Rod Ball

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Rigid rods

File:Rigidrod.jpg

Rigid rod motion?

I'm still of the opinion, that you are making a severe error in your presentation of the rigid rod and the BSP problem.

I'd prefer no to further fill the Talk:Bell's spaceship paradox page with this discussion but we can have a discussion here, starting with your picture and the theses you presented on it -- if you agree. In the (hopefully consensual) end, we can report our results, if relevant, at Talk:Bell's spaceship paradox.

Pjacobi 16:58, 3 May 2006 (UTC)

Not interested? --Pjacobi 20:12, 7 May 2006 (UTC)

I've only just found this item (I thought it was just some stuff about sourcing diagrams and hadn't scrolled down before). I slightly reworded it this morning, so what don't you agree with ? Rod Ball 13:58, 8 May 2006 (UTC)

Can we start with agreeing (or disagreeing) on some definitions (and direct consequences of them):

Proper time is time as measured by the clock for an observer who is traveling through spacetime. In SRT, if the path is giving in cartesian coordinates in some inertieal system, the proper time difference between start and end point of a path P is given by

$\Delta \tau =\int _{P}{\sqrt {dt^{2}-dx^{2}-dy^{2}-dz^{2}}}$ (if we take c as 1)

And this gives the same result for any intertial system.

Proper acceleration is the acceleration measured in the comoving system, and in any inertial system given as

$a_{p}=a\,\gamma ^{3}={a \over (1-v^{2})^{3 \over 2}}$

Do you agree?

Pjacobi 15:13, 8 May 2006 (UTC)

First item - I would say accompanying an observer rather than "for" (I'm not contradicting, just being as clear as possible). (I think we could drop the y and z coords also for this one dimensional prob.) But yes I would agree although bear in mind that for the ends of a rod or string ( I mean the ends of the proper length) the path length for the integral is different. Second item - I think one has to be very careful here but I'll save my reservations for later. The formula is acceptable for acceleration of individual points taken in isolation but "a" needs to be defined carefully when considering correlated points such as ends of proper length that move disproportionately in x-t space. That is, for a given increment of proper time, dx and dt are proportionately greater at one end than the other.

Just briefly, to help me see your point of view, am I right in thinking that we agree that the proper length (ie. as measured in its own frame) of the rod is constant and that it has the same velocity at each end at all proper times ? I hope we ageree this is so, in which case I wonder how you reconcile that, with the ends of the same proper length having different accelerations ? Rod Ball 19:51, 9 May 2006 (UTC)

interjection

Interjection: The two ends of an accelerating rod are only in 'the same frame' in the same sense that the bottom and top of a tall building are in 'the same frame' I suppose that someone has made a good definition of an accelerated frame somewhere, but I just want to make sure you know that 'the same frame' is not an inertial frame. i.e. it's beyond my own limited conceptual ability at this time. I can only think of a frame in terms of one observer at a time. The persons at top and bottom of the building will not agree about simultaneity, but they will both agree about the height of the building. On the other hand, if you somehow take a building into outer space, and hook rockets to the bottom of it so that it accelerates upward at 9.8 m/s^2, and watch from the distance, you'd see the building falling and decelerating until it stopped, then accelerating upward again. It would acheive its full un-contracted length at the moment when the entire building achieved a standstill at exactly the same moment. Yes exactly the same moment, because if it weren't all stopped at exactly the same moment, then people in the building would see the top and bottom moving relatively to one another. So the building goes from being length contracted, to noncontracted, and back to being length contracted again. What does this say about the relative velocity of the top and bottom of the building from the view of the inertial observer? I believe I have determined that the bottom of the building must be moving faster than the top at all times. I was writing a computer simulation of all this a couple years ago which I never quite got done. Let me know if you would like to see it. JDoolin 04:12, 26 August 2006 (UTC)

back to the show

Yes, a in the case if the rigid rod, the rod in comoving coordinates has constant lengths, that is exact the definition of rigidity. In SRT there is only a very limited set of rigid motions possible, but uniform acceleration is one of them, see Born rigidity.

I'm a bit confused about your reservations in the a case. The acceleration can be defined for each point separately.

Pjacobi 20:05, 9 May 2006 (UTC)

Yes, but an increment of proper time is an increment of angle about O that a) increments the velocity the same amount at each end and b) sweeps a greater path length on the hyperbola by exactly the inverse ratio of the separate "a" for each curve. There's no coincidence about this. The true acceleration of a curve depends on how fast you move along it. For concentric circles the accn. is proportional to r for a common radius but quite different if you just use cartesian coords on bits of the arc length.

I don't quite understand your first comment. If you have constant p.length and identical v at each end, does that alone not imply identical proper accn. at each end ? Rod Ball 07:59, 10 May 2006 (UTC)

If and only if both ends have equal proper time, and this notion is not equivalent to both ends being at the same time coordinate in the co-moving frame.

I assume, if we can agree on the definitions of proper time and proper acceleration (or you are at least willing to see what follows from these definitions, we should continue to worked example with concrete values to see what happens.

Taking still c=1, we can at first look at the two points travelling with x²=t²+3² and x²=t²+5² (in the lab frame), as pictured in your diagram above. OK to proceed with this?

Pjacobi 09:10, 10 May 2006 (UTC)

Sure. Rod Ball 11:38, 10 May 2006 (UTC)

I'm in a hurry and offline tomorrow, so let my throw in some conclusions from x²=t²+3² (for positive t and x):

• $x={\sqrt {t^{2}+3^{2}}}$
• ${dx \over dt}={t \over {\sqrt {t^{2}+3^{2}}}}$
• $t={\sqrt {x^{2}-3^{2}}}$
• ${dt \over dx}={x \over {\sqrt {x^{2}-3^{2}}}}$
• ${d\tau \over dt}={\sqrt {({dt \over dt})^{2}-({dx \over dt})^{2}}}={\sqrt {1-{t^{2} \over t^{2}+3^{2}}}}={\sqrt {3^{2} \over t^{2}+3^{2}}}$
• Integrating gives $\tau (T)-\tau (0)=\int _{0}^{T}{\sqrt {3^{2} \over t^{2}+3^{2}}}dt=3\,arcsinh({T \over 3})$
• If we choose τ (0) = 0, reverting to t as variable, and omitting the argument of τ this reads $\tau =3\,arcsinh({t \over 3})$
• This now gives $t=3\,sinh({\tau \over 3})$
• And $x={\sqrt {3^{2}sinh^{2}({\tau \over 3})+3^{2}}}={\sqrt {3^{2}cosh^{2}({\tau \over 3})}}=3\,cosh({\tau \over 3})$

So, that should give a solid base for some numerical examples and pictures. Please check my calculations, I'm notorous for having typos in formulas. Also point out, whether any of these mathematical steps look physically unsound to you.

Pjacobi 21:27, 10 May 2006 (UTC)

This seems reasonable, and in general... (x/y)=cosh(tau/y), (t/y)=sinh(tau/y), where y=x(o)

(I corrected a few minor typo's) Rod Ball 10:36, 12 May 2006 (UTC)

Thanks for the corrections.

Before dusting off my Python and Matplotlib skills to make some more diagrams, I'd like to interrupt the mathematics for a short break to discuss physics, or even philosophy. The rationale for this is the notion of "proper length", you mentioned above. "Proper time" and "proper acceleration" are observer local effects, but proper length, for example between both ends of the rods, when the observer is at one end, is not local. It requires a notion simultanity. Which point of the world line of the other end is simultaneous to a given point on the worldline of the observer?

It's at the core of relativity theory, that there is no absolute simultanity, the only invariant notions are, whether two spacetime points are space-like or time-like separated. Now, for inertial observers, there is a natural choice, the Einstein synchronisation.

Einstein synchronisation

Interjection: I think that might be the region of constant t which I have been trying to say is a nonambiguous meaning of simultaneity. The fact is that it can be defined for each observer at any given moment (event), and once you do so, much more meaningful conversation can take place.

I recently found to my surprise that his synchronization method was not clearly defined as I expected in his 1905 paper. I have read about using a method of sending a signal from halfway between two observers to create synchronous events, I think from several different books or articles.

Sorry about these extra headers.

But even in that case it is considered a convention only - at least by significant faction of philosophers and physicists, see the literature and links of that article, especially [1].

For accelarated observes no single choice of simultanity has all the nice properties of the intertial case. The most common convention is, to use at each point of the wordline the simultanity hyperplane of an inertial observe with the same position and velocity. This is the concept underlying Born rigidity. The Rindler coordinates are another example. But another possibility are Märzke-Wheeler coordinates a.k.a. Radar time, see [2].

Fortunately, it is my opinion that neither for the rigid rod nor for BSP these complications doesn't make a significant difference (and I'd consider those authors, who base their arguments on either of these coordinate choices, to be confused or confusing). Two arguments:

• If in doubt, we can always switch off drive for some time and make measurements resp. calculatuinb in inertial frames.
• The difference between different simultanity conventions gradually disappear when going near the observers world line: As we more and more "zoom in" the world line more and more looks like a straight one. And whereas we tend to use "large distances" (length times acceleration comparable with c²), to make the diagrams better showing the effects, we can always use a small l·a for calculations.

Pjacobi 21:28, 12 May 2006 (UTC)

You say "no absolute simutaneity". Agree but this means between relatively moving reference frames. You seem to be taking it too far and possibly denying a notion of simultaneity within a single inertial frame. There is no problem establishing simultaneity among different points in the same inertial RF, but it breaks down and becomes "shifted" as between RF's moving relative to one another. Rod Ball 18:36, 13 May 2006 (UTC)

As I've said, in inertial frames there is natural (but argueably still conventional) notion of simultanity. But regarding general observations in non-inertual frames, there is not. But sorry to be confusing myself. I just wanted to point out, that the problem of non-unique definitions of simultanity will not change the results here. --Pjacobi 20:08, 13 May 2006 (UTC)

Rubicon reached?

Despite patient efforts to explain matters to you, you are still pushing your strange POV at Bell's spaceship paradox. Your article space edits can easily be reverted but the the endless discussions on the talk page are even worse. Making a bilance, your current Wikipedia edit behaviour just drains resources (edit time of contributing physicists). I concede that you seem have read quite a lot articles on the subjects, but your failure of understanding basic SR facts, leave me puzzled, how you can become an asset and not an obligation for Wikipedia.

Perhaps you just should try editing a completely different subject (and perhaps and after a significant pause only re-read the BSP arguments and a textbook)?

Pjacobi 22:26, 16 August 2006 (UTC)

You are hardly in a position to explain things to me, rather it's the other way around. I have deeply researched this topic and know and understand it better than the four of you. This is quite evident from the comments that are made in the talk page. Your contribution has been little else than to keep restating the equations of hyperbolic motion which have no bearing on the problem at all since it is only stipulated that the acceleration regimes be the same, not that they take any particlar profile. Remember also that ChrisH had never heard of the problem before and I had great difficulty persuading him to even consult the literature, such was his arrogance. He didn't understand the problem and thought the 2nd s'ship unnecessary because he wanted to model the string elasticity with concatenated springs !! I particularly didn't like his dishonesty in blustering and not acknowledging some elementary errors when they were pointed out to him. He even denied not having read the topic before, when he eventually got round to doing so. His analysis is incorrect due partly to errors and partly to omitting to include relativity.

Against incessant repetition of unconnected statements and unsupported assertions of the correctness of D&B and Bell, I have managed to pursue a variety of arguments and approaches on the talk page that have considerably clarified the issues and shown that the divergence of opinion on string-breaking is due to the unconscious use of different conceptual versions of relativity. As I describe in my most recent entries, because of the near-identity of Lorentz's theory and Einstein's SR for constant motion, it has become not uncommon for some physicists to think of SR in terms of the more common-sense notions of Lorentz's theory. This is, of course, openly stated at length by Bell and has been adopted more widely, although not always knowingly.

However what has not been generally recognised is that for accelerated motion, Lorentz's theory and SR differ markedly in their predictions. In particlar in Bell's problem where Lorentz's theory has the string contracting and the empty space between s'ships unable to, both being accurately observable from launch, in SR the string does not actually contract but is only measured as doing so from the launch frame and this corresponds exactly to the s'ship distance and measurements of it from launch. In other words I show that the statement that the s'ships "cannot get closer from the launch frame unless they have different accelerations" (which seems to be the main plank of your argument) is demonstrably false in the context of special relativity, where one does not always expect things to be as simple as in Newtonian physics.

You complain that I am draining resources of contributing physicists. What arrogance !! What makes you think that you (and Harald & Ed) are any better qualified to edit Wikipedia than I ?Any contributor, whether professional scientist, or degree level (like myself), or hobbyist has at best one to a few areas of specialisation in which they may have expert knowledge, whilst perhaps having a "rough and ready" acquaintance with a broader range. This can also change somewhat as a result of intense research or prolonged disengagement. I sense that SR for many years, or decades even, has been neglected due to understandable eagerness to get stuck into the hot topics of GR & cosmology, and is all too often treated in a sloppy and superficial way because it is thought to have been completely worked out and done and dusted prior to WWII.Far from failing to understand basic SR facts, as you put it, I am clarifying what are SR facts by distinguishing contaminating ideas from Lorentz's theory that have infected much SR thinking. A muddled mixture of the two theories is worse than either on its own. If you do not have sufficient interest or detailed knowledge in BSP & SR, perhaps it is you who should think of moving to a different topic where you can contribute more usefully. Rod Ball 11:22, 18 August 2006 (UTC)

For bringing the problem to the attention of more eyes and hearing more opinions, I opened a user conduct RfC, see Wikipedia:Requests for comment/Rod Ball. You are invited to expose your view in the "Response" section. This is a step withing the Wikipedia:Conflict resolution frameworj, you may want to explore some policy and process pages linked from that page. --Pjacobi 19:24, 19 August 2006 (UTC)

You say that I am "pushing my strange POV". Well, what POV is that ? If you mean the view that contradicts D&B and Bell by denying the string would break, then that is not merely my POV (nor is it "strange") but was held by the formidable body of expert opinion called the "CERN Theory Division" not to mention Nawrocki, Hsu & Suzuki and the "many physicists and university professors who teach relativity" and who contradicted Matsuda & Kinoshita. If on the other hand you mean my many analyses and explanations, then these were provoked and invited in response to contrary remarks in the course of discussion in the talk page. I would not have felt obliged to pursue them if you had not taken the extreme and unscientific position of denying the legitimacy of any alternative view to your own and thus dismissing the above-mentioned substantial opinion as "dissident" or in some way cranky, irrational or even anti-SR. Worst of all you seem determined, like some Orwellian truth ministry, to suppress and erase all mention of such "heresy" by presenting the D&B/Bell line as the only one. Because I can see both sides of the argument and indeed, see why there are two sides to the argument, I have striven to open your eyes to the errors in D&B/Bell and present a clear and simple analysis that does not deviate from SR and yet shows no string breakage.

The two main faults with D&B/Bell's arguments are:

(1) Failure to distinguish SR from Lorentz's "absolute motion" theory that pre-dated it.

(2) Failure to distinguish normal Doppler shift from the shift that results from changing velocity during signal transit, and which involves no change in separation between transmitter and receiver.

If the discussion has been prolonged, it is not my fault but due to the three of you taking turns to conduct your own arguments and being unable to agree among yourselves. There would no sooner be an emerging compromise between two of us, than another of you would jump in and provoke disagreement again - as you yourself did recently.

May I remind you again that Wikipedia is an open resource and not the private fiefdom of a tiny coterie that can regard all articles as subject to their complete approval, even down to the smallest detail. If you want that level of control I suggest you get together and write your own textbook. Rod Ball 12:47, 21 August 2006 (UTC)

RfC

Rod - Peter and I have initiated an RfC against you. See Wikipedia:Requests_for_comment/Rod_Ball. --EMS | Talk 20:45, 22 August 2006 (UTC)

3RR

You are in violation of WP:3RR at Bell's spaceship paradox. Please stop. --Pjacobi 21:40, 25 August 2006 (UTC)

So are you - and you started it ! It's up to you to stop. I'm restoring constructively, you are just vandalising what you don't like. Rod Ball 19:06, 27 August 2006 (UTC)

First, I only count 3 reverts by Jacobi in a 72 hour period or so. Second, even if Jacobi had also been violating 3RR that would not make your violation acceptable. Third, do not call edits vandalism simply because you don't agree with them. Thank you. JoshuaZ 19:13, 27 August 2006 (UTC)

Blocked

I've blocked you for 24h to give you a chance to think about the views expressed against your position on the RFC William M. Connolley 09:15, 28 September 2006 (UTC)

Re your mail: things are better discussed here William M. Connolley 10:14, 28 September 2006 (UTC)

Alright then but briefly, to deal with the most recent edit "skirmish", I added a reference comprising just one line to the end of the BSP article. It was to a Springer-Verlag book in which at a specified page the author refers specifically to "Bell's spaceship paradox" and puts a point of view contrary to Bell's own, as a number of theoreticians (eg. CERN, etc) have previously done on different occasions. I also adjusted the terms "mainstream" and "dissident" to "supporting Bell" and "contradicting Bell" in order to restore NPOV and dropped a reference (Nicolic) that had nothing to do with Bell's paradox.

Pjacobi promptly deleted my edit by reversion claiming the Nicolic result is a "natural corollary" of BSP and that the author of my reference, Vesselin Petkov, was writing "completely non-canonical" (ie. non-standard) SR and that his papers were "obviously not accepted for publication".

Both these claims are entirely false. Springer-Verlag are one of the most reputable academic publishers in the world and manuscripts peer-reviewed prior to publication. I pointed out that Pjacobi had no basis for his denigration of Vesselin Petkov nor for deleting the reference and I quoted a link to Petkov's recent publications as follows: http://www.math.u-bordeaux.fr/~petkov/publications/publi1.html

I consequently restored the Petkov reference and the "mainstream/dissident" adjectives with "supporting/disagreeing with" Bell BUT this time I left the Nicolic reference that Pjacobi likes in, while shifting it separate from the direct Bell spaceship references. I also explained in talk page why Nicolic is not connected with Bell's spaceship problem.

Pjacobi then promptly reverted again, removing my amendments without any explanation.

I restored the changes I had just made (previous para) and Pjacobi did not revert but briefly asserted on the talk page that BSP follows immediately from Nicolic (note the reversal from his previous claim that 'Nicolic is a natural corollary of BSP').

Nearly six hours later EMS steps in to delete my changes and revert back again without explanation.

The next day I restored my changes again preserving the Nicolic reference and objecting to abrupt unexplained removal by EMS.

The same day EMS removed them again claiming my edits were "inappropriate" but not saying why.

The following day I restored my changes again because I was essentially only adding one legitimate reference and I was not going to be "bullied" by two editors with highly dogmatic views who were suppressing what they didn't agree with, without giving account of themselves.

14 minutes later Pjacobi again reverted my edit without explanation, shortly after which I restored them again and gave a fuller explanation on the talk page of why BSP does not follow from Nicolic nor vice versa - but while as before keeping the Nicolic reference in.

Less than a half hour later Pjacobi reverted again, removing my small edit without comment and subsequently I found myself blocked from further contribution.

Wikipedia is supposed to be an "open resource" and I have consistently applied myself to it constructively and striving for a NPOV whilst allowing the edits of others as far as possible as they do not distort facts or present a biased article. What I have just described is unfortunately typical of the conduct of Pjacobi, EMS and one or two others of like mind who seek to brow-beat honest editors like myself and enforce their own views to the exclusion of others, regardless of the stature or experience of those holding counter opinions. The tactics they use to exert total control of articles down to the last word, are the highly inappropriate ad hominem attacks that claim others to be ignorant of the subject, and when their arguments fail, to mis-use Wikipedia OR and POV labels to smear opponents before seeking to have them blocked for taking up too much of their valuable time !! [All this can easily be verified by consulting the archives and edit history at Bell spaceship]

I cannot see how Pjacobi, EMS et.al. are in any way conducting themselves in accordance with either the spirit or the letter of Wikipedia policy. They are far too dogmatic to be good editors and they greatly overestimate their expertise in special relativity generally and the topic in hand especially. This is particularly noticeable in the way they bring little or no textual support to their arguments and choose to ignore, dismiss or denigrate standard reputable textual references I have used or quoted from. It is also significant that they consider the opinion of the whole CERN Theory Division as of no consequence, and the work of Professor Hsu with two relativity textbooks to his name (World Scientific) as equally to be swept aside.

This is certainly not the way that science is supposed to operate and surely it cannot be good for Wikipedia either. Rod Ball 13:58, 28 September 2006 (UTC)

That wasn't brief. I've looked at the talk page and RFC: there is lots of discussion. total control of articles down to the last word is completely over the top: have another go, but be briefer, don't pretend there is no discussion, and don't go OTT. This is certainly not the way that science is supposed to operate - quite right: we're *not* doing science here. We are describing pre-existing science William M. Connolley 14:13, 28 September 2006 (UTC)

Describing pre-existing science requires the same qualities of objectivity and open-mindedness as science itself. If the history and current state of science are misrepresented, it can only ultimately do harm to science itself. Censorship of opinion is as disreputable in the presentation of science as it is in the conduct of science itself.

I don't think "down to the last word" is over the top. In the example quoted they won't allow a pertinant reference from a reliable source (as detailed above) but will not say why, despite it being just a single line. They insist on the loaded terms "mainstream" and "dissident" when there is absolutely no statistical evidence, however vague, to support such a distinction. On the contrary the only meagre evidence is that Bell himself was contradicted by the whole CERN Theory Division, and Matsuda & Kinoshita's paper was opposed by the "many physicists including university professors who appear to teach relativity" in Japan (as quoted in their own paper). Thus it seems more likely that "mainstream/dissident" should be reversed but I'm content with the NPOV 'supporting/contradicting' Bell. Previous examples in the edit history show similar excessively zealous control of wording, phraseology and emphasis applied to nearly every sentence. Rod Ball 14:43, 28 September 2006 (UTC)

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