Talk:Length contraction

LT given incorrectly?

Hm, looks to me as if the Lorentz transformation states $x'=\gamma \cdot (x-vt)$ with $\gamma ={\frac {1}{\sqrt {1-{\frac {v^{2}}{c^{2}}}}}}.$

So setting t = 0 yields $x'={\frac {x}{\sqrt {1-{\frac {v^{2}}{c^{2}}}}}}$, which would describe quite the opposite effect.

What's wrong?

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You have to set t' = 0, not t.

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The equation above is correct. The moving observer measures the length of a rod as the rest length $l_{0}$ (all measuring rods are comtracted) so $x^{\prime }=l_{0}$. The rest frame measures the length of the rod $x-vt$ as contracted. Hence $x-vt<l_{o}$. Fot $t=0$ and $x<x^{\prime }$.

I don't know since when these comments are sitting here and who wrote them, but they are utterly faulty.

In the frame in which the rod is moving, the length is measured by subtracting the distances to the end points when measured simultaneously. In the rest frame of the rod its length is measured by subtracting the distances to its end points at arbitrary times. When we decide to use the equation $x'=\gamma (x-vt)\,$ we assume that one end point is measured at event (x,t) = (x',t') = (0,0), and another endpoint at some event (x,t) for which the x'-coordinate is given by this transformation equation. Since the variable t' is not present in the equation, it is arbitrary, and the equation therefore establishes the (x',t')-frame as the rest frame of the rod. The (x,t)-frame is the frame in which the rod is moving. This also establishes x' as the proper length and x as the coordinate length.

So, to make sure that in the (x,t)-frame the distances to the endpoints are measured simultaneously, we have to put t = 0 in the equation, and get $x'=\gamma x\,$ , giving $x=x'{\sqrt {1-v^{2}/c^{2}}}<x'\,$ , or in coordinate free language: coordinate length < proper length. DVdm 14:01, 20 January 2007 (UTC)

New section

Was imported by me from Ehrenfest paradox during my second rewrite of that article. In that and other contexts (e.g. Thomas precession), two spatial dimensions are essential, hence discussion of E^1,2 rather than E^1,1.

I realize the present exposition has shortcomings and will eventually try to address these, e.g. by writing a background article explaining more fully the three trigonometries, their relation with Kleinian geometry and Cayley's projective metric.---CH 15:05, 5 June 2006 (UTC)

Merge?

The articles called Lorentz-FitzGerald contraction hypothesis and Length contraction are both rather short and partly discuss the same subject. As the title "Length contraction" is a bit ambiguous, I propose to merge the articles into a new article called Lorentz contraction. Harald88 14:46, 11 July 2006 (UTC)

I second that motion, 14 Nov 2006

• • Comment: This message is unsigned. Please sign all messages.

• This is a bad idea. Everything should be merged into Length contraction as it is simple, more popular, and less prone to argument. Moving the page to one that does not have a history and credits Lorentz but does not credit FitzGerald's contribution will not work out. I am going ahead and merging it.--JEF 02:31, 20 January 2007 (UTC)

Talk:Lorentz–FitzGerald contraction hypothesis

There is one phrase that I left but think is erroneous:

"Lorentz was not particularly satisfied with his hypothesis because he realized that it was ad hoc and not testable by experiment."

Anyone has a direct reference? I think to have read the contrary, which is consistent with fact that it was *not* ad-hoc, as explained. Thus I will take it out if after some time nobody proves its correctness; or if I find the source I read, I'll adppt it accordingly and include the ref. Harald88 06:56, 14 October 2005 (UTC)

OK I found it: http://www.mpiwg-berlin.mpg.de/litserv/diss/janssen_diss/Chapter3.pdf - in particular p.41. I'll rewrite that part accordingly to the here presented facts. Harald88 18:47, 17 October 2005 (UTC)

It IS "ad-hoc". Please read the final resolution given by the Trouton-Rankine experiment that proves that, contrary to what Lorentz belived, the contraction is "aparent" , not "real". The TR experiment was the final nail in the coffin for the FitzGerald contraction.

"Ad-hoc" is nonsence, as explained in the above reference as well as in this article. And I have read Trouton-Rankine; with others I tried to explain the logical flaw in your reasoning, but you didn't pay attention. Here is another try: please formulate the Kennedy-Thorndike experiment as seen from the solar frame, accounting for the fact that time dilation is as "real" as the Ives-Stillwell experiment demonstrated. Harald88 17:02, 8 January 2006 (UTC)

Harald, looks like you are mixing up Lorentz's theory with FitzGerald's. I explained the error in your thinking:

1. Lorentz (at least in the current acception) is "subjective" (i.e. it is an artifact of judging the experiment from a frame moving wrt to the frame of the experiment)

2. FitzGerald is "objective", i.e. the contraction really "happens" (or at least, this is what FitzGerald thought) within the frame of the experiment. Interestingly enough, Lorentz thought the same thing, at least until he accepted Einstein's explanation. Your post is conveniently missing this "detail" leaving the reader with the wrong impression that Lorentz died clinging to his theory.

Now, since you asked, here is BOTH MM and KT explanation as viewed from the Sun:

http://www.wbabin.net/sfarti/sfarti12.pdf

Hope that this will clear any lingering confusion.

PS: it would be good if you made the logical separation between the FitzGerald and the Lorentz contraction. they are not the same thing.

PPS: You are also somewhat confused about Ives-Stilwell. The time dilation is real , not "real" (as in "subjective"). For an explanation, please check here:

http://www.wbabin.net/sfarti/sfarti17.pdf

If you don't mind me asking, are you a relativist or an "aetherist"? Reading your posts I am having a hard time figuring out.

[all the above apparently written by no-name, 12.36.122.2]

12.36.122.2, to me it is clear that you confuse a single hypothesis with a complete theory. Waht is, according to you, "subjective" about the "real" expansion of an object? The impression that Lorentz saw no reason to replace his metaphyisics for that of Einstein the general opinion as supported by his writings.

from your answer on my question about your explanation with an internet article, does that mean that you are the author? I think that you mistakingly gave the wrong link, as I could not find a description of the KT experiment in the light of Ives-Stillwell.

About "real", I put it like that, as it has different meanings for different people. Einstein's "real" was apparently more like "reality" as in the film Matrix. What Lorentz at first overlooked but later understood from Poincare and Einstein is that --assuming that the theory is correct-- for consistency reasons, length contraction and time dilation must be equally real. That was also an important argument of Ives.

And for your question: some die-hard Etherists call me "Relativist", while some die-hard Relativists call me "Etherist". Instead, I am a technical physicist. True scientists are against dogmas. And may I ask, what are you? Harald88 22:38, 9 January 2006 (UTC)

"as I could not find a description of the KT experiment in the light of Ives-Stillwell." What? This question seems to make no sense at all.You must mean accounting for time dilation. It is all there, read the MM+KT paper. Anyway, what I gave you are my own explanations of KT and IS. I am a die-hard relativist (to use your terms) and I see no reason in the ambiguity that is perpetrated by "etherists" (we can explain this experiment if, and we can explain that experiment if..., and Lorentzian relativity would be perfectly equivalent to STR if ....)

"The impression that Lorentz saw no reason to replace his metaphyisics for that of Einstein the general opinion as supported by his writings.". Yes, right. Check this out:

"If I had to write the last chapter now, I should certainly have given a more prominent place to Einstein's theory of relativity (p 189) by which the theory of electromagnetic phenomena in moving system's 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 only had to be considered as the true time and that my local t' must be regarded as no more than an auxiliary mathematical quantity." in "The Theory of Electrons," by H. A. Lorentz second edition (1915). Page 197 in the original 1915 edition, page 321 in Dover Publications 1952 reprint.Ati3414 19:08, 2 February 2006 (UTC)

[who wrote this last comment? I get tired of unsigned comments, and it's against the rules... Harald88 00:25, 10 January 2006 (UTC)]

It is clear who wrote it, it is a continuation of my posting (ati3414).

Obviously I am part of neither camp. The fact is that according to KT as well as mainstream literature, the Lorentz contraction and time dilation are a pair, and this combined Lorentz contraction and time dilation was assumed to have been demonstrated (thanks for the above citation, that was what I meant further above with "later understood" - concerning physics). Thus whatever you may think, it's up to you to show that your opinion can be found in respectable literature, and that it is notable. Harald88 00:25, 10 January 2006 (UTC)

"The fact is that according to KT as well as mainstream literature, the Lorentz contraction and time dilation are a pair, and this combined Lorentz contraction and time dilation was assumed to have been demonstrated"

Yes, the time dilation and length contraction of STR form a pair in the explanation of the KT experiment. This does not mean that they always form a pair (look at the MM experiment, time dilation is not needed in explaining the experiment). Though that they are both part of STR, as I explained to you numerous times time dilation is objective (as per IS experiment) while length contraction is subjective (as demonstrated by TR experiment). I don't know exactly how to sign this, so I will add my name: ati3414

You are here turning a historical account into a philosophical debate, but without referring to this debate. The article already cites Lorentz' final opinion; a citation of a different opinion by a notable scientist could be interesting. Harald88 08:08, 10 January 2006 (UTC)

"The chief cause of my FAILURE was my CLINGING to the idea that the variable t only had to be considered as the true time and that my local t' must be regarded as no more than an auxiliary mathematical quantity." by....H.A.Lorentz

Harald, I gave you Lorentz CONCEDING speech,IN PRINT, from HIS OWN BOOK, what else do you need? ati3414

Hi Ati, I am not the only editor here; but I'm the only one who bothers to reply to your personal interpretations, which differ from the common one. I already told you that I refered to that passage in my reply to you. That still doesn't ring a bell? Lorentz had inconsistenly regarded time dilation as somehow more [oops, I meant LESS] real than Lorentz contraction. Now you try to suggest that a similar (only, inversed) inconsistency would be the general opinion. To the cvontrary: KT would have concluded the absence of time dilation if they had assumed that Lorentz contraction does not occur, and Ives would not have regarded his positive time dilation result as evidence for the reality of Lorentz contraction. Harald88 19:07, 10 January 2006 (UTC)

Harald, the concession I am referring to is that Lorentz admits SR's superiority. The reference to time dilation is incidental, ok?

Harald, I am having a hard time following your logic, especially when you put words in my mouth. I am a "mathematical formulas" man , so I let my math do the speaking for me. As to what I believe to be the truth, I found it encapsulated on another wiki posting, here:

http://en.wikipedia.org/wiki/Lorentz_ether_theory

This is the view I ascribe to. OK? ati3414

Ati, I think that that article describes it pretty well, and your above citation may be a useful complement to Lorentz ether theory. Note that, as mentioned, no "LET" was known at the time: it is revisionist history. Similarly, we could invent a "MET" for Maxwell Ether Theory, and state that it has been replaced by Electrodynamics. Also, the LET article isn't about the math, and thus it shouldn't speak according to you. Your recent argument is definitely not about the formulas but about your personal metaphysics.

I reformulated your words in the way that makes sense to me, to let you know what I received. Again, in my words: it is very much inconsistent, in the same way as Lorentz had been inconsistent, to propose that according to SRT t and l in the same equation would not have similar reality for the same physical description.

I have nothing else to add. I repeat: if you can find a respectable article's opinion to your taste, you may cite that and see if others agree that it improves the article (applicable, notable, balanced). Harald88 22:13, 10 January 2006 (UTC)

OK : applicable,notable,balanced and reputable:

http://www2.slac.stanford.edu/vvc/theory/relativity.html

If you look at the caption at the bottom, under Length Contraction it is clear that these people do not think in terms of rods shortening (actually every place on the web gives a resounding NO to this question for SR and YES for LET, you know many of these places since you've posted your ideas there). They think in terms of particle flightpath shortening as a reciprocal to time dilation (particle lifetime lengthening). So, from the perspective of Trouton-Rankine AND from the perspective of SR , rods DO NOT GET SHORTER, and ATOMS DO NOT BECOME OBLATE (Cleonis, are you reading this?). The internal clock of the particles does run slower, though therefore the particle lifetime gets longer. I know that you, like any physicist likes symmetries but this is a subtle case, there is symmetry but it is not perfect.

Ati:

- you disagree with Einstein (see my quote on the other talk page where he argues that atoms flatten)

Really? can you give me the link?

Look at my replies to you of yesterday or the day before...

Ah, I found it.

BTW, according to Einstein, For v=c all moving objects --VIEWED from the "stationary" system-- shrivel up into plane figures.

VIEWED is key. As in "aparent". I have said it numerous times that I agree with SR, there is an "apparent" length contraction. Now, how did you divine from the above that "see my quote on the other talk page where he argues that atoms flatten"? He certainly is saying something DIFFERENT.

Now, the funny thing is that, had he lived a few more years , he could have read Terrell's paper that says that VIEWED from another reference frame an object does not appear only forshortened but also rotated. The LET proponents haven't caught on on this one yet to incorporate it. So SR and LET might show some differences after all :-)

Maybe I'll write an entry on Terrell's paper :-) ati3414

- you suggest an asymmetry that I never found in literature (you do claim that time dilation is real, but that length contraction is an artifact, right?); thus your metaphysics is your personal POV, and apparently original research.

He,he,he you've been told about this by many others in many other places where you posted on the web. But, no, you wouldn't accept it. To refresh your memory:

"Does the length of the object really change? According to SR, No. According to ether theory, Yes. John Anderson "

Come on , Harald, you are not impartial, you are clearly a LET epigone, hoping that maybe one day, when SR/GR continues to falter in the difficult and not yet attained quest of unification with QM, LET will spring back to life (see your earlier posting on this). So, keep LET in a refrigerated state awaiting the opportunity to supplant SR/GR.

Ati, there is a never ending debate in mainstream literature about relativistic effects being "real" or not, and what "real" means. But sorry to break the news to you, your asymmetrical approach is entirely yours -- and thus not notable for Wikipedia. Harald88 23:34, 11 January 2006 (UTC)

- as many people, you confuse the principle theory that Einstein labeled "special relativity" with Einstein's interpretation of it; and you confuse Einstein's interpretation of that theory with that of others.

Well, it is not the first time you are resorting to personal attacks when you don't get your way. You started this way, when I first posted, you are ending this way (see this last posting). So, what's wrong with the Stanford Linear Accelerator link I gave you?

That's fruitless: it's you who attemps to make this a personal matter; I won't cooperate with turning this Wikipedia page into a boxing match. At first sight that link is not bad for its purpose: teaching the physics of special relativity.Harald88 23:34, 11 January 2006 (UTC)

On a different topic, have you ever wondered why M.Janssen spent hundreds of pages on the Trouton-Noble experiment just to conclude that SR gives a more ellegant and natural explanation than LET while he made not one mention of Trouton-Rankine? Not one page. Not one reference. Nothing. Regards from ati3414

It's a different experiment, involving different physics. Probably he deemed tit wise to leave that for someone else's thesis subject of another 200 pages. Maybe you want to try it? But I warn you, one page won't do! ;-)

Nope, not interested. It was me who suggested it first for other people. ati3414

I leave further comments to other editors. Good luck.

Harald88 23:34, 11 January 2006 (UTC)

Regards, Harald

I have a question for you, Harald:

Suppose that I have a spring . I look at the spring and then I decide to run very fast by it. Does the spring compress and if so, will it push an object next to it when I stop running? Ati3414 19:10, 2 February 2006 (UTC)

This may seem like a dumb posting, especially in the midst of all out philosophical war, but unequivocally sidestepping interpretational issues of the hypothesis itself, who want's to rename the effect, the "FitzGerald-Lorentz contraction hypothesis". I'm not aware of any physical institution that states any preference, it is just habit. The physical community has a shameful tendancy to forget the contributions of less successful physicists, and Lorentz himself always accredited the hypothesis to FitzGerald alone. So, let's give FitzGerald his due.

Ati3414, stealing Harald's question, I don't think the spring extends past it's equilibrium position in either frame (although that equilibrium distance will itself contract). Thus, no forces will be exerted from anyone's point of view ( I hope!).

Krea 20:41, 10 March 2006 (UTC)

I'm worried that the section on "A trigonometric effect?" may be badly sourced. Not to disparage Hughston, but the source listed for that section is co-authored by that author and does not discuss the issues listed in that section. Additionally, I'm not sure that the geometry of the transformations is really that modern and interpretation; it seems very basic geometry, but I'm not up on the specific history of that discussion. It would be nice to have a reference to the development of the geometry here if it is to presented as a "modern view". (Worryingly, the image in the section is similar to a figure in Minkowski's original paper on the subject.) BangPhys Feb 20, 2008 —Preceding comment was added at 18:41, 20 February 2008 (UTC)

Merge?

The articles called Lorentz-FitzGerald contraction hypothesis and Length contraction are both rather short and partly discuss the same subject. As the title "Length contraction" is a bit ambiguous, I propose to merge the articles into a new article called Lorentz contraction. Harald88 14:45, 11 July 2006 (UTC)

This is a good idea. --EMS | Talk 18:51, 15 August 2006 (UTC)

• This is a bad idea. Everything should be merged into Length contraction as it is simple, more popular, and less prone to argument. Moving the page to one that does not have a history and credits Lorentz but does not credit FitzGerald's contribution will not work out. I am going ahead and merging it.--JEF 02:29, 20 January 2007 (UTC)

I have suggested a merge for the article space contraction as well, since it is a synonym for Lorentz contraction. Tnxman307 (talk) 14:57, 11 December 2007 (UTC)

Space contraction is not really a synonym but in fact the contrary: if a ruler contracts, the measured space increases as illustrated by for example bell's spaceship paradox. Thus space contraction is really a misnomer. However, it may be useful to mention it inside the length contraction article, if the term is notable in the literature. Harald88 (talk) 15:52, 6 April 2008 (UTC)

First person plural tone

This article reads like a professor's lecture with two occurrences of the word "we" and its plural first person viewpoint. I feel it would better represent the subject if passive voice were used. I've tagged the article for inappropriate tone. Binksternet (talk) 17:40, 21 November 2008 (UTC)

The "object's length" , not "the object"

The sentence: "Note that in this equation it is assumed that the object is parallel with its line of movement." should be changed to "Note that in this equation it is assumed that the object's length is measured parallel with its line of movement."

I vote for leaving the tone of the article the same. One of the virtues of the Wikipedia is that it can emphasize being useful information as opposed to being dry and "authoritative" information. It's never going to be authoritative. The sponsors have grown very defensive, however. You even see the Wikipedia warning banners in mathematics articles when the authors give examples. How silly. —Preceding unsigned comment added by 4.240.141.41 (talk) 17:25, 27 February 2009 (UTC)

Length is not an appropriate term for all objects

Not all objects can be said to have 'length'. A sphere, for example, does not have length, because its dimensions are all equal and/or equitable. 'Length' is a term applied to everyday objects where one dimension is much bigger than the others. Thus I believe that a more universal term would be 'size' or c. Majopius (talk) 15:20, 29 March 2009 (UTC)

You are right about 'length' being a term applied to objects where one dimension is much bigger than the others. However, traditionally the object in question is rod-shaped and (silently) aligned with the direction of motion, so length is of course the only meaningful dimension. Your 'size' or 'distance' suggestions fail because they effectively hide the (implicit) direction of motion prerequisite. Tricky, but sticky <== double pun intended :-) DVdm (talk) 16:22, 29 March 2009 (UTC)

Why is the object in question a rod? If the terms "size" and "distance" do not work (I'm fine with them!), then maybe a better term would be "the dimension parallel to the direction of motion". If you meant that my suggestions don't work because they might mean ALL the dimensions, not only one, than this term clearly states ONE direction. Neither is length always parallel to the direction of motion - the object could be moving sideways. So I think that the term 'length' fails too. Majopius (talk) 03:41, 31 March 2009 (UTC)

"Why is the object in question a rod?" => Perhaps our great-grandfathers took a rod because it was a short word and because rods have only one interesting dimension, automatically implying direction of motion. But yes, perhaps they expected far too much goodwill from their audience. Maybe all the books should be rewritten and "length contraction" replaced with "dimension parallel to the direction of motion contraction", and then, a few years later we can finally change this article's name into dimension parallel to the direction of motion contraction. I'm sure we could find a suitable replacement for "time dilation" as well. DVdm (talk) 13:18, 31 March 2009 (UTC)

For me, the object of investigation is a ball. And for a sphere, length and height are the least appropriate terms.Majopius (talk) 03:11, 14 April 2009 (UTC)

I don't see any Length Contraction in the following ??

Consider two space ships A and B of same length instead of train in the following link. http://www.youtube.com/watch?v=wteiu...eature=related

Both A and B started their same computerized journey from stationary observer “Os” station but moving in opposite direction to each other in a closed loop. All clocks as shown below, used by respective observers are synchronized at Os station before their journey into their respective ship. After certain time A and B crosses each other at the crossing facility in a loop such that one is exactly above the other (front of upper ship is exactly above the rear of lower and rear of upper is exactly above the front of lower). Here is the detail of crossing facility (For simplicity imagine a parallel circuit diagram for crossing)

“A” leave the normal loop and move up grade, straight, down grade and then enter the normal loop from where“ B” left

“B” leave the normal loop from opposite direction but move down grade, straight, up grade and then enter the normal loop from where “A” left.

            End------------------------ship A---------------------------Front
           LSae, Mae, e, Cae, Oae _______________________f,Caf, Oaf, LSaf,Maf

           Mbf, LSbf, f, Cbf, Obf,________________________e,Cbe, Obe,Mbe, LSbe
          Front------------------------ship B---------------------------End                                  

Where e = end of ship, f = front of ship, Af = A front, Bf = B front, Ae = A end, Be = B end

Oae = Observer of A at its e, Oaf = Observer of A at its f, Obe = Observer of B at its e, Obf = Observer of B at its f.

LSae = Light Source at the bottom of A at its e (emit downward vertical flash), LSaf = Light Source at the bottom of A at its f (emit downward vertical flash), LSbe = Light Source at the top of B at its e (emit upward vertical flash), LSbf = Light Source at the top of B at its f (emit upward vertical flash).

Mae = Mirror at the bottom of A at its e which detect LSbf during line up of Bf/Ae, Maf = Mirror at the bottom of A at its f which detect LSbe during line up of Af/Be, Mbe = Mirror at the top of B at its e which detect LSaf during line up of Af/Bf, Mbf = Mirror at the top of B at its f which detect LSae during line up of Bf/Ae.

Cae = Clock of A used by Oae during line up of Ae/Bf, Caf = Clock of A used by Oaf during line up of Af/Be, Cbe = Clock of B used by Obe during line up of Be/Af, Cbf = Clock of B used by Obf during line up of Bf/Ae.

For Os, in elevation or top view

LSae is well above Mbf and Mae is well above LSbf, LSaf is well above Mbe and Maf is well above LSbe.

As for Os both A and B are equally longer therefore he would see both new flashes from the f and e of both ships at the same time. And also at the same time

Downward vertical flash of LSae is detected by Mbf and upward vertical flash of LSbf by Mae, Downward vertical flash of LSaf is detected by Mbe and upward vertical flash of LSbe by Maf.

Now consider the event from A frame of reference

For Oaf, the front light strike the Af/Be followed by Ae/Bf. This means Mbe is struck by downward vertical flash of LSaf and that Maf by upward vertical flash of LSbe Caf is paused by Oaf when Af even with Be but Since Oae is still waiting for Bf to be even with Ae, therefore Cae is not yet paused by Oae, and Downward vertical flash of LSae hasn’t yet touched B and or Mbf while Upward vertical flash of LSbf has touched A but not yet reach Mae and thus Oae is still waiting for the event to be occurred at Ae

Obf and Obe have an exactly symmetrical experience but sees flash Bf/Ae first followed by Be/Af

Here is the detail of event as seen from B frame of reference

For Obf, the front light strike the Bf/Ae followed by Be/Af. This means Mae is struck by upward vertical flash of LSbf and Mbf by downward vertical flash of LSae Cbf is paused by Obf when Bf even with Af but Since Obe is still waiting for Be to be even with Af, therefore Cbe is not yet paused by Obe and Upward vertical flash of LSbe hasn’t yet touched A and or Maf while Downward vertical flash of LSaf has touched B but not yet Mbe and thus Obe is still waiting for the event to occurred at Be

Later on both Oaf and Obf come back from their mission to Os station and starts claim for observing first front strike Both are right in their perspective frame of reference but still there is disagreement between two

Oaf claim that he has paused his Caf before Obf while Obf also claim that he has paused his Cbf before Obf

Now Os advises Oaf and Obf to compare their Caf and Cbf reading. Since Oaf is the witness for the Af even with Be ( For the front strike of Af and rear strike of Be) Obf is the witness for the Bf even with Ae (For the front strike of Bf and rear strike of Ae) So both Caf and Cbf should show same reading because they went through the same computerized journey and thus there should no length contraction

Here is the answer about those clocks from one of reputable physics forum. It's true that when lightning struck next to Af, A's clock at that location read -5, and when lightning struck next to Bf, B's clock there read -5, but since these are clocks from two different observers this does not mean the strikes were simultaneous in either frame--this is your crucial mistake, each observer only defines simultaneity using multiple clocks of his own at different locations”.

So here are my questions..

If each front observer deny the lining up of the front of the other ship with the end of his ship then how comes abovementioned mirrors detects all those vertical flashes from their respective opposite light sources??? OR

Event from A frame of reference

If Oae is still waiting for Bf to be even with Ae, then how come Mae was struck by upward vertical flash of LSbf and Mbf by downward vertical flash of LSaf from B frame of reference

Event from B frame of reference

If Obe is still waiting for Af to be even with Be then how come Mbe was struck by downward vertical flash of LSaf and Maf by upward vertical flash of LSbf from A frame of reference?? 96.52.178.55 (talk) 04:14, 12 May 2009 (UTC)khattak