HPS 2590 Einstein 1905

Tuesdays, 9:30-11:55am, 2004. G28 CL
John D. Norton, 1017CL, 4-5896, jdnorton@pitt.edu

Department of History and Philosophy of Science
University of Pittsburgh

The fine print
Einstein's corpus of 1905
Advance work
Sources and readings
Projects
Schedule
Possible Readings


The fine print. Participants in this seminar are expected to attend regularly, read the assigned readings and take their turn in presenting material. The final grade is based on these presentations and on an essay to be submitted on Friday April 23 in 1017CL by 4:45 pm. My policy is NOT to issue incomplete grades, excepting in extraordinary circumstances. I really do want your essays completed and submitted by the end of term. I do not want them to linger on like an overdue dental checkup, filling your lives with unnecessary worry and guilt. In return for the rigidity of the deadline, the seminar will not meet in the final week of term (Tuesday April 20). The essay may be on any subject of relevance to the seminar. To assist you in commencing work, I ask you submit an essay proposal to me by Tuesday March 23. The proposal need only be brief. It should contain a short paragraph describing the topic to be investigated and give a brief indication of the sources you intend to use. Do talk to me about possible topics!

Einstein's corpus of 1905

This seminar will center on the reading of Einstein's papers of 1905, his annus mirabilis, and their interpretation in the history of science literature. The papers comprising the corpus are:

"A New Determination of Molecular Dimensions" (Einstein's doctoral dissertation) (30 April 1905)
Buchdruckerei K. J. Wyss, Bern, 1906.
Also: Annalen der Physik, 19(1906), pp. 289-305.
This is Einstein's doctoral dissertation, submitted after much delay to the University of Zurich. In it he uses available physical data on the diffusion of sugar in solution and the effect of dissolved sugar on the solution's viscosity to determine the size of sugar molecules and Avogadro's number. The analysis makes the kinetic theory of heat more definite, in so far as it provides a measure of the real size of molecules, so that they cannot be dismissed as easily as useful fictions. It is the least impressive of Einstein's work of 1905 although, curiously, the most cited.
"On the motion of small particles suspended in liquids at rest required by the molecular-kinetic theory of heat." (Brownian motion paper) (May 1905; received 11 May 1905)
Annalen der Physik, 17(1905), pp. 549-560.
In this paper Einstein reports that the kinetic theory of heat predicts that small particles suspended in water must execute a random motion visible under the microscope. He suspects this motion is Brownian motion but has insufficient data to affirm it. The prediction is a powerful test of the truth of the kinetic theory of heat. A failure to observe the effect would refute the theory. If it is seen and measured, it provides a way to estimate Avogadro's number. The domain in which the effect is observed is one in which the second law of thermodynamics no longer holds, a disturbing result for the energeticists of the time.
"On the electrodynamics of moving bodies" (special relativity) (June 1905; received 30 June 1905)
Annalen der Physik, 17(1905), pp. 891-921.
Einstein develops the special theory of relativity in this paper. His concern, as he makes clear in the introduction, is that then current electrodynamics harbors a state of rest, the ether state of rest, and the theory gives very different accounts of electrodynamic processes at rest or moving in the ether. But experiments in electrodynamics and optic have provided no way to determine which is the ether state of rest of all inertial state of motion. Einstein shows that Maxwell-Lorentz electrodynamics has in fact always obeyed a principle of relativity of inertial motion. We just failed to notice it since we tacitly thought that space and time had Newtonian properties, not those of special relativity.
"Does the inertia of a body depend on its energy content?" (E=mc2) (September 1905; received 27 September 1905) Annalen der Physik, 18(1905), pp. 639-41.
Written as a brief follow-up to the special relativity paper, this short note derives the inertial of energy: all energy E also has an inertia E/c2.
"On a heuristic viewpoint concerning the production and transformation of light." (light quantum/photoelectric effect paper) (17 March 1905)
Annalen der Physik, 17(1905), pp. 132-148.
While the victory in the 19th century of the electromagnetic wave theory of light over Newton's corpuscle view is undeniable, Einstein shows that its success is incomplete. The theory gives incorrect results for the analysis of heat radiation. He looks at the thermodynamic properties of high frequency heat radiation and finds that this radiation behaves just like a collection of many spatially localized units ("quanta") of energy of magnitude hf (h=Planck's constant, f=frequency). He proceeds to show how this quantum view of light makes sense of several experiments in electrodynamics and optics, the best know being the photoelectric effect. He then described the paper as "revolutionary."

Advance work.

Here is what I want you to do prior to my presentation on each of these papers.

"A New Determination of Molecular Dimensions" (Einstein's doctoral dissertation)

Read the paper. Einstein is using known properties of sugar solutions to fix values for the size of sugar molecules P and Avogadro's number N. One might have hoped that data on diffusion of sugar alone might be sufficient. But it turns out to give an expression for NP only. Einstein needs a second relation between N and P to recover individual values. He arrives at it from his analysis of the effect of solutes on the viscosity of a solution. The analysis is in Sections 1-2. It is very tough going and should be skimmed (on a first read). The conlcusion that matters is stated in the last paragraph of Section 2. "If very small spheres are suspended in a liquid, ..."

What is Stokes' law? Under what conditions does it obtain?
What is osmotic pressure?What law relates osmotic pressure to temperature?
How is the coefficient of diffusion defined?

What is Einstein's stated purpose?
Find two approximations used in his calculations. Are the approximations licit?

"On the motion of small particles suspended in liquids at rest required by the molecular-kinetic theory of heat." (Brownian motion paper)

Read the paper. The central results of the paper are in Sections 4-5. In Section 4, a stochastic model of Brownian motion is used to generate the expression for the root mean square displacement of particles. In Section 5, the expected magnitude of the motion is computed from values of the size of particles and Avogadro's number. Sections 1-3 play the supporting role of generating an expression for the diffusion coefficient used in Sections 4-5 in terms of Avogadro's number and particle size. The analysis of Section 2 is independently noteworthy in that it reveal the extremely general statistcal mechanical basis of the ideal gas law and its reappearance as the law governing partial pressures in dilue solutions. (The analysis is very similar to the core argument of the light quantum paper.)

What is Brownian motion?
What is free energy? How is it used to express the condition of thermal equilibrium for a system maintained at constant temperature? How can it be used to recover an expression for the pressure of a thermodynamic system?
What is the diffusion equation? What are its typical solutions?

How does the Brownian motion paper build on and improve the analysis of Einstein's dissertation?

"On the electrodynamics of moving bodies" (special relativity)

Read the paper. The first "kinematical" part contains the developement of the special theory of relativity as a new theory of space and time. It is the most celebrated part of the most celebrated scientific paper of the 20th century and should be studied closely. It is mathematically easy, excepting a somewhat overcomplicated derivation of the Lorentz transformation in Section 3. (Almost any other development will give a simpler derivation.) The second "elctrodynamical" part is tougher going. In it, Einstein applies the new theory of space and time to Maxwell's electrodynamics. The principal goal is to show that the theory already conforms to the principle of relativity, once we recognize that space and time behave according to special relativity. The most important calculation is in Section 6 where Einstein shows the Lorentz covariance of Maxwell's equations and that the electric and magnetic fields get mixed under transformations between inertial frames. Note that the E field has components (X,Y,Z) and the H field has components (L,M,N).

The key to special relativity is the relativity of simultaneity. Make sure you understand the notion, as laid out in Sections 1 and 2 and how Einstein shows that attending to the relativity of simultaneity in our measurement operations leads to the relativity of lengths.

The demonstration of the Lorentz covariance of Maxwell's equations of Section 6 is the most important result of the paper. If you have the math, reconstruct the proof.

In Section 10, Einstein talks of transverse and longitudinal mass. What are they? Why do they cause him trouble and what should he have used?

"Does the inertia of a body depend on its energy content?" (E=mc2)

Read the paper. The argument is short and simple, although slightly complicated by Einstein's use of transverse and longitudinal mass in electrodynamics. The main thing to see is that the goal is a relation between inertia and energy for all forms of matter, not just electromagnetic. The use of electromagnetic theory is merely the path Einstein takes to the general result.

How does Einstein manage to have his result apply to all forms of matter?

"On a heuristic viewpoint concerning the production and transformation of light." (light quantum/photoelectric effect paper)

Read the paper. The core arguments are in Sections 5 and 6. In Section 5, Einstein gives an especially lucid demonstration of this result: if a system consists of many, independent energy elements, its entropy varies with the logarithm of its volume. In section 6, Einstein notes that the entropy of high frequency radiation does vary logarithmically with volume so that it has the characteristic fingerprint of a system of many independent energy elements. The remaining Sections 7-9 give three experimental demonstrations of the localization of energy in radiation; the photoelectric effect is the best known. Earlier sections provide supporting results, including the expression for the entropy of high frequency radiation. Section 1 contains a lucid demonstration of the failure of classical physics to accommodate black body radiation.

Find Einstein's complete statement of the light quantum hypothesis in the paper. Note how it is carefully hedged.
Why does Einstein restrict his analysis to high frequency radiation? Does this mean low frequency radiation is not quantized?
If radiation turns out to be quantized, how does Einstein explain the great success of Maxwell's wave theory of light?
Planck, the lore holds, quantized energy in 1900. Is there any evidence in this paper that Einstein knows this? To what does "quanta" in the title of Section 2 refer?
Note the similarities between Einstein's argument of Section 5 and his statistical mechanical derivation of the expression for osmotic pressure in the Brownian motion paper.

Sources and readings

Einstein's Papers

John Stachel et al., eds., The Collected Papers of Albert Einstein: Volume 2: Writings, 1900-1909 Princeton University Press, 1989.
Contains facsimiles of the originals of Einstein's papers of 1905 in German. This is the standard source, with extensive editorial headnotes introducing the material and footnotes that correct minor errors in the text and develop background materials. This editorial apparatus provides the authoritative introduction to Einstein's work of 1905.

Anna Beck, translator; Peter Havas, consultant. The Collected Papers of Albert Einstein: Volume 2: Writings, 1900-1909 Princeton University Press, 1989. English translation volume.
Translation volume does not have any editorial apparatus.

John Stachel, ed., Einstein's Miraculous Year: Five Papers that Changed the Face of Physics. Princeton University Press, 1998.
English translations of the Einstein 1905 corpus. Editorial material follows Papers, Vol. 2 but in simplified form.

Albert Einstein et al., The Principle of Relativity. Dover.
A standard edition of Einstein's "On the electrodynamics of moving bodies" and "Does the inertia of a body depend on its energy content?" (E=mc2)

Albert Einstein, Investigations on the Theory of the Brownian Movement. Dover.
A standard edition that contains Einstein's Brownian motion paper and his dissertation as well as other related papers.

D. Ter Haar, ed., The Old Quantum Theory Pergamon, 1967.
Translation of Einstein's 1905 light quantum paper, along with earlier and later papers by others. Long introductory historical essay.

Secondary Literature

Abraham Pais, Subtle is the Lord: The Science and Life of Albert Einstein.Oxford: Clarendon, 1982.
The standard scientific biography of Einstein's work.

Albrecht Foelsing, Albert Einstein: A Biography. Viking, 1997.
One of the best of the many Einstein biographies.

Wolfgang Pauli, Theory of Relativity.Dover.
A reprint of Pauli's 1921 Teubner Encyclopedia article. It is both an introduction to relativity theory and a survey of the literature. An invaluable historical resource.

Max Born, Einstein's Theory of Relativity. Dover.
A reprint of Born's work, first published in 1924. It is a popular exposition but gives much of the historical background in a very accessible form.

Arthur Miller, Albert Einstein's Special Theory of Relativity Addison-Wesley, 1981.
An expansive collection of material on Einstein's paper, the background in electrodynamics preceding and subsequent developments. The exposition is not always helpful. Has a translation of the 1905 special relativity paper.

Edmund Whittaker, A History of the Theories of Aether and Electricity. Dover.
A venerable standard history. Slight idiosyncrasy in attributing special relativity to Lorentz and Poincare.

Olivier Darrigol, Electrodynamics from Ampere to Einstein. Oxford, 2000.
A more recent, solid history of 19th century electrodynamics.

Don Howard and John Stachel, eds., Einstein: The Formative Years, 1879-1909.Boston: Birkhaeuser, 1998.
Collection of new papers on Einstein's early years.

Peter Galison, Einstein's Clocks and Poincare's Maps: Empires of Time.Norton, 2003.
Pursues parallels between Einstein's 1905 treatment of clock synchrony and methods used to synchronize railroad clocks.

John Stachel, Einstein from 'B' to 'Z'.Boston: Birkhaeuser, 2002.
Collection of essays on Einstein by our leading Einstein expert.

John D. Norton, "Einstein's Special Theory of Relativity and the Problems in the Electrodynamics of Moving Bodies that Led him to it." (New version, January 17, 2004.)
Popular essay prepared for Cambridge Companion to Einstein, M. Janssen and C. Lehner, eds., Cambridge University Press.

Stephen G. Brush, The Kind of Motion We Call Heat: A History of the Kinetic Theory of Gases in the 19th Century. 2 Vols. Amsterdam: North Holland, 1976.
Stephen G. Brush, Statistical Physics and the Atomic Theory of Matter, from Boyle and Newton to Landau and Onsager. Princeton Univ. Press, 1983
Standard histories of statistical physics.

Mary Jo Nye, Molecular Reality: A Perspective on the Scientific Work of Jean Perrin. London: MacDonald, 1972.
A standard account of the atomic debates, focussing on Perrin's contribution.

Max Jammer, The Conceptual Development of Quantum Mechanics.New York: McGraw-Hill, 1966.
A standard history of quantum theory.

Projects

Some suggestions for research projects.

Pais, Subtle is the Lord:... p.89 reports that Einstein's dissertation was his most cited paper in 1970-74. Check whether this is still so and try to come to some determination over what it tells us about the relative quality and value of Einstein's papers.

Einstein's methods in his dissertation seem very fragile.
(a) Einstein's entire analysis depends on the assumption that sugar molecules are spheres. They are not.
(b) He recovers the viscosity of a sugar solution by looking at energy dissipation in one very specialized case of a fluid with spheres. How can it adequately model a sugar solution? Should we expect that a fluid, laden with spheres, continues to behave like a Newtonian fluid for which the ordinary notion of viscosity is applicable?
(c) Einstein's recovers the force on a moving sugar molecule from Stokes law. But Stokes law was derived for spheres moving uniformly in a fluid. The motion of sugar molecules in diffusion is not unidirectional or constant in magnitude.
Yet his results and methods seem to have staying power. How is this possible?

In Australia in 1905, William Sutherland independently discovered results of Einstein's 1905 dissertation on the diffusion of sugar. Compare Sutherland's work to Einstein's.

The lore is that a mighty battle was fought over the reality of atoms around 1905. Was it?

Einstein's dissertation and Brownian motion paper was part of a larger tradition of work on the reality of atoms. Review that tradition, noting the place of Perrin and the 1911 Solvay conference.

Why did Einstein choose sugar for this dissertation work?

Einstein makes much use of the relation Entropy = k log Probability, which he calls Boltzmann's principle. The principle must be used with extreme caution, since it only holds in the right contexts. Investigate Einstein's use of the principle and grounds for its applicability.

Who discovered Boltzmann's Principle? Boltzmann? Planck? Einstein?

Fluctuation phenomena, such as Brownian motion, demarcated the boundary of applicability of thermodynamics. How was this threat to thermodynamics received?

Before his concentration moved to Lorentz's version of Maxwell electrodynamics, Einstein had studied Hertz' electrodynamics. What might he have found there of relevance to his discovery of special relativity.

In his recent book Einstein's Clocks, Poincare's Maps, Galison describes a similarity between the definition of simultaneity of the Einstein's 1905 special relativity paper and the method of clock synchronization used for railroad clocks. Assess the significance of this similarity.

Einstein's 1905 work on the light quantum was derived from a statistical mechanical analysis. His 1909 elaboration of wave particle duality proceeded from an interpretation of the thermal fluctuations of radiation. How might Einstein's earlier work in the foundations of statistical physics (1902-1904) have figured in these discoveries?

Kuhn has argued that Planck did not introduce quantum discontinuity in 1900, but that it was really introduced by Einstein in 1905. Assess this claim.

Schedule of Readings for HPS 2590 Einstein 1905

Date Reading Presenter
6 January Introductory meeting
13 January The statistical papers: doctoral dissertation Norton
20 January Doctoral dissertation.
Brownian motion		 Norton
27 January Brownian motion. Norton
3 February The light quantum. Norton
Prize awarded to anyone who can equal or better my best candidate for an unexpected use of the statistical mechanical analysis of equilibrium in a field in Einstein's published papers.
...and the winner is Alexandre Guay.
10 February The light quantum. Norton
17 February The light quantum. Norton
24 February and later Special relativity and E=mc2 Norton
2 March Special relativity and E=mc2 Norton
9 March Spring recess--no classes.
16 March Special relativity and E=mc2 Norton
23 March Essay proposals due.
Nuggets from headnotes in Einstein Papers, Vol. 2. Everyone
30 March Laszlo Szabo, "Does special relativity tell us anything new about space and time?"
Michel Janssen, "Reconsidering a Scientific Revolution: The Case of Einstein versus Lorentz," Physica in Perspective, 4(2002), pp. 421-446. 		Balazs Gyenis
Poincare's analysis of clock synchronization. Extracts from The Value of Science Alexander Afriat
6 April Einstein's argument in the light quantum paper.
Jon Dorling, "Einstein's Introduction of Photons: Argument by Analogy or Deduction from the Phenomena?" British Journal for the Philosophy of Science, 22 (1971), pp. 1-8. 		John Anders
Einstein's use of entropy and S=k log W in the argument for the light quantum. Bl**dy Norton again.
13 April John D. Norton, "Einstein's Investigations of Galilean Covariant Electrodynamics prior to 1905"
(Easy background reading: John D. Norton, "Einstein's Special Theory of Relativity and the Problems in the Electrodynamics of Moving Bodies that Led him to it.") 		Norton
Wrap up of survey of Einstein's 1905 corpus
John Stachel, "Introduction to Einstein: The Formative Years, pp. 1-22 in Don Howard and John Stachel, eds., Einstein: The Formative Years, 1879-1909.Boston: Birkhaeuser, 1998.		 Norton
(Very unlikely that we have time for it.) Sahotra Sarkar, "Physical Approximations and Stochastic Processes in Einstein's 1905 Paper on Brownian Motion," pp. 203- 229 in Don Howard and John Stachel, eds., Einstein: The Formative Years, 1879-1909.Boston: Birkhaeuser, 1998. Norton
20 April Reprieve. No class meeting.
Friday 23 April Papers due in 1017CL by 4:45pm

Possible Readings

Statistical physics

"Einstein on the Foundations of Statistical Physics," Papers, Vol. 2, pp. 41-55.

"Einstein's Dissertation on the Determination of Molecular Dimensions," Papers, Vol. 2, pp. 170-182.

"Einstein on Brownian Motion," Papers, Vol. 2, pp. 206-222.

Sahotra Sarkar, "Physical Approximations and Stochastic Processes in Einstein's 1905 Paper on Brownian Motion," pp. 203- 229 in Don Howard and John Stachel, eds., Einstein: The Formative Years, 1879-1909.Boston: Birkhaeuser, 1998.
Juergen Renn, "Einstein's controvery with Drude and the Origin of Statistical Mechanics: A New Glimpse from the 'Love Letters'," pp. 107-157 in Don Howard and John Stachel, eds., Einstein: The Formative Years, 1879-1909.Boston: Birkhaeuser, 1998.

Steven Brush, "Brownian Movement," Ch. 15 in The Kind of Motion We Call Heat: A History of the Kinetic Theory of Gases in the 19th Century. Vol. 2. Amsterdam: North Holland, 1976.

and more...?

Special relativity

"Einstein on the Theory of Relativity," Papers, Vol. 2, pp. 253-74.

John Stachel, "Einstein and Ether Drift Experiments," pp. 171-76 in John Stachel, Einstein from 'B' to 'Z'.Boston: Birkhaeuser, 2002.

Michel Janssen and John Stachel, "The Optics and Electrodynamics of Moving Bodies," in John Stachel, Going Critical.

John Stachel, "Einstein and Michelson: The Context of Discovery and the Context of Justification," pp. 177-190 in John Stachel, Einstein from 'B' to 'Z'.Boston: Birkhaeuser, 2002.

Robert Rynasiewicz, "The Construction of the Special Theory: Some Queries and Considerations," pp. 159-201 in Don Howard and John Stachel, eds., Einstein: The Formative Years, 1879-1909.Boston: Birkhaeuser, 1998.

Olivier Darrigol, "The Electrodynamic Origins of Relativity Theory," Historical Studies in the Physical and Biological Sciences, 26(1996), pp. 241-312; Ch. 9 of Electrodynamics from Ampere to Einstein. Oxford, 2000.

John D. Norton, "Einstein's Investigations of Galilean Covariant Electrodynamics prior to 1905"

Michel Janssen, "Reconsidering a Scientific Revolution: The Case of Einstein