Talk:Bell's spaceship paradox/Archive 6

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A weakness in the problem setup given in the lead.

In the lead we say, '...two identically accelerating spaceships. Both rockets and the thread all move at all times with the same velocity in S'. The second sentence, 'Both rockets and the thread all move at all times with the same velocity in S', is a correct description of the condition that we wish to impose. The first bit however, 'two identically accelerating spaceships' is vague and potentially misleading. Should we not say, 'Two spaceships having identical coordinate acceleration', or 'Two spaceships having the same acceleration at all times as measured in frame S'? Martin Hogbin (talk) 16:21, 8 October 2013 (UTC)

Thanks, I now summarized both sentences into a single one, in order to emphasize your point. --D.H (talk) 20:02, 8 October 2013 (UTC)

On reading the article it looks as though Dewan and Beran did not fully appreciate this fact, They say, 'Since the rockets are constructed exactly the same way, and starting at the same moment in S with the same acceleration, they must have the same velocity all of the time in S. Thus they are traveling the same distances in S, so their mutual distance cannot change in this frame.' They are seem to be saying that two identical spaceships would be measured to have the same coordinate acceleration in the starting frame. This is not correct. Two identical spaceships would have the same proper acceleration and would have the same velocity all of the time in a comoving inertial frame.

To maintain a fixed distance in frame S, the rear spacecraft would need to progressively reduce its power.

In fact whether the rope breaks or not depends on whether we have identical rockets (in which case it does not) or whether the rockets are controlled to produce a constant coordinate acceleration in frame S (in which case it does). Maybe that resolves some of the arguments about this subject.Martin Hogbin (talk) 21:57, 8 October 2013 (UTC)

Your comment "Two identical spaceships would have the same proper acceleration and would have the same velocity all of the time in a comoving inertial frame", is not correct. When you try to maintain the same distance in a comoving frame, then you are talking about Born rigidity, which needs different proper accelerations.
More precise: Proper acceleration (as opposed to coordinate acceleration) can be directly measured by an accelerometer, and in Bell's example the proper acceleration is the same for both ships due to identical programs and construction. However, this alone says nothing about the question, whether the measured distance between two ships remains the same or not, because it depends on when we initiate the same acceleration programs (this time varies due to relativity of simultaneity). As you can read in many sources, same proper accelerations lead to an increased rest length as in Bell's example, as opposed to Born rigidity which needs different proper accelerations. For instance:

• Tartaglia, A.; Ruggiero, M. L. (2003). "Lorentz contraction and accelerated systems". European Journal of Physics. 24 (2): 215–220. arXiv:gr-qc/0301050. doi:10.1088/0143-0807/24/2/361.{{cite journal}}: CS1 maint: multiple names: authors list (link). "p.4: Fig. 1: The world lines ζR and ζF of two objects accelerated with the same proper acceleration and for the same proper times up to t = t0 are shown. Afterwards both objects continue to move inertially at the same constant speed. The distance between the objects as seen by a static observer maintains its initial value l, but the proper distance increases to become l0 . The length l corresponds to the Lorentz contracted l0 . The dashed line represents the light cone."
• Semay, Claude (2006). "Observer with a constant proper acceleration". European Journal of Physics. 27 (5): 1157–1167. arXiv:physics/0601179. doi:10.1088/0143-0807/27/5/015.: p.11:"FIG. 5: World lines (in bold), in an inertial frame, of two observers with the same proper acceleration A. The distance between the two observers is constant in the inertial frame (L) but increases in the proper frame of the first observer (X(t)). [..] From the point of view of an observer in the first spaceship, the distance increases between the two ships. This in agreement with the reasoning sustained above about the rod. This phenomenon is due to the fact that the spaces of simultaneity for an observer on board the first space ship are different from the spaces of simultaneity for a stationary observer in the inertial frame."
• Styer, Daniel F. (2007). "How do two moving clocks fall out of sync? A tale of trucks, threads, and twins". American Journal of Physics. 75 (9): 805–814. Bibcode:2007AmJPh..75..805S. doi:10.1119/1.2733691.: "p. 808: The situation “two clocks undergo identical acceleration programs in the lab frame” is the same as “two clocks undergo identical acceleration programs as deter mined by their own clocks.” But such acceleration programs are not identical in any other frame. [..] p. 810: We have established that if two clocks, at rest in the lab frame and separated by distance l_i, carry out identical acceleration programs (identical in the lab frame or identical as determined by their own clocks, see the discussion following Eq. 19), then at the end of the program the clocks remain separated by distance l_i in the lab frame, but are separated by a longer distance l_i*γ in their own rest frame. The two clocks might be in identically programmed space ships, but they might also reside at the nose and tail of a truck. Thus if all parts of a truck undergo identical acceleration programs, the truck’s proper length stretches as it accelerates.
• Franklin, Jerrold (2010). "Lorentz contraction, Bell's spaceships, and rigid body motion in special relativity". European Journal of Physics. 31 (2): 291–298. arXiv:0906.1919. Bibcode:2010EJPh...31..291F. doi:10.1088/0143-0807/31/2/006.: "For two spaceships having equal accelerations, as in Bell’s spaceship example, the distance between the moving ships appears to be constant, but the rest frame distance between them continually increases. This means that a cable between the two ships must eventually break if the acceleration continues. For rigid body motion in special relativity, the rest frame acceleration throughout the body will vary as in Eq. (23), but this will preserve the rest frame dimensions of the object."
• Mathpages: Born Rigidity and Acceleration: "This is the magnitude of the constant proper acceleration which the leading end of the rod must undergo in order to meet the stated conditions. Also, the reciprocal of this value represents the distance of the leading end of the rod from the pivot event. Trailing sections of the rod must undergo a greater acceleration in order to maintain Born rigidity with the leading end, and the required acceleration is inversely proportional to the distance from the pivot event. [..] Of course, nothing prevents us from accelerating every part of an arbitrarily long rod, all in the same direction, in unison, but this sort of acceleration does not maintain Born rigidity. The instantaneous rest length of the rod increases, i.e., the rod is stretched."

Regards, --D.H (talk) 10:21, 9 October 2013 (UTC)

No, I think Martin Hogbin is on the right track ! His statement at the start of his last paragraph is absolutely correct !!

Martin Hogbin wrote:

"In fact whether the rope breaks or not depends on whether we have identical rockets (in which case it does not)..."

Reminder -

The stipulation in the original problem by both Dewan & Beran and by J.S.Bell is simply that the rockets (or spaceships) are identical in construction and have identical pre-programmed acceleration (i.e. no in-flight adjustment !). Therefore the two rockets are exactly equivalent to launching just one rocket twice from two different positions a distance L apart in the direction of travel, and considering that the entire (x,t) trajectory profile is simply displaced by a distance L.

Any other inertial frame from which L appears to be shorter or longer does not affect the physical distance between them and is purely the effect of changing coordinates, especially in this case changing to obliquely oriented coordinates.

Note that the x-axis can be considered (as it customarily is) as being horizontal, so that the rockets travel horizontally close to the (extended) launch platform. This means that throughout their travel the rockets pass closely over any arrangement of clocks and/or marker posts that can be envisaged downrange of the launch position in the pre-launch frame.

Thus at any time during and most especially after acceleration, the time taken according to either launch frame clocks or on-board clocks to reach any chosen x-position, can be compared. Because the rockets and rocket trajectories are identical, it follows immediately that either rocket reaches the same x-distance from its own launch position in the same time interval by either launch frame clocks or by on-board clocks. (The time by on-board clocks being less due to time dilation.)

Hence by both launch clocks and on-board clocks the rockets reach the same distance they started from in the same time interval, which means they remain exactly the same physical distance apart as they were at launch !

So where does the (erroneous) impression that they 'move apart' come from ? Almost always, as in the unreliable references listed by D.H., it comes from confusing coordinate distance with 'proper', or physical distance. In the 2nd. diagram in the article, many people think that the dotted line A'----B" is the comoving 'proper' distance between the rockets - but it isn't ! The rockets are at A' and B' so the line A'----B" is merely the comoving coordinate distance between the trajectories i.e. from the rocket at A' to the future trajectory of B' at B".

It is clear that perpendicular to the dotted 'equal time' line A"----B", the rocket B' is retarded by a time interval in the comoving coordinates. When this is taken into account the 'proper' physical distance Δs between the rockets can be calculated by the standard definition: Δs² = Δx²+Δy²+Δz² - (cΔt)² and when this is done the result is again L as one would expect. Desiderata9 (talk) 18:14, 9 October 2013 (UTC)

Thanks for the refs DH. Let me have a read and come back to you. Martin Hogbin (talk) 23:13, 9 October 2013 (UTC)

Do we (and the sources) agree on this?

Martin Hogbin (talk) 08:13, 10 October 2013 (UTC)

Yes, Martin, at least in most sources published in peer-reviewed journals such as AJP or EJP as mentioned above and in the article (the article already cites about 20 examples of them, much of them in the last decade), as well as the PhysicsFAQ. The point where one finds disagreement lies in the question whether this result has something to do with the "reality" of "physicality" of length contraction, or not (Petkov, Franklin). But even those physicists agree that the rest length will increase. --D.H (talk) 09:44, 10 October 2013 (UTC)

I will come to that point soon. At the moment I amtrying to find something that we can all agree on. Martin Hogbin (talk) 09:56, 10 October 2013 (UTC)

No, I disagree (as do many other physicists), they will stay a fixed distance apart anyway if the rockets are identical etc. - Why do you think that the rope will break ? Desiderata9 (talk) 08:24, 10 October 2013 (UTC)

Because, if the distance stays fixed in the original frame, then the proper length must increase in order for length contraction to do its work and keep the measured coordinate distance constant in that original frame, in which the system is moving faster and faster. If the proper length keeps increasing, the rope must —trivially— break. - DVdm (talk) 08:55, 10 October 2013 (UTC)

Below is an example of DVdn' argument for Desiderata9 .

Consider this case. At the start the leading spaceship tows a rope of length $L$ (as measured in the starting inertial frame S), which just reaches the rear spaceship which is exactly a distance $L$ (in frame S) behind the first ship but is not attached to it. The two spaceships start simultaneously (in frame S) and then are defined to both accelerate so maintain a distance $L$ between them as measured in frame S.

Some time later, when measured in frame S, the distance between the two spaceships is still $L$ (because we have defined the spaceships to move so that this is the case) but the rope will be measured to have contracted to a length$L/\gamma$. Do you agree so far? Martin Hogbin (talk) 09:11, 10 October 2013 (UTC)

I see where you are going, but in your scenario these are not identical spaceships. Dbfirs 09:17, 10 October 2013 (UTC)

I will come to that. Do you not agree that, in the above example, the rope will contract? Martin Hogbin (talk) 09:25, 10 October 2013 (UTC)

No, the rope will not really contract (of course) but I agree that it will be measured to be shorter. Apologies for butting into the argument. I don't want to confuse the flow, and I'm not expert in relativity, so I'll allow DVdm to continue. Dbfirs 09:40, 10 October 2013 (UTC)

I'll just turn the argument around. If the rope would not break, then the proper distance between the rockets would not increase. So, in the original frame, in which the system is moving faster and faster, the measured coordinate distance would decrease. But —by design— it does not decrease. So the rope will break. A trivial no-brainer, really. - DVdm (talk) 09:27, 10 October 2013 (UTC)

Yes, we agree but I would like to get the agreement of others on this page if possible. Note that in my example the rope will not break because it is not attached to the rear spaceship. It simply will not reach the rear spaceship because, in frame S it will be contracted but the distance between the sips will be the same (by definition).

So Dbfirs and Desiderata9, do you agree that the rope will be measured to have contracted to $L/\gamma$? Martin Hogbin (talk) 09:56, 10 October 2013 (UTC)

I don't think this is the place for such discussions - see wp:TPG. We should discuss the article here, not the subject. Perhaps you could do this on some user talk page? ^{(-: Not mine :-)}. Cheers - DVdm (talk) 10:05, 10 October 2013 (UTC)

I agree with DVdm that this is probably not the place for the argument. We should find good references for the differing views (and I'm still convinced that they are just different ways of looking at the situation) and report these in the article. ( ... and of course I agree with the apparent contraction, but that contracted length will be the exact distance between identical spaceships unless they are programmed to keep a constant distance apart as measured in the original reference frame. ) Dbfirs 10:28, 10 October 2013 (UTC)

Over twenty references have been given already in the article (see the section on "discussions and publications"), and in the peer reviewed literature lots of papers state that the string will break - the article reflects this circumstance. There is some disagreement whether this result is related to the "reality" of length contraction (see Petkov or Franklin), but both authors don't dispute the result that the string will break (also this is mentioned in the article). PS: I agree with DVdm (see wp:TPG), this is not the place for private discussions on this paradox, a real forum or newsgroup is the appropriate place. Or one should write a paper and send it to peer review, when it is accepted we can refer to it in the article. --D.H (talk) 10:59, 10 October 2013 (UTC)

This is the correct place for discussion on how to improve this article. At the moment, partly due to my own recent comment, the article does not clearly state the full paradox or give a clear exposition of the generally accepted resolution.

I am happy to leave the philosophical (and in my opinion meaningless) question of the "reality" of length contraction (as discussed Petkov or Franklin) as it is but I would like to improve the article.

I am happy to take the discussion with Dbfirs and Desiderata9, who seem to disagree with generally accepted physics to my talk page (iwill copy the above discussion there for those interested). There are issues that should be discussed here concerning the best way to present the paradox and its resolution as described in reliable sources.

We are writing an encyclopedia not a literature review so, whilst everything we say must be supported by reliable sources, we no not have to present the information in the exact words of the sources so long as there disagreement over what the sources are saying.

Can we now move on to presenting and resolving the paradox in the article

Apart from, Dbfirs and Desiderata9, we seem to agree that if the two rockets are defined in the problem setup to move so as to maintain a fixed distance apart in the original frame S then the rope will break. This is very simple physics, as DVdm points out.

Specifying the problem this way though (as we now do after DH changed the text at my suggestion) does not properly present the full paradox. We need to consider what would happen in the case of two identical rockets (we can for simplicity take it that both rockets have identical and constant proper accelerations). I said above, "Two identical spaceships would have the same proper acceleration and would have the same velocity all of the time in a comoving inertial frame". AS DH pointed out, with abundant references, this is incorrect. I am sure that I knew that once when I looked at this page some time ago but I this time made the mistake if assuming that the relativity of simultaneity would mean that the two rokets would not be in step in frame S. The result though may be surprising to many people and it forms an essential part of the paradox. I shall wait for comments from others before suggesting any changes to the article. Martin Hogbin (talk) 12:10, 10 October 2013 (UTC)

Thanks, you clearly understand the paradox and its solution (in agreement with the sources provided above), and it's indeed simple physics. Please improve the formulations in the article if you can state the paradox and its solution more clearly. --D.H (talk) 12:25, 10 October 2013 (UTC)

(edit conflict)x2 I wasn't actually disagreeing with the (now clarified) statement of the paradox, but I was supporting Desiderata9's argument about pre-programmed identical accelerations (measured in their own frames). I can see five different sets of instructions for the pilots: 1) Follow the commands from base station and adjust accelerations so that base-station measures the separation to be constant (and the string will break, as in the basic paradox); 2) Follow the acceleration instructions given before leaving (and identical for both craft); 3) The first pilot adjusts his acceleration so that his measured distance ahead of the second ship remains constant in his reference frame; 4) The second pilot adjusts her acceleration so that her ship remains a constant distance behind the lead craft in her (second ship) reference frame; 5) Follow the commands from base station (who are aware of Lorentz contraction) and aim to keep the rope taut without breaking. (They can also think ahead and issue instructions ahead of time so that communications are not a limitation). The more I think about the situation, the more complicated it gets. Will any of my five sets of instructions produce the same result? Dbfirs 12:46, 10 October 2013 (UTC)

Dbfirs, this is interesting but many think it is not appropriate to discuss this here as it is not directly about improving the article. I have copied your comment to my talk page where I will be happy to give you my thoughts on the subject. Martin Hogbin (talk) 13:23, 10 October 2013 (UTC)

Dbfirs, I appreciate that you accept that the string will break in scenario 1. Therefore I've responded to you on Martin's talk page. --D.H (talk) 14:42, 10 October 2013 (UTC)

DH my original comments, which started this section, were based on a misunderstanding that I had. The original paradox refers to two identical rockets and does not define them to maintain a constant separation on the frame S. We should therefore amend the article to give the paradox in this form rather than as I suggested.

For the resolution we first need to show that two identical rockets (say which maintain the same fixed proper acceleration) will also maintain the same coordinate acceleration at every given time in their starting frame. This may seem unintuitive to some (as it did for a while to me) but it is a fact clearly described by at least one of your quoted sources. It is actually very simple to show when viewed in the right way. For the first rocket, the coordinate acceleration at any time can be measured using synchronised clocks in the frame S. Using only the generally held assumption of translational invariance we can deduce that the second (and identical) rocket would have exactly the same acceleration vs coordinate time profile as the first when measured by the clocks of frame S. Thus in frame S both rockets will have the same coordinate acceleration at all times. I have not checked if this argument is given in any of the sources you have listed, perhaps you will know, but it seems very simple and bomb-proof to me. Maybe some sources considered it too obvious to mention but I think we do need to give an argument of some kind in the article. Martin Hogbin (talk) 13:43, 10 October 2013 (UTC)

It already follows directly from the initial condition, that ships with the same acceleration profile always have the same velocity only in the frame in which they are accelerating simultaneously. If there are persons who don't understand that ships of same velocity maintain their distance in this frame, then we can tell them nothing at all.... What is more confusing to the people, is the circumstance that the constant distance in S is indeed consistent with the length contraction formula. Of course the solution to this "problem" is the relation to the increasing rest length $L'=\gamma L$, and its consistency is mentioned at the end of the math section ($L_{contr.}=L'/\gamma =\gamma L/\gamma =L$), with sources such as Petkov (2009) and Styer (2007). --D.H (talk) 14:22, 10 October 2013 (UTC)

Yes, I know it follows but it is not necessarily obvious to everyone. Some of your references explicitly make this point. The paradox need to be covered as a whole from the original setup with two identical rockets. Some may find the first step (that two rockets with equal and constant proper acceleration will maintain equal distance in their starting frame, but not as you point out in any other) obvious but other may not. Some may consider the fact that the rope shrinks but the gap does not a no-brainer. This is a well know paradox so there must be something difficult to follow somewhere. I see no advantage in leaving out part (as given in reliable sources) of the resolution of the paradox just because some people think that it is obvious. Martin Hogbin (talk) 14:59, 10 October 2013 (UTC)

If you want to state those things (consistent with the sources), then do it. I most likely will agree with it since I know that you understand the paradox and the sources. --D.H (talk) 15:24, 10 October 2013 (UTC)

I have noticed that we currently have, ' If we suppose that at a prearranged time both rockets are simultaneously (with respect to S) fired up, then their velocities with respect to S are always equal throughout the remainder of the experiment', which is almost what I want. I will have a think about improvement and maybe make some changes later. Martin Hogbin (talk) 14:49, 11 October 2013 (UTC)

Can I point out a few things that show that this problem is still an unsettled issue and that the divergences in 'explanation' (as well as whether the string breaks or not) are very relevant for any 'presentation' of the article.

First of all, Dewan & Beran originally formulated the problem as equivalent to unmanned rockets with no "pilots" aboard to do anything to affect rocket motion. They refer only to passive "observers" aboard and speculate about how things "appear" to them. Also Dewan & Beran originally claimed that SR distinguishes between material lengths in motion and the empty space between two objects in identical motion, in the sense that the former contract but the latter does not.

Bell, while switching to "spaceships" & "thread" instead of "rockets" & "string", essentially followed the same argument, but hinted that he advocated Lorentz-FitzGerald 'aether' theory rather than SR for analysing such problems [a belief he makes more explicit elsewhere eg.in "The Ghost in the Atom" pp.48-50 (CUP 1986-91 & Canto 1993-04) edited by PCW Davies & JR Brown].

Since then, modern treatments of SR have emphasized that "length contraction" is a space-time phenomenon and not an effect on the object concerned, so would apply to spaces between moving objects as well as to the objects themselves.

As a result of this, those that choose to believe the string will break have focussed attention on the identical rockets or spaceships and, while acknowledging that the identical setup & identical pre-programmed acceleration will automatically mean they stay the same distance apart in the original launch frame (for obvious reasons of translational invariance & isotropy of space), nevertheless use a kind of "backward reasoning" to suppose that in the co-moving frame of the rockets/spaceships - they must have physically moved apart !

However, a Lorentz transformation between the original launch frame and the co-moving frame, followed by a calculation of the 'proper distance' in each case (according to the standard formula: Δs² = Δx² - (cΔt)² ) shows this not to be so. Desiderata9 (talk) 14:01, 10 October 2013 (UTC)

You have chosen not to respond to my very simple question, which I have now copied to my talk page. Please respond there. — Preceding unsigned comment added by Martin Hogbin (talk • contribs)

This attempted relativity physics paradox solution receives a grade of F

The reader is referred to E.M Purcell's Electricity and Magnetism, which is Volume II of the old Berkeley Physics course, used in college freshman physics courses in the 1970s. The text describes the Lorentz contraction effects which give rise to A CHANGE IN THE SPACING BETWEEN ELECTRICAL CHARGES in two current carrying wires, demonstrating that the force we call magnetism is consistent with the Special Theory of Relativity as it applies to moving electric charges.

The scenario is the same as in "Bell's Paradox", except that instead of a length of tether being contracted, we have spaces between electric charges (which changes the charge densities, depending on the frame of reference used.

E.M. Purcell is a Nobel Laureate who, among other things, developed Magnetic Resonance Imaging technology for medical diagnostic applications. Danshawen (talk) 22:25, 29 April 2014 (UTC)danshawen

Does Purcell mention this connection? Paradoctor (talk) 23:58, 29 April 2014 (UTC)

Danshawen, the case that you describe is, in some ways, the inverse of the spaceship paradox. In the spaceship paradox, the distance between the two spaceships, as measured in the starting frame, remains constant. The contraction of the rope is the equivalent of the change in spacing between the electrical charges. Martin Hogbin (talk) 08:55, 30 April 2014 (UTC)

A pity this whole article is misconceived & incorrect

This discussion has been closed per talk page guidelines. Please do not modify it.

What a shame that readers are being misled by the sort of nonsense perpetuated by this article ! The question of whether the string breaks or not is easily settled under either of the two possible paradigms - Lorentz/Fitzgerald theory or Special Relativity. Under the Lorentz-Fitzgerald theory of absolute motion it is certainly arguable that the string would break due to a genuine physical contraction arising from motion with respect to an absolute stationary frame. However, this is definitely not the conclusion if one tries to adopt the rather more dubious paradigm of Special Relativity ! This is because in Special Relativity all inertial frames are perfectly equivalent, from which it follows rigorously that for two such frames A & B, any contraction of an object in B, observed from A would necessarily mean there would be an identical contraction of an object in B, observed from A ! This reciprocity is an unavoidable and essential feature of SR and means quite unequivocally that the observed "contractions" are all merely "apparent" and not physically real. They are nothing more than apparent artifacts of the measurement process where "relativity of simultaneity" interferes so as to make locating end points of a measured moving length non-simultaneous in the moving object's frame, thus making it "appear" shorter. The very use of the terms describing 'from this frame' or 'from that frame' as used in the article, are a clear acknowledgement of the apparent nature of the effects. (Otherwise one runs smack into fatal contradictions of the A<B whilst B<A type.) Consequently, according to Special Relativity, there would be no reason at all for the string to snap, and it would not do so ! — Preceding unsigned comment added by 146.200.47.246 (talk) 11:11, 14 February 2015 (UTC) 146.200.47.246 Articles in Wikipedia should explain subjects acccording to mainstream science and as supported to reliable sources. If you cannot supply a reliable source to backup your personal opinion then it has no place here. That is why your comments have been repeatedly deleted. You are free to register and have more general discussions on your talk page with anyone willing to participate but this page is strictly for improving this article based on mainstream science and what is said in reliable sources. (Please feel free to delete this reply after 146.200.47.246 has had a chance to read it). Martin Hogbin (talk) 09:42, 15 February 2015 (UTC) For a start, Mr.Hogbin, this topic is not in any sense a part of what you like to call "mainstream science". For instance, of all the many hundreds of textbooks published over the years on Special Relativity, you'll be hard pushed to find more than 2 or 3 that even give it a mention ! Secondly, the article itself refers to Petkov and Franklin - Petkov denying string breaking in a published Springer-Verlag textbook and later elsewhere at least denying physical reality of contraction in much the same way I am doing. These viewpoints are merely mentioned in the article and I see nothing wrong in elaborating some reasoning behind them in the talk page ! (An additional bias is that while Dewan and Beran's view is presented at great length, Nawrocki's rebuttal of their analysis at the time is denied any explanation or consideration.) Thirdly, the lack of any "mainstream" support for the view as presented in the article is further evidenced by the fact that Bell was flatly contradicted by the whole of the CERN theory division - a formidable body of eminent physicists, both theoretical and experimental, most of whom would have more direct involvement in relativity applications than Bell himself ! [Again, the article further alludes to a similar situation in Japan, where Matsuda and Kinoshita's article was met with a barrage of criticism and contradiction from Japanese physicists, also better qualified than Matsuda and Kinoshita who were at the Earth and Planetary Sciences at Kobe and the Japan Meteorological Agency respectively.] Fourthly, in Bell's article he makes it clear that he is an advocate of Lorentz-Fitzgerald theory which he prefers to Einstein's Special Relativity, and is arguing specifically from the Lorentz-Fitzgerald theory point of view. If you have any doubt about this, I recommend you refer to the interview chapter with Bell himself published in "The Ghost in the Atom" by P.C.W.Davies and J.R. Brown, where Bell explicitly denies the validity of Einstein's Special Relativity in favor of Lorentz-Fitzgerald theory !! So the suggestion that Bell's view is "mainstream" is far from the truth, and the alternative view that seems to be advocated by a majority of physicists such as those contradicting Bell or Matsuda and Kinoshita, is one not sufficiently represented in the article and which I am merely trying to rectify by airing it in the talk pages. I do not see anything inappropriate in doing so !! — Preceding unsigned comment added by 146.200.47.246 (talk) 09:03, 16 February 2015 (UTC) Why then do you not cite a reasonably recent reliable source which supports what you say. Martin Hogbin (talk) 11:14, 16 February 2015 (UTC) Don't be ridiculous !! I am using mostly some of the same sources as are used by the article itself, and are therefore equally legitimate. In addition I referred to "The Ghost in the Atom" by P.C.W.Davies & H.R.Brown (Prof.Davies being an eminent physicist and well established author of popular and semi-popular books on modern physics), which was published first by Cambridge University Press in 1986 to 1991 and subsequently by Canto in 1993-4. [Note that Bell died in 1990 and his theorem has been proven with even more exquisite precision since, thus more accurately representing his views and position regarding Lorentz-Fitzgerald vs Special Relativity in regard to the article topic is certainly relevant and well worth pointing out. You are showing a lamentable indulgence in personal bias ! See User_talk:146.200.47.246#Bell.27s_Spaceship_Paradox Martin Hogbin (talk) 16:31, 18 February 2015 (UTC) Moved to bottom. Final warning for talk page disruption at User talk:146.200.47.246. - DVdm (talk) 10:03, 15 February 2015 (UTC)

Clocks Within Each Ship

I think that the fact that the clocks in the two ships appear synchronized to the initial observer in S distracts us and makes us think of the situation in non-relativistic terms. In general, most SR paradoxes can be eased by remembering the relativity of simultaneity. Let's say that the 2 spaceships have clocks at their centers, and the observer in S finds them to be synchronized throughout. What jolts us back into an SR view of the situation might be to point out that for that observer in S, a clock in the back of each ship appears to be set later than the clock in the front of that same ship. The "sameness" of the clocks in the two ships now appears much more artificial and "set up." MistySpock (talk) 00:06, 22 March 2015 (UTC)

The above comment is incorrect. There are two errors, one being more an unspecified assumption.

Firstly, if any extra clocks in the rear or front of the spaceships were also synchronized before launch in the same way as any 'main' clocks, then from the point of view of S, they would of course remain synchronized with the main clocks and with each other during flight, just as the main clocks in each ship remain synchronized with each other, provided they were left undisturbed.

However, if after acceleration & having acheived inertial flight, the clocks in front, middle & rear of either ship are re-synchronized by those aboard, some slight adjustment will be found necessary to bring the front & rear clocks back into synchrony with the main clock in the center. Only after this procedure will an observer in S (where S is the original 'stationary' frame) find that the front & rear clocks of each ship are out of whack with the middle clock.

Now it turns out that the adjustment is the opposite of that stated - namely that in order to synchronize the three clocks aboard each ship, the rear clock will need to be advanced slightly, and the front clock retarded slightly, to bring them into synchrony with the middle clock.

Thus, from the point of view of S, after on board re-synchronisation the clock in the back of either spaceship will be set earlier than the clock in the middle which itself will be set earlier than the clock in the front.

[ Incidentally, it is precisely this re-synchronization that causes a ship observer to measure lengths in the original launch frame S to appear to be contracted. Obviously no lengths in S actually contract because S remains stationary throughout. But the shift in a moving observer's clock synchronization means that fixing the end-points of a length in S 'simultaneously' from the moving observer's point of view will yield an apparently contracted value.

The stationary S observer will rightly say that the end of a length in S towards the rear of the ship was 'marked' by the moving observer slightly before the end towards the front of the ship, thus leading to the two marked end-points being closer together for the ship observer than they actually are in S.] — Preceding unsigned comment added by 87.114.12.87 (talk) 12:52, 27 March 2015 (UTC)

"Distinguished" as a terminus technicus

Bell reported that he encountered much skepticism from "a distinguished experimentalist" when he presented the paradox.

Was the experimentalist canonical? Meaning, was he introduced abtrarily or was he defined as part of the structure? If not, he probably introduced a bias. 89.217.6.172 (talk) 13:22, 29 April 2015 (UTC)

New primary reference

There is a new primary reference on this topic - it is a relativity textbook published by Springer in April 2017. The book was written by a former collaborator of John Bell and it contains a whole chapter on Bell's spaceship paradox. Before you ask, I have a personal connection to the author - prof. Rafelski (he is my research adviser), but in my opinion this reference should be cited here. I tried to add following paragraph to the "Discussions and publications" section of this article, but it was taken down, so I would like to open it for consideration of other contributors to this article:

A contemporary discussion which arose from the conversations with Bell and which emphasizes the importance of the physical reality of the Lorentz FitzGerald body contraction can be found in the relativity textbook by Rafelski (2017). In many examples Rafelski points out that the body contraction is consistent with relativistic (Lorentz) coordinate transformations. This consistency depends on specific measurement prescription. The separation between end beacons of a string measured at equal observer time reproduces the body contraction result. Therefore the Bell's spaceships paradox can be explained in terms of either gentle acceleration or a Lorentz transformation. In either case the seperation between rockets will be greater than the length of the string except for the original rest frame where they were set to be equal. — Preceding unsigned comment added by Andune88 (talk • contribs) 15:37, 20 April 2017 (UTC)

Please put new talk page messages at the bottom of talk pages and sign your messages with four tildes (~~~~). Thanks.

I have moved the comment to the bottom and signed it for you. Note that I've also added a local talk page reflist template and formatted the refs for repetition. This might be handy if you end up adding the text in the article.

Note to other contributors: see also User talk:DVdm#Bell's rockets. - DVdm (talk) 16:33, 20 April 2017 (UTC)

@Andune88: It's a textbook by the proponent of this argument, making it a primary source. In order to judge whether or not this argument has made inroads into the professional physics community, secondary sources are required. Also the paragraph is given WP:UNDUE weight by placing it in the lede of the article, since there's no evidence it is widely accepted. Kleuske (talk) 08:50, 21 April 2017 (UTC)

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Breaking due to length contraction?

I'm having a hard time understanding why the thread would break due to being length contracted. The thread begins with speed = 0 and is forced to gain speed as the frontmost ship accelerates. Length contraction at low speeds, is known to be negligible, so provided the two ships accelerate at exactly the same speed, unless the thread's ability to withstand stretching is lowered to ridiculous levels, it should be fine. By the time length contraction kicks in in a measurable way, the thread's speed will be matched to that of the ships, so there would be no length contraction relative to them. What am I missing here? --uKER (talk) 19:04, 18 June 2018 (UTC)

Not really the place to discuss this here (per wp:TPG). Best place to ask is our wp:Reference desk/Science. Good luck there . - DVdm (talk) 19:16, 18 June 2018 (UTC)

Nah, I could have easily asked about it on /r/Physics. I did it here just under the impression that the explanation here is a bit flimsy, but never mind. Cheers. --uKER (talk) 19:41, 18 June 2018 (UTC)

Proper acceleration

I've rewrote and expanded the section on constant proper acceleration recently added in order to bring it into accordance with the other wiki articles, and added some new images for both the scenario using immediate acceleration, as well as some to describe the Rindler horizons of Born rigid accelerations and equal proper accelerations. --D.H (talk) 09:34, 18 July 2018 (UTC)

After a user wanted to remove some of the older section, he now wants to completely remove the old sections which stayed here for years. He also replaced my variant directly discussing rigid frames and Rindler frames as per the sources with his own version (actually, his version gives some correct information, but it contain no source directly discussing the paradox, and he included his own unsourced remarks and conclusions, see WP:OR). Are there other opinions? --D.H (talk) 07:11, 19 July 2018 (UTC)

Incoherent writing

Lost in all of the argument over the years about this subject is a basic error in the writing of this article: The A, B, and C labels for things change halfway down the article with no notice to the reader. Jonathan de Boyne Pollard (talk) 05:52, 2 October 2021 (UTC)

kinetic energy of string?

I'm not a physicist. But my understanding is that the kinetic energy of the string would cause a length contraction of space. Perhaps that could mean that the distance through the string between the two ships is less than it is outside the string? Unhandyandy (talk) 16:28, 21 June 2023 (UTC)