> > "Martin Ouwehand" <see....@end.of.post.ch> wrote in message > > news:43313e74$1@epflnews.epfl.ch... > >> In article <1126626847.877636.161...@g43g2000cwa.googlegroups.com>, > >> "Juan R." <juanrgonzal...@canonicalscience.com> writes:
> >> Another example: "the Lorentz transformation replaces the real electron > >> in motion by an ideal electron at rest."
> It seems to me like a debate about words: Einstein also uses "ruhendes > System" (= system at rest) because of didactic reasons, and Poincaré used > ether because of didactic reasons and because he has known, that this is > allowed.
> >> It is definitely not the same as > >> Einstein's. For instance in his 1908 article (available from > >> http://www.soso.ch/wissen/hist/SRT/srt.htm -- BTW thank you Homo Lykos > >> for the link !),
> > BTW, also that german link reminds us of the fact that Poincare spoke > > about real clocks and not just about mathematical manipulations: > > "Im zweiten Büchlein findet man als Kapitel 2 wieder seine Arbeit von > > 1898 über die Zeitmessung, wo er das Konzept der Relativität der > > Gleichzeitigkeit erstmals deutlich formuliert hat"
> >> I understand from his arguments around pages 565-566 > >> that he uses the following transformation:
> >> x' = (x - v * t) / sqrt(1 - v^2/c^2) (Lorentz contraction) > >> t' = t - (v * x) / (c^2 - v^2) ("local time")
> >> (x', t') is what is actually measured by an observer in motion with > >> respect to the ether, (x, t) are the coordinates in the ether frame > >> (beware that in his formula for the local time, he expresses x in term of > >> x', resulting in a slightly different formula). With the help of this > >> transformation, he is able to explain the null result of the Michelson > >> experience: the time of travel of a light pulse along a given distance > >> doesn't depend on the direction. But the transformation rule for the > >> speed of light (last equation on page 566 -- BTW there is a misprint: t > >> should be replaced by tau) is:
> >> c' = c * sqrt(1 - v^2/c^2)
> Such a nonsense you don't find on page 566.
Indeed.
> My interpretation (for the present) of this (strange) page 566:
> 1. This paper is written in a popular manner (almost no equations and > no real proofs, he don't makes use of setting V = 1 as in his papers of > 1905)
> 2. His "popular proof" of Michelson/Morley seems to me with respect to his > own theory of 1905 incorrect.
Most likely (in general), that is due to a misunderstanding on your part. I'll wait with giving my opinion until I understand how he meant it.
> " Supposons que la différence entre le temps vrai et le temp local en un > point quelconque soit égale à l'abscisse de ce point multipliée par la > constante: e/(V sqrt(1-e^2)) "
> Poincaré gives no explanation for this (and speaks only of supposons(=we > suppose)) and I - at least in this moment - can't understand it.
> 3. If it is really only a (strange) error - as I believe now - it's not > possible to derive any conclusions.
> >> which doesn't respect the principle of relativity (by measuring the speed > >> of light in different frames, it's possible to tell which is moving > >> fastest whith respect to the ether.)
> > - I did not see the misprint (duration= t, apparent duration= tau), but > > the last AB on the copy certainly was AB'.
> No
Yes! He wrote that AB' was part of that equation. In the copy we only see AB in that equation. I'm quite sure that AB' isn't AB with a beautiful piece of dirt next to it at exactly the right spot. Thus the AB in the equation certainly was AB'.
> >> do you know of an earlier reference where > >> Poincaré actually mentions it *in words* and says something like "Hey ! > >> motion has an influence on the *rate* of clocks !" ?
> > I also don't remember having seen that he expressed that in words. > > Maybe Einstein was the first to verbally point out that the effect on > > clocks implies that "moving clocks" "go more slowly"?
> I think too, that Einsteins (popular) explanations of all these things were > clearer and more specific then the explanations of Poincaré; but from > Poincaré Einstein had first learned these more philosophical ideas about > space and time. Now I copy older citations of Poincaré in this context:
> The strong general statement of 1898 in La Mesure du Temps:
> " La simultanéité de deux événements, ou l'ordre de leur succession, > l'égalité de deux durées, doivent être définies de telle sorte que l`énoncé > des lois naturelles soit aussi simple que possible. "
> More specifically 1904 in St. Louis (Bull. des Sciences Mathématiques, > deuxième Série, tomé XXVIII):
> " .... Pour un observateur, entraîné lui-même dans une translation dont il > ne se doute pas, aucune vitesse apparente ne pourrait non plus dépasser > celle de la lumière; et ce serait là une contradiction, si l'on ne se > rappelait que cet observateur ne se servirait pas des mêmes horloges qu'un > observateur fixe, mais bien d'horloges marquant le "temps local". "
That's a nice one, but it doesn't show that he understood that this local time implies a different rate.
In article <4332845...@epflnews.epfl.ch>, I wrote:
] I understand from his arguments around pages 565-566 ] that he uses the following transformation: ] ] x' = (x - v * t) / sqrt(1 - v^2/c^2) (Lorentz contraction) ] t' = t - (v * x) / (c^2 - v^2) ("local time")
I made a mistake (it should be x-vt in the equation for t'), the full transformation between ether frame (unprimed [x, y, t]) and moving frame (primed [x', y', t']) is:
Let me show how this is consistent with what Poincaré says on pages 565-566 of the article http://www.soso.ch/wissen/hist/SRT/P-1908.pdf. He considers two events: A (emission of a light wave) and B (detection of the light on an arbitrary point of the wave front at some later time). Let the space-time coordinates of A and B in the ether frame be:
with ellipcity e = v/c and center [-vt * sqrt(1 - v^2/c^2), 0], corresponding to the picture on page 566.
Next I compute Poincaré's AB and AB':
AB = sqrt(x_B'^2 + y_B'^2) = t * (c - v * cos(a)) / sqrt(1 - v^2/c^2) AB' = x_B' = t * (c cos(a) - v)/ sqrt(1 - v^2/c^2)
and check that indeed:
AB + v/c * AB' = ct * sqrt(1 - v^2/c^2)
which is the second equation on page 566. Then I can find the next-to-last equation for the local time by rewriting:
tau = t_B' = (t - (vct cos(a)/c^2)) / (1 - v^2/c^2) = (t - t* v^2/c^2 + t * v^2/c^2 - (vct cos(a)/c^2))/(1 - v^2/c^2) = t - ((ct cos(a) - vt)*v/c^2)/(1 - v^2/c^2) = t - ((AB' v/c) / c sqrt(1 - v^2/c^2))
Finally, it's easy to check that:
AB = c tau sqrt(1 - v^2/c^2)
which is the last equation (with t corrected to tau -- that this is a misprint can be seen by comparing the next-to-last and the second equation).
As AB is the distance travelled by the ligth wave and tau the time of travel, *as measured by an observer in the moving frame*, I deduce that the speed of light for that observer is:
c' = AB / tau = c sqrt(1 - v^2/c^2)
While it is true that "you don't find such a nonsense" (as Homo Lykos says) in the article, it's just a division away :-/
Now I'd like to follow-up to some remarks by Harry and Homo Lykos.
In article <4332845...@epflnews.epfl.ch>, Harry <harald.vanlin...@epfl.ch> writes:
] > you seem to be saying that after discovering Special Relativity in 1905, ] > he changed his mind... It is easy to see that what is missing in his 1908 ] > article is time dilatation: ] ] I am flabbergasted - "time dilatation" is represented by the tau on page ] 566.
there is "time delay" but no time dilatation in the equation linking t and tau: for an observer at rest in the moving frame (hence: constant AB') a phenomenon won't start at the same time as for an observer in the ether frame (because of the second term -- that's time delay), but its *duration* will be the same (t and tau come with the same unit factor in the equation.) Hence, in Poincaré's theory time durations have an absolute meaning. Not so in Einstein's theory.
In article <4335d73e$...@news.bluewin.ch>, Homo Lykos <ly...@lykos.ch> writes:
] Especially strange for me: ] ] " Supposons que la différence entre le temps vrai et le temp local en un ] point quelconque soit égale à l'abscisse de ce point multipliée par la ] constante: e/(V sqrt(1-e^2)) " ] ] Poincaré gives no explanation for this (and speaks only of supposons(=we ] suppose)) and I - at least in this moment - can't understand it.
if you compute in the ether frame the correction needed to synchronize moving clocks, you get a term vL/(c^2 - v^2) where L is the distance between the clocks projected on the direction of the motion measured in the ether frame -- you get Poincaré's expression if you use the distance as measured in the moving frame but corrected for the length contraction.
Note that Einstein uses the same synchronisation procedure as Poincaré (who must indeed be credited for this nice idea) but comes to different conclusions because he postulates that the speed of light is the same in all inertial frames.
-- | ~~~~~~~~ Martin Ouwehand ~ Swiss Federal Institute of Technology ~ Lausanne __|_____________ Email/PGP: http://slwww.epfl.ch/info/Martin.html _____________ The right question to ask is sometimes better than the right answer to the wrong question [Clifford Truesdell]
> Let me show how this is consistent with what Poincaré says on pages > 565-566 > of the article http://www.soso.ch/wissen/hist/SRT/P-1908.pdf. He considers > two events: A (emission of a light wave) and B (detection of the light > on an arbitrary point of the wave front at some later time).
.....
> Finally, it's easy to check that:
> AB = c tau sqrt(1 - v^2/c^2)
> which is the last equation (with t corrected to tau -- that this is a > misprint
This is no misprint, but Poincarés mistake in his "popular proof" of Michelson-Morley, as one can see by comparison with the text, what I did in an other note. So he was incorrectly thinking that his assumption (supposons ..) would be a good one without controlling all this a second time or carefully enough.
> In article <4332845...@epflnews.epfl.ch>, I wrote:
> ] I understand from his arguments around pages 565-566 > ] that he uses the following transformation: > ] > ] x' = (x - v * t) / sqrt(1 - v^2/c^2) (Lorentz contraction) > ] t' = t - (v * x) / (c^2 - v^2) ("local time")
> I made a mistake (it should be x-vt in the equation for t'), the full > transformation between ether frame (unprimed [x, y, t]) and moving frame > (primed [x', y', t']) is:
Dear Martin, Poincare certainly didn't abandon the Lorentz transformations.
And pasting here what you concluded with:
> Note that Einstein uses the same synchronisation procedure as > Poincaré (who must indeed be credited for this nice idea) but > comes to different conclusions because he postulates that the > speed of light is the same in all inertial frames.
Note also that Einstein postulated what Poincare had concluded, so that they could not disagree about that.
According to Poincare, the full transformation between the measured values in any moving inertial frame and in the ether frame as well as between those in any set of inertial frames is:
The sign depends on the choice of which coordinates one chooses as the primed ones. Thus, according to your interpretation, there is an error in the time calculation of his M-M example. Logically, any interpretation of explanations by Poincare in the context of Lorentz' theory that disagrees with the LT must be either due to an interpretation error or an error in the text.
In order to not contradict his Lorentz transformation, tau must be equal to t*sqrt(1-v^2/V^2), so that he had to end with the last equation just as it appeared in print (BTW, I misread that the first time):
AB = V*t*sqrt(1-v^2/V^2)
>From that he concluded that Michelson's experiment will yield an *apparent
transmission duration* that is proportional to the apparent distance (independent of the angle).
I'll now follow you and also have a closer look at it, to try to spot where the error is. See below.
> Let me show how this is consistent with what Poincaré says on pages 565-566 > of the article http://www.soso.ch/wissen/hist/SRT/P-1908.pdf. He considers > two events: A (emission of a light wave) and B (detection of the light > on an arbitrary point of the wave front at some later time).
I read: the light goes "de B en A", which I think can only mean from B to A.
Also, I had some difficulty with:
"We choose the contraction law, such that the point S is at the base of the meridian section of the ellipse."
It's in cursive, thus important. I think that he meant that we shift the local time such that the contraction ellipse is apparently centered around the source. Then, the detector A is located at the source S, and we look at the light that returns from the apparent position of B back to A.
Note that this apparent position is due to length contraction and time offset, while still using absolute time. Apparently, he wanted to illustrate local time measurement by at first not accounting for it - IMO a bit cumbersome, but typical for him. As he stated:
"How will we then proceed, to evaluate the time that the light takes to go from B to A?"
Thus IMO he does not, at that point, use his Lorentz transformations, but instead he illustrates the consequences for local time measurement, taking the well-known assumption of length contraction for granted.
IOW, fig.2 sketches only half of the Lorentz transformation, as he uses local (apparent) coordinates A and B with the true duration t (watch out: this "t" is *not* a time coordinate; it corresponds to duration delta_t of the Lorentz transformations!).
That is confirmed by his second equation on p.566:
> with ellipcity e = v/c and center [-vt * sqrt(1 - v^2/c^2), 0], > corresponding to the picture on page 566.
> Next I compute Poincaré's AB and AB':
> AB = sqrt(x_B'^2 + y_B'^2) = t * (c - v * cos(a)) / sqrt(1 - v^2/c^2) > AB' = x_B' = t * (c cos(a) - v)/ sqrt(1 - v^2/c^2)
> and check that indeed:
> AB + v/c * AB' = ct * sqrt(1 - v^2/c^2)
> which is the second equation on page 566.
> Then I can find the > next-to-last equation for the local time by rewriting:
> tau = t_B' > = (t - (vct cos(a)/c^2)) / (1 - v^2/c^2) > = (t - t* v^2/c^2 + t * v^2/c^2 - (vct cos(a)/c^2))/(1 - v^2/c^2) > = t - ((ct cos(a) - vt)*v/c^2)/(1 - v^2/c^2) > = t - ((AB' v/c) / c sqrt(1 - v^2/c^2))
> Finally, it's easy to check that:
> AB = c tau sqrt(1 - v^2/c^2)
> which is the last equation (with t corrected to tau -- that this is > a misprint can be seen by comparing the next-to-last and the > second equation).
You overlooked that that would not only contradict everything he said before but even his conclusion in the next paragraph.
Now I'll do a first attempt to finish following Poincare's reasoning, instead of yours:
The direction of motion is along PP'. His first equation is trigonometry with v/V=e, the excentricity.
Next he states that, as there is no effect on lateral dimensions,
OQ = Vt
I first didn't spot his mistake, but here it happened! Ironically, it's the same mistake that Michelson made in 1881 and that Lorentz corrected before Michelson repeated it with Morley. He should have stated:
He states in words (no symbols, so I generate them here but it's inconvenient as the symbol t is already taken, leading to confusing notation - which is no doubt why he skipped it):
Supposing that the difference between true and local time at a point in time and space depends on the location of the clock along PP' as well as on a constant that is a function of the speed, as follows:
tau_p - t_p = x'_p * C
With tau_p and t_p indicating instances, and C = e/(V*sqrt(1-v^2/V^2))
(Note: here I corrected what looks like sloppy phrasing, as from his words I first guessed that he meant "t_p - tau_p", but then the sign doesn't come out right. Thus that would be a little glitch on his part.)
>From that the apparent duration of the transmission from B to A is as
follows:
tau_A - t_A = x'_A * C tau_B - t_B = x'_B * C -------------------------- - tau_A - tau_B - t_A + t_B = (x'_A - x'_B) * C
tau_A - tau_B = t_A - t_B + (x'_A - x'_B ) * C
So that, going back to his notation,
tau = t - AB' * C
He next claims that from that follows that :
AB = V*t*sqrt(1-v^2/V^2)
However, this is in direct contradiction with his second equation, due to his mistake in that second equation. Perhaps he was so sure that it would work out (as he knew that it should), that he didn't bother to verify it.
Concistency check (I won't bother to derive it):
Taking the correct equations and writing g for 1/sqrt(1-v^2/c^2),
AB + e *AB' = V*t/g^2 } t = tau + e* AB' /(V/g) }
AB + e *AB' = V*t/g^2 } t *(V/g) = tau*(V/g) + e*AB' } ----------------------------------- - AB - t *(V/g) = V*t/g^2 - tau * (V/g)
With tau = t/g we get:
AB - t *(V/g) = V*t/g^2 - t/g * (V/g) AB - t *(V/g) = 0
> As AB is the distance travelled by the ligth wave and tau the time of > travel, *as measured by an observer in the moving frame*, I > deduce that the speed of light for that observer is:
> c' = AB / tau = c sqrt(1 - v^2/c^2)
> While it is true that "you don't find such a nonsense" (as Homo > Lykos says) in the article, it's just a division away :-/
> Now I'd like to follow-up to some remarks by Harry and Homo Lykos.
> In article <4332845...@epflnews.epfl.ch>, > Harry <harald.vanlin...@epfl.ch> writes:
> ] > you seem to be saying that after discovering Special Relativity in 1905, > ] > he changed his mind... It is easy to see that what is missing in his 1908 > ] > article is time dilatation: > ] > ] I am flabbergasted - "time dilatation" is represented by the tau on page > ] 566.
> there is "time delay" but no time dilatation in the equation linking t and > tau: for an observer at rest in the moving frame (hence: constant AB') > a phenomenon won't start at the same time as for an observer in the ether > frame (because of the second term -- that's time delay), but its *duration* > will be the same (t and tau come with the same unit factor in the
equation.)
Many people, incl. Poincare, sometimes use t for duration and sometimes for point in time. IMO that's not good practice, as some may overlook it, as now happend to you:
"t [étant] la durée de transmission".
Thus you were right to state that tau is the "time of
...
>> I think too, that Einsteins (popular) explanations of all these things >> were clearer and more specific then the explanations of Poincaré; but >> from Poincaré Einstein had first learned these more philosophical ideas >> about space and time. Now I copy older citations of Poincaré in this >> context:
...
>> More specifically 1904 in St. Louis (Bull. des Sciences Mathématiques, >> deuxième Série, tomé XXVIII):
>> " .... Pour un observateur, entraîné lui-même dans une translation dont >> il ne se doute pas, aucune vitesse apparente ne pourrait non plus >> dépasser celle de la lumière; et ce serait là une contradiction, si l'on >> ne se rappelait que cet observateur ne se servirait pas des mêmes >> horloges qu'un observateur fixe, mais bien d'horloges marquant le "temps >> local". "
> That's a nice one, but it doesn't show that he understood that this local > time implies a different rate.
How do you think it is possible to have the same velocity of light (in the sense of the limiting velocity) in different systems without a different rate but with "standard-Lorentz-contraction"? Moreover (if you don't think that Poincaré here was speaking about a real constant c): At least since about mai 1905 Poincaré was setting c=1 - as he had written to Lorentz and as he did in his june- and july-work - and this is possible only if c is assumed as beeing constant independently of the observer/system.
But it is correct that this idea for Poincaré was not in the same sense fundamental as for Einstein, because Poincaré was normally thinking in mathematical more abstract pictures, and this - I think - is the main reason, that he made this grave, but now very well understandable mistake in his "popular proof" of Michelson. But on the other hand exactly this mistake shows, that Poincaré has known, that clocks in different systems must have different rates.
> > > - I did not see the misprint (duration= t, apparent duration= tau), but > > > the last AB on the copy certainly was AB'.
> > No
> Yes! He wrote that AB' was part of that equation. In the copy we only see AB > in that equation. I'm quite sure that AB' isn't AB with a beautiful piece of > dirt next to it at exactly the right spot. Thus the AB in the equation > certainly was AB'.
Sorry, I somehow misread that part, as "d'ou" means "from which".
Anyway, it's clear that :
AB + e*AB' = c*t*sqrt(1-e^2) and AB + 0 = c*t*sqrt(1-e^2)
> > My interpretation (for the present) of this (strange) page 566:
> > 1. This paper is written in a popular manner (almost no equations and > > no real proofs, he don't makes use of setting V = 1 as in his papers of > > 1905)
> > 2. His "popular proof" of Michelson/Morley seems to me with respect to his > > own theory of 1905 incorrect. Especially strange for me:
> > " Supposons que la différence entre le temps vrai et le temp local en un > > point quelconque soit égale à l'abscisse de ce point multipliée par la > > constante: e/(V sqrt(1-e^2)) "
> > Poincaré gives no explanation for this (and speaks only of supposons(=we > > suppose)) and I - at least in this moment - can't understand it.
I did an attempt to interpret it in my reply to Ouwehand, but although at first sight it seemed to work out, possibly I didn't correctly understand that part. Anyway, I notice that I spent a lot of time on this while it doesn't really matter for this discussion. Even if he had been affected by mad cow disease at that time and stated that cows fly, it hardly matters for the subject at hand. ;-)
> > 3. If it is really only a (strange) error - as I believe now - it's not > > possible to derive any conclusions.
> 4. His error is very probably, that he has written by mistake t instead of > tau in the last equation of page 566. So he believed to have shown the > following relation between true (t) and apparent duration (tau): > tau = t sqrt(1-e^2). > Only so I can understand the first sentence on page 567, which is directly > following the (wrong) equation for the apparent distance AB:
> " c'est-à-dire que la durée apparente de transmission est proportionelle à > la distance apparente. "
> Without this mistake one would have the following nonsense: tau = tau > sqrt(1-e^2).
> Homo Lykos
Very close, but not quite:
- I fully agree that "he believed to have shown the following relation between true (t) and apparent duration (tau): tau = t sqrt(1-e^2)."
- The last equation must be correct as it expresses exactly the above: AB/V = t * sqrt(1-e^2) = tau. (local duration of light transmission equals local distance divided by the speed of light).
>> "Homo Lykos" schrieb im Newsbeitrag news:4335d73e$1_2@news.bluewin.ch... > Anyway, I notice that I spent a lot of time on this while it doesn't > really matter for this discussion. Even if he had been affected by mad cow > disease at that time and stated that cows fly, it hardly matters for the > subject at hand. ;-)
I did not spend a lot of time, because I lost the interest, when I became convinced, that's only an error because of "cow disease" or other reasons.
>> > 3. If it is really only a (strange) error - as I believe now - it's not >> > possible to derive any conclusions.
>> 4. His error is very probably, that he has written by mistake t instead >> of tau in the last equation of page 566. So he believed to have shown the >> following relation between true (t) and apparent duration (tau): >> tau = t sqrt(1-e^2). >> Only so I can understand the first sentence on page 567, which is >> directly following the (wrong) equation for the apparent distance AB:
>> " c'est-à-dire que la durée apparente de transmission est proportionelle >> à la distance apparente. "
>> Without this mistake one would have the following nonsense: >> tau = tau sqrt(1-e^2).
I add: Without his t-tau-mistake he would have seen, that his proof could not be correct because of this "tau-contradiction".
>> Homo Lykos
> Very close, but not quite:
> - I fully agree that "he believed to have shown the following relation > between true (t) and apparent duration (tau): tau = t sqrt(1-e^2)."
> - The last equation must be correct as it expresses exactly the above: > AB/V = t * sqrt(1-e^2) = tau. > (local duration of light transmission equals local distance divided by the > speed of light).
Poincaré thought so, but this not follows from his "proof".
> > Anyway, I notice that I spent a lot of time on this while it doesn't > > really matter for this discussion. Even if he had been affected by mad cow > > disease at that time and stated that cows fly, it hardly matters for the > > subject at hand. ;-)
> I did not spend a lot of time, because I lost the interest, when I became > convinced, that's only an error because of "cow disease" or other reasons.
> >> > 3. If it is really only a (strange) error - as I believe now - it's not > >> > possible to derive any conclusions.
> >> 4. His error is very probably, that he has written by mistake t instead > >> of tau in the last equation of page 566. So he believed to have shown the > >> following relation between true (t) and apparent duration (tau): > >> tau = t sqrt(1-e^2). > >> Only so I can understand the first sentence on page 567, which is > >> directly following the (wrong) equation for the apparent distance AB:
> >> " c'est-à-dire que la durée apparente de transmission est proportionelle > >> à la distance apparente. "
> >> Without this mistake one would have the following nonsense: > >> tau = tau sqrt(1-e^2).
> I add: Without his t-tau-mistake he would have seen, that his proof could > not be correct because of this "tau-contradiction".
You missed out that: - it's not a "proof" but a messed-up example. - I showed in my other posting that there wasn't a t-tau contradiction, but a simple error in his calculation of the light path - the very same error that Michelson made in 1881.
BTW, I now found that he gave the same example in his other 1908 publication, Science et Methode, but without adding the for Michelson-Morley irrelevant clock time considerations - and thus without this error.
> > Very close, but not quite:
> > - I fully agree that "he believed to have shown the following relation > > between true (t) and apparent duration (tau): tau = t sqrt(1-e^2)."
> > - The last equation must be correct as it expresses exactly the above: > > AB/V = t * sqrt(1-e^2) = tau. > > (local duration of light transmission equals local distance divided by the > > speed of light).
> Poincaré thought so, but this not follows from his "proof".
His proof dates from 1905 and is based on group theory.
>> > Anyway, I notice that I spent a lot of time on this while it doesn't >> > really matter for this discussion. Even if he had been affected by mad >> > cow disease at that time and stated that cows fly, it hardly matters >> > for the subject at hand. ;-)
>> I did not spend a lot of time, because I lost the interest, when I >> became convinced, that's only an error because of "cow disease" or other >> reasons.
>> >> > 3. If it is really only a (strange) error - as I believe now - it's >> >> > not possible to derive any conclusions.
>> >> 4. His error is very probably, that he has written by mistake t >> >> instead of tau in the last equation of page 566. So he believed to >> >> have shown the following relation between true (t) and apparent >> >> duration (tau): >> >> tau = t sqrt(1-e^2). >> >> Only so I can understand the first sentence on page 567, which is >> >> directly following the (wrong) equation for the apparent distance AB:
>> >> " c'est-à-dire que la durée apparente de transmission est >> >> proportionelle à la distance apparente. "
>> >> Without this mistake one would have the following nonsense: >> >> tau = tau sqrt(1-e^2).
>> I add: Without his t-tau-mistake he would have seen, that his proof could >> not be correct because of this "tau-contradiction".
> You missed out that: > - it's not a "proof" but a messed-up example.
a (wrong) "proof" or explanation of this exemple.
> - I showed in my other posting that there wasn't a t-tau contradiction, > but a simple error in his calculation of the light path - the very same > error that Michelson made in 1881.
I think all is only a misunderstanding, because I have spoken only about the t-tau-error in his calculation (which ended by chance in a correct result) and not about the primary error, which - as I think too - you have found now. The second (I had forgotten to say so explicitely) error in my opinion was only the reason, that he had not realised, that something (before) was wrong.
> BTW, I now found that he gave the same example in his other 1908 > publication, Science et Methode, but without adding the for > Michelson-Morley irrelevant clock time considerations - and thus > without this error.
>> > Very close, but not quite:
>> > - I fully agree that "he believed to have shown the following relation >> > between true (t) and apparent duration (tau): tau = t sqrt(1-e^2)."
>> > - The last equation must be correct as it expresses exactly the above: >> > AB/V = t * sqrt(1-e^2) = tau. >> > (local duration of light transmission equals local distance divided by >> > the speed of light).
>> Poincaré thought so, but this not follows from his "proof".
> His proof dates from 1905 and is based on group theory.
Sure: That's the reason, that mostly I have spoken in this context about "popular proof" (of this exemple).
> "harry" <harald.vanlin...@epfl.ch> schrieb im Newsbeitrag > news:1128274691.068382.179260@o13g2000cwo.googlegroups.com... SNIP > >> >> 4. His error is very probably, that he has written by mistake t > >> >> instead of tau in the last equation of page 566. So he believed to > >> >> have shown the following relation between true (t) and apparent > >> >> duration (tau): > >> >> tau = t sqrt(1-e^2). > >> >> Only so I can understand the first sentence on page 567, which is > >> >> directly following the (wrong) equation for the apparent distance AB:
> >> >> " c'est-à-dire que la durée apparente de transmission est > >> >> proportionelle à la distance apparente. " SNIP > >> I add: Without his t-tau-mistake he would have seen, that his proof could > >> not be correct because of this "tau-contradiction".
SNIP
> > - I showed in my other posting that there wasn't a t-tau contradiction, > > but a simple error in his calculation of the light path - the very same > > error that Michelson made in 1881. > I think all is only a misunderstanding, because I have spoken only about the > t-tau-error in his calculation (which ended by chance in a correct result) > and not about the primary error, which - as I think too - you have found > now.
SNIP
> >> > - The last equation must be correct as it expresses exactly the above: > >> > AB/V = t * sqrt(1-e^2) = tau. > >> > (local duration of light transmission equals local distance > >> > divided by the speed of light).
OK, I see what you mean now: we meant the same thing but looked at it from another angle.
> All that's required is that the Lorentz transformations constitute the > unique solution that satisfies all constraints. And Poincare solved > that problem. The rest is just didactical stuff for human consumption. > It only gives people the illusion they grasp something about it.
LoL. Let me guess, you have never actually done any research in theoretical physics?
Hilbert wrote down the equations of GR before Einstein but didn't understand what they told him, Poincare wrote down the equations for SR before Einstein but didn't realize what they implied. t'Hooft wrote down the formula for Asymptotic freedom before Gross, Politzer and Wilczek did, but didn't understand that he held the answer to a deep problem, St=FCckelberg came up with precursor theories to Pathintegrals but didn't understand completely how to cast them into a consistent mathematical AND physical picture (He also came up with the Yukawa interaction before but didn't publish due to Heisenbergs objections), something at which Feynman succeeded. Schr=F6dinger wrote down the Klein-Gordon equation but dismissed it as unphysical.
> >> I think too, that Einsteins (popular) explanations of all these things > >> were clearer and more specific then the explanations of Poincaré; but > >> from Poincaré Einstein had first learned these more philosophical ideas > >> about space and time. Now I copy older citations of Poincaré in this > >> context:
> ...
> >> More specifically 1904 in St. Louis (Bull. des Sciences Mathématiques, > >> deuxième Série, tomé XXVIII):
> >> " .... Pour un observateur, entraîné lui-même dans une translation dont > >> il ne se doute pas, aucune vitesse apparente ne pourrait non plus > >> dépasser celle de la lumière; et ce serait là une contradiction, si l'on > >> ne se rappelait que cet observateur ne se servirait pas des mêmes > >> horloges qu'un observateur fixe, mais bien d'horloges marquant le "temps > >> local". "
> > That's a nice one, but it doesn't show that he understood that this local > > time implies a different rate.
> How do you think it is possible to have the same velocity of light (in > the sense of the limiting velocity) in different systems without a > different rate but with "standard-Lorentz-contraction"? Moreover (if you > don't think that Poincaré here was speaking about a real constant c): At > least since about mai 1905 Poincaré was setting c=1 - as he had written > to Lorentz and as he did in his june- and july-work - and this is > possible only if c is assumed as beeing constant independently of the > observer/system.
> But it is correct that this idea for Poincaré was not in the same sense > fundamental as for Einstein, because Poincaré was normally thinking in > mathematical more abstract pictures, and this - I think - is the main > reason, that he made this grave, but now very well understandable > mistake in his "popular proof" of Michelson. But on the other hand > exactly this mistake shows, that Poincaré has known, that clocks in > different systems must have different rates.
I largely agree with you, as also may be clear from my analysis of the mistake in his example. I simply admit that when one does not read into his words what he didn't explicitly state, then it's not impossible that in 1904 he didn't consider the effect on clock rates - which had not been tested. And even in 1908 Poincare apparently focussed on explaining past experiments, not future experiments.
> > All that's required is that the Lorentz transformations constitute the > > unique solution that satisfies all constraints. And Poincare solved > > that problem. The rest is just didactical stuff for human consumption. > > It only gives people the illusion they grasp something about it.
> LoL. Let me guess, you have never actually done any research in > theoretical physics?
> Hilbert wrote down the equations of GR before Einstein but didn't > understand what they told him, Poincare wrote down the equations for SR > before Einstein but didn't realize what they implied.
I agree with you that also the application must be understood (which goes less far than to demand that all implications should be dished up). Now, I don't know about Hilbert, but Poincare clearly understood the main implications of the PoR and Lorentz's theory, eventhough Lorentz didn't yet understand so much of it himself. The main direct application that he implied without explicitly mentioning it before Einstein is time dilation.
> t'Hooft wrote > down the formula for Asymptotic freedom before Gross,
That's interesting. And he didn't understand it? That's possible - in fact, we can ask him!
> Politzer and > Wilczek did, but didn't understand that he held the answer to a deep > problem, St=FCckelberg came up with precursor theories to Pathintegrals > but didn't understand completely how to cast them into a consistent > mathematical AND physical picture (He also came up with the Yukawa > interaction before but didn't publish due to Heisenbergs objections), > something at which Feynman succeeded. Schr=F6dinger wrote down the > Klein-Gordon equation but dismissed it as unphysical.
> That's just from the top of my head.
Interesting collection in your head, it may be worth writing an article about that. :-)
>> >> I think too, that Einsteins (popular) explanations of all these things >> >> were clearer and more specific then the explanations of Poincaré; but >> >> from Poincaré Einstein had first learned these more philosophical >> >> ideas about space and time. Now I copy older citations of Poincaré in >> >> this context:
>> ...
>> >> More specifically 1904 in St. Louis (Bull. des Sciences Mathématiques, >> >> deuxième Série, tomé XXVIII):
>> >> " .... Pour un observateur, entraîné lui-même dans une translation >> >> dont il ne se doute pas, aucune vitesse apparente ne pourrait non plus >> >> dépasser celle de la lumière; et ce serait là une contradiction, si >> >> l'on ne se rappelait que cet observateur ne se servirait pas des mêmes >> >> horloges qu'un observateur fixe, mais bien d'horloges marquant le >> >> "temps local". "
>> > That's a nice one, but it doesn't show that he understood that this >> > local time implies a different rate.
>> How do you think it is possible to have the same velocity of light (in >> the sense of the limiting velocity) in different systems without a >> different rate but with "standard-Lorentz-contraction"? Moreover (if you >> don't think that Poincaré here was speaking about a real constant c): At >> least since about mai 1905 Poincaré was setting c=1 - as he had written >> to Lorentz and as he did in his june- and july-work - and this is >> possible only if c is assumed as beeing constant independently of the >> observer/system.
>> But it is correct that this idea for Poincaré was not in the same sense >> fundamental as for Einstein, because Poincaré was normally thinking in >> mathematical more abstract pictures, and this - I think - is the main >> reason, that he made this grave, but now very well understandable >> mistake in his "popular proof" of Michelson. But on the other hand >> exactly this mistake shows, that Poincaré has known, that clocks in >> different systems must have different rates.
> I largely agree with you, as also may be clear from my analysis of the > mistake in his example. I simply admit that when one does not read into > his words what he didn't explicitly state, then it's not impossible that > in 1904 he didn't consider the effect on clock rates - which had not > been tested. And even in 1908 Poincare apparently focussed on explaining > past experiments, not future experiments.
I think it was a more philosophical reason, that Poincaré named the Lorentz-contraction an astonishing fact, but never (?) has directly spoken about time-dilatation: In la mesure du temp you can see, that Poincaré had no (a priori-)feeling/understanding for a universal time and this is in clear contrast to his thinking about space, as you can see in La Science et l'Hypothèse in chapter 5; especially interesting in this context is the begin of La géométrie et l'astronomie and the last part L'expérience ancestrale. Here Poincarés ideas are very near to my own thinking and I wonder why he thought so differently about time. But this difference - as I think and felt very strongly by reading - explains why time-dilation in contrast to Lorentz-contraction for Poincaré was never an "interesting" fact to speak about.
A general remark: It seems, that Poincaré never changed his mind about these more philosophical ideas and this is the main reason, that it is impossible to understand Poincaré, if one not knows, what he has written about these tings between about 1898 and 1904. Also about ether (chapter 10) he never changed his mind, as some people think. Ether was for Poincaré in principle a useless concept, except for didactical reasons. In this point he was nearer to Einstein than to Lorentz. But he has known and always emphasized - in clear contrast to Einstein - that (an infinity of) ether models are in principle possible, if the principle of least action is valid. So he has konwn, that it's allowed to make use of the ether-picture for better understanding and he made use of it.
Frank Hellmann wrote: > Hilbert wrote down the equations of GR before Einstein but didn't > understand what they told him, Poincare wrote down the equations for SR > before Einstein but didn't realize what they implied. t'Hooft wrote > down the formula for Asymptotic freedom before Gross, Politzer and > Wilczek did, but didn't understand that he held the answer to a deep > problem, Stückelberg came up with precursor theories to Pathintegrals > but didn't understand completely how to cast them into a consistent > mathematical AND physical picture (He also came up with the Yukawa > interaction before but didn't publish due to Heisenbergs objections), > something at which Feynman succeeded. Schrödinger wrote down the > Klein-Gordon equation but dismissed it as unphysical.
> That's just from the top of my head.
> Frank.
Unfortunately, this thread is becoming too repetitive. You would read evidence was presented here (even if you has no time for reading innumerable references cited alog this thread!) before submit.
> Hilbert wrote down the equations of GR before Einstein but didn't > understand what they told him.
This is not correct!
In Jürgen Renn and John Stachel. "Hilbert's Foundation of Physics:
>From a Theory of Everything to a Constituent of General Relativity"
pprnt 118 (1999). [Max Planck Institute for the History of Science]
The work is exhaustive and one can understand the physics underlying Hilbert research methodology:
"Hilbert presented his contribution as emerging from a research program that was entirely his own -the search for an axiomatization of physics as a whole creating a synthesis of electromagnetism and gravitation."
Curiously, it was Einstein who do not understand the physical structure of GR (Einstein, of course, understood physical *implications* but not the basis). As noted by Ivan T. Todorov (arXiv:physics/0504179 v1)
On 25 November Einstein proposes /without derivation/ the correct GR equation. This was just after of receiving Hilbert proof. "Einstein chooses not to mention Hilbert's name in the published paper."
"Later commentators have a hard time to understand what was Einstein's argument at the time to include the trace term."
In fact, Einstein did not know the physics underlying that crucial '(1/2) trace' term and in posterior works -i have documented but people ignore (as if newer were published)- Einstein *claimed* other versions with (1/4) trace term, etc.
> Poincare wrote down the equations for SR before Einstein but didn't realize > what they implied.
This is also just the inverse. It has been extensively discussed and cited here:
- Poincaré understood relativistic theory (Einstein returned to many Poincare arguments in posterior years) as i documented here extensively.
- Not only Poincare offered to us correct *NEW* equations, he also interpreted correctly the physics of those equations: New simultaneity concept in mechanics, Lorentz 'local time' was *real* time read by a clock, clocks could be sinchronized using light signals, c was a maximum velocity could not be achieved by bodies (Poincaré explicitely compared this limitation with the zero absolute of thermodynamics, I already cited his words here), no posibility for detecting absolute motion, time *is* relative, and a large, the four momentum and velocity, the four component of force, the PoR, etc.
- Poincaré applied his relativity theory to gravitation and compared with experimental data when Einstein was still working with EM. Poincaré was able to reduce the 43'' of Mercury to 36'' (now we know that total explanation needs of a more general theory of relativity, but part of the 43'' computed now with the aid of GR are, obviously, from the SR effects incorporated into GR).
- Poincaré understood the group property of the LT and was able to formulate the 4D spacetime view of relativity. Einstein newer did that, this is the reason that part of relativity has been traditionally attributed to Minkoski, but recent documents, (i cited) show that Poincaré achieved spacetime and the invariant element of line ds before.
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