poincare's "similitude" idea
Rajarshi Ray
Poincare in discussing the concept of "Absolute Space" says that if all
dimensions of all objects were to increase tenfold we still would not
notice anything amiss. This would be because we ourselves would undergo
the extension in dimensions.
However, I think he is wrong. First of all, I know that if only I were
to get ten times bigger my legs would break under my weight; my mass
increases by a factor of thousand while the surface area on which it is
supported only increases by a factor of hundred, hence the pressure is
now ten times higher.
If EVERYTHING were to get ten times bigger, including the Earth, then
the situation would be far far worse since now the gravity acting on me
would also be increased by a factor of thousand! I would be pretty
crippled! So I don't think it would be difficult to tell the difference
if everything were to increase in size tenfold.
So, in this sense Poincare is wrong. The only way his conclusion can be
recovered is if we consider that SPACE itself increases in dimension by
ten times. In that case all the inter-atomic and inter-molecular spaces
would increase tenfold. If all the constants determining the forces
between these atoms and molecules were also to adjust properly, only
THEN would we not notice any difference. But the only way we have
recovered Poincare's conclusion is by considering something like
"Absolute" space in his argument, exactly what Poincare set out to show
does not exist!!
Does all this make sense?? Or is there something I'm missing out?
-Rajarshi Ray
Androcles
Rajarshi Ray <raja...@home.com> wrote in message
news:38545689...@home.com...
> Hi,
>
> Poincare in discussing the concept of "Absolute Space" says that if all
> dimensions of all objects were to increase tenfold we still would not
> notice anything amiss. This would be because we ourselves would undergo
> the extension in dimensions.
>
> However, I think he is wrong. First of all, I know that if only I were
> to get ten times bigger my legs would break under my weight; my mass
> increases by a factor of thousand while the surface area on which it is
> supported only increases by a factor of hundred, hence the pressure is
> now ten times higher.
Your legs are ten times stronger.
You are correct that the pressure is ten times greater. It takes ten times
longer for you to feel it. UNLESS your mass remains as before, in which case
you are 1000 times less dense. Did Poincare assert that your mass would be
ten times greater (in all directions)? Or was that your assertion?
Androcles
Rajarshi Ray
back to it when you're feeling more sober.
Joe Fischer
: Rajarshi Ray <raja...@home.com> wrote in message
: > Poincare in discussing the concept of "Absolute Space" says that if all
: > dimensions of all objects were to increase tenfold we still would not
: > notice anything amiss. This would be because we ourselves would undergo
: > the extension in dimensions.
I have been waiting for this article, but I can't
wait any longer, can you give a specific reference or title?
If size is changing, it must change constantly and
smoothly, indefinitely. This seems to make a discussion
of "absolute space" rather moot.
: > However, I think he is wrong. First of all, I know that if only I were
: > to get ten times bigger my legs would break under my weight; my mass
: > increases by a factor of thousand while the surface area on which it is
: > supported only increases by a factor of hundred, hence the pressure is
: > now ten times higher.
No, if size was changing, it would be at the atomic
and molecular level, your mass, density, volume and size
would always measure what they do now. The lenght of
the second would also have to lengthen, but wouls seem
as it does now.
This is a reasonable conjecture, and I would like
to read what Poincare had to say.
: The dimensions to use are mass, length and time.
Mass, distance, size and time.
: Your legs are ten times stronger.
: You are correct that the pressure is ten times greater.
: It takes ten times longer for you to feel it.
That was a problem the world's tallest man had. :-)
: UNLESS your mass remains as before, in which case
: you are 1000 times less dense. Did Poincare assert
: that your mass would be ten times greater
: (in all directions)? Or was that your assertion?
: Androcles
I wish that original article would get here,
you guys with cable modems make me green with envy. :-)
Joe Fischer
Rajarshi Ray
> ...
> I have been waiting for this article, but I can't
> wait any longer, can you give a specific reference or title?
It can be found at: http://home.mira.net/~gaffcam/phil/
> No, if size was changing, it would be at the atomic
> and molecular level, your mass, density, volume and size
> ...
I said something like that at the end. That's the only way Poincare's
argument can hold realistically. But he doesn't clarify this issue.
Happy reading!
Chris Hillman
On Tue, 14 Dec 1999, Rajarshi Ray wrote:
> Poincare in discussing the concept of "Absolute Space" says that if all
> dimensions of all objects were to increase tenfold we still would not
> notice anything amiss. This would be because we ourselves would undergo
> the extension in dimensions.
Just to be clear, a "similitude" is a linear transformation of form
(x,y,z) -> a (x,y,z)
for some constant a > 0. Sometimes translations are also allowed, and
then a synonym is "homothety" ("same angles" in psuedo-Greek).
> if only I were to get ten times bigger my legs would break under my
> weight; my mass increases by a factor of thousand while the surface
> area on which it is supported only increases by a factor of hundred,
> hence the pressure is now ten times higher.
Right, this was first pointed by Gallileo! In the same book, GG narrowly
missed discovering the concept of "scaling dimension" (including fractal
dimensions). Think how -that- could have changed history!
> So, in this sense Poincare is wrong. The only way his conclusion can be
> recovered is if we consider that SPACE itself increases in dimension by
> ten times.
That's what he meant. Oddly enough, I have recently been arguing on
sci.physics.research about this and similar passages, which I insist are
merely mathematical jokes in which Poincare (who according to many
contempary accounts had a sardonic sense of humor concerning people less
intelligent than himself) was more or less trolling the idgits, who
indeed, down to the very time in which we live, have taken these passages
with utmost gravity. So to speak ;-)
> Does all this make sense?? Or is there something I'm missing out?
No, I think the "argument" given by Poincare was obviously tautological
and that he knew this very well, and that he laughed his head off when the
idjits took him seriously. See also his "heated disk model" of the
hyperbolic plane. These are all more or less tautological, something
which any mathematician instantly realizes. That's why I am so sure that
Poincare was joking.
Here is another very well known example where Poincare showed his sardonic
sense of humor. Some of his greatest early mathematical work involved the
beautiful connection between what are now called Fuchsian functions and
the geometry of the hyperbolic plane. A minor mathematician called Fuchs
(Germany and France were mathematical rivals in those days) complained
loudly that in one of Poincare's paper on something else, Poincare had
failed to acknowledge the prior contribution of Fuchs, which was "trivial"
by comparison, which Poincare well knew. Poincare's reply to Fuchs'
unpleasant if absurd allegations that Poincare had "stolen" a
one-hundredth baked idea from Fuchs was to name what we know call Fuchsian
functions after Fuchs, precisely -because- Fuchs worked on -entirely-
different stuff. He was having fun at Fuchs's expense, because he knew
that everyone (math was a very small world then) would immediately
understand that Poincare was saying:
(i) Fuchs had about as much to do with the work whose priority he
disputed as he had to do with "Fuchsian" functions, namely -nothing-,
(ii) Poincare could "afford" to name -anything- after -any- idgit,
because he had already made so many great contributions to mathematics by
the age of 25 that he didn't need to worry about priority, as a person who
has only one good idea in his entire life might. Poincare had so many
good ideas he could "give the names away", and indeed the name Fuchsian
function instantly "stuck", even though everyone knew that Poincare was
simply taunting Fuchs by introducing this terminology.
There are many other examples which show Poincare's tendency to insert
private jokes into his papers and books. Again, in the case of his
clearly tautological arguments, I am sure that he was, to adopt the phrase
of Gauss, "trolling the Boetians" who were still worried about whether
noneuclidean geometry made any sense, while mathematics had already, in
the hands of Poincare and Klein (a more serious rival), passed far beyond
this stage. At the other extreme, Poincare at times was given to making
cryptic remarks without precise statement or proof which have only been
understood a hundred years later to have been uncannily prescient. So it
was not out of character for him to speak to people a hundred years afer
his time in one paragraph, and people (philosophers of space and time) who
were a hundred years -behind- his time in the next (e.g., still taking
Kant seriously).
For those who don't know, although Rajarshi didn't give a citation (by the
way, can you give a citation?), AFAIK all the joke passages aimed at the
philosophers occur in popular books, of which Poincare wrote several.
These were "bestsellers" in their time, kind of like the turn of the
century equivalent of the popular books by Hawking, who also has a good
sense of humor, although more mischevious than sardonic. Probably if one
combed through Poincare's collected papers one could find many similar
sardonic jests, only more sophisticated.
Anyway, I feel sure that Poincare's motivation for writing these passages
with a straight face in his popular books were akin to Kibo's motivation
for trolling Archie. Some targets are just too easy, ya know? :-)
Chris "Atom!" Hillman
Home Page: http://www.math.washington.edu/~hillman/personal.html
Gerry Quinn
Poincare was obviously considering only geometric measurements. The
rulers scale, the objects that are measured scale: no observed
difference. (No difference at all, in fact, since Poincare is talking
about geometry rather than physics, and just using an analogy from
everyday life.) There is no reason to assume that he was joking, or
that, if someone had pointed out Galileo's observation that he would not
have said "Yes, yes, but I am speaking here of geometry only." Nobody
did, and he may have imagined that overly-clever people would not
nitpick his text in search of unintended meanings, or if they did, that
their cleverness would extend to understanding the sphere in which his
example was applicable, which does not include mechanics.
>> Does all this make sense?? Or is there something I'm missing out?
>
>No, I think the "argument" given by Poincare was obviously tautological
>and that he knew this very well, and that he laughed his head off when the
>idjits took him seriously. See also his "heated disk model" of the
>hyperbolic plane. These are all more or less tautological, something
>which any mathematician instantly realizes. That's why I am so sure that
>Poincare was joking.
>
Who exactly are these "idgits" who are taking his simple examples
seriously? I've only seen you, the poster you are responding to, and
some guy who was complaining about Einstein's "unsoundness on
foundational matters". All Poincare was doing was suggesting some
simple visualisations of his mathematical discussions. Perhaps he felt
that visualisation in terms of homely examples was a good way - or the
best way - to understand mathematics.
- Gerry Quinn
z@z
| Here is another very well known example where Poincare showed his sardonic
| sense of humor. Some of his greatest early mathematical work involved the
| beautiful connection between what are now called Fuchsian functions and
| the geometry of the hyperbolic plane. A minor mathematician called Fuchs
| (Germany and France were mathematical rivals in those days) complained
| loudly that in one of Poincare's paper on something else, Poincare had
| failed to acknowledge the prior contribution of Fuchs, which was "trivial"
| by comparison, which Poincare well knew. Poincare's reply to Fuchs'
| unpleasant if absurd allegations that Poincare had "stolen" a
| one-hundredth baked idea from Fuchs was to name what we know call Fuchsian
| functions after Fuchs, precisely -because- Fuchs worked on -entirely-
| different stuff.
Did Poincaré call "Lorentz transformation" the transformations presented
by Lorentz 1904 or only the more straightforward and symmetric version
presented by (himself and/or) Einstein 1905.
As far as I have read and understood on these newsgroups, the formulas
presented by Lorentz are quite different from Einstein's transformation,
but can be transformed into the latter if somehow combined with the
Galilei transformation. Am I right or wrong? How did Lorentz express
length contraction. Einstein's variant suggests for the moving frame
at first sight rather length increase than length contraction.
x' = gamma (x - vt) gamma > 1
In order to derive lenght contraction, either relativity of simultaneity
must be taken into consideration or the ether coordinate x must be
expressed as a function of the coordinates of the moving frame.
x = gamma (x' + vt') --> x' = x / gamma if t' = 0
Which transformation variant used Poincaré himself in his papers? Did
he derive his relativistic velocity addition formula of 1905 from
Lorentz's variant or did he use Einstein's variant (or an equivalent
one) before Einstein?
Cheers, Wolfgang
Jim Carr
... note followups to s.p.relativity ...
Chris Hillman wrote:
}
} Here is another very well known example where Poincare showed his sardonic
} sense of humor. Some of his greatest early mathematical work involved the
} beautiful connection between what are now called Fuchsian functions and
} the geometry of the hyperbolic plane. A minor mathematician called Fuchs
} (Germany and France were mathematical rivals in those days) complained
} loudly that in one of Poincare's paper on something else, Poincare had
} failed to acknowledge the prior contribution of Fuchs, which was "trivial"
} by comparison, which Poincare well knew. Poincare's reply to Fuchs'
} unpleasant if absurd allegations that Poincare had "stolen" a
} one-hundredth baked idea from Fuchs was to name what we know call Fuchsian
} functions after Fuchs, precisely -because- Fuchs worked on -entirely-
} different stuff.
In article <83dml9$5j2$1...@pollux.ip-plus.net>
"z@z" <z...@z.lol.li> writes:
>
>Did Poincaré call "Lorentz transformation" the transformations presented
>by Lorentz 1904 or only the more straightforward and symmetric version
>presented by (himself and/or) Einstein 1905.
What Lorentz presented in 1904 _was_ the "straightforward" version
that was derived by Einstein in 1905. The difference between what
Lorentz did and what Poincare' sketched in 1905 (and published in
1906) was how lambda=1 was obtained. Lorentz used the physical
properties of his model of the electron (that was the main point of
his 1904 paper, the full derivation found in "Theory of Electrons"
was published piecemeal in journals) to get this result, while
Poincare' used group theory. Part of Einstein's derivation can
be understood more easily from group theory, but he did it all in
one fell swoop.
>As far as I have read and understood on these newsgroups, the formulas
>presented by Lorentz are quite different from Einstein's transformation,
>but can be transformed into the latter if somehow combined with the
>Galilei transformation. Am I right or wrong?
Wrong. Lorentz combined them.
This might not be clear to persons not used to reading physics or
mathematics papers (see below) because of the terse notation he used.
That is, in his paper Lorentz writes x' = gamma x [I use modern notation
and suppress the scale factor that is later proved to be 1] and uses
words to say what "x" is, in "Theory of Electrons" he makes this very
clear by writing x_r = x - vt [again I use v to be consistent with
modern notation] and then defines x' = gamma x_r and thus obtains
the x' = gamma ( x - vt ) transformation.
>How did Lorentz express length contraction.
Note well that Lorentz did more than one thing. He expressed
"length contraction" just as FitzGerald did -- back when he first
did it. The 1904 paper is about transformations of coordinates
between the ether frame and any relatively moving frame and a
proof (velocity addition) that you don't need to know which
coordinate system is the ether one.
>Einstein's variant suggests for the moving frame
>at first sight rather length increase than length contraction.
>
> x' = gamma (x - vt) gamma > 1
>
>In order to derive lenght contraction, either relativity of simultaneity
>must be taken into consideration or the ether coordinate x must be
>expressed as a function of the coordinates of the moving frame.
Which is, if you understand coordinate systems, exactly what you
must do to define a length measured at a particular time t' in
a particular coordinate system. Lorentz understood coordinate
transformations, and assumed his readers were similarly educated
(he wrote for physicists, not a general audience), so this is
just done with essentially no explanation in the paper. In "Theory
of Electrons", which is a monograph derived from lecture notes, he
gives more pedagogical details which make this clear. See above
for just one example.
--
James A. Carr <j...@scri.fsu.edu> | Commercial e-mail is _NOT_
http://www.scri.fsu.edu/~jac/ | desired to this or any address
Supercomputer Computations Res. Inst. | that resolves to my account
Florida State, Tallahassee FL 32306 | for any reason at any time.
Rajarshi Ray
>
> Who exactly are these "idgits" who are taking his simple examples
> seriously? I've only seen you, the poster you are responding to, and
> some guy who was complaining about Einstein's "unsoundness on
> foundational matters". All Poincare was doing was suggesting some
> simple visualisations of his mathematical discussions. Perhaps he felt
> that visualisation in terms of homely examples was a good way - or the
> best way - to understand mathematics.
So what's your point? Even if Poincare doesn't have his facts straight
it's OUR fault when we notice since Poincare "obviously" didn't mean it
that way?? So Poincare is right even when he's wrong! Now that's funny!
Dwight Thieme
There are not-to-serious speculations that the red shift is due to a
universal shrinkage.
Ike
Chris Hillman
On Fri, 17 Dec 1999, Gerry Quinn wrote:
> There is no reason to assume that he was joking,
Seems to me that I gave some reasons to assume just that, but since
Poincare is no longer with us, I guess we'll have to agree to disagree on
this point.
> or that, if someone had pointed out Galileo's observation that he
> would not have said "Yes, yes, but I am speaking here of geometry
> only." Nobody did, and he may have imagined that overly-clever people
> would not nitpick his text in search of unintended meanings, or if
> they did, that their cleverness would extend to understanding the
> sphere in which his example was applicable, which does not include
> mechanics.
Huh?!
> Who exactly are these "idgits" who are taking his simple examples
> seriously?
In this instance, people who don't follow the math of guys like Poincare,
but feel compelled to go on and on about what their intuition tells them
Nature is like, in blissful ignorance of the fact that known theorems tell
a very different story.
In general, when I refer to "idgits" I mean "people who just don't get
it", including cranks. The group of idgits in the preceeding paragraph is
obviously a much more sophisticated bunch and includes some philosophers,
but at a higher level of discourse, they still count as idgits.
(Definition: a crank is a person who endlessly repeats flagrantly
erroneous claims, despite repeated corrections).
Chris Hillman
Home Page: http://www.math.washington.edu/~hillman/personal.html
Chris Hillman
On Fri, 17 Dec 1999, z@z wrote:
Hang on right there. I have question for you, Wolfgang. Why so
mysterious? What's with this z@z business?
> Chris Hillman wrote:
>
> | Here is another very well known example where Poincare showed his sardonic
> | sense of humor.
[snip]
>
> Did Poincaré call "Lorentz transformation" the transformations presented
> by Lorentz 1904 or only the more straightforward and symmetric version
> presented by (himself and/or) Einstein 1905.
AFAIK the terminology"Lorentz group" and "Poincare group" was introduced
by others.
> As far as I have read and understood on these newsgroups, the formulas
> presented by Lorentz are quite different from Einstein's transformation,
> but can be transformed into the latter if somehow combined with the
> Galilei transformation. Am I right or wrong?
Well, not having Lorentz's papers on electrodynamics in front of me, I am
not sure what difference you are referring to. It could be something as
trivial as writing
t' = t cosh p + x sinh p
x' = t sinh p + x cosh p
y' = y
z' = z
versus
[t'] [ cosh p sinh p 0 0 ] [t]
[x'] = [ sinh p cosh p 0 0 ] [x]
[y'] [ 0 0 1 0 ] [y]
[z'] [ 0 0 0 1 ] [z]
> Which transformation variant used Poincaré himself in his papers?
Same comment. I don't have the original papers in front of me and I have
no memory of any significant difference between what Poincare and Einstein
had to say (I never really read Lorenz's papers, but I don't have that in
front of me either).
Chris Hillman
Home Page: http://www.math.washington.edu/~hillman/personal.html
z@z
: Did Poincaré call "Lorentz transformation" the transformations presented
: by Lorentz 1904 or only the more straightforward and symmetric version
: presented by (himself and/or) Einstein 1905.
:
: As far as I have read and understood on these newsgroups, the formulas
: presented by Lorentz are quite different from Einstein's transformation,
: but can be transformed into the latter if somehow combined with the
: Galilei transformation. Am I right or wrong? How did Lorentz express
: length contraction. Einstein's variant suggests for the moving frame
: at first sight rather length increase than length contraction.
:
: x' = gamma (x - vt) gamma > 1
:
: In order to derive lenght contraction, either relativity of simultaneity
: must be taken into consideration or the ether coordinate x must be
: expressed as a function of the coordinates of the moving frame.
:
: x = gamma (x' + vt') --> x' = x / gamma if t' = 0
:
: Which transformation variant used Poincaré himself in his papers? Did
: he derive his relativistic velocity addition formula of 1905 from
: Lorentz's variant or did he use Einstein's variant (or an equivalent
: one) before Einstein?
In the meanwhile I have read Poincaré's paper of June 1905. Because
it is the last important paper concerning SR which appeared before
Einstein's relevant papers it can be considered a pre-relativistic
summary of the Ether theory advocated by Lorentz and Poincaré.
Here some translated extracts which seem relevant to me:
"... It seems that this impossibility of determining the absolute
motion is a general law of nature.
An explanation has been proposed by Lorentz who introduced the
hypothesis of a contraction of all objects in direction of the
motion; ... Lorentz tried to complete and modify his hypothesis
in order to make it consistent with the postulate of the full
impossibility of determining the absolute motion. ...
The essential point, established by Lorentz, is that the equations
of the e.m. field do not change under a certain transformation
(which I'll call Lorentz transformation) and ...
... These transformations, ..., must form a group; however, for
this to be so, it is necessary that l = 1; hence we are led to
assume that l = 1 and this is a consequence which Lorentz had
found by a different way. ...
Lorentz was also led to assume that the moving electron takes the
form of a compressed ellipsoid; ...
... and at the same time [one gets] a possible explanation of the
electron contraction, in assuming that the electron, deformable
and compressible, is subject to a kind of exterior constant
pression whose effect [travail] is proportional to the variations
in volume. ...
But that is not enough: Lorentz considered it necessary to
complete his hypothesis by assuming that all forces, of any
origin, are affected in the same way by a translation as the e.m.
forces and that therefore the effect of a Lorentz transformation
is once again defined by the equations (4)."
If we replace l by 1 then Poincaré's formula (1) takes in modern
notation the form
x' = gamma(x + beta t), y'=y, z'=z, t' = gamma(t + beta x)
Formally this is equivalent to Einstein's variant:
x' = gamma(x - vt), y'=y, z'=z, t' = gamma(t - v/c^2 x)
But whereas SR is essentially based on giving up absolute
simultaneity, Poincaré does not even mention either time (apart
from t=time) nor simultaneity, far less relativistic velocity
addition which requires relative simultaneity.
Therefore it seems rather improbable to me that Poincaré interpreted
x' = gamma(x) in the same (modern) way as Einstein did, namely as
length increase. http://www.deja.com/=dnc/getdoc.xp?AN=562477376
As far as I know, Lorentz never accepted the simultaneity concept
of SR. Instead, he believed in absolute ether simultaneity. The fact
that the Lorentz transformation forms group does not necessarily
entail SR simultaneity, because there are two different ways time
offsets (coordinates) can be interpreted.
http://www.deja.com/=dnc/getdoc.xp?AN=550248591
http://www.deja.com/=dnc/getdoc.xp?AN=560576844
Lorentz Ether Theory based on absolute simultaneity (with
different times = clock readings in moving frames at the same
absolute time) cannot be not equivalent to Special Relativity.
On the other hand, LET based on the SR simultaneity concept is
essentially SR + preferred frame.
Wolfgang Gottfried G.
Liechtenstein, n9:363.96 (IC time)
APPENDIX (The originals of the translated extracts):
'
' "... Il semble que cette impossibilité de démontrer le mouvement
' absolu soit une loi générale de la nature.
'
' Une explication a été proposée par Lorentz, qui a introduit
' l'hypothèse d'une contraction de tous les corps dans le sens du
' mouvement terrestre; ... Lorentz a cherché à compléter et à
' modifier son hypothèse de facon à la mettre en concordance avec
' le postulat de l'impossibilité complète de la détermination du
' mouvement absolu. ...
'
' Le point essentiel, établi par Lorentz, c'est que les équations
' du champs électromagnétique ne sont pas altérées par une certaine
' transformation (que j'appelerai du nom de Lorentz) et ...
'
' ... L'ensemble de toutes ces transformations, ... , doit former
' groupe; mais, pour qu'il en soit ainsi, if faut que l = 1; on est
' donc conduit à supposer l = 1 et c'est là une conséquence que
' Lorentz avait obtenue par une autre voie. ...
'
' Lorentz est amené également à supposer que l'électron en mouvement
' prends la forme d'un ellipsoide aplati; ...
'
' Mais avec l'hypothèse de Lorentz, l'accord entre les formules
' ne se fait pas tout seul; on l'obtient, et en même temps une
' explication possible de la contraction de l'électron, en supposant
' que l'électron, déformable et compressible, est soumis à une sorte
' de pression constante extérieure dont le travail est proportionnel
' aux variations du volume.
'
' Mais ce n'est pas tout: Lorentz, dans l'Ouvrage cité, a jugé
' nécessaire de compléter son hypothèse en supposant que toutes les
' forces, quelle qu'en soit l'origine, soient affectées, par une
' translation, de la même manière que les forces électromagnétiques,
' et que, par conséquent, l'effet produit sur leurs composantes
' par la transformation de Lorentz est encore défini par les
' équations (4)."
'
Poincaré, "Sur la dynamique de l'électron.", Comptes rendues 140