Talk:Bell's spaceship paradox

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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)

Pjacobi, please stop. If you can't get it that the open question is whether the string breaks or not, you are out of place here.

This is science, not supporting sports teams. The object is to fairly represent currents of opinion, not belittle, insult and squeeze out of existence perfectly legitimate contrary opinion.

The reason you deny the legitimacy of counter-arguments is because, as I have noted before, you do not understand the issues involved. Rod Ball 12:34, 24 July 2006 (UTC)

Stop it now for good. --Pjacobi 12:52, 24 July 2006 (UTC)

archived

I now archived the talk page, giving CH's essay a separate link on this page. I hope that we can still find a way to use it. Harald88 10:02, 22 July 2006 (UTC)

Dishonest

It is dishonest and POV pushing to present a problem which is SR textbook level as an open problem with two possible solutions. The Nawrocki analysis was notably the last dissenting analysis published in a peer reviewed journal and that's now over 40 years ago. Note that the strange papers by Fields all are rejected.

Please look into your SR textbook of choice under hyperbolic motion or uniform acceleration.

Pjacobi 10:24, 22 July 2006 (UTC)

The reason it has two possible solutions is because there are two possible relativity theories that can be applied. Bell makes it crystal clear in his article that he is using Lorentz's rather than Einstein's theory. Since it seems you do not appreciate the difference I'll point out just two important features. In E's "SR" there is never any contraction w.r.t. an observer at relative rest whereas in L's theory there is, but it is undetectable to the observer due to identical contraction of everything else in his ref. frame. This might seem an unimportant distinction but it means that in E's SR measurement of empty spatial intervals will also show contraction but in L's theory they will not. Unfortunately, many physicists today do not take care when using SR and dip into either theory in an ad-hoc way to suit whatever purpose is in hand.

Moreover it is your honesty that is in question when you seek to push your rigid POV to the exclusion of all others, including far better qualified specialists than yourself. Rod Ball 13:01, 24 July 2006 (UTC)

We of course agree with you, except for the issues above on which you srangely enough didn't comment. Thus here again:

• 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.

From your last comment I take it that you suggest that his calculations can be found in your textbook. Which one is that?

Harald88 14:05, 22 July 2006 (UTC)

Fine. I didn't read the current version of the article as agreement. But perhaps I'm only overinpreting.

As you may have noted in some comment from me months ago, I'm not 100% comfortable with CHs treatment. But presenting the worldline of spaceship A in Rindler-coordinates "of spaceship B" isn't creative enough to be excluded as OR.

What you can copy verbatim from any textbook with an explicit chapter on hyperbolic motion (uniformly accelarted motion is):

Wordline of spaceship A

x(τ) = (cosh (ατ) - 1) / α

t(τ) = sinh (ατ) / α

Wordline of spaceship B

x(τ) = (cosh (ατ) - 1) / α - l

t(τ) = sinh (ατ) / α

Where is α the proper acc. and l the distance at start in the lab frame

(I assume I have written this somewhere in Archive 1 already)

So all the remaining the problems are

• how to best present this in the article
• how far to go into the historical detail and errands of the dissenters

Pjacobi 20:02, 22 July 2006 (UTC)

Good - now you're up-to date with the discussion. :-) If we include your textbook as reference, we could for example add that to the discussion of Bell, to illustrate what "most people" typically do, therewith demonstrating that there is no need for any "new" such derivations.

However, going deeply into that kind of description implies IMO (and probably also in the opinions of Dewan and Bell) to give in to a misconception: as if a calculation that uses a description that is correctly derived from SRT could somehow differ from a calculation that uses the inertial frame description of SRT itself, and in such a case even be more reliable. Such mathematical hobbyism could throw sand in the eyes of the readers.

Meanwhile, as there isn't any dispute on this page about accuracy (to the contrary, corrections are welcome!), I modify the banner accordingly.

About the AAPPS bulletin: it seems to be peer reviewed, and it has big aspirations, but I couldn't find it in Web of Science nor in Scopus...

Harald88 01:59, 23 July 2006 (UTC)

Can we state some fixpoints to avoid doing useless discussions over and over again? Can every serious contributor agree that (a) the equations of motion above correctly describe hyperbolic motion and that (b) the question of the equation of motion for hyperbolic motion is fairly settled for decades, if not for a century, and is standard textbook stuff. --Pjacobi 13:03, 24 July 2006 (UTC)

Why do you keep pushing this ? Where were the equations of hyperbolic motion disputed ? The fact that you think the problem is simply a matter of veryfying the hyperbolic motion would indicate you have completely missed the whole point of it and are oblivious of the issues involved. You might as well ask why Dewan & Beran didn't confine themselves to the 4 or 5 lines necessary ! Rod Ball 13:22, 24 July 2006 (UTC)

Rod - Pjacobi has made a very serious allegation in claiming that your viewpoint has not been taken seriously in decades. I really think that the first order of business is to verify that claim, as I am much more comfortable treating your viewpoint as a common misconception than a respected alternative. Certainly there is no question in my mind that the string breaks, but Wikipedia is about what is known instead of what is true. (Note that what Pjacobi is saying is that it is known that you are wrong.)

BTW - One known aspect of accelerated frames of reference is that someone lower down in an accelerated box feels a larger proper acceleration, and needs it to "keep up" with the top of the accelerated box. In this "paradox", the spaceships both have the same proper separation, and so of course they should diverge. --EMS | Talk 13:40, 24 July 2006 (UTC)

It is hardly a "very serious allegation" !! He merely wants to ignore the CERN Theory Division, JH Field's analysis, the opposition that Matsuda & Kinoshita experienced that upset them so much, and Hsu & Suzuki's paper. But of course if all these are not serious people then you could say it hasn't been taken seriously for four decades.

Although not directly relevant, your BTW is wrong. He does not feel a larger proper acceleration. His velocity is the same as the top and the distance constant. The relativistic effects are only apparent to outside inertial observers UNLESS of course, you are using the Lorentz theory instead of Einstein's ! Rod Ball 14:37, 24 July 2006 (UTC)

Rod - In an accelerated box, time dilation is given by $t'=t(1-gh)$, where

• t is the proper time rate at the top of the box,
• t' is the proper time rate at the bottom of the box,
• g is the proper acceleration at the top of the box, and
• h is the proper height of the box.

In addition, going the other way we have $t=t'(1+g'h)$, where

• g' is the proper acceleration at the bottom of the box.

We also expect that $t=t'/(1-gh)$. So

$1+g'h=1/(1-gh)$

$g'h=1/(1-gh)-1=gh/(1-gh)$

$g'=g/(1-gh)$.

I trust that this settles the issue. --EMS | Talk 15:49, 24 July 2006 (UTC)

Not at all. If the box dimension is unchanged for someone inside it then such an observer must find t'=t & g'=g since top & bottom are in an identical situation. Again, it is only the outside inertial obs. who, plotting the locus of contracted measurements with increasing v, perceives the front & rear accelerating differently. Rod Ball 11:36, 25 July 2006 (UTC)

$t'=t$ means that you do not believe in gravitational time dilation. If that is the case, then I have grounds for calling you an anti-relativist :-). Your argument is moot as the top and bottom exist at different potentials in the accelerated frame of reference experienced by the observers, and therefore are different situations. As for the external (inertial) observers: Given that the box must contract due to the Lorentz contraction of course the external observer also finds the "rear" (or lower potential) end of the box being accelerated more. It all works together very nicely (although "nice" may not be your idea of an argument that means that the string must break). --EMS | Talk 13:07, 25 July 2006 (UTC)

Not quite. You are invoking a rather strong form of the equivalence principle which is unverified experimentally or theoretically. True Gravitational fields are non uniform & have "tidal" effects. The supposed equivalent of constant & equal acceleration would be a hypothetical field uniform (ie.identical at successive spatial intervals) in the direction of motion. I do not think there are good grounds for expecting time variation along this direction. Rather that grav. time dilation is due to variation in grav. field strength (ie. curvature) which is not mimicked for a comoving observer for whom front and back do not contract. Rod Ball 14:57, 25 July 2006 (UTC)

Now you have truly impeached yourself. I strongly advise seeing Einstein's 1911 article on the proagation of light in a gravitational field and the articles on the equivalence principle and gravitational time dilation. Simply put, curvature and tidal effects are wholely irrelevant to gravitational time dilation. The only variable needed is gravitational potential. In accelerated box that gravitational potential is $\Phi =gh$. In the vicinity of a massive object, $\Phi =-m/r$, which leads to $t'=t{\sqrt {1-2m/r}}$ of the Schwarzschild solution.

I do not know of any evidence for what you are saying. On the contrary, Einstein writes: "Of course we cannot replace any arbitrary gravitational field by a state of motion of the system without a gravitational field..." [Annalen der Physik, 49, (1916)] - whilst J.L.Synge writes: "...I have never been able to understand this [equivalence] principle...Does it mean that the effects of a gravitational field are indistinguishable from the effects of an observer's acceleration ? If so, it is false. In Einstein's theory, either there is a gravitational field or there is none, according as the Riemann tensor does or does not vanish. This is an absolute property; it has nothing to do with any observer's world line..." [ "Relativity; The General Theory", North-Holland, (1971) p.ix-x ]. A standard textbook says: "Local experiments can distinguish between a reference frame at rest in a gravitational field and an accelerated reference frame far away from all gravitational fields. Gravitational effects are not equivalent to the effects arising from an observers acceleration....", [Ohanian and Ruffini, 1994, p. 53].

Remember that atomic clocks have been centrifuged for prolonged periods at very high G without showing any sign of "gravitational time dilation" due to acceleration. Furthermore, how on earth could you define the "potential" anyway for uniform acceleration ? Also consider comparing an observer close to an asteroid with an observer very far away from a massive black hole - they could certainly compare their local gravitational field, but how could you arrive at any comparison of "potential" ? Rod Ball 12:31, 26 July 2006 (UTC)

I can only hold my nose at the "stuff" that you are shoving at me. The source of the gravitational field very much matters geometrically, but that is irrelevant to the issue at hand. For example, with the centrifuged atomic clocks, there is time dilation. Externally, it is velocity time dilation. But what if you are in the center of the centrifuge and spinning with it? Then you will detect a gravitational field (due to the acceleration of the centrifuge) and assign the time dilation to it. As for your question about potential, this issue was settled by Newton in his work on gravity. (BTW: I am using "geometrical" units such that c=G=1 in my writing. I hope that this is not causing confusion. So fully written out, $\Phi =-MG/r$ near a massive body, and the time dilation formula with respect to a distant observer is $t'=t{\sqrt {1-2MG/rc^{2}}}$.)

You are grasping at straws here. You shouldn't need to contest the fundamentals of general relativity or even Einstein's 1911 article on accelerated frames of reference in order to defend your viewpoint. --EMS | Talk 13:48, 26 July 2006 (UTC)

I take it you "go your own way" in GR. If you are rotating with the centrifuge, you will also observe points upward and downward in the "field" moving at different velocities, unlike the uniform case in hand. You apparently want to use Newton's potential in GR ? In Newton's gravitation there is no time dilation as time is absolute. My earlier question still stands.

What you are saying is that because there is T.D. (time dilation) in a gravitatioonal field then there must be T.D. across an accelerated box. You are assuming an extreme and invalid form of the equivalence principle, which only really says that Inertial and Gravitational Mass are measurably indistinguishable. I've provided ample references to the fact that gravitation and acceleration are not generally "equivalent" and it must be especially not so when the acceleration is uniform so as to not even superficially bear a resemblance to any conceivable gravitational field. Rod Ball 14:18, 26 July 2006 (UTC)

The judgement on J.H. Field is not done by us, but by the anonymous reviewers and the journal editors who refuse to publish the vast majority of his pappers [1]. Also I have to still to see someone else than Fields citing his papers -- except as bad example. --Pjacobi 17:29, 24 July 2006 (UTC)

Might I inquire what evidence there is that the "vast majority" of his papers are refused publication ? (I honestly don't know how to check on this)Rod Ball 11:40, 25 July 2006 (UTC)

Because of that I had already removed reference to Field. As according to general opinion Nawrocki's note had been debunked by Dewan's second article, only Hsu et all remains as a possible serious notable counter opinion. All of us except Rod have no doubt that they are mistaken, but that doesn't count for Wikipedia. IMO, The fact that their publication is in a journal that can't be found in common indexes makes it of less encyclopedian value; and a corresponding comment is at its place - its obscurity may cause that nobody will even try to debunk it, giving a false impression of correctness.

Harald88 21:53, 24 July 2006 (UTC)

Wrong again ! I was earlier going to point out that Dewan actually fails to address the first and third of Nawrocki's points, plus apart from your view I don't know of any opinion, much less "general opinion", that Dewan had "debunked" Nawrocki - any references ?.

Remember Matsuda & Kinoshita is in the same journal as Hsu & Suzuki and was so far from obscure that it provoked considerable controversy in Japan ! Hsu, incidentally has had two books published on relativity and is a professor of theoretical physics so why is his opinion so much less worthy than Dewan & Beran, two air force engineers at Bedford, Massachusetts ?. I cannot see any "balance" in your reasoning. Rod Ball 12:02, 25 July 2006 (UTC)

I think that the status of the "counter-view" is definintely coming into more and more focus. My thanks the Pjacobi and Harald. I hope that Rod will be willing to have some respect for the consensus of those researching this topic, in spite of his strong bias on this issue. --EMS | Talk 02:18, 25 July 2006 (UTC)

Reality check: it was in fact me that introduced the second Dewan reference, the JE Romain reference and the Austin Gleeson link - all of which follow D&B. I am not trying to expunge their or Bell's analysis & conclusions. I am not trying to exclude any mention that perfectly respectable and sane physicists still do disagree with Dewan & Beran.

Strong bias ? I think you should look closer to home for that. Rod Ball 12:12, 25 July 2006 (UTC)

I won't deny a bias here. You don't come into a situation like this without one. However, the real issue is how you deal with your bias.

I am getting the impression that you are giving those who would agree with you more credit than they deserve. Right now I do not have time to study the literature myself, but the other editors (whom I trust on issues of the literature) are not finding anything to recommend the idea that your view remains commonly held. --EMS | Talk 13:25, 25 July 2006 (UTC)

It is definitely worth looking closely at the literature. Particularly D&B's papers where there are quite a few errors. In particular I might draw your attention to Dewan's later paper and the formulae & calculation he uses on page 2 (p.384). The additional v(delta)t term is quite wrong as during (delta)t the relative velocity rises from zero to only a fraction of final v before the other rocket launches.Rod Ball 15:05, 25 July 2006 (UTC)

Time dilation and GR

Rod Ball (talk · contribs) wrote above:

What you are saying is that because there is T.D. (time dilation) in a gravitatioonal field then there must be T.D. across an accelerated box.

That is 100% correct.

Rod then continues:

You are assuming an extreme and invalid form of the equivalence principle, which only really says that Inertial and Gravitational Mass are measurably indistinguishable.

This is not true at all. The original point of the equivalence principle was the free-fall and inertial motion are equivalent. That is why inertial and gravitational masses are equivalent. It is also why gravitational time dilation applies in both the accelerated box and between the top and bottom floors of a tall building on the Earth. Please see this tutorial, and most relevantly section 10.5. Also you need to read "On the influence of gravitation on the propagation of light", reprinted in "The Principle of Relativity" (which is often available at large bookstores such as Borders). In that article, Einstein uses the accelerated box to demonstrate the existance of gravitational time dilation.

Finally Rod says that:

I've provided ample references to the fact that gravitation and acceleration are not generally "equivalent" and it must be especially not so when the acceleration is uniform so as to not even superficially bear a resemblance to any conceivable gravitational field.

In that case, the issue is whether the 1911 accelerated box exercise and its time dilation prediction applies to the gravitational fields of massive objects. However, that is not germane to the issue of Bell's paradox.

Rod - My little piece of math is really acid on your case if it means that you must tear down GR and the insight that freefall is inertial motion for your view to hold. It's time to admit that you have lost. You are human, Rod - It's all right to be wrong. --EMS | Talk 18:24, 26 July 2006 (UTC)

But we know free fall & inertial motion are not equivalent because of tidal effects. The idea of equivalence of acceleration & gravity served as inspiration (it has been referred to as "midwife" to GR) for general relativity but is not only not essential to it (ie. I, or rather the prevailing idea I'm expressing, is not "tearing down" GR) but theoretically and experimentally incorrect. In Hafele & Keating's "clocks around the world" experiment of 1971 they added gravitational T.D. to the special relativistic effects to match their results, so that the S.R. effects cannot "stand in for" the gravitational as you suggest for the centrifuged clocks. I would further emphasize that we are not even dealing with rotation in Bell's problem, so that as I said before, one cannot even pretend that it is "like" gravitation, let alone equivalent. Here's another quote:

"It is very important to notice that in a freely falling frame we have not transformed away the gravitational field since the Riemann tensor will not vanish and we will still measure relative acceleration ….. The first thing to note about the 1911 version of the principle of equivalence is that what in 1911 is called a uniform gravitational field ends up in general relativity not to be a gravitational field at all – The Riemann tensor is here identically zero. Real gravitational fields are not uniform since they must fall off as once recedes from gravitating matter." [ Principle of Equivalence, John R. Ray, Am. J. Phys., 45(4), pp. 401-402 (1977) ]

( Incidentally, had you not noticed that the tutorial you refer to is actually arguing against the equivalence principle ? ) Rod Ball 08:52, 27 July 2006 (UTC)

You keep missing the point here. Gravitational red shifting has nothing to do with tidal effects. It is a matter of being in an accelerated frame of reference, just as the spaceships are when they are firing their engines. --EMS | Talk 11:36, 27 July 2006 (UTC)

Again you skirt all the issues and just assert what you wish to believe. Gravitational red shift is a matter of being in a gravitational field.The connection with Bell's problem, before we lose sight of that, is that you claim the back end of an accelerated box must must have higher acceleration than the front merely to keep at the same distance from it. This is simply not the case but results from a slip in reasoning. The box is uncontracted for an observer inside it - it only appears (by measurement) to become contracted for an outside inertial observer. Thus for the inside observer(s) the acceleration "felt force" is the same front and back whereas it is only for the outside inertial observer, who measures more and more contraction, that the front apparently seems to be accelerating less than the rear, or vice versa, the rear more than the front, but he can't tell which. Is this clear enough ? Rod Ball 12:31, 27 July 2006 (UTC)

This is sick! The basis of the proper acceleration calculation was time dilation in an accelerated box as proven by Einstin in a readily available 1911 article which uses only special relativity (just as Bell's paradox does) and which I gather that you have chosen not to read. So here is a simple proof of the red-shift: By the time a signal goes from the bottom on the box to the top of the box, the top observer has accelerated to another frame of reference moving away from the frame of reference of the source of the light when it was emitted. Hence this is just a Doppler shift effect. However, since the observers are static, this red shifting also corresponds to a time dilation effect of the same magnitude. Going the other way, you get a blue shift. Notice that length contraction has nothing to do with it, and this exercise is being doine entirely within the box. (However, as you alluded to above, it can also be inferred for the external observer via the length contraction effect. This is appropriate as all observers must agree on the value of a proper acceleration even if they determine it by different means.) --EMS | Talk 23:22, 27 July 2006 (UTC)

I agree with your description of the Doppler-type of shift resulting from acceleration. I refer to Doppler-type because Doppler AFAIK is invariably used for relative motion between source and observer whereas here it is the increase in velocity of observer during signal transit. What you were saying earlier, however, is that the time at each end of the accelerated box will differ, which is surely wrong. The T.D. to which you refer is a characteristic of a gravitational field and not of acceleration. In a Gr. field the lower clock actually runs slower whereas in equal acceleration the clocks are in synchrony but there is a Doppler type shift instead. For an idealised "uniform" field neither of these effects involve a change in distance between the two points. What the "equivalence" principle says is that the two effects are of the same magnitude so that when they are both present in a "contra" way as in free fall, they cancel out and the observers cannot distinguish themselves from "inertial". Take away the Gr. field and you remove the T.D. so that the otherwise accelerated box has the same proper time at each end but with the Doppler-type shift that merely makes it "seem" that the clock rates differ. If you were to claim a proper T.D. as well for acceleration, then you would double the effect and the equiv. principle would no longer work.

Since you brought up the equivalence principle in this way, I thought it an interesting alternative way to consider the Bell problem by replacing the s'ships by two weights connected by a string and free-falling in a uniform Gr. field. It should be a bit clearer to see that the weights do not move apart ( remember this is a uniform field where "tidal forces" which disobey the equiv. principle are rendered negligable ). An observer freely falling with the system can regard it as inertial with no "relativistic stresses" and no string breaking. Replacing gravity with identical powered s'ships will only revert the clock rates back to synchrony. The string can hardly be broken by a change in clock rates any more than by a Doppler-type shift that does not involve relative motion.

BTW what is it that Pjacobi disputes about article neutrality ? At a rough estimate the "pro" description is currently about three and a half times the length of the "counter-opinions". What ratio does he have in mind, or is that all mention of counter opinions should be erased from the record ? Bear in mind that when I first wrote it a short while back, it was only a bit more than half its current length, but due to a minor quibble with Harald over the CERN view, longer and longer verbatim quotes got included that rather "beefed it up". Since it doesn't essentially say anything different from before, I'd be happy to edit it down slightly. The pro argument could be clarified further but I don't see any lack of neutrality at the moment. Rod Ball 18:37, 30 July 2006 (UTC)

Rod - In relativity, an acceleration field is a gravitational field. You are now reduced to asserting that time at both the "top" and "bottom" of an accelerated box run at the same rate, in spite of Einstein having shown that this is not the case in "On the influence of gravitaition on the speed of light" in 1911. Once again, please find Minkowski, H. The principle of relativity. ISBN 0-486-60081-5. {{cite book}}: Unknown parameter |coauthors= ignored (|author= suggested) (help). At this point, I see no reason to continue this discussion. If you cannot be bothered to research and learn relativity, then there really is no point to this.

As for the {{NPOV}} tag, I think that it is best I Pjacbi would explicitly state his reasons for placing it there. I for one would be happy to help deal with his objections. --EMS | Talk 22:19, 30 July 2006 (UTC)

The tag is meant to state, that it is dishonest and contrary to our encyclopedic misson statement to present the "dissenters' opinion" as a possible alternative and not as an easily refutable error (validity of SR assumed). Especially citing the last article of the "dissenters" which got published in a significant journal (40 years ago!) in the intro -- without giving this context -- is misleading. --Pjacobi 08:57, 31 July 2006 (UTC)

To EMS: You are totally wrong. In relativity, acceleration is definitely not the same as a gravitational field. I suggest you update your knowledge somewhat from 1911. Einstein retracted much of what he wrote then, in 1912 when he realised that gravity and acceleration are only equivalent (not the same) in a sufficiently small region. Later still, in 1915, he even joked about himself - "That fellow Einstein suits his convenience. Every year he retracts what he wrote the year before." As I said above the T.D. of the Gr. field compensates for the "Doppler" shift of acceleration to make free fall resemble an inertial system. By itself, without gravity, equal acceleration of two separated bodies involves no difference in proper time - something even ChrisH would agree with from his "identical path length gives equal proper time" argument.

The equivalence is good enough for a 3-story building (like the one the Pound-Rebka experiment was done in) to be effectively an accelerated box. Also, free fall does not "resemble" and inertial system -- Instead free fall is an inertial system! Finally, your proper time statement is both correct and irrelevant. So all that you have just shown is that you don't know what you are talking about. --EMS | Talk 14:31, 31 July 2006 (UTC)

3-storeys! Compared to radius of Earth? "Effectively an accelerated box"? - not quite (see before) one is T.D. the other is a Doppler-like shift. Free-fall is not inertial - it approaches closer and closer to inertial for ever smaller regions. try researching the topic, the problem seems to be your understanding of it. Rod Ball 10:46, 7 August 2006 (UTC)

To Pjacobi: I think it is your honesty that is in doubt. "Dissenters" is your description - intended to imply minority view, when Matsuda & Kinoshita as well as Bell's own article reveal, if anything, quite the opposite. You also claim the counter opinion has not been taken seriously in 40 years, when it clearly has; and indeed, Dewan & Beran's articles themselves were disregarded for seventeen years before Bell took them up. You refer to "easily refutable error" when no error has been refuted. You talk about "validity of SR" when Bell clearly states he's demonstrating Lorentz's absolute motion theory and not Einstein's Special relativity. The only detailed analysis of the problem is that in D&B's papers and they do not successfully address the contrary argument, which they raise themselves !

What is misleading is to selectively regard those journals as "signifant" or otherwise according to which contain articles supporting your view. Rod Ball 13:53, 31 July 2006 (UTC)

Rod - Coming from someone who calls Bell an "anti-relativist", I am most unimpressed. I have looked at the article of Hsu and Suzuki, and they go through a lot of contortions to get their result. Most disturbing is their conclusion that the distance between the spaceships as viewed from the launching frame contracts. That is not the way the exercise is set up. --EMS | Talk 14:31, 31 July 2006 (UTC)

Why quotation marks around "anti-relativist" when it's not a quotation, nor even a fair interpretation ? I pointed out that Bell himself avers preference for Lorentz's theory. The exercise is set up as identical s'ships & same engine thrust. Anything else is derived, deduced, calculated or assumed. Point: "viewed by" is inappropriate. Apart from Penrose & Terrell's (1959) paper there is the sheer invisibility of anything moving at partial 'c'."As measured by" is what is meant, and the measurement would presumably be made the same way as a measurement of the string length - and would arguably give the same result. Rod Ball 14:49, 31 July 2006 (UTC)

I feel I should add that Pjacobi's main stumbling block to appreciating that there could conceivably be any other rational viewpoint, is that he does not perceive the difference between Lorentz's and Einsteins's theory. He said some time ago that all of SR could be derived from Lorentz's ether based theory where contraction occurs even w.r.t. relatively stationary observers. This is simply not true. For one thing there would be no reciprocity - a distinct and paradoxical feature of Einstein's theory where if A measures B's lengths as contracted, B will also measure A's lengths as contracted. This does not occur in Lorentz's theory, where if B has a higher velocity than A w.r.t. absolute rest, B will measure A's lengths as increased. Another difference is that in Einstein's theory all coordinate distances in the observed frame, when measured from a relatively moving frame, appear to be reduced in length, whereas in Lorentz's theory only connected lengths of coherent material can contract and empty spatial distances cannot. It is this latter distinction that makes an alternative view possible to that presented by Bell in his article. It is simply no good to just keep asserting the equations of hyperbolic motion to "prove" the s'ship trajectories must be parallel. What is important is s'ship distance versus string length and the above considerations make it possible to regard all measurements of, and statements about the s'ship distance as equivalent to, and replaceable by measurements of and statements about the string length. Rod Ball 11:22, 1 August 2006 (UTC)

Wrong again, Rod. By the time Lorentz was done refining LET, he had incorporated the relativity of simultaneity into it. At that point, he had an aether whose rest frame cannot be detected, and an effective spacetime geometry imposed by it such that length contraction always exists for the rod in relative motion as perceived by an arbitrarily chosen "stationary" observer.

Beyond that, we are talking about SR anyway, and hyperbolic motion is an inate part of it, and shown by Hermann Minkowski in 1908. Yet even without hyperbolic motion: If the acceleration of the ships are identical at any given time t in a given frame of reference, and at t=0 the ships are at rest and separated by L, then it follows that at any subsequent time t' that the ships must have the same velocity v and retain the initial spatial separation L. This is the same (within a given frame of reference) in SR as in classical mechanics.

Then again, I am probably wasting my time noting such things. You have already shown that you will cavalierly toss out a relevant calculation and refuse to look at relevant literature. --EMS | Talk 14:30, 1 August 2006 (UTC)

I can't imagine how you dreamed up your first paragraph, which is factually incorrect throughout. Since you disbelieve on principle anything I say, I'd better include a quote. Lorentz wrote in the 1916 edition of "The Theory of Electrons": "If I had to write the last chapter now, I should certainly have given a more prominent place to Einstein's theory of relativity by which the theory of electromagnetic phenomena in moving systems gains a simplicity that I had not been able to attain. The chief cause of my failure was my clinging to the idea that the variable t can only be considered as the true time and that my local time t' must be regarded as no more than an auxiliary mathematical quantity. In Einstein's theory, on the contrary, t' plays the same part as t."

As I pointed out above, in all such "reasoning" as your second paragraph, all mention of "s'ships" and "s'ship distance" can be interchanged with the same statements about "string endpoints" and "string length". Inability to see this is due to an automatic assumption that only the string "contracts" which of course it does in Lorentz's theory, but in Einstein's SR it is only the relatively moving observer's direct measurements that are shorter. I admit that Lorentz's theory is conceptually simpler and you have every right to stick with it, but you cannot claim it is the same as SR, nor that the above alternative analysis is some kind of crazy error committed by people who's sanity needs to be questioned. Rod Ball 12:30, 3 August 2006 (UTC)

Rod, Lorentz agreed with Einstein - his theory was a perfection of the electron theory of Lorentz.

There is no operational difference. It's a starting assumption of physics that the position coordinate doesn't matter for the laws of physics - if it did, it would be a big mess. That implies a distinction between contraction of objects and distances between such objects, as explained in the article. Harald88 16:18, 3 August 2006 (UTC)

You make it sound like he just applied the finishing touches ! "No operational difference" eh! - what about the transverse Doppler effect and the Einstein-Laub effect ? (It beats me why you all argue so vociferously on a subject you know so little about.)

You're referring to the assumption of isotropy of space. That you actually think this implies a distinction between contraction of objects and the spaces between them shows a serious lack of reasoning. Try to get hold of the notion that Lorentz's and Einstein's theories are different. You can't take "contraction in the object's frame" from Lorentz and pretend it's a part of Einstein's SR where there is only contraction "from the observer's frame". SR makes no distinction between lengths of objects and lengths between objects. Rod Ball 09:59, 7 August 2006 (UTC)

Time to move on

Peter -

What edits do you suggest be done to this page to resolve the "NPOV" issues? (I put NPOV in quotes as I see this a more of an accuracy issue personally, but either way it needs to be dealt with.) --EMS | Talk 15:59, 31 July 2006 (UTC)

Essentially would you said in above 14:30, 1 August 2006 (UTC) comment, stating this as scientific fact and rephrasing the "dissenters" views as typical error in thinking about the so-called paradoxa of SR. Noting the fact that as late as 1960 a dissenters view got published in a significant journal as curious fact. --Pjacobi 19:17, 1 August 2006 (UTC)

At this point, I think that you should go ahead and edit the article to suit yourself. I won't guarentee 100% support for said edits, but I do agree that the Dewan, Beran, & Bell interpretation is correct, and more importantly that this is generally accepted as such (at least amongst those who have researched the issue). I do advise against outright saying the the "dissenters" are "in error" (as this in not NPOV), but saying that the mainsteam view considers the dissenters to be in error (and stating the reasons) is very much works IMO. --EMS | Talk 21:42, 1 August 2006 (UTC)

"Generally accepted as such (at least by those who have researched the issue)" ?? Well, I know I've researched it but I haven't seen much evidence on your part, and certainly not from Pjacobi ! Rod Ball 12:36, 3 August 2006 (UTC)

Rod - You don't understand relativity and most certainly do not understand this thought experiment. At this point, I don't care how much you have researched this. You disregard items that do not conform to your pre-conceived notions, and don't seem to recognize that that impulse as a foolish defense mechanism. You quote Lorentz above on t and t' but do not seem to fully understand how Einstein related the two, nor the relevance of that relationship to Bell's paradox. You correctly note that Einstein's full GR superseeded the SR-based predictions of the 1911 article that I keep asking you to look at, but ignore the fact that the prediction of time dilation as a function of gravitational potential was carried forward in GR. Overall, I'm tired of dealing with someone who not only does not understand what is going on in the exercise, but who also does not want to understand it. --EMS | Talk 16:10, 7 August 2006 (UTC)

What you're tired of it seems to me, is having your false notions contradicted and errors exposed. There's a good deal of projection in your accusations. I have, as anyone can read in the previous entries, addressed all of the issues put to me, sometimes more than once as they are repeated as if not previously answered. It is rather you and often your colleagues who choose to ignore many of the "awkward" points and issues that I raise, most recently the suggestion to compare the situation of two weights connected by a string and falling in a uniform Gr. field. There were many earlier ones too. As for defence mechanisms, I am not defending anything other than fair representation of opinion against an illegitimate attempt to expunge perfectly rational counter-views by well qualified experts who happen to differ from yours. What I keep coming up against is an almost fanatical "knee jerk" reaction to throw any fact, diversion, argument or insult, no matter how irrelevant or irrational, at anyone who even seems to be questioning your interpretation of SR, even where your ground is decidedly shaky.

Your comments above concerning t and t' as well as the prediction of T.D. (which I didn't ignore BTW) are not obviously relevant to the previous discussion. You were trying to assert that acceleration is exactly the same thing as a Gr. field and I pointed out that you were wrong, even supplying authoritative reference quotes to the same effect which you "held your nose at" and chose to ignore. I understand perfectly well both sides of the argument concerning Bell's problem but it is quite obvious that you are quite unable to grasp the POV that contradicts Bell's conclusion. Further, you also choose to ignore the plain unambiguous fact that Bell views relativistic problems from the perspective of Lorentz's theory and not SR. The two theories have significant conceptual differences that become pronounced operational differences when treating acceleration of extended (ie. not single point) systems. It is I who has reason to be tired of dealing with false notions, faulty arguments, non-sequiters, diversions, repetitious restatements and avoidance tactics. Have any of you considered a career in politics ? Rod Ball 11:02, 8 August 2006 (UTC)

Rod - You wrote:

You were trying to assert that acceleration is exactly the same thing as a Gr. field and I pointed out that you were wrong.

I won't say that the above is not true. You correctly pointed out the existance of tidal effects. But you then asserted that gravitational time dilation is due to the tidal effects, and I pointed out that you are wrong about that. You also state that

Bell views relativistic problems from the perspective of Lorentz's theory and not SR

but I do view it from an SR standpoint (as do Harald88 and Pjacobi) and we all agree that the Bell analysis is correct in SR too. I use the accelerated frame of reference as a sanity check, and find that the $g'=g/(1-gh)$ relationship shows that the string must break. I am done with arguing with you. I am quite satisfied that D&B and Bell are correct, and that you don't know what you do not know. Argue that the ships get closer over time as viewed from the launcher's frame if you like, but that simply is not correct. --EMS | Talk 15:21, 8 August 2006 (UTC)

Whilst I acknowledge that SR & Lorentz's theory may seem to be operationally identical for constant motion situations ( although there are subtle differences it would not be profitable to quibble further about ), I believe that the conceptual differences lead to manifestly different predictions where accelerated motion is concerned. In Lorentz's theory there is a very real contraction that is undetectable to comovers due to similar contraction of all comoving apparatus. This is why the question of molecular or sub-molecular mechanisms to cause or allow such contraction is an issue worthy of consideration. However, in his theory there is a true absolute time for a stationary system and other moving observers are tricked into mis-synchronising their clocks due to the speed of light being c-v or c+v respectively with or against the direction of motion. This is rather well described by Bell in the last two or three pages of his article.

In SR alternatively, the speed of light is constant in any direction, synchronisation of clocks in inertial systems have equal status and there is no actual contraction (not simply undetectable) for comoving observers. This means that the measured contraction must be an artifact of the measurement operation between relatively moving systems, for the comover is not assumed to merely be unable to detect the contraction but will always genuinely verify all rest lengths to be unchanged.

These consideration imply the primacy of length contraction in Lorentz's theory while the time dilation is a secondary artificial effect, which is why Lorentz referred to "true time" in distinction to "local time" which for him was an auxiliary mathematical variable. In SR on the contrary, with a constant speed of light, time dilation has primacy and length contraction appears as an effect of the general measurement process with standard rods and synchronised clocks in relative motion.

In Bell's problem Lorentz's approach does indeed predict string breaking as generally described because the string actually does contract but the empty space between the s'ships could not possibly do so. With SR however, where the string does not actually contract, there would be no difference between measuring the length of the moving string and measuring the length of the moving inter-spaceship distance. The measurement process from launch frame would be the same and both distances would be genuinely unchanged for comoving observers. It is misleading to think of the trajectories as sort of visible smoke trails that should be identical from the launch frame. The "trajectories" in x-t space should rather be regarded as loci of potential s'ship to s'ship distance measurements that might be made at any intervals along the launch frame. In this way the "true" (or "proper") s'ship trajectories would be identical and the proper s-s distance constant while as measured from the launch frame, the s-s distance yields diminishingly shorter results and a locus of such measurements would suggest dissimilar "trajectories" in the same way as for the string ends.

I do not expect you to be in any way convinced by these arguments, but I am trying to show that the situation is not as clear cut as you are convinced it is. I think that when a clear distinction is drawn between the conceptual approach of Lorentz's theory and SR, it is possible to see operational differences arise for accelerated motion that would not be suspected in the usual constant motion presentations. One does not therefore have to be irrational or anti-SR to dispute the outcome of Bell's problem, which is why a number of perfectly well qualified physicists do just that.Rod Ball 14:53, 14 August 2006 (UTC)

You can't have the ships getting closer in the launcher frame unless they have different accelerations. It is that way as seen from the launcher frame. As my time-dilation math shows it is also that was as experienced in the spaceships themselves (meaning that the ships indeed have different proper accelerations). All that you are doing above is a bunch of hand-waving. As I now see it, the refutations are not Bell expercises at all, as they treat the ships like an accelerated box, and beacause of the proper acceleration differences that is a different exercise. --EMS | Talk 16:19, 14 August 2006 (UTC)

I think the statement that the s'ships cannot "get closer in the launch frame unless they have different accelerations", whilst blindingly obvious in a non-relativistic context, is highly questionable to say the least in a relativistic context. Consider two objects travelling at constant velocity (w.r.t. a given observer) and a fixed distance L apart. The observer will measure the separation of the objects to be L/gamma just in the same way as if it were a "rigid" rod of length L. Now consider two objects also L apart at a higher velocity and which will be measured by the observer to be less than the previous L/gamma apart ( ie.L/gamma* ). Now consider any number of pairs of objects, each pair the same distance L apart and all pairs moving at different incremental fractions of the speed of light. As measured by the original observer their separations will be measured as progressively reduced by the factor L/gamma according to their velocity. Now if we consider the objects accelerating in the way of rockets with identical mass & engine thrust, then clearly they will pass through each of the incremental velocity stages considered above, yet their separation will be measured as steadily decreasing with increasing velocity. If we take care to stick with SR and not Lorentz's theory, (where the string actually shortens), then the string of length L will contiue to span the distance between the rockets during acceleration, while both string and separation distance are measured as progressively shorter from the launch frame. I don't see that there is any hand-waving in this straightforward analysis.

Concerning the "time dilation", I thought I'd pointed out earlier that there is no gravitational field involved so there can be no time dilation other than the normal SR one between either s'ship and the observer. This is Euclidean space and what we do have is simply a doppler shift between clocks running at the same rate in each s'ship, where both s'ships have increased their velocity between transmission and reception of any signal. Hence a signal from the forward s'ship is received by the rear "blue shifted" and a signal from the rearward is received by the front "red shifted". No difference in clock rates nor change in s'ship separation is implied. Rod Ball 12:57, 16 August 2006 (UTC)

Concerning the edits:

I am restoring the accurate version again because the version with "initially" and "by Hsu & Suzuki" is at best misleading and arguably downright false. "Initially" carries an implication of a later change, as in "when offered either tea or coffee, he initially chose tea", which is not justified in the context. "At the time he...presented" is reasonably neutral without future implication.

The criticism Matsuda & Kinoshita suffered was not simply by Hsu & Suzuki. I quote verbatim from their article.....

"The present authors discovered the interesting phenomenon that many physicists, including university professors who teach relativity, fail to understand the problem and insist that the distance between two spaceships should undergo Lorentz contraction."

They were so upset about it they go on at greater length on the next page.......

"The present authors published papers presenting the above two spaceships paradox in a Japanese physics journal, although we do not refer to the papers since they are written in Japanese. We discovered a very interesting phenomenon: many physicists, including university professors who appear to teach relativity, fail to understand the problem but instead claim that the distance should be L'. Some of them stick to the wrong answer and published papers criticizing us ( in Japanese therefore we do not refer to them neither ). Moreover in order to give their wrong comprehension something to stand on, they presented lots of nonsensical arguments."

On the last page they again return to the theme.......

"After our Japanese papers and a few papers criticising our argument appeared in the Japanese physics journal "Parity", we discovered that a very similar argument was discussed by Bell, and that it was met with similar criticism that we are. This means that, unfortunately, many physicists did not, have not and still do not understand the real meaning of the Lorentz contraction even after almost 100 years of the introduction of special relativity by Einstein."

Of course I would say it is Matsuda & Kinoshita who do not understand the problem and do not realize that, like Bell, they are using Lorentz's pre-SR "relativity", unaware that it's prediction of string breaking differs from that using SR - with which I'm sure their critics would have been far more familiar.

It's interesting to note that I have never come across such whingeing in a scientific paper before and the pettiness of it does not reflect well on Matsuda & Kinoshita themselves. Rod Ball 10:51, 17 August 2006 (UTC)

Based on the above, I must conclude that Harald88's wording (which I am reverting back to) is more concise and NPOV.

BTW and FWIW - 11 years ago, I too was claiming that Einstein's work not understood, albeit in the area of GR instead of SR. When the resultant alternate theory went up in smoke the next year, I returned to square one and quickly saw how foolish I had been. Now I will admit that claiming that a known crackpot like Edward Schaefer (i.e. myself) does not know relativity is one thing, but when you find yourself also being opposed by the likes of Pjacobi and Chris Hillman (CH), that is quite another. So please be advised that I have been in your shoes, and that you are strongly counseled to go back to square one and find a new pair. --EMS | Talk 15:05, 17 August 2006 (UTC)

Editorial changes

You might quibble over "initially" but the other part is inadmissable. For one thing Hsu & Suzuki's approach bears no resemblance to Nawrocki's and more importantly, Matsuda & Kinoshita complain about criticism prior to their 2004 paper which could not possibly refer to Hsu & Suzuki's 2005 paper. This is a matter of facts not point of view. Is this sudden switch to editorial quibbling your way of avoiding the issues around Lorentz versus SR applied to Bell's problem, as discussed above ? Rod Ball 15:17, 17 August 2006 (UTC)

I have no more desire to argue with you, at least not here in Wikipedia. The offer to e-mail me remains open but I will not discuss the technical details of this problem further with you here. I am quite satisfied that you are satisfied with your current "knowledge" of relativity. I have found many times that the "anti-" has to convince himself of it when they are wrong. Having eaten crow a number of times as part of my own relativity research I know that it is no fun, but for me learning is more important than saving face.

BTW - I have remove the Hsu and Suzuki mentions. Their extended Lorentz transformations have no currency in the fields as a whole, and mentioning that here makes it appear that their work is significant. The important point is that controversy over this issue continues to this day. --EMS | Talk 14:18, 18 August 2006 (UTC)

A refernce at end is not "undue weight". At least relevant, unlike Nicolic which does not address BSP at all. Rod Ball 14:55, 18 August 2006 (UTC)

With something like this "extended Lorentz transformation" business either you do or you don't. Keeping the reference makes it a "stealth" entry. If it is not obvious why the reference is there, it does not belong there. The removal of its mention from the main text as inappropriate therefore demands the same of its reference. --EMS | Talk 20:03, 18 August 2006 (UTC)

I think your objection is invalid. An article entitled "Extended Lorentz transformations for accelerated frames and the solution of the "Two-spaceship paradox"", written in response to an article titled "A paradox of two space ships in special relativity", and published in the same journal has an obvious relevance and a clear right to be included in the list of references. It is not necessary and seldom the case that all relevant references are discussed in the article. Removing references you happen to disagree with is hardly NPOV. Rod Ball 11:38, 21 August 2006 (UTC)

IMO, that reference is effectively OR. I must admit that even the entry it is rebuting is somewhat questionable given its place of publication, but it does make the legitimate point that debate is ongoing, and for that reason is valuable. The other entry admitedly is also proof of the same. However, you are giving their extended Lorentz transformations undue weight. I will not abide by that. --EMS | Talk 00:59, 22 August 2006 (UTC)

I'm afraid whether or not you can "abide" articles you disagree with is of no consequence whatever. A published article on the specific topic in hand is perfectly relevant whether you like it or not. If you took the trouble to study (by which I mean read, understand and remember) the Wikipedia policy you might realize that whether the reference is OR is completely irrelevant. All knowledge was at some time OR. I am at times disconcerted by your apparent disengagement from scientific thinking. Rod Ball 09:55, 22 August 2006 (UTC)

I certainly agree that all currently accepted knowledge was at some point WP:OR. However, that is a very, very poor reason not to respect that standard! For accepted knowledge, some event happenned to transition it away from being OR. SR itself was OR in 1905, but by the end of 1908, the work of Hermann Minkowski and the endorsement of Max Plank had made that theory a object of strong scientific interest. I see no evidence of any such transition for this article. Instead I see it being favored by an editor who does not understand relativity. --EMS | Talk 20:37, 22 August 2006 (UTC)

Published peer-reviewed articles, even in unnotable journals, are certainly not WP:OR. Either we delete all references to that journal because it's not deemed notable by any(?) citation index, or we must, in accordance with WP:NPOV include both opinions - eventhough we know that one is wrong. Including erroneous but notable opinions is necessary to get used to. Harald88 21:18, 22 August 2006 (UTC)

Are you sure that this article is notable? That is effectively the issue that is bugging me about it. I see the one article as making the basic point that there is still debate about this paradox, and being useful in terms of illustrating that. I see the other article as not only redundant in that regard, but as its also being given a soapbox for this "extended Lorentz transformation" business, which IMO is very much OR. BTW - The idea of removing the other reference too is acceptable to me. I think that the other references and text do a decent job of describing the issues here. --EMS | Talk 01:48, 23 August 2006 (UTC)

That is the discussion that I started several times: I don't see how articles in a journal that isn't even indexed can be called "notable". Harald88 06:19, 23 August 2006 (UTC)

For goodness' sake ! Please stop trying to remove sources you don't happen to agree with. Have some respect for Wikipedia policy. The rules about OR do not apply to references, except where those references were themselves written by the editor (or possibly a close friend or relative). Dewan & Beran was OR in the sense EMS wants to use it. The OR stricture applies only to the content of the edit itself. As for journals, they do not have to be "notable" or "indexed" nor do they even have to be peer-reviewed (it is only said that such are "preferable"). It should be clear that a journal is acceptable if it is widely consulted by people working in the relevant field, within its area of publication. Rod Ball 09:03, 23 August 2006 (UTC)

The AAPPS Bulliten is not "widely consulted by people working in the relevant field". That is fairly obvious from its context and its content. So you and Harald have convinced me that the last sentense from the article and both references have to go. --EMS | Talk 19:45, 23 August 2006 (UTC)

EMS - You are behaving childishly. If you are unable or unwilling to conduct reasonable discussion of the topic in the talk page, it is nothing short of peevish petulance to pursue a negative vendetta of erasing perfectly legitimate references just because you disagree with what they say. Either try and be more constructive or leave the page alone - no-one is forcing you to change your opinion but you must learn to live with the fact that yours is not the only POV that matters. Rod Ball 10:35, 25 August 2006 (UTC)

Rod - You are totally arrogant and totally mistaken. I am not impressed by your business of "Lorentz's theory instead of Einstein's". Nor am I impressed by your using GR to reject the math I showed you: This is a purely SR exercise to being with! (Your claim that the gravitational red shift does not exist in the absense of spacetime curvature is also evidence of your ignorance BTW.) It has become painfully obvious that you do not understand either relativity or Wikipedia. --EMS | Talk 15:51, 25 August 2006 (UTC)

It is arrogance I am battling against !

(1) You do not have to be impressed - note my comment that your POV is not the only one.

(2) Again you try to reverse. It was you who introduced GR arguments - I simply responded to them. If you look back you'll see I have been regularly saying it is an SR problem needing only clear SR reasoning.

(3) Gravitation=Spacetime curvature and Spacetime curvature=gravitation - see Misner Thorne and Wheeler for example. A perfectly uniform and constant Gr. field is a hypothetical construct so your point is moot. My argument did not depend on this anyway - There is no desynchronisation of clocks between the two s'ships accelerating in Euclidean space but there is a signal blue-shift front to back and redshift vice versa simply due to increasing v of both s'ships in tandem. No difference in clock rates or increase in separation is involved. If the s'ships were in free fall in a Gr. field instead of using engines, the Gr. time dilation would exactly compensate for the frequency shift just mentioned so that it would be effectively "inertial" for a passenger aboard. Think about it.

(4) Wikipedia does not reject references on the grounds that 2 or 3 people don't like them because they think they're wrong. Have I tried to remove any references that support D&B ? On the contrary, I added some. How much scientific integrity is there in trying to eradicate reference to published work by well qualified physicists with prominent academic positions ? Rod Ball 19:24, 25 August 2006 (UTC)

On point (3), you do get desynchronization in Euclidean space due to the relativity of simultaneity. On point (4), two references (one for and one against Bell's interpretation) are being rejected as a set due to AAPPS not being a repectable publication. I fail to see the POV in that. --EMS | Talk 21:28, 25 August 2006 (UTC)

You are wrong on both (3) and (4). Rod Ball 19:04, 27 August 2006 (UTC)

re pont (3): $t'=(t-vx/c^{2})/{\sqrt {1-v^{2}/c^{2}}}$. Note the "$-vx$" part. --EMS | Talk 00:15, 28 August 2006 (UTC)

You are referring to difference in time rates between s'ships and ground. There can be no absolute difference in on-board proper time between the s'ships as they are travelling at the same velocity by construction so that their relative velocity, v, is zero and t=t'.

It is even more crashingly obvious that the on-board clock rates cannot differ because translational invariance dictates that a clock must behave identically whether launched at X1, X2 or Xn where the Xi are colinear points in the inertial launch frame. Rod Ball 09:53, 26 September 2006 (UTC)

You are jumping between frames of reference like mad. Both statements are correct, but they do not mean that Bell was wrong. The second statement is the key: All rocket clocks synchonized in the launch frame remains synchronized in the launch frame in this exercise. However, because of the -vx term noted above, they are not synchronized in the final coasting frame of reference. After that, all that your first statement shows is that the clocks tick at the same rate in the new frame, and can be resynchronized for their current frame if the ship's captains should wish to do so. In any case, your claim in item (3) above that "[t]here is no desynchronisation of clocks between the two s'ships accelerating in Euclidean space" is totally incorrect. --EMS | Talk 15:19, 27 September 2006 (UTC)

Restored references section

I have restored the older version of the references section created by Chris Hillman. This does include the contested AAPPS references. Given the Chris had them in his version, I am assuming the he endorsed their presense. More important is the organization of this section. It groups the entries and noted what the significance of each group is. I find this to be a much better form that the "flat" one that had been present more recently. --EMS | Talk 00:29, 28 August 2006 (UTC)

CH may have endorsed them, but I find them highly doubtful. In any case, self-published articles (such as arxiv) are unacceptable as independent source; consequently I'll delete those. Harald88 19:54, 19 September 2006 (UTC)

arXiv.org has had an "endorsement" system in place since January, 2004. While this is not peer review, it none-the-less is a filter that keeps people from willy-nilly "self-publishing" on it. More importantly, many good articles which have been published in respectable journals are placed there also. So an article in arXiv.org should at the least be judged on its own merits, not on the suitablility of the site! I will take a look at the arXiv articles soon, but unless I see a good reason not to, I will put those references back into this article. --EMS | Talk 02:02, 20 September 2006 (UTC)

Good articles that have been published in journals may be linked to its arxiv version, that's not the issue. Arxiv articles are self-published - that's its very purpose! Authors are endorsed (only if they are new authors), but not the papers themselves. They are not to be considered a "reliable source" - imagine the mess Wikipedia would become with such self-published sources. It's not up to editors (either you or Rod) to judge that the information in a certain arxiv article is "correct" or "bad", see WP:NOR and WP:V. In a nutshell: "Articles should rely on credible, third-party sources with a reputation for fact-checking and accuracy ". Harald88 10:15, 20 September 2006 (UTC)

I have looked at the arXiv abstract pages for those articles, and they are not listed as having been published ni a journal.  :-( I'm still not sure what to make of them. They are evidence for the "contra" view. Perhaps we need to settle on a reasonable POV and style for this article. For example, using the new footnoting scheme would allow these references to be attached to text expressing that they represent a contrary and discredited viewpoint. --EMS | Talk 19:46, 20 September 2006 (UTC)

That was my point. OTOH, including a link to such an article inside a sentence as a means to verify that such "dissident" viewpoints continue to appear (but without discussing it)is IMO a different thing althogether, I can go along with that. It would not give those the same status as standard references, thus less likely leading to POV complaints as below on this page.

As a matter of fact I similarly gave support to having a link in the Big Bang article to verifiable opposition to that theory but that was opposed by ScienceApologist who replaced such with unverifiable loose statements (see [2]) - I may return to that issue, using your argument; or perhaps you want to try it yourself. ;-)

Still, the article now does reference the contra-view in a recent published paper. Thus I wonder if we really need more references, instead IMO we should simply reinsert a sentence on that. Harald88 20:46, 20 September 2006 (UTC)

The arXiv endorsement system didn't saved us from http://arxiv.org/abs/physics/0507193

Giving Fields' http://arxiv.org/abs/physics/0403094 as a <ref></ref> isn't the worst idea. It is not only a reference for the disssident views floating around,but is also evicence, that they don't get published anymore: I would like to thank [...] and an anonymous referee, of a journal that rejected this paper for publication, for pointing out a serious error in the Eqns(2.26)-(2.28) of an earlier version.

Pjacobi 21:11, 20 September 2006 (UTC)

Bad article

I have to totally agree with the previous comments that this is a very bad article, which gives "undue weight" to extreme minority positions and will tend to confuse students and lay readers alike. There are not two different solutions to the Bell paradox.

For now I'm just going to stick an NPOV and an EXPERT tag on it, to warn unwary readers, while I read the various comments on the talk page and think about the issue more, to see if there is any way to save it. Pervect 20:04, 17 September 2006 (UTC)

You may want to compare two old versions with the current one:

• 2005-10-11, after I tried to clean it up to a short but correct article. You may say that the minoroty position has undue weight also in that version, but I just tried to report correctly their non-acceptance.
• CH's large version, where he tried to give an extensive technical treatment

Pjacobi 20:34, 17 September 2006 (UTC)

There is only need for enough editors to counterweight one editor who, when others don't pay much attention, gives according to everyone else "undue weight" to a minority opinion.

Meanwhile I'll rework it back to a more balanced version, keeping the NPOV banner (thanks for bringing this to our attention). In particular, there will be no references to Arxiv papers and at most minor mention of articles that appeared in a journal that apparently is not mentioned in any science index.

Note that there is no need for additional experts, the positions are clear and there are no doubts.

Harald88 20:08, 19 September 2006 (UTC)

I think any of the previous articles would be an improvement. The Hillman version goes into the most depth, but I'd like to see a treatment that didn't use covariant derivatives if possible. It's possible and desirable to address the problem using only the methods of introductory SR. Since it's possible, it's desriable, I think, because that is where the issue is going to have the most impact (on students confused about SR). By the time a student has mastered covariant differentiation, there's a good chance he's figured these issues out already.

I think that where I'm going to focus my efforts for the time being is to expand the stub on hyperbolic motion, or possibly a new article on Born rigid motion. Something along the lines of http://www.mathpages.com/home/kmath422/kmath422.htm perhaps. Showing that two spaceships that maintain a constant distance apart must have differeing accelerations is at least as clear a way to resolve the "paradox", IMO, as saying that two spaceships with the same acceleration separate.

The logical thing to do would be to link this article from the new article I'm thiniking about working on. I've been feeling unmotivated recently, but after I write the new article, I'll worry about trying to get this article in such a shape that I would not feel bad about linking to it.

As far as educational value goes, it seems to me that there isn't much educational value in showing that people publish silly things in non-peer reviewed articles. There are many examples of such on the internet :-). It's a little more educational to show that even peer review doesn't gurantee non-sillyness, I suppose. Pervect 21:04, 23 September 2006 (UTC)

You're welcome as long as you abstain from WP:NOR and stick to WP:V. Mathpages looks great but is anonymous, it's IMO not acceptable as reference (but they are great examples indeed). Harald88 21:09, 24 September 2006 (UTC)

Would there be any objection to including the mathpage webpage as an external reference? Or is this a can of worms best left unopened? I agree that this particular webpage is of high quality, but there are many webpages on relativity that are not of high quality. For the moment, I've left it out, as I do not want to set a precedent for including random webpages on relativity, but I'm willing to be convinced that this particular web page is "OK". Pervect 01:52, 29 September 2006 (UTC)

For the accelerated rigid rod, IMHO http://arxiv.org/abs/physics/9810017 suggests itself as reference. Born rigidity and Hyperbolic motion already exists BTW. --Pjacobi 21:42, 24 September 2006 (UTC)

Pjacobi: As I've pointed out before, the Nicolic reference you seem so fond of is concerned with trying to show a difference between pushing and pulling a "rigid" rod at relativistic speeds and has therefore got nothing whatever to do with the issue of "Bell's problem" and the controversy over what happens. Nicolic's article is also easily seen to be incorrect in that he derives expressions for the same length using (x-L) & (x) on the one hand and (x) & (x+L) one the other and mistakenly presumes that the superficially different formulae represent physically distinct situations. Rod Ball 09:03, 26 September 2006 (UTC)

The case of the rigid rod is the natural corollary of the BSP. Equal accelartions <=> rope breaks, connection is rigid <=> different acc. at front and back.

The book by Petkov is, ahem, interesting. But of course it's completely non-canonical in the treatment of relöativity. His papers obviously are not accepted for publication.

Pjacobi 09:36, 26 September 2006 (UTC)

Bluffing won't work ! "Corollary" = "a proposition inferred immediately from a proved proposition with little or no additional proof, something that naturally follows" [Merriam-Webster]. Nicolic is asserting a difference in contraction for a rod pulled compared to pushed, which does not in any way follow from either conclusion of Bell's problem. Bell's problem is to do with the behaviour of the two s'ships so has no connection with distinguishing pushing from pulling a rod. [The paper is also bunkum for the reasons I previously stated.]

Your comment on Petkov's book suggests you have not consulted it and you stray further into make-believe with your derogatory and false claim that his paper's are not published viz:

http://www.math.u-bordeaux.fr/~petkov/publications/publi1.html

[How many papers have you published ?] Rod Ball 10:18, 26 September 2006 (UTC)

The pull/push dicrepancy is only one point of Nikolic's paper. And yes, the BSP result follows immediately, without further proof from the rigid rod result.

And as has been established, per Wikipedia:Requests for comment/Rod Ball, that you lack the necessary understanding of the topic, please stop to interfere now, before formal arbitration or other measures have to be taken.

Pjacobi 11:12, 26 September 2006 (UTC)

No, actually it's the main point and the only original, if incorrect, content. The BSP result does not at all follow, although you were claiming the reverse, that Nicolic follows from BSP, so it seems you're a little confused. In either case, if you think one follows from the other then your reasoning is seriously at fault so perhaps you'd care to specify the step(s) that make one an automatic consequence of the other.

All that RfC established was that the criticism of myself was both groundless and especially in the case of ChrisH, maliciously false. Both in terms of literature research and argument both EMS and yourself have so far failed to prevail but merely adopted an ostrich-like stance that pretends the substantial opposition to Bell's view does not exist. Unlike Bell's scenario, which is purely hypothetical, the substantial opinions of those who contradict his conclusion are very real and factual, and cannot be wished away by narrow minded and ill informed editors. Rod Ball 11:52, 26 September 2006 (UTC)

The only comments in Wikipedia:Requests for comment/Rod Ball which support that position are your own. Given that you had not bothered with this article in a while I was happy to let the RfC and a possible Request for arbitration rest. Do note that RfC's are intended to provide a framework for reaching a resolution to a conflict prior to using the arbitration process. That it failed to resolve the issue simply means that we can proceed to arbitration in good faith. --EMS | Talk 19:23, 26 September 2006 (UTC)

I have clearly shown that almost all the (few) comments are mistaken and unfounded. The ridiculous semi-coherent tirade from ChrisH I utterly refuted by quoting his own self-damning talk page comment from 29th April (and I could have included his even sillier stuff from the days before that). It's a pity you don't spend as much time on improving the main body of the article. If the viewpoint you believe in were as clear-cut as you claim, then a well written presentation of it ought to be completely convincing and you wouldn't need to fret so much over any mention of counter-opinion. The main article has long been in poor shape but remains neglected while you endlessly quibble over the minutiae of reference inclusion. Rod Ball 08:46, 27 September 2006 (UTC)

It is a shame that we have to fight you over the Nikolić reference, which is highly relevant. In fact, it is a shame that we have to fight you at all. You don't know relativity, and event worse is that you have shown that you do not care to know it. --EMS | Talk 14:58, 27 September 2006 (UTC)

"Highly Relevant" ? Despite lacking anything to do with D&B or Bell's setup of s'ships and string or anything remotely similar, and also D&B/Bell's problem having nothing to do with pushing/pulling a nominally rigid rod ? It is accepted as basic SR that either the string or a "rigid" rod would be measured as contracted from the relatively moving launch frame. In BSP the issue concerns what the distance between two effectively unconnected identical s'ships would be whereas the Nicolic paper is claiming that contraction differs between a rod pulled from one end or pushed from the other, due to a shift of the centre of mass forward or backward respectively. I do not see any relevant connection between the two issues.

Claiming that I "don't know relativity" when I clearly do, seems just your way of avoiding having to argue a case, at which you have not been successful hitherto, having had to blindly reject or ignore the range of textual support I've supplied including reputable textbooks and history of SR. Rod Ball 09:07, 28 September 2006 (UTC)

Perhaps if you considered that the string is being pulled by the leading spaceship you will see the relevance of the Nicolic paper. However, the truly relevant point in that the back end of the rod perceives a shorter but stronger acceleration. Otherwise, the rod is placed under mechanical tension and must get longer or break.

As for whether you know relativity: That you don't is well established by your contention that "[t]here is no desynchronisation of clocks between the two s'ships accelerating in Euclidean space". Even when I first began to deal with you, it was obvious that you have no conception of what the relativity of simultaneity is. Now you have said so as clear as day. You don't understand relativity! You really, really, don't. --EMS | Talk 14:44, 28 September 2006 (UTC)

Look, this is quite simple. That either a string or a rod appears increasingly contracted at increasing speeds from lab/launch frame is not contested and has been a commonplace for a century. That Nikolic uses it in his article is of no significance as it's the basis for all discussions of Lorentz "contraction" effects. The gist of the Nikolic paper (ie that which he might regard as original) is that for a given rocket thrust, if the rod is pushed from behind the rest of the rod is apparently slowing up very slightly due to apparent contraction of front end towards the rear. Vice versa if the rod is pulled from the front then the rest of it will seem to be slightly speeding up as the rear end "contracts" towards the front. Thus if the centre-of-mass or average velocity of the rod is compared to apparent length, a slightly different profile would occur for pushing or pulling and it would seem that the rod could be accelerated to a higher velocity for a given thrust by pulling as opposed to pushing.

In the BSP it is accepted that the string will appear Lorentz contracted from launch frame and the contested conclusion of the problem centres around whether the distance between two identical unconnected in-line rockets would also appear contracted from launch or not. Thus it should be clear that there is no relevance of either problem to the other and the only connection is that they both start from the same traditional concept of Lorentz contraction.

My take on Nikolic is that he's dressed up a triviality and mistakenly believes they are physically distinct situations rather than a superficial formulaic difference resulting from coordinate labelling. He consequently claims an observer on the rod would feel a stronger inertial force at the rear end. This is quite wrong as according to SR there will be no contraction of the rod for an observer riding on it, so the arguments applied from the launch frame don't apply and the inertial "felt force" will be uniform along the rod.

Another way of convincing you that there is no de-synchronisation of clocks between the two s'ships is the same argument that you use to claim constant distance & equal acceleration observed from launch frame. By using (translational) symmetry your argument is that the trajectory of s'ship A must be an exactly translated copy of s'ship B. This argument also implies that a clock aboard A cannot differ from a clock aboard B - everything is identical and the clock obviously can't behave differently when launched from Xb as opposed to Xa. Although during acceleration the Doppler-like effect previously discussed makes A think signals from B are speeding up and B think signals from A are slowing down, once they revert to constant velocity ( for example after their identical amounts of fuel are exhausted ) they will become inertial and verify identical clock rates and identical elapsed times. This must be so as if there were any difference one would re-launch A from location B and thus prove either they were non-identical contrary to assumption, or that spacetime in the region between A & B is non-isotropic contrary to Euclidean assumption. Rod Ball 11:43, 29 September 2006 (UTC)

Standard textbooks clearly show that you are wrong about the syncrhonization issue, if I understand you correctly. Consider the following quote from (Misner, 1973: 165)

"At distances l away from his world line, strange things of dimensionless magnitude gl happen to his (ed: the accelerated observer's) lattice - e.g, the acceleration measured by accelerometers differs from g by a fractioanal amount gl (exercise. 6.7); also, clocks intially synchronized with the clock on his world line get out of step (tick at different rates) by a fractional amount ~gl (exercise 6.6). Pervect 00:50, 30 September 2006 (UTC)

Your argument applies to incremental clock rates, not accumulated clock times. It also misses the most basic point: If the clocks stayed synchronized in the launch frame (and they do), then they are unsynchronized in the final spaceship frame. You cannot transfer synchrony in the lauch frame to the final spaceship frame. It is that simple. --EMS | Talk 16:55, 29 September 2006 (UTC)

Save the Hillman version.

I would like to propose "saving" the Hillman version of this article, by merging it with the current article. I'm willing to do the work, but I'm concerned about Rod Ball making the task prohibitively difficult :-(. Hillman's version is a bit advanced, but I think that we can merge the less technical current article together with Hillman's larger and more technical version, keeping Hillman's excellent space-time diagrams to expand the introductory portion.

Question: do we do this the straightforwards way by just editing it, most likely starting an "edit war", or is there an arbitration process that we should do first? I'm a bit reluctant to just start an edit war, but reading the RFC's has convinced me that Rod Ball is indeed alone in his position. Pervect 02:56, 29 September 2006 (UTC)

Let's see what you can produce. I don't think that Rod will be much of a problem as the three of us can take turns reverting his reverts as needed, and since Rod is more concerned with pushing his own POV than in suppressing ours. (Rod did not interfere with Chris' version much anyway. It was archived due to a consensus that it was too advanced, and not due to Rod.) --EMS | Talk 03:46, 29 September 2006 (UTC)

Have none of you noticed that the formulae given immediately after "Advanced Analysis" are faulty ? In the triple expressions after " T = { " the third formula should begin " sinh(k sigma)/k " and not " [cosh(k sigma)-1]/k " as written. The error is duplicated in the second set immediately below. There are also other problems.....Rod Ball 14:22, 29 September 2006 (UTC)

I didn't notice, but you actually have a good point here. I've asked Chris about the issue. Pervect 00:50, 30 September 2006 (UTC)

Rod - I find it hard to believe that Chris does not know what he is doing here. I will expand those equations if I get a chance and verify them, but you can't just eyeball hyperbolic trig equations like those and say that they are not consistent.

My big problem is that this is a huge step backwards. This is OR in that it appears to me to be novel treatment of this paradox, and brings out all of the Chris' abilities. On one level, it is a masterpiece. However, Wikipedia articles should be accessible to readers who are reasonably educated in the related subject. This math is so advanced that some who has read and understood the special relativity article probably has little chance of understanding this advanced analysis.

Pervect - What is your goal here? Are you using Chris' version as a stepping stone to something better? If so, are you sure that you should be playing with it here instead of working it over in a subpage in your user space (such as user:Pervect/Bell's spaceship paradox)? --EMS | Talk 17:09, 29 September 2006 (UTC)

My goal here was, as I stated earlier, to save the original Hillman version. It's essentially a cut and paste job, combining my earlier edited version of the article with Hillman's. I thought Hillman's contributions contained valuable advanced insights. I think I did add a few additional editorial changes to both Hillman's text and the main article in the process, mostly very minor changes. You may notice that the formulas in the main article are a bit more legible now.

If it turns out that people don't like the Hillman version, because it was OR, my effort was wasted :-(. I had the impression that you at least liked the Hillman version, but perhaps now that you've seen it again you've changed your mind?

The fact that my initial edits were done in a sandbox don't have anything to do with the issue as far as I can tell - that was done for my convenience. Basically, I wanted to a) avoid cluttering up the history of the article with many versions and b) avoid interference with the article by other editors while I was initially combining the articles, a time during which I did not want random input. Now that I've completed preparing it, I expect that it will undergo the usual wiki process. Usual process in my opinion includes a certain amount of "sitting" on Rob Ball's viewpoints so that they do get a fair mention, but do not dominate the article the way they have in the past, as we have discussed on the talk page. Usual process definitely includes input from other editors, that's the point of wiki.

In that vein, I would like to see some direct quotes from the Petkov reference, which I do not have, here on the talk page, before including a mention of it in the main article. I don't have any objection personally to including Petkov in the references sections without mention - it appears to be a creditable, though not particularly noteworth, reference. I would need to see some quotes from it to see why it is noteworthy. I've currently given Rob Ball's objections a slightly higher visibility than I think they actually merit, by quoting "his" references in the lead part of the article. This is the first I've heard of the Petkov reference, of course I have only come into this mess recently. Pervect 19:40, 29 September 2006 (UTC)

I both like and don't like the "Hillman version". As a proof that Bell was correct, it is marvelous. For anyone who can handle the math, it totally nails the case for it. The catch is that you almost need an advanced degree in mathematics to be able to handle the math. I need to exert a real effort to sort my way through it, and that is a red flag that the average reader is being just snowed by it. (I'm nowhere near as good a mathematician as Chris, but I am still much better than most people in that regard.) IMO, the "good stuff" is in your edits to the initial section about the problem. Those are helping to explain to people what is going on here. OTOH, bringing in "Rindler observers" and "Bell observers" and graduate-school-level math to support their description only leaves most readers holding in their hands a piece of math that they cannot understand, and really should not be expected to understand. That just is not proper for Wikipedia.

On the Petkow reference: This is new to me also. Based on past experience, Rod cannot be trusted as he will interpret stuff to suit his own POV. OTOH, given the history of this issue it is not impossible that this is valid and a good reference. So I also want to see he relevant passages quoted. --EMS | Talk 20:18, 29 September 2006 (UTC)

Petkov may be a fine philosopher, even asking good questions about the philosophical implications of SR, but he advances his very own theory of SR, which includes predictions differing from standard SR. I don't think he got published any SR paper in a physics journal. The Springer Frontier series is very inclusionist.

So whether it is wise to mention Petkov, boils down to a question of notabiliy.

Pjacobi 20:50, 29 September 2006 (UTC)

Lovely. This all comes back to the question of the extent to which controversy on this issue remains, and how to deal with it. For a near-majority of relativists, that Bell was right is obvious, and the matter nicely settled by the prior work of D & B. However, there are these regular outliers with a differing opinion, and Pektov is just the latest in the set. --EMS | Talk 22:02, 29 September 2006 (UTC)

Personally, I think that I need to see some of the quoted material by Petkov before I can make any rational decision. Pervect 00:33, 30 September 2006 (UTC)

OK, a status update. I have to reluctantly admit that the Hillman article, as-is, is flawed. CH is totally burned out on wikipedia, and isn't interested in fixing it - in fact, he suggests I'm wasting my time. I should add that I've been thinking about the appeal of his version of the article to me, and come to the conclusion that the main appeal is that it serves as a worked example or the techniques of geodesic congruences, rather than for the light that these techniques throw on the Bell spaceship problem.

Therfore, for these reaons, I'm going to go back to my original Before Hillman version, with a few significant additions that have just occurred to me. This will essentially combine the analysis given in the current article with the scenario where both spaceships stop accelerating and compare their lengths in an inertial frame.

As far as Petkov goes, I need to see at least one quote demonstrating why this author is relevant before including him. If he's relevant he deserves at least a mention in the references section, possibly more if he's very relevant. But I'm not going to do anything at all until I see some a quote. Pervect 18:36, 30 September 2006 (UTC)

I found a paper by Petkov His relevance would seem to be as another example of someone being mistaken. Perhaps the most interesting aspect of the paradox is that so many get it wrong, at least at first. Gregory Merchan 19:39, 30 September 2006 (UTC)

Wow - if this is representative of his published work, he's one confused puppy. If it can be confirmed (a quote will do) that Petkov actually said that the string does not break, and this statement was made in a peer-reviewed journal (even an inclusive one), I'll add his name in the article. After looking again at the references, I see that we've only included papers specifically about spaceships and strings in our papers section, so I'm not quite sure what to do with the "Frontiers" reference if it's not specifically about the Bell paradox and the breaking of the string. Pervect 23:34, 30 September 2006 (UTC)

I wouldn't say that Frontiers book series is peer reviewed in th usual meaning of the word. Looking for articles by Petkov in peer reviewed journals, I didn't found any (this search only founds unpublished preprints on arXiv). BTW, no that you've had some exposure to Petkov, would you mind giving Andromeda paradox a look? --Pjacobi 12:08, 1 October 2006 (UTC)

The intro is/was factually incorrect. I am trying to correct it back to what was for a long time a truthful version acceptable all round. The two errrors I'm seeking to remove are that:

(1) There are not "a family of problems" under the name "Bell spaceship paradox" but just one that is quite specifically defined in the opening paragraph of the Bell reference. Varying the rate of the acceleration or considering whether the engines are switched off at some point does not constitute a different problem.

(2) The Dewan & Beran is not an "earlier version", but it is the seminal version, of which all and every subsequent appearance including Bell's is to a lesser or greater extent an abbreviated copy. It would have been polite for Bell to mention this in his opening remarks in addition to citing Dewan & Beran as a source at the end refs. Rod Ball 10:47, 2 October 2006 (UTC)