of the peer reviewed objections, "eventhough" you agree with them! Harald88 20:01, 4 July 2006 (UTC)

There seems to be some confusion in your account. You've mixed up 2 different arguments. For the comoving frame the s'ships also launch simultaneously but D&B argue they gradually move apart. In D's 1962 it is from constant v (during launch and throughout) ref. frame that they start at different times. For this observer remember, the string length is also increasing so another mechanism is required. Also comoving is adequate and accurate - "series of instantaneously..." is only needed if inertial LT's are to be used. Also it's the observed, measured or actual length that contracts or not. The maximum sustainable length is the elastic limit length which is supposed reached when the normal length is hindered from contracting. Rod Ball 12:48, 5 July 2006 (UTC)

Rod, you're absolutely right that I mixed up two slightly different descriptions - I'll correct that immediately.

Apart of that, I'd say that in pure SRT only inertial frames are to be used, but accelerating frames can be emulated by a series of instantaneously comoving inertial frames (ignoring dynamic effects). -> I now notice that a section about acceleration is lacking in special relativity!

About EMS's "max. sustainable length": I'm sure that it's correct but perhaps unclear, see below. When the normal length is hindered from contracting, stress starts to build up. It takes some more relative extension before the elastic limit is reached.

Harald88 19:27, 5 July 2006 (UTC)

Actually, Harald, I've noticed the mixing up occurs in D&B where they refer to a number of observers arranged along the track, each at a higher constant v, and say that they will observe s'ships at increasing distance and to have started at different times. So your account of what they say was a fair one. Nevertheless I agree with you that it's better to clarify D&B's position, which may be what Dewan was (partly) doing in his follow up.

Presumably, if max. sustainable... is a few % more than L, it will also be same % more than any contracted L/gamma, so I suppose it does itself "contract" or stay the same in proportion to L. But all this is unnecessarily speculative and encumbers the wording for no good reason when it's perfectly clear to say just "length" instead. Rod Ball 08:49, 6 July 2006 (UTC)

Todo list; students beware

I created the May version of this article and had been monitoring it, but I am leaving the WP and am now abandoning this article to its fate.

Just wanted to provide notice that I am only responsible (in part) for the last version I edited; see User:Hillman/Archive. I emphatically do not vouch for anything you might see in more recent versions. In particular, I believe the changes by Rod Ball (talk · contribs) and Harald88 (talk · contribs) are in some respects factually inaccurate and in general are seriously misleading. See the archived talk pages for some details of my dispute with them over the content of this article.

The expert tasks in the todo list were notes to myself which probably won't make sense to other users, so I have removed them as a courtesy.

Good luck to all students in your seach for information, regardless!---CH 22:41, 30 June 2006 (UTC)

Thanks a lot for your contributions and for your hint to check the archives; but before you go, please indicate what in the new lead (based on the German Wikipedia but with a few corrections by EMS and myself) is not OK according to you? Amazingly, you claim to have in the past "disputed" with me "over the content of this article", while in fact (easy to verify!) you never discussed it with me and I only recently discovered it! You certainly need a break.

Regards, Harald88 00:24, 1 July 2006 (UTC)

"Bell observers"?

The article now has a section called "Bell observers" to indicate the moving observers in this example. Who coined that term?

Bell stressed that:

[the example's] special merit is to drive home the lesson that the laws of physics in any one reference frame account for all physical phenomena, including the observations of moving observers. And it is often simpler to work in a single frame, rather than to hurry after each moving object in turn.

To me "Bell observer" suggests the contrary of what he tried to make clear. IMO, "moving observer" would be an appropriate lable.

Harald88 09:43, 1 July 2006 (UTC)

Rod - Do the rewrite elsewhere

Rod -

Please do not replace this article until we have a version that we agree is acceptable. I know that your version will not be adequate on its own, and it is my hope that by working with myself and Harald that we can create a reasonable, accessible article on this subject and the relevant viewpoints. Once again, please use User:Rod Ball/Bell's spaceship paradox for the rewrite. Just click on the red link and start the article. Then let myself and Harald comment on it.

Also, be aware that I have interspersed comments in your text in the "Proper distance" thread above. I also am not impressed that you have refused to respond to my specific arguments about how this "paradox" works with technical arguments of your own. In any case, I await your opinions of the physical significance of X and T. --EMS | Talk 14:58, 5 July 2006 (UTC)

On second thought I may have mistaken Harald's additions and Rod's removal of Chris' math for a rewrite attempt. Even so, I must ask that Chris' math stay in place until we know what will replace it. --EMS | Talk 16:27, 5 July 2006 (UTC)

Chris's sections on Bell observers & Rindler observers etc. can and should be jettisoned as they are in blatant breach of WP:OR. No published source supports either his approach or his arguments, quite apart from the fact that they contain errors and severely lack sufficient detail for verifiability. Given the low technicality of the primary and subsequent sources on the problem, what exists now (sans ChrisH's) is a perfectly adequate version and it will be improved and added to bit by bit as is expected for Wikipedia articles. Why not transfer ChrisH's stuff to the talk page, where the same rules don't apply as long as the material is relevant.

I have refused to respond. (On the contrary several of my arguments have been ignored throughout these discussions.) About 3 paragraphs above "New Lead" your point (2) reads; "The proper distance between the ships increases in their own frames of reference as they accelerate". I then pointed to an earlier simple LT calc. that showed this was not the case. You then claimed I hadn't calculated the proper distance but something else. I briefly referenced that I had whereupon you admitted I'd calculated the proper distance but you wanted to use another different proper distance claiming mine was w.r.t. wrong frame. I then pointed out that the proper distance is so called because it's the same for any inertial frame.

I have to say you don't seem to quite understand proper distance in SR. The "proper" length or distance between two events is at first the length or distance in a frame w.r.t. which it is at rest. It is the maximum length or distance that can be measured from any relatively moving inertial frame. It can however be calculated from any such frame by using the "hyperbolic triangle" formula from the coordinate x-difference and t-difference etc. You cannot just take the x-difference from the LT and simply wave a wand to make the t-difference go away. What meaning can you attach to a distance between one coordinate fixed this morning and the other in the afternoon if you're in relative motion ? Rod Ball 13:14, 6 July 2006 (UTC)

Rod - You wrote

You cannot just take the x-difference from the LT and simply wave a wand to make the t-difference go away.

That is a good point, but is totally misleading. Whether the string breaks or not is give by the simultaneous proper distance between the ships. Note the word "simultaneous", meaning "at the same time". You are finding the proper distance between the events at which the ships cut off their engines to be L. That is fine since those events are simultaneous in the frame of reference of the launcher. However, in the rest frame of reference of the ships, we have Δ X = γ L and Δ T = γ v L. The non-zero Δ T means that, in the frame of the ships, the shutdown of the engines is not simultaneous. However, whether the string will break is based on its length at a given time in that frame of reference! Fundamentally, since this is the rest frame of the ships, the X coordinate gives the at-rest rod distance between the positions, and this is what the string experiences (or is being asked to experience).

In other words, you cannot use arbitrary events to determine the mechanical length that the string must stretch to go between the ships. Instead you must use simultaneous events. For example, look at how the length contraction of a rigid rod works: In the rest frame its length is L. When in a "moving" frame, the same events that gave it a rest length of L are still separated by a proper length of L, but they are no longer simultaneous. Instead, using the position of the ends of the rods which are simultaneous one finds that the rod is length contracted.

So answer some questions:

Do you agree that ΔT = 0 is the simultaneity condition in the final rest frame of the spaceships?

Do you agree that ΔX is a simultaneous distance as measured using at-rest standard rods in the rest frame of the spaceships?

Do you agree that the string's mechanical attributes are based on the simultanous distance between the spaceships?

Please answer the above explicitly. I need to see your answers to deal with the disagreement about the result of this exercise. (Look at it this way: If you are right, your answers will allow me to see it and change my mind.) Thank you.

BTW - I agree that Chris' work is probably WP:OR, but would like a chance to look over the referenced literature myself. I assure you that it is correct, but it is not accessible, nor is it encyclopedic IMO. However, I want some agreement on what will replace Chris' work instead of letting it be removed unceremoniously. --EMS | Talk 14:41, 6 July 2006 (UTC)

I'll get back tomorrow on the simultaneity points as I want to be as clear as possible about where you're going wrong and also about not expressing things unintentionally ambiguously.

BTW - How can you assure me? Have you noticed the error in the 3rd expression for T (at start) which should be sinh(k.sigma)-1 over k ? Have you tried calculating the expansion tensor ? I calculate (&check&check) it to be zero like the vorticity. There's no "probably" about it breaching WP:OR - it's heavily biassed, unverifiable and reflects no published argument. And its also badly written ("to assuage any remaining misgivings.." & other tortuously condescending prose). Perhaps "ceremonially" tranfer it to the talk page ? Rod Ball 15:42, 6 July 2006 (UTC)

If there is an error in Chris's discussion, it is a transcription error instead of a math error. I have gone over it carefully as I can, and see no problems with it. I also suspect that your calculation of zero expansion is based on the same simultaneity issue that bedevils the rest of your calculations. (After all, in the frame of reference of the launcher, there is zero expansion, but that is not the issue.) I will technically disagree about Chris' work not being verifiable, but needing an advanced degree to do the verification is not appropriate to Wikipedia.

Let's give this process a bit longer before transfering Chris' stuff over here. Overall, it is a good plan, but I'm not sure that it is time for that yet. The current article without it looks a little scimpy to me. At the least, I want to hear Harald's opinion on this -- If he thinks that it is time to remove Chris' math here then I will go along with it, although I would like to some discussion in the article of the math you posted at the top of this page in the article. (I agree with the math, but not your interpretation of it. Given some use of that math in the literature, I would like to be in the article.) --EMS | Talk 16:16, 6 July 2006 (UTC)

My take on this: I had not yet carefully looked at that math, and assumed that it's similar to the contents in one of the referenced textbooks. Thus I hoped that at least some of it can be kept, and that we'd work out a simplified presentation with which to replace it.

I suggest that if in the coming days we are unable to find any description in the literature that roughly resembles it, then it should be all moved to the Talk page (or perhaps to a separate, linked Talk page called "CH's math"). The article is already more than a stub without those math sections. Harald88 12:18, 7 July 2006 (UTC)

I've just noticed in my second paragraph at the top of this section I started "I have refused to respond" - sorry I wasn't being ironic, I meant to write "I have not refused to respond" but lost the "not" somehow.

I don't think the article is too skimpy as a starting version - just look how short Bell's own presentation is !!

There's no simultaneity issue in calc.of expansion tensor, just slightly laborious calc. of covariant derivative components.

In any case "verifiability" means verifiable as a published method of solution, not whether it's correct or not - obviously original research could be verified as correct but would still be inadmissable.

I don't think it's a good idea to intersperse comments (or worse, questions) in earlier sections above. One can't trawl through all previous stuff each day, they're hard to spot, and break the sense of what's already written, so a reply to something said before suddenly looks like a reply to a new comment added ata later date - and no longer makes sense.

The answers to your questions are Yes, No and No, although the second can be converted to Yes for the right ΔX as follows.

We want to have ΔT =0 so (using same symbols as before)....

x(A) = γ( X(A) + v.T(A) ) and x(B) = γ( X(B) + v.T(B) )

So x(B) - x(A) = L = γ.( X(B) - X(A) ) for T(B) - T(A) = 0

That is X(B) - X(A) = L/γ

[ Of course there is now a time difference in launcher's t coordinates but this is expected, as always, since we know that it is a difference in simultaneity that leads to measured "contraction".]

Why do we find the distance contracted ? Because the "events" x(A),t and x(B),t are fixed points in launcher's coordinate system for all values of t, so s'ships moving at relative v should find them all (including the blast-off positions) contracted by gamma.

If, however we parametrize t so as to be co-moving with the s'ships, then the relative velocity becomes zero, γ equals 1 and X(B) - X(A) = L.

To emphasize the sleight-of-hand in the Bell-D&B view, let me put it another way. When they assert in the context of SR that s'ships at equal but increasing v maintain constant distance in launch frame, they are denying that the usual length contraction effect applies to empty space between moving objects. If so, then they cannot then claim that the s'ships "move apart" in their own frame by taking L & applying reverse LT to "de-contract" the distance to γL. Either empty space shows contraction or it doesn't, you can't have it both ways - no contraction between 0 and v for launcher, and de-contraction between v and 0 for s'ships is just disguised self contradiction. Rod Ball 09:42, 7 July 2006 (UTC)

Rod, which paper(s) are you summarising here? Harald88 12:31, 7 July 2006 (UTC)

Ed ( if I may hazard a less abstract appellation ) has asked me 3 questions to explain my position and moreover accused me of refusing to respond to earlier queries, which I'm more than happy to. Remember that talk pages are not subject to the same tight restrictions as articles. Rod Ball 13:33, 7 July 2006 (UTC)

That's OK within certain limits - however, by now IMO those limits are far exceeded, as these pages should not -- and therefore certainly not mainly! -- be used for such newsgroup discussions. The same space, time and energy could be used to everyone's advantage for discussing the arguments the literature.

BTW, please indent comments (using ":"), as I now did with yours and mine. Harald88 18:47, 7 July 2006 (UTC)

[Insert] Harald, I have to say that your recent amendments are increasingly garbling what was before at least intelligible. You're also introducing errors, the instantaneously comoving observers find A & B launch simultaneously - consider comoving observer at velocity 0+epsilon. The later comovers are conjured up to check situation from inertial POV at higher v - they would have to refer back to much earlier times (when not comoving) to have seen staggered take-off (and thus disagree with 0+epsilon observer). The viewpoint is more clearly dealt with by Dewan as a seperate constant v observer. Also the "According to SR..." para. is bizarrely expressed. Rod Ball 14:42, 7 July 2006 (UTC)

Rod, I see that there was an ambiguity, you probably interpreted instantaneously co-moving as not moving at t=0 - I'll expand that sentence to avoid such a misunderstanding, as it is about separate constant v observers, and not about continuously co-moving observers. Harald88 18:47, 7 July 2006 (UTC)

???. Rod - You seem to have a very odd view of simultaneity in relativity. In the frame of reference of the launchers, A and B launch simultaneously. In the velocity ε frame, they do not. This is a matter of two different views of the same events. There is no "refering back" to an earlier time. BTW - DO NOT assume that the clock of A and B (which were synchronized in the launcher frame) will remain in sync as they accelerate. Instead, as their velocity increases, A 's clock becomes synchronous with earlier times on B 's clock due to the relativity of simultaneity. That is why the instantaneous proper distance increases as the ships accelerate. --EMS | Talk 14:57, 7 July 2006 (UTC)

Rod - Your derivation above (and I gather that it is in accord with the Nawrocki logic mentioned in the article) has a flaw: You are asserting ΔT = 0 instead of deriving it using the LT. Also, you are overlooking the fact the the ships take of in the (x,t) system and accelerate at the same rate in the (x,t) system. This means that their velocity in the (x,t) system is the same at any given time t, which in turn means that their distance is constant (at L). There is no need to use the Lorentz contaction on their x separation the initial description of the ship's actions is given entirely in terms of the (x,t) system. Note that the use of the LT gives a non-zero ΔT, and that the events which are simultaneous in the (x,t) frame therefore at not simultaneous in the (X,T) frame. So you need to go to the (X,T) frame first and then find events that are simultaneous.

At this point, I once again ask you to e-mail me as described above, and take this conversation off-line. Otherwise, we may just need to agree to disagree and to respect the literature in working on this article. --EMS | Talk 14:36, 7 July 2006 (UTC)

Nonsense ! My calculation is qite correct. What you say at the end of your first paragraph is precisely what I did. The diff. is that you wanted to take an equ. where ΔT was already non-zero due to another condition (delta(t)=0) and just set it zero. What I did was set it to zero in the variable equ. as the first and only condition to fix and find the ratio of the other parameters. Your comment "there is no need to use..." is absurd. Please try drawing a few diagrams - you seem to be confusing yourself with awkward phraseology & unclear concepts.Rod Ball 15:14, 7 July 2006 (UTC)

Let's see. Above you wrote:

T(A) = γ( t(A) - v.x(A) ) and T(B) = γ( t(B) - v.x(B) )

where γ = gamma, t(A) = t(B) and x(B)-x(A) = L

thus T(B) - T(A) = -γv.L

Also X(A) = γ( x(A) - v.t(A) ) and X(B) = γ( x(B) - v.t(B) )

so X(B) - X(A) = γ.L

This I agree with. Then in this thread you write:

x(A) = γ( X(A) + v.T(A) ) and x(B) = γ( X(B) + v.T(B) )

So x(B) - x(A) = L = γ.( X(B) - X(A) ) for T(B) - T(A) = 0

That is X(B) - X(A) = L/γ

So you now have an inconsistency here. In fact, your second exercise asserts that which you are trying to prove. It is the first exercise, and its X(B) - X(A) = γL, which is correct. Note that the spaceships end up being at rest in the (X,T) frame. That is why I can assert ΔT = 0 in the (X,T) frame to obtain an instantaneous proper distance of γL --EMS | Talk 16:21, 7 July 2006 (UTC)

No, it's the first one that is appropriate for the purpose at hand, which is finding ratio of distances at T(B)-T(A)=0 rather than at t(B)-t(A)=0 (which was ok for invariant "proper" distance). It's standard textbook (eg. d'Inverno) and what you asked for, ie., distance in spaceship frame for T(B)-T(A)=0.

The best way to exhibit the problem with Bell/D&B's "obvious" answer is with a diagram - and it's only fair that I ask you to explain something. Look at these...

File:Rocket1.jpg

Consider first the launch site POV in the first diagram, where the bold lines show hyperbolic x-t trajectories of the front rocket (B1-B2) and the trailing end of the rope/string/thread (A1-A2). The bold dashed line shows Dewan/Bell's proposed trajectory for 2nd rocket at constant distance w.r.t. launchsite.....

File:Rockets2.jpg

Now consider the POV of constant v observer (as described by Dewan in his 1962 paper) in the second diagram, using appropriate parts of the same hyperbolae and where the thick lines again show trajectories of the ends of the "de-contracting" string. It is obvious that the string cannot break between time B1 & "A launches" as these are simultaneous in launchsite frame. The different launch times clearly play no part in the issue. Worse still is that the rear rocket is caught between two contradictions. The dashed trajectory between A2 & B2 which maintains "constant distance" as per Bell/D&B, slackens the string in contradiction to breaking it, whereas the dashed trajectory to the left of A2 is clearly on the one hand in violation of the "constant distance" idea and on the other is diverging at something like γ² compared to the thick lines expanding at γ. Also it is clearly a sharper deceleration & thus in contradiction to the condition of identical s'ships/rockets. Note that the only trajectory consistent with both diagrams is where the rear rocket follows the same bold line of the end of the thread, so that it neither breaks nor grows slack. Is there any other way you can resolve the 2nd diagram ? .Rod Ball 21:14, 7 July 2006

Lovely diagrams. However, if the first one you are ahowing dis-similar accelerations. Do note that it is a known feature of accelerated frames of reference that an observer at a lower potential needs to use a greater proper acceleration of keep up with the observer at a higher gravitational potential. For the second drawing I think that you have the rockets stopping at the same time, and that just does not happen if they start at different times and their flights are identical.

I like to say that the "anti-" has to convince himself of it when he is wrong. It is something that I have seen in myself, and whenever I lose track of it I later find that I have wasted a bunch of time and energy needlessly. Rod - You are working way too hard to justify your view. It's time to analyze what I have been trying to tell you. The dashed line in your first drawing is the correct one. That is what the exercise calls for. Just step back, and you will see that. --EMS | Talk 21:12, 7 July 2006 (UTC)

Hmm, initially I said the thick lines are the ends of the string (and the front one the front s'ship also - it makes sense to have the "weak point" of the string at rear attachement), and the dashed line the rear vehicle. The "velocity A=v" label was added after my conclusions from diag.2 - I should have left it off as it looks looks a prior assumtion.

Since displacement of simultaneity is proportional to the relative velocity - the greater relative v is, the more "simultaneous" events become displaced in time. So it seems reasonable that as the s'ships increase v and approach observer v, their relative velocity is decreasing (to zero) and so their "difference in time" should similarly diminish. Rod Ball 08:49, 10 July 2006 (UTC)

What are you trying to say? After all, in any given inertial frame of reference, the time difference between corresponding events in spaceships A and B will hold constant. So in the inital frame of reference, A and B both take off and turn off their engines at the same time. Similarly, in the final rest frame of A and B, they both take off and turn off their engines at times separated by γ v L. --EMS | Talk 14:52, 10 July 2006 (UTC)

Note that A and B are also the starting positions of the ends of the string which certainly arrive at the same velocity v at the same time by their own clocks and according to the pre established inertial v observer. Rod Ball 12:51, 13 July 2006 (UTC)

I'm done with this. You have shown that you cannot or will not adopt my view of the situation, and at the same time I find that every sanity test that I care to use supports the Bell view of this exercise, while impeaching your view. For example, the idea that the launcher frame distance between the ships is contracted is contradicted by the way the exercise is set up. (The reason for the "paradox" is that this is not allowed, after all.) So let's get back to brass tacks, and the issue of how to organize this article.

At this time, I will support the removal of Chris' version to the talk pages. You are right in that it is an original exercise, and also IMO is way too technical for the subject matter. As long as we can focus on the issue of what the literature says ahout this and have some respect for the difference of opinion between ourselves, the article should end up being OK. --EMS | Talk 14:34, 13 July 2006 (UTC)

I cannot & will not simply because I'm quite certain you are wrong. I think "sanity" is overdoing it but every rationality criterion I can think of shows that Bell's argument & conclusion are (1) from a non-SR viewpoint and thus (2) wrong. The exercise set-up dictates the situation in the comoving s'ship frame, not the non-s'ship frame left behind dwindling into the distance. Rod Ball 12:40, 18 July 2006 (UTC)

Tweeking intro

In the intro, "while the maximum sustainable length of the string is contracted" is IMO a bit heavy on the reader. "thus the string cannot contract" is IMO easier to understand and it's closer to the phrasing in the original paper by Dewan&Beran. Apparently EMS objects to that; Please clarify and do a suggestion! Harald88 18:24, 5 July 2006 (UTC)

What we need to communicate is that the molecules of the string are being contracted. As a result, the string will break even though the distance between the ships (in the launcher's frame of reference) is not increasing. This is where things get tricky, since technically the string is not being permitted to contract, yet its substance must given the Lorentz contraction.

I am open to suggestions and ideas here, but we need to communicate and that communication needs to be as accurate as possible. --EMS | Talk 19:23, 5 July 2006 (UTC)

I beg to differ. I see no need to communicate any behaviour of molecules. Not only is such mechanical explication no part of special relativity but it has no bearing on the problem. In any case isn't "contraction" supposed to be a simple direct consequence of relativity of simultaneity ? I thought we agreed, (or at least Harald seems to) that contraction only happens for the relatively moving observer and not at all for observers stationary w.r.t. length concerned. hence no molecular distortions are needed. You seem to be trying to introduce inappropriate theories, (or are you having difficulty with "string breaking" ?). See also my reply to Harald above. Rod Ball 08:58, 6 July 2006 (UTC)

Rod - One way or another the behavior of molecules is the issue if/when the string breaks. Whether that needs to be stated explicitly is another issue. Do note that I changed the wording to "elastic limit" in the article, and see my previous response above. Thank you. --EMS | Talk 14:48, 6 July 2006 (UTC)

Did you read the two quotations I put in the Proper Distance section ? You seem to be arguing (a) old-style Fitzgerald-Lorentz theory has to be used to derive string-breaking and (b) old-style F-L theory is exactly equivalent to SR so (c) it must also be true in SR. This doesn't work. SR needs no molecular or mechanical support for contraction since it doesn't happen to the body in it's own frame. F-L theory is also not equivalent to SR. If string-breaking occurs it should be predictable from true SR without any molecular nonsense.

You are falling into Chris's mistake of thinking that you have to model the elasticity & vibration etc. Nothing of the sort is relevant to whether the string snaps, just the usual SR arguments about what contacts, when it contracts and from whose viewpoint it contracts. Rod Ball 15:21, 6 July 2006 (UTC)

The Lorentz-Fitzgerald contraction is explained by SR and is therefore a part of it. Also do realize that I am describing the situation as seen from the frame of reference of the launcher, making your "no contraction in the string's own frame" argument moot. Also recall that in the string's frame the distance between the ships in increasing according to Bell (whose viewpoint I support). So once again the string comes under increasing stress. As for the use of full SR: Agreed. However, you need to answer my questions above (and I thank you for promising to do so) before we can come to agreement on what that means. Thank you. --EMS | Talk 19:17, 6 July 2006 (UTC)

This is later note (7 July) relating to above. The "Fitzgerald" contraction in the rest frame is certainly no part of SR. It was an earlier (pre-Einstein) partial relativity theory that is distinct from, and cannot be combined with, SR. Have a look at Arthur I. Miller's well-known classic on early history & emergence of special relativity. Rod Ball83.244.164.35 12:07, 7 July 2006 (UTC)

"Elastic limit" is certainly better, I can live with that.

Alternatively (and very close to the original): "According to special relativity the string should contract; however, the distance between the ships remains constant. Thus the string cannot contract and at a certain point in time it should break." Harald88 19:04, 6 July 2006 (UTC)

We can use our own words here, and in this case would prefer to do so. I don't see your version as communicating what is going on very well. Do recall that Wikipedia:Wikipedia is not a reseach journal. So not only are we not obliged to use the wording of the original text, but if it is technical enough we are even prohibited from doing so. --EMS | Talk 19:24, 6 July 2006 (UTC)

any possible disagreement?r

The following phrase was not opinion of Dewan but meant to be general information to the Wikipedia readers about SRT:

Under special relativity, the string must appear contracted in S if it is to appear undeformed in a frame relative to which the string is resting.

Is there any possible disagreement about how the LT work, or any ambiguity in that sentence? If so, in what way?

Harald88 07:05, 10 July 2006 (UTC)

If Rod Bell can live with that, then good. Since there is a controversy, a blanket statement starting with "under special relativity" raises a potential POV concern. However, the rebuttal to the standard view seems to be that the distance between the ships should also appear contracted, as opposed to the string not being contracted. Since this appears to be an area of agreement between the views, it may well be quite acceptable. --EMS | Talk 14:55, 10 July 2006 (UTC)

It's only that the wording is rather awkward. D&B actually say "...contracted in S because it has a velocity with respect to S." Shorten, diminish, contract etc. are ok but "deformed" is too far off to be used as a synonym, and the sense of above is 'in order to appear undeformed when at rest...' -almost reversing the logic without mention of velocity.

Secondly, there's the usual "shimmy" in reasoning that goes from "must appear contracted" to "...s'ships prevent the string contracting" - er, hang on ! What happened to "appear" ? If the s'ships only prevent the string from "appearing" to contract" perhaps there only "appear to be stresses". Can there be real effects from apparent causes ? Rod Ball 08:55, 11 July 2006 (UTC)

Rod, thanks for the precisions. The speed is already mentioned in the foregoing discussion; and the point is that when an object appears not contracted in S (as D&B have it), according to SRT it must appear stretched in the co-moving frame. Thus in such a case, according to all observers the object will be under mechanical stress - the length may be "relative", but the deformation relative to its normal length is an absolute. AFAIK there is no disagreement about such things in the (peer reviewed) literature.

If you have problems with "appear": such words are to remind the reader of the fact that in SRT length and time measurements are not absolutes, and Einstein also used that term.

Later I'll have a look at it to see if I can formulate it clearer. Harald88 13:50, 11 July 2006 (UTC)

[The re-wording is better] I don't have any problem with appear - others do, which is why they drop it like a hot potato as soon as possible because it would spoil the conclusion they want to reach. Yes Einstein uses "erscheinen" quite a bit. The reason is not what you claim but most specifically to distinguish between a "real" (ie.,non-apparent ) measurement made by an observer moving with the object, and a measurement of apparent length from a less reliable observation made whilst in relative motion.

The stipulations of identical accelerations, identical velocities therefore constant distance apply first and foremost in the moving frame of the s'ships themselves. The relativistic consequences of apparent observations made from the relatively moving launch site can only then be worked out. The s'ship distance can only "un-contract" if it has first been contracted. Just notice how often in relativity "reasoning" the word appear attached to a measurement is conveniently and surreptitiously made to disappear so as to firm up the status to a measure of "real" length and thus enable "stresses" to be conjured up. Rod Ball 12:12, 13 July 2006 (UTC)

Was that the argument of Nawrocki? If so, please add it to the article.

The primary frames, on which SRT is based, are inertial frames. Just as with Newtonian calculations, one can calculate - using inertial frames - what will be experienced in accelerated frames. If next a calculation with such derived frames contradicts calculations with primary frames, it would be a logical error to conclude that therefore the derived frame calculation must be right. Instead, obviously an error is made somewhere, and most likely in the more complicated calculation. Harald88 13:44, 18 July 2006 (UTC)

PS I now have both Nawrocki's letter as well as Dewan's rebuttal. Harald88 22:33, 18 July 2006 (UTC)

messed up explanations

I notice that Rod messed up the main points of the explanations by Dewan and Bell, which best defend their POV. Possibly because he doesn't understand their arguments, or possibly because he dislikes hearing them. Moreover, his suggestion that the CERN scientists continued to disagree with Bell runs contrary to Bell's suggestion that they didn't (except if we should assume that those scientists never looked deeply into the matter). Thus I partly revert.

Rod, if you don't understand their arguments, instead of deleting them please ask here and we can try to explain it more in the article. Harald88 12:58, 21 July 2006 (UTC)

In fact I understand the arguments a lot better than you! I removed your short paragraph that directly contradicted the 5th para. of the opening statement beginning "They obtained...". It is you that is confused by the two D&B explanations. The inertial observer considered by Dewan is any inertial observer travelling at any v w.r.t. launchsite and for all of whom the string is increasing in length after take-off at perceived differing times. A truly "co-moving" observer or a sequence of momentarily co-moving observers considered at the moments that each of them is comoving would see simultaneous launch and constant string length. Each of the prolonged inertial observers would have "seen" the string smoothly increasing its length, whereas the comovers are an infinite collection of momentary inertial observers every one of which finds the same unchanged string length. The two explanations do not "blend".

Also your obsessive bias prevents you from reading plain english correctly as written by Bell. He does not say the CERN theorists changed their minds. He refers to "many people". As far as I know Bell was a reasonable chap and the CERN people were his colleagues. Having stated that they flatly disagreed with him in an explanation that he calls "obvious", he would surely have specifically commended their good sense in coming round to his POV if they had done so. The fact that he does not refer to them but vaguely to "many people" would, if I wanted to push the point, suggest if anything, that they remained unconvinced. Rod Ball 15:19, 21 July 2006 (UTC)

Rod, since I merely summarized what they wrote, the contradiction (if it were) would be theirs. However, there isn't any. Insofar as you see a contradiction, it only requires clarification (and not deletion of an argument!). In a momentarily co-moving observer frame along the way (which is moving!), simulataneity differs from that in the launch frame. Dewan spent most of an entire article on trying to get that point through. I agree that the phrasing of both rather similar explanations can be improved, and I will do that now.

Apart of that, indeed I also didn't write that Bell stated that the CERN theorists changed their minds - probably there wasn't a second opinion poll. Bell only stated what he knew, which is that many who looked into it deeper, agreed with him (as indeed also happened with the reviewers). In any case, it's not up to us to do such guessing or to distort his account in order to suggest the opposite of what his point was.

Harald88 23:33, 21 July 2006 (UTC)

Rod - You certainly are making some interesting points. I regret that I am busy with worldly duties at this time, and cannot devote more effort to this page. One point that needs some looking into is in how D&B characterized the inertial observers and the string. I will admit that I need to read the articles, but it appears to me that you have he interial and the sequence of momentarily co-moving observers confused. The prolonged observers view a constant spatial separation between the ships after launch, while the sequence of moemtarily co-moving observers finds that string length increasing. Otherwise it makes no sense that D&B are arguing that the string breaks. --EMS | Talk 15:54, 21 July 2006 (UTC)

Stop

Rod, please stop. If (a) this article is your only interest in Wikipedia and if (b) you can't get it, that there are no open questions in BSP, you are out of place here. --Pjacobi 15:40, 21 July 2006 (UTC)

IMO the biggest question is if we can accept the AAPPs bulletin as Wikipedia source. Moreover, it would be nice if we can find a source for at least part of CH's calculations. Harald88 00:03, 22 July 2006 (UTC)