> Almost interestingly, perhaps for the "econophysics"
> crowd, Einstein gets all the credit for this, but it
> was actually an economist who invented the equations.
> Louis Bachelier's PhD dissertation "Theorie de la
> Speculation" invented the Brownian motion equations to
> describe an early version of the Efficient Markets
> Hypothesis.
that's interesting.
i looked at Pais' bio of Einstein and found zip for Bachelier in the section on Brownian motion, though Pais does admit at one point that all of E.'s work in this area was not necessarily first-of-kind. I'd be curious to see what Bachelier did to compare with E. Can you recommend a paper on his stuff i could look through?
contents of his thesis: http://www.gabay.com/sources/Liste_Fiche.asp?CV=9
more on finance: http://cepa.newschool.edu/het/schools/finance.htm http://cepa.newschool.edu/het/profiles/bachelier.htm
hmmm, Poincare on Bachelier: http://www.iaes.org/journal/aej/sept_99/dimand/dimand.htm
something bothers me about this article, but its perhaps of interest: http://www.linguafranca.com/9712/9712hyp.html
my guess would be, until i see Bachelier's stuff and compare and snoop around some, is that Einstein probably did not even know about his work. After all, E. hadn't even read Lorentz's paper when he wrote his first on Special Relativity. So, i can see someone trying to clear up the notion that all of E.'s work was completely novel (and after all, who's is?). But it appears from reading stuff at these links that even economists didn't pick up on Bachelier's stuff right away (Samuelson in the 60's???). and i am wondering whether B.'s work was too early in the history of financial markets to be of significance in the same way that E.'s stuff hit just at the time when the atomic and quantum shit hit the fan <question mark>
from: http://www.isye.gatech.edu/cap/96-workshop/reading-list.html
"It is easy to pinpoint the birth of mathematical finance: the thesis "Theory of Speculation," presented to the Faculty of Sciences of the Academy of Paris on March 29, 1900, by Louis Bachelier for the degree Docteur es Sciences Mathematiques. Bachelier not only made a brilliant application of mathematics to the problem of evaluating the price of a call option, but he invented what came to be called Brownian motion for the purpose of modeling the price of the underlying stock. Unfortunately, Bachelier's fantastic work was ignored and forgotten for half a century. It is unclear why he did not receive more credit for inventing Brownian motion, but perhaps he received little attention for his option pricing model because Brownian motions become negative, whereas stock prices do not. "
of course, by now, we have random walks with reflecting walls, directed random walks, etc.
mandelbrot, Bachelier, Physics in economics: http://guava.physics.uiuc.edu/~nigel/articles/mandelbrot.html (scum suckers)
sci-am article: http://www.sciam.com/1998/0598issue/0598stix.html
interesting physics critique of Bachelier (Gaussian or not): http://backissues.worldlink.co.uk/articles/08091999111756/04.htm
the most comprehensive take on Bachelier i could find in 30 minutes of searching: http://www.aros.net/~vlyon/tfme/1tfme13.htm
be curious to hear what the resident econs say on this one, i don't know beans about economics, other than that supply-and-demand curves and equilibria sound fishy to me.
so, back to my point, which was mainly that Einstein had no problem using statistical techniques and viewpoints in his work, and in fact is noted for a number of such contributions.
d^2's comments on Bachelier made me go back and hone up a little more on the history of E.'s statistical work, its (i'm tempted to add 'of course') broader than i first alluded to.
Abraham Pais' wrote a bio on E: Subtle is the Lord, The Science and the life of Albert Einstein. Pais himself is a physicist, and also knew E. personally at Princeton. I think they even collaborated briefly on some things.
There's so much here its hard to condense without another long email, but if this interests anyone, Pais' book has a whole section, chapters 4 and 5, devoted to E's. Statistical Theory's, and its relation to quantum physics. see also the Introduction pp. 18 through the middle 0f 20. One of the interesting things about the work on Brownian motion, as Pais points out, is the numerous times E. makes connection with the for then modern experimental results. this is a place where it would be interesting to compare Bachelier's work with E, to see in what ways B. made deep connections to the ""experimental sciences"" around him.
>From Pais:
"As we now know, although it was not at once clear then, in the early part of the twentieth century, physicists concerned with the foundations of statistical mechanics were simultaneously faced with two tasks. Up until 1913, the days of the Bohr atom, all evidence for quantum phenomena came either from blackbody radiation or from specific heats. In either case, statistical considerations play a key role . Thus the struggle for a better understanding of the principles of classical statistical mechanics was accompanied by the slowly growing realization that quantum effects demanded a new mechanics and, therefore, a new statistical mechanics. The difficulties encountered in separating the two questions are seen nowhere better than in a comment Einstein made in 1909: Once again complaining about the complexions [les: the counting of micro-states and their contributions to thermodynamics quantities], he observed, 'Neither Herr Boltzmann nor Herr Planck has given a definition of W'. Boltzmann, the classical physicist, was gone when those words were written. Planck, the first quantum physicist, had ushered in theoretical physics of the twentieth century with a new counting of complexions which had absolutely no logical foundation whatsoever -- but which gave him the answer he was looking for. Neither Einstein, deeply respectful and at the same time critical of both men, nor anyone else in 1909 could have foreseen how odd it would appear, late in the twentieth century, to see the efforts of Boltzmann and Planck lumped together in one phrase.
In summary, Einstein's work on statistical mechanics prior to 1905 is memorable first because of his derivation of the energy fluctuation formula and second because of his interest in the volume dependence of thermodynamic quantities, which became so important in the discovery of the light-quantum. [snip] Out of his concern with the foundations of statistical mechanics grew his vastly more important applications to the theoretical determination of the Boltzmann constant. These applications are the main topic of the next chapter, where we meet Einstein in the year of his emergence, 1905. One of the reasons for his explosive creativity in that year may well be the liberation he experienced in moving away from the highly mathematical foundation questions which did not quite suit his scientific temperament."
a perhaps not inappropriate quote in closing, one of my favorite, and an eloquent (to a physics buff) call for getting a grasp on the need for a history of science. the nub to me is in the phrase "__had to be__ introduced", speaking on the history of the idea of quantum spin:
"It was a little over fifty years ago that George Uhlenbeck and I introduced the concept of spin...It is therefore not surprising that most young physicists do not know that spin had to be introduced. They think that it was revealed in Genesis or perhaps postulated by Sir Isaac Newton, which most young physicists consider to be about simultaneous."
Samuel A. Goudsmit, address to American Physical Society (Feb. 1976), quoted on p. 424, An Introduction to Quantum Physics, French and Taylor
thanks for the heads up, dd.
les schaffer
p.s. a few pages later French and Taylor, in a nice historical touch, have a photograph of the front and back of the actual postcard sent from Walter Gerlach to Niels Bohr detailing the first results from the Stern-Gerlach experiment, showing 'the experimental proof of directional quantization'. (1921)
The back of the card itself has two pasted-on photos of the glass plate on which silver atoms collected after passing through a region first without, then with, a magnetic field. Each looks schematically like this:
Ag atoms Ag atoms
deposited deposited
on plate on plate
| / \
| / \
| / \ <-------
| \ / magnetic field
| \ / (stronger in center)
| \ /
no field "how the hell does each
one know to go left or
right?"