Sunday, April 29, 2007

Henri Poincaré


Today is the birthday of Henri Poincaré. Physicist know the Poincaré group of translations and Lorentz transformations, and the Poincaré conjecture about the topology of 3-spheres became widely known last year as the one millennium problem that has been its proofed by a reclusive Russian named Perelman.

But the man behind these concepts is probably not as well know as he deserves to be, considering that he contributed enormously to diverse areas of mathematics and physics. He is better known in France, where he was born on April 29, 1854, in Nancy in Lorraine, but beware: If you see a place, or street in France called Poincaré, it is most probably named after his cousin Raymond Poincaré, who was premier minister and president of the French Republic in 1913-1920.

In physics, Henri Poincaré is most famous for his contributions to the three-body problem, and, of course, to the theory of the electron and the special theory of relativity.


Poincaré discussing with Marie Curie at the 1911 Solvay Congress, while Einstein stands behind. (Source: Solvay Congress 1911)


It is not so easy today to form an unbiased opinion of what Poincaré achieved with respect to relativity, and to give a fair tribute to his and Einstein's respective work and results. That's in part because his original papers about the special theory of relativity are not easily available - I had been searching for a long time before finding some scanned copies to have a glimpse in his 1905 paper, "Sur la dynamique de l'electron", Comptes Rendues 140, 1504-8, and his 1906 paper "Sur la dynamique de l'electron", Rendiconti del Circolo matematico di Palermo 21, 129-176.

It seems that although Poincaré stated a version of the principle of relativity, understood the problems involving simultaneity, formulated the group property of the Lorentz transformations, and postulated the invariance of the laws of physics with respect to different inertial frames, he stayed convinced that all this was a consequence of the detailed dynamics of matter in the rest frame of the ether. A good description of the current understanding of this issue by a historian of science is The Mystery of the Einstein Poincaré Connection, by Olivier Darrigol in Isis 95 (2004) 614–626. Alas, his birthday is to short, even using apparent time, to read all these papers, or the book by Galison, Einstein's Clocks, Poincaré's Maps, which discusses all these topics and contains a biographical sketch of Henri Poincaré...




TAGS: , ,

20 comments:

Frank said...

In a recent conversation me and a friend hit upon the role deconstruction playsin physics. Within the language of structuralism, it is clear that empiricsmprovides us with a center for our structures. They are not in free play, however the inversion characteristic in deconstruction, that reversal of hierarchies in which that which was to be deduced becomes the new center from which the original assumptions can now in term be deduced, is characteristic of many of the greatest insights of modern physics, especially in the beginning of the last century.

I always thought, when reading about Poincare/Einstein debate, the Einsteins achievement with special relativity was just this sort of inversion, or more prosaically put: He turned the theory of Poincare from it's head onto it's feet.



It is funny that the structural philosophical terminology to describe these insights was developed 50+ years later, out of entirely different motivations.

fh

Thomas Larsson said...

A couple of years ago I found a book by Poincare in my father-in-law's library. In this book, printed in 1911 (Swedish translation printed in 1911, didn't say when French original was printed), Poincare discusses Lorentz' modifications of ether theory with great enthusiasm and in great length, whereas he never mentions Einstein.

On a related note, ether theory was alive, if not well, when Paul Ehrenfest gave his inaugural speech in 1912, 25 years after the Michelson-Morley experiment and seven years after 1905.

Anonymous said...

I became familiar with Poincare's achievements more through his work in the three-body problem, rather than his work in relativity. Indeed, it seems Poincare may have been the first person to get the earliest glimpse of chaos theory.

changcho

Pioneer1 said...

I like Poincare's essays. But in the link that you posted to the book Einstein's Clocks, Poincaré's Maps http://www.fas.harvard.edu/~hsdept/bios/galison-einsteins-clocks.html the first sentence is "True time would never be revealed by mere clocks--of this Newton was sure." Then it goes on to imply that clocks measure time or that "Times" replace "time".

I doubt that Poincare would have believed that clocks measured time. To believe that comparison of two oscillators is anything other than a comparison of two oscillators is like believing that following celebrities is astronomy. Calling an oscillator "clock" does not make it a measurer of time neither calling a human "star" makes that human a celestial body.

stefan said...

Frank,

I don't understand a word of what you try to say ;-)... the "prosaic formulation", however, is probably too easy to be correct. For example, Poincaré writes in "La Science et l'Hypothèse" (1902), as cited in the Darrigol paper:

It matters little whether the ether really exists; that is the affair of the metaphysicians. The essential thing for us is that everything happens as if it existed, and that this hypothesis is convenient for the explanation of phenomena. [...] no doubt, someday the ether will be thrown away as useless.

Einstein's special relativity indeed starts from the assumption of principles, that of relativity, and of the constancy of the speed of light, wile Poincaré's work is anchored in the dynamical theories of the electron. However, Darrigol also cites form "La Science et l'Hypothèse" that Poincaré generally pleaded for a "physics of principles" that organized theories around stable principles, rather than attempting the sort of arbitrary, molecular constructions found in the older, Laplacian physics..

So, the differences, and congruences, of the views of both Einstein and Poincaré are quite sublte... I guess that's one of the reasons why Darrigol has chosen the title "The Mystery of the Einstein-Poincaré Connection" for his paper...

Best, stefan

stefan said...

Thomas,

Poincaré has written several semi-popular books, which seem to have been quite well-known and much read at the time. The book you mention could have been a translation of his 1902 "La Science et l'Hypothèse", which contains a description of Lorentz theory. The french text is available from the Archives Henri Poincaré at the University of Nancy - unfortunately, the link to the English translation is broken.

So, no wonder that Einstein is not mentioned in the book - it seems, on the contrary, that Einstein has read it and may have been influenced by it. This point is dicussed in more detail in the Darrigol paper.

However, also after 1905 both Einstein and Poincaré did not explicitly mention the respective contributions of the other.

Thanks for the reference to Ehrenfest! - The Wikipedia link says that the title of his inaugural lecture was "About the crises of the light-ether hypothesis" - that seems to be a fair title for such a speech in 1912, when many physicists still hold to the ether ;-)... think of Victor Jakob, the hero of the Night Thoughts of a Classical Physicist...


Best, stefan

stefan said...

changcho,

thank you for reminding us of Poincaré's discovery of deterministic chaos! Somehow, that's more apart from the physics I have been in touch with lately, so I nearly forgot about it... but indeed, I first heard of Poincaré in relation with Poincaré sections and Poincaré maps and their fractal structure in expositions of chaos theory I read in the late eighties...

Ivar Peterson cites from Poincaré's 1908 essay "Science and Method" that

... it may happen that small differences in the initial conditions produce very great ones in the final phenomena. A small error in the former will produce an enormous error in the latter. Prediction becomes impossible, and we have the fortuitous phenomenon.

- that's deterministic chaos!

Best, stefan

stefan said...

Pioneer,


I strongly doubt that your doubt that Poincare would have believed that clocks measured time is justified...

I am not an expert on Poincaré, but just about time and simultaneity, in all his writings he emphasizes the role of conventions to establish these very concepts.

So, would you not agree that the statement that exact clocks measure time, or, even more strongly, that clocks establish time, pefectly fit into this conventionalistic way of thinking that was a trademark of Poincaré? As he states about the ether - everything else "is the affair of the metaphysicians"...


Best, stefan

Pioneer1 said...

Hi Stefan, thanks for your reply.

I may be confusing Poincare with Mach. I think it was Mach who said that time was an abstraction.

But I question, regardless of Poincare's belief, that "clocks measure time."

How do physicists test if a quantity is measurable?

There was a physicists at MIT, the story goes, who was trying to duplicate Big Bang in his basement. He also invented a gadget to measure soul. To test his gadget he took it to a James Brown concert and he observed how the needle behaved.

After the concert, he did extensive error analysis and he concluded that more measurements were needed because the needle did not move in a statistically significant way. So he set out to build a more precise version of his apparatus measuring soul.

This all sounds like nice physics. But how do you convince a non-physicist that soul is not a quantity which can be measured with a gadget? I would say that notions such as soul, cool, time are concepts which cannot be measured with an oscillator because there is no proof that they interact with the measuring instrument.

Is there a method physicists use to test what is measurable and what is not?

Thanks, for thought provoking post.

Bee said...

Hi Pioneer,

the idea is not to measure 'time' itself (I too wouldn't know how to do it), but to measure observables against observables, that is relations in which time only appears in intermediate steps but not as an entity by itself. (There is a name for that but I forgot, sorry, will let you know if it comes to my mind.) To give you an example: you measure the redshift of an object (may it be a star or an ambulance) and you measure the intensity (may it be the brightness of the star or the volume of the sound). Now you can attempt to understand both as a function of time. But this isn't necessary. You can instead examine the redshift as a function of the amplitude (or vice versa), which are both direct observables and the relation between both you want to predict with your theory - whether or not you 'know' what time is. Subsequently, if you have done so, you can use them to define a notion of 'time' - if you want to.

Hope this helps. Best,

B.

Pioneer1 said...

Bee, thank you for your reply.

I cannot agree with your statement that "the idea is not to measure 'time" itself..." In physics time is defined as "time is what clocks measure." http://www.pitt.edu/~gbelot/Courses/06-1/0610/3slides.pdf Do you agree with this definition?

I am unable to agree with your statement that "time only appears in intermediate steps but not as an entity by itself." If you write a term and then cancel it that term is superfluous and it should not be included in the derivation. Cancelling terms are placeholders which cannot be measured.

Neither measurement of redshift nor the measurement of volume of sound involves the measurement of time.

I don't understand what you mean by "which are both direct observables and the relation between both you want to predict with your theory..."

What is my theory?

I think there is a difference between defining "a notion of 'time'" and measuring time. Defining is not measuring.

It appears that you are saying that you define time as a useful label. I am interested in the relationship of "time" and "clocks." I don't think your answer clarifies this issue.

Is there a test in physics which can test if time is a measurable quantity?

Thanks for replying.

Bee said...

Hi Pioneer,

What is my theory?

Well, I don't know what 'your theory' is. My sentence was supposed to say 'this is what the theory one wants to test needs to predict'. Sorry for being sloppy with the wording. Also, I have to apologize, please keep in mind: I am not a native speaker. I do my best, but its not always sufficient.

I cannot agree with your statement that "the idea is not to measure 'time" itself..." In physics time is defined as "time is what clocks measure." http://www.pitt.edu/~gbelot/Courses/06-1/0610/3slides.pdf Do you agree with this definition?

No, because it's not a definition. As I've pointed out elsewhere, it's a meaningless statement unless one clarifies what a clock is.

You kind of miss the point I was trying to make. What time is, is an open question. One of THE open questions in quantum gravity. There is no answer I can give you, and I doubt you have one. What I was trying to point out is that one can do physics nevertheless. As I have explained above, by relating direct observables to observables. Yes, for this, time is nothing but a useful label.

It appears that you are saying that you define time as a useful label. I am interested in the relationship of "time" and "clocks." I don't think your answer clarifies this issue.

No, it doesn't. If you want to find out what the relation between 'clocks' and 'time' is, I would recommend you start with defining both. Best,

B.

Pioneer1 said...

Hi Bee,

it's a meaningless statement unless one clarifies what a clock is.

I agree with your assessment that this is a meaningless statement. It is a double definition like Newton's definition of force with mass and mass with force. But this is the accepted definition of both time and clock in physics as explained here (note 1)

-------
We can get around [the problem of defining time without knowing what it is] by defining time operationally. This means that we're not going to worry about what time "really" is, we're just going to figure out how to measure it, and call whatever we're measuring "time." So, the operational definition of time (and the definition we're going to use) is: "Time is what you measure with a clock."

So what is a clock?

If time is something you measure on a clock, then what is a clock? One good definition of a clock is something that measures regular intervals of time. Is this circular? You bet....but since we don't "really" know what time is, it is very difficult to avoid circular definitions."
------

What I was trying to point out is that one can do physics nevertheless.

I agree too that one can do physics without time. But this is not relevant to the problem of meausuring time. I am trying to find out about how time is measured by clocks while it is not known if time is a measurable quantity.

If you want to find out what the relation between 'clocks' and 'time' is, I would recommend you start with defining both.

I am not really looking to define time or clock. It is a given in physics that time is measured by clocks. I believe that in this case physicists are confusing timekeeping with measuring time. What physicists are doing is timekeeping not measuring time.

And also, if a physicist associates an oscillator with soul then I would like to know if soul is a measurable quantity. If a physicist associates time with an oscillator then I would like to expect the physicist to prove first that time is a measurable quantity. There is no scientific evidence that an oscillator measures time.

Is there a test physicists use to test if time is a measurable quantity by an oscillator?

This is interesting subject so I posted the thread for reference in my Mediawiki that I just got installed. Also, I think you are a great writer who is able to explain difficut subjects with clarity and to the point. I should be the one apologizing for not reading what you wrote carefully.

Thanks again for your reply.

Bee said...

Hi Pioneer,

But this is the accepted definition of both time and clock in physics as explained here (note 1)

I couldn't care less what some guy writes in his notes that you found somewhere in the web, and I doubt very many of my colleagues would agree that this is 'an accepted definition of both time and clock in physics'. I have tried to point out that indeed many physicists are scratching their head about the question what time is, and you are more than welcome to think about it. However, as I have said before, for almost all cases one can do without defining it. Or, to put it more precisely, it doesn't matter what time is. One way or the other, this is not my field. Best,

B.

Pioneer1 said...

I just wanted to say that my quote was taken from lecture notes from University of Illinois and represents the official view of time in physics. That time is what clocks measure is taught to students in the physics classroom. I believe that your view on time is an unorthodox one. This is not surprising to me since this is what Perimeter Institute is about.

The fact that some physicists consider that physics can be done without time does not eliminate the fact that other physicists measure time with oscillators. There is no scientific justification for the assumption that oscillators labeled clocks measure time. You may reject it but Relativity theories are based on this assumption. Future generations will be puzzled why physicists of today were so active in the study of paranormal and mystical such as measuring time with oscillators.

Bee said...

Pioneer,

I just wanted to say that my quote was taken from lecture notes from University of Illinois and represents the official view of time in physics.

I just wanted to say that your idea of an 'official view' in physics is bullshit. If there was one, you'd definitely not find it by googling for somebody's lecture notes.

I believe that your view on time is an unorthodox one. This is not surprising to me since this is what Perimeter Institute is about.

As I've tried to say repeatedly, my view is not unorthodox at all. For practical purposes it is sufficient to treat time naively as what is measured by a clock. This works in almost all areas. This is also what you would teach beginning students (at least I would. I most definitly wouldn't start a lecture on GR saying we don't know what spacetime is anyhow). On a deeper level however, one might want to understand how that comes that time is what it is, what we observe about it and why. There are not many people working on this, true. But this doesn't mean the rest thinks there is an definition of time. It means that the rest (including me) rather works on something different.

Best,

B.

Thomas Larsson said...

Whereas I agree that time is what a clock measures, things become more subtle when you take quantum mechnics into account. Let me quote from quant-ph/0303106:

"Time is widely recognized as a parameter in quantum mechanics, and no one emphatically asserts this conviction in recent times more than Sakurai’s assertion in his well known textbook—“The first important point we should keep in mind is that time is just a parameter in quantum mechanics, not an operator. In particular, time is not an observable. It is nonsensical to talk about the time operator in the same sense as we talk about the position operator.”1 On the other hand, the scalar status of time has been seen as a weakness of quantum theory. Von Neumann has much earlier categorically expressed this view—“First of all we must admit that this objection [time being just a number] points at an essential weakness which is, in fact, the chief weakness of quantum mechanics. In fact, while all other quantities are represented by operators, there corresponds to time an ordinary number-parameter t, just as in classical mechanics.”2"

My own understanding is that there are tacit assumptions about the mass of the observer: in QM, the observer is heavy so that a clock-measuring experiment produces a c-number, while in GR the observer is light not to disturb the gravitational field.

Pioneer1 said...

Hi Bee,
For practical purposes it is sufficient to treat time naively as what is measured by a clock.

To me physics is an experimental science. I would not teach a known falsehood for "practical purposes." If time is not a measurable quantity and if some physicists are claiming to have measured it by using oscillators, then, this reduces physics into magic. If physicists routinely measure unmeasurable quantities then physics' reputation as an experimental science needs to be reevaluated.

As far as I know there is no test which tests if time is a measurable quantity. I understand that this is not what you are working now. Thanks for replying.

Thomas,

if you believe that "time is what a clock measures" do you have the answer to my question: Is there a test physicists use to convince themselves that time is a measurable quantity? Thanks.

Thomas Larsson said...

Pioneer1,

The rate that my children grow up and my hair turn grey is undeniablly a measure of time.

Pioneer1 said...

The rate that my children grow up and my hair turn grey is undeniablly a measure of time.

Thanks. The example you give may indeed be a measure of time. But your hair does not measure time. My hair may be greying faster than yours, does that mean that time is running faster? And someone whose hair is not greying would tell us that time is not changing. Same with any oscillator. By comparing the periods of two oscillators you only measure the difference of periods, not time.

Can oscillators measure time because they are named clocks? In order for an oscillator to measure time, time needs to interact with the oscillator. How do physicists test that time is a quantity measurable by clocks?