Reading Group
The reading group of the quantum history project meets every second Wednesday at 11 am to study and discuss important source texts in the history of quantum theory. On the alternating Wednesdays, we have presentations of work in progress by guests and locals.
25/24.02.2011, , MPIWG: Workshop The Crisis of the Old Quantum Theory
Reading Material:
Helium
Born, Max. 1923. "Quantentheorie und Störungsrechnung." Naturwissenschaften 11: 537-542.
Correspondence in 1923
Born-Bohr-Correspondence 1923 AHQP BSC 9.2
General Reflection
Pauli, Wolfgang. 1926. Parts 24-27 of "Quantentheorie." In Hans Geiger and Karl Scheel (ed.), Handbuch der Physik, Bd.23. Berlin: Springer, 1-278: 147-169.
Precirculated material for discussion
Protocoll of the first Discussion on crisis
28.04.2010, 10 a.m., MPIWG: Bohr's Correspondence Principle
Reading Material:
There are English translations of both papers. They can be found in the Bohr Collected Works, Vol. 3 (in Jaume Navarro's office).
21.4.2010, 11 a.m., MPIWG: Quantum Conditions and Correspondence Principle.
We will be looking at material for the treatment of quantum conditions in the book. Since the primary literature is extensive, and I am not aware of a very comprehensive overview from the time, I propose to look at the standard historical treatments and some examples of historical sources.
Reading Material:
P. 93-118 of Jammer, Max. 1989. The Conceptual Development of Quantum Mechanics. 2nd ed. New York [u.a.]: McGraw-Hill. Note that the download contains all of chapter 3. For our discussion you only need to read the first two sections.
Supplementary reading:
Ehrenfest, P. and Tolman, R.C. 1924. Weak Quantization. Physical Review 24, 287-295.
Bokulich, Alisa. 2008. Three Puzzles about Bohr's Correspondence Principle. Preprint.
3.2.2010, 11 a.m., MPIWG: The Crisis of the Old Quantum Theory.
This will be a brainstorming session to decide what issues we want to address in the section in our book. As primary material I have somewhat randomly selected a few statements by theoreticians from 1923/24 that addressed the current status of quantum theory. But I want to encourage everybody to look for other material of relevance.
Reading Material:
Max Born, "Quantentheorie und Störungsrechnung." Naturwissenschaften 11 (1923),537-542.
Secondary literature:
25.11.2009, 11 a.m., MPIWG: The Construction of the Time-Dependent Schrödinger Equation
We will discuss the notebook by Schrödinger in which he derives for the first time the time-dependent Schrödinger equation and compare it with the text of the fourth communication.
Reading Material:
Schrödinger, Erwin. 1926. Research Notebook 18-12 (pdf file of the whole notebook).
The pdf is quite highly compressed. If you want a higher resolution, you can also look at the individual pages on our viewer:
Schrödinger, Erwin. 1926. Research Notebook 18-12 (page viewer).
11.11.2009, 11 a.m., MPIWG: Perturbation Theory in Wave Mechanics.
We will look at the sections on perturbation theory in Schrödinger's Mitteilungen zur Wellenmechanik (communications on wave mechanics). In the third communication, Schrödinger tackles time-independent perturbation theory (pp. 437-457) and applies it to the Stark effect. In the fourth communication, he develops time-dependent perturbation theory and treats dispersion theory on pp. 112-132.
Reading Material:
28.10.2009, 11 a.m., MPIWG: Perturbation Theory in Matrix Mechanics.
We will look at the sections on perturbation theory in the first papers on matrix mechanics.
Reading Material:
Heisenberg, Werner. 1925. "Über die quantentheoretische Umdeutung kinematischer und mechanischer Beziehungen." Zeitschrift für Physik 33: 879-893.
Relevant here is the treatment of the anharmonic oscillator on p. 887-890.
Born, Max and Jordan, Pascual. 1925. "Zur Quantenmechanik." Zeitschrift für Physik 34: 858-888.
The anharmonic oscillator is treated on p. 875-883.
Born, Max, Heisenberg, Werner and Jordan, Pascual. 1926. "Zur Quantenmechanik II." Zeitschrift für Physik 35: 557-615.
Perturbation theory is treated on pp. 565-572 and 585-590.
Additional material:
Born, Max. 1924. "Über Quantenmechanik." Zeitschrift für Physik 26: 379-395.
This contains Born's treatment of perturbation theory in his pre-1925 paper on discrete calculus in quantum theory. It might be an interesting piece of evidence about the transition from old QT to QM.
14. 10. 2009, 11 a.m., MPIWG: Perturbation Theory in the Old Quantum Theory.
We will look at the chapter on perturbation theory from Born's textbook, in an attempt to understand the historical background of perturbation theory.
Reading Material:
Born, Max. 1925. "Störungstheorie." In: Vorlesungen über Atommechanik. Berlin: Springer, 282–341.
30. 9. 2009, 11 a.m., MPIWG: The Born-Hückel Paper.
We continue to study the so-called applications of the new formalism of quantum mechanics in fields outside atomic physics, with a focus on the contribution of developments in quantum chemistry, solid-state physics, or nuclear physics, to the ongoing conceptual development of quantum mechanics. After studying the Heitler and London paper on the covalent bond last time, we have decided to go back in time and take a look at the 1923 paper by Born and Hückel.
Reading Material:
Secondary literature:
16. 9. 2009, 11 a.m., MPIWG: The Heitler-London Paper.
We will study the 1927 paper by Heitler and London as an example for the "application" of quantum mechanics.
Reading Material:
Secondary literature:
Supplementary material:
12. 8. 2009, 4 p.m., MPIWG: The measurability of quantum fields.
We will have a special session with Anja Skaar Jacobsen and Don Salisbury on the debate between Landau/Peierls and Bohr/Rosenfeld about the measurability of quantum fields:
Secondary literature:
8.7.2009, 11 a.m., MPIWG: John von Neumann's "Mathematical Foundations of Quantum Mechanics": Measurement and Reversibility.
We will study chapter 5 and 6 of John von Neumann's book:
Neumann, Johann von. 1932. Mathematische Grundlagen der Quantenmechanik. Berlin: Julius Springer.
The scan comprises the whole book, so you can orient yourself. The relevant passages for our discussion are pages 184-237.
24.6.2009, 11 a.m., MPIWG: John von Neumann's "Mathematical Foundations of Quantum Mechanics"
We will study chapter 3 and 4 of John von Neumann's book in comparison to his papers:
Neumann, Johann von. 1932. Mathematische Grundlagen der Quantenmechanik. Berlin: Julius Springer.
The scan comprises the whole book, so you can orient yourself. The most relevant passages for our discussion will presumably be pages 101-134 and 157-183.
10.6.2009, 11 a.m., MPIWG: John von Neumann's statistical foundation of quantum mechanics (continued)
After our excursion into the realm of models and analogy, we will return to the discussion of John von Neumann's statistical foundation of quantum mechanics.
Readings are the same as for our May 20 session.
3.6.2009, 11 a.m., MPIWG: Models and Analogy in Physics
Following our discussion of the use of analogy in Schrödinger's research, we decided to devote a special session to some background reading on models and analogy in physics, from a broader perspective.
The entry on Models in Science (Roman Frigg, Stephan Hartmann) in the Stanford Encyclopedia of Philosophy might also be helpful.
27.5.2009, 11 a.m., MPIWG: Christian Joas and Shaul Katzir, Analogy, Extension and Novelty: Young Schrödinger on Dielectric Phenomena
Erwin Schrödinger's contributions to quantum mechanics have received a lot of attention in the historical literature. The same cannot be said about his earlier theoretical work. Our paper, tentatively titled "Analogy, Extension, and Novelty: Young Schrödinger on Dielectric Phenomena," not only discusses the ambitious novel theory of solids Schrödinger advanced in 1912, but also his style of research and, especially, his fertile use of analogies that would also play a role in his later contributions to quantum mechanics.
Schrödinger, Erwin. 1912. "Studien über Kinetik der Dielektrika, den Schmelzpunkt, Pyro- und Piezoelektrizität." Sitzungsberichte der kaiserlichen Akademie der Wissenschaften in Wien. Mathematisch-naturwissenschaftliche Klasse (IIa) 121: 1937-1972. This is the main source discussed in our talk.
Joas and Katzir, "Analogy, Extension and Novelty: Young Schrödinger on Dielectric Phenomena," our working paper which will be presented in our talk.
Joas and Katzir, "Reconstruction of Schrödinger’s 1912 Paper on Dielectrics," a modern reconstruction of the calculations in Schrödinger's 1912 paper.
20.5.2009, 11 a.m., MPIWG: John von Neumann's statistical foundation of quantum mechanics
We will study the second paper by von Neumann on quantum mechanics:
Secondary literature:
Redei, Miklos. 1996. "Why John von Neumann did not like the Hilbert space formalism of quantum mechanics (and what he liked instead)." Studies in History and Philosophy of Modern Physics 27: 493-510.
(This has a much wider scope, but seems to contain some interesting remarks about von Neumann's aims in the paper.)
22.4.2009, 11 a.m., MPIWG: Jordan's "Neue Begründung"
We will return to Jordan's "Neue Begründung" once more.
08.04.2009, 11 a.m., MPIWG: Jordan's "Neue Begründung"
We will discuss the two following papers by Pascual Jordan:
Secondary literature:
In addition, the following primary sources are provided as supplementary material for further reading:
25.3.2009, 11 a.m., MPIWG: John von Neumann's Hilbert space formalism for quantum mechanics
We will study the first paper by von Neumann on the Hilbert space formalism:
Additionally, the previous paper of Hilbert, Nordheim, and von Neumann, might help to understand the background:
Secondary literature:
11.3.2009, 11 a.m., MPIWG: The reception of Dirac’s quantum electrodynamics
We will discuss the reception of Dirac's second quantization using Fermi's overview paper and a textbook chapter.
Fermi, Enrico. 1932. "Quantum Theory of Radiation." Rev. Mod. Phys. 4: 87-132.
25.2.2009, 11 a.m., MPIWG: Dirac’s quantum electrodynamics revisited
We will return to Dirac's quantum electrodynamics once more.
11.2.2009, 11 a.m., MPIWG: Dirac’s quantum electrodynamics revisited
We will return to Dirac's quantum electrodynamics once more, trying to understand his aims and methods in comparison with his work on transformation theory.
Secondary literature:
For the specialists, also the following application of Dirac's quantum electrodynamics to the issue of dispersion might be interesting:
28.01.2009, 10 a.m., MPIWG: Quantized matter waves - General Discussion.
We will attempt to sum up our discussions of the beginnings of quantum field theory from the last few months. Reading is the material from before, especially from the sessions on 1.10., 29.10., and 12.11. Dieter Fick has pointed out to me an overview paper by Jordan on the light quantum hypothesis, which might help to gain a general perspective. It can be found at:
21.01.2009, 11 a.m., MPIWG: Scott Walter will give a talk on the following subject:
The prehistory of Thomas precession in relativistic kinematics
The support provided to Uhlenbeck and Goudsmit's 1925 hypothesis of a
spinning electron by L.H. Thomas's calculation of a relativistic
precession effect -- which gave rise to "Thomas precession" -- has a
negative twin of sorts in the early history of Minkowskian
relativity. My talk will discuss the work on relativistic kinematics in
1913 by Émile Borel in Paris, and by Ludwig Föppl and P.J. Daniell in
Göttingen. Geometric illustrations of velocity composition, I will
suggest, lent additional credence to Thomas's classical picture of the
spinning electron.
Monday, 12.1.2009, 11 a.m., MPIWG: Pauli and Jordan on the exclusion principle and quantized matter waves.
Sources:
Pauli, Wolfgang. 1926. "Über Gasentartung und Paramagnetismus," Zeitschrift für Physik 41: 81-102.
17.12.2008, 3:30 p.m., MPIWG: Marta Jordi will give a presentation on the following subject:
From classical to quantum physics through optical dispersion
In this session of the reading group I will present a project proposal for my PhD dissertation, which deals with the role of the relation between theoretical models and experiments on optical dispersion in paving the way for the matrix mechanics.
I will give a long historical perspective, arguing that a satisfactory physical explanation of optical dispersion did not become possible until the advent of quantum mechanics, although it was already known and analyzed since Newton and Descartes. This will allow me to present it as a borderline problem between theories of light and matter, as a good understanding of the phenomenon requires a model of both as well as of their mutual interaction, a task more challenging that the construction of models of light and matter separately.
I will then focus on the relation between new experimental data and theoretical insights in continuous reevaluation during the period between the late 19th century and the 1920s, from the point of view of a more general understanding of the interaction between the emerging quantum theory and inherited classical knowledge. The secondary literature addressing the issue in these terms is scarce. I will conclude with some open questions and observations to be answered in the further development of my PhD project, in order to get suggestions and feedback from the audience on the general approach.
I will conclude with some open questions and observations to be answered in the further development of my PhD project, in order to get suggestions and feedback from the audience on the general approach.
Finally, I will also present the idea of a small workshop to be held next year at the Max Planck Institute for the History of Science aimed at exploring from this epistemological perspective the history of optical dispersion from Newton to quantum mechanics.
Secondary literature:
Before the reading group session it could be useful to read the third part (“The dispersion theory as the bridge between the quantum old theory and matrix mechanics“) of the following paper:
03.12.2008, 11 a.m., MPIWG: Arianna Borrelli will give a presentation on the following subject:
Dirac's bra-ket notation and the notion of quantum state
In the early history of quantum theories, the introduction of mathematical forms whose features were not fully determined (q-numbers, operators) and the employment of non-rigorous mathematical procedures (manipulation of infinite matrices, divergent integrals) were the rule rather than the exception. The present paper attempts a more positive assessment of what is often negatively described as “vague physical concepts” and “non-rigorous mathematics”, evaluating their contribution to the emergence of non-classical notions, and focussing in particular on the role played in this context by changes in mathematical-physical notation.
The example discussed is the “bra-ket” notation for quantum theory, which Paul Dirac introduced in 1939 claiming that it “provides a neat and concise way of writing, in a single scheme, both the abstract quantities themselves and their coordinates, and thus leads to a unification of ideas”. The new formalism, while in some ways problematic, closely matched and reinforced a style of quantum-theoretical thought focussing not on physical objects, but rather on states and transitions. It could help students interiorize this form of thought and, with its peculiar graphic structure, it lent itself to non-rigorous extensions used by experimentalists and philosophers, and, occasionally, also by theoreticians.
26.11.2008, 11 a.m., MPIWG: Anja Skaar Jacobsen will give an account of her current work in progress. No preparatory reading material is required.
Rosenfeld in early quantum field theory
In my talk I will briefly present my book project with the tentative title Niels Bohr’s “paper tiger”: Léon Rosenfeld in physics, ideology, and history. I will then proceed to topics from my project that seem most relevant from the point of view of the quantum physics reading group, viz., Rosenfeld’s involvement with early quantum field theory while in Zurich working with Pauli, and later his collaboration with Bohr in Copenhagen in the early 1930s. When Rosenfeld began to work part of each year in Copenhagen he was immediately involved in a controversy between Bohr and Landau-Peierls about the consistency of quantum electrodynamics. The controversy resulted in the Bohr-Rosenfeld paper of 1933, famous and notorious among physicists, on the measurability of the electromagnetic field. However, Landau and Peierls seem never to have been convinced by it. I will end by a brief outline of the work I will be doing on the Bohm-Rosenfeld controversy during the Cold War while I am in Berlin.
12.11.2008, 11 a.m., MPIWG: Jordan and quantized matter waves II.
Sources:
Jordan, Pascual and Pauli, Wolfgang. 1928. "Zur Quantenelektrodynamik ladungsfreier Felder," Zeitschrift für Physik 47: 151-173.
Secondary literature (as before):
29.10.2008, 11 a.m., MPIWG: Jordan and quantized matter waves.
Sources:
Jordan, Pascual. 1927. "Zur Quantenmechnik der Gasentartung." Zeitschrift für Physik 44: 473-480.
Jordan, Pascual. 1929. "Der gegenwärtige Stand der QED", Physikalische Zeitschrift 30: 700–713.
Secondary literature:
15.10.2008, 11 a.m., MPIWG: Christoph Lehner will give an account of his current work in progress. No preparatory reading material is required.
Einstein on Reality and Quantum Mechanics
One of the standard charges levelled against Einstein's critique of the Copenhagen interpretation of quantum mechanics is that it is based on a "naive" concept of reality that is not only out of touch with the philosophical sophistication of modernity, but simply has been disproven by modern physics. Various critics of Copenhagen have argued that Einstein's realism is not philosophically naive at all. However, its exact meaning has been difficult to pin down. Going back to Einstein's reflections on the meaning of relativity in his two theories of relativity, I will offer a new analysis of Einstein's concept of "physical reality". Rather than being disproven by the developments of twentieth century physics, I argue that Einstein's considerations throw light on the theoretical apparatus of modern physics up to this day. I will discuss Einstein's critique of the Copenhagen interpretation in the light of this concept of physical reality.
1.10.2008, 11 a.m., MPIWG: Dirac’s first paper on quantum electrodynamics
Secondary literature:
18.06.2008, 10 a.m., MPIWG: The 1927 Solvay Conference II
We will look at the general discussion at the Solvay Conference, p. 478-523 of the Bacciagaluppi/Valentini manuscript. Since there was interest in looking at experimental data available in 1927,
I propose that we also look at the talk by A. H. Compton, in Bacciagaluppi/Valentini, p. 331-374.
4.06.2008, 10 a.m., MPIWG: The 1927 Solvay Conference
We want to look at the discussions about how to understand quantum mechanics at the 1927 Solvay Conference. We will look at the contributions by de Broglie, Born and Heisenberg, and Schrödinger, and at the general discussion. An English translation of the text can be found at, thanks to Guido:
Please note that I put up all of the book manuscript, this also includes a historical introduction and a discussion of the main topics. As secondary literature we can look at the introduction, p. 30-150.
If you would rather look at the German manuscripts of Schrödinger, Born and Heisenberg, you have to study them on microfilm, since the AHQP reel that they are on has not been scanned yet. (It is in the AHQP supplements Richardson collection). We have also ordered a copy of the French original volume.
21.05.2008, 10 a.m., MPIWG: Bohr's Complementarity Principle
Bohr, Niels. 1928. "The Quantum Postulate and the Recent Development of Atomic Theory." Nature 121: 580-590.
Secondary literature:
Kalckar's introduction to Volume 6 of Niels Bohr's Collected Works constitutes a good source of information about the discussions around Bohr's argument.
7.05.2008, 10 a.m., MPIWG: The Uncertainty Principle
Heisenberg, Werner. 1927. "Über den anschaulichen Inhalt der quantentheoretischen Kinematik und Mechanik." Zeitschrift für Physik 43: 172-198.
Secondary literature:
A standard account is
Jammer, Max. 1989. "The Copenhagen Interpretation (Chapter 7)." In The Conceptual Development of Quantum Mechanics. New York [u.a.]: McGraw-Hill, 343-383.
For the discussion with Bohr following the publication of Heisenberg's paper:
Murdoch, Dugald. 1987. "The Uncertainty Principle." In Niels Bohr's Philosophy of Physics. Cambridge: Cambridge University Press, 46-54.
23.04.2008, 10 a.m., MPIWG: Transformation theory of Dirac and Jordan
As agreed in the previous session, we will continue following the history of transformation theory, and will discuss the paper in which John von Neumann formulated Quantum Mechanics in terms of Hilbert spaces:
Neumann, Johann von. 1927. "Mathematische Begründung der Quantenmechanik." Nachrichten von der Gesellschaft der Wissenschaften zu Göttingen: 1-57.
This paper is rather long and full of mathematical details, but we might focus on those parts in which the physical interpretation is discussed. The structure of the paper is the following:
§ I: Statement of the problem and methodology
§§ II-IV: Step-by-step introduction of Hilbert spaces
§§ V-VI: Statement and proof of the properties of Hilbert spaces
§§ VII-X: Operators and Eigenvalue problems in Hilbert space
§ XI (erroneously labeled IX!): Definition of the absolute value of an operator
§§ XII-XV: New formulation of quantum mechanics
Mathematical appendixes.
In my opinion, the most interesting parts for our present discussion thread are §§ I-IV, with the arguments for introducing Hilbert spaces, and §§ XI-XV, with the new formulation of QM.
An additional suggested reading for this session is:
Hilbert, David, Neumann, Johann von and Nordheim, Lothar. 1928. "Über die Grundlagen der Quantenmechanik." Mathematische Annalen 98: 1-30.
The two papers are independent form each other, but it may be interesting to compare the two approaches. The Hilbert et al. paper was based on lectures by Hilbert prepared by Nordheim, and von Neumann only contributed to it mathematical computations.
In addition, Michel has pointed out that it might be worthwhile to take a look into:
Lacki, Jan. 2000. "The Early Axiomatizations of Quantum Mechanics: Jordan, von Neumann and the Continuation of Hilbert's Program." Archive for the History of Exact Sciences 54: 279-318.
9.04.2008, 10 a.m., MPIWG: Transformation theory of Dirac and Jordan
Dirac, Paul Adrien Maurice. 1927. "The Physical Interpretation of Quantum Dynamics." Proceedings of the Royal Society, Series A 113: 621-641.
Jordan, Pascual. 1927. "Über eine neue Begründung der Quantenmechanik (1)." Zeitschrift für Physik 40: 809-838.
Jordan, Pascual. 1927. "Über eine neue Begründung der Quantenmechanik (2)." Zeitschrift für Physik 44: 1-25.
Secondary literature:
Jammer, Max. 1989. "Statistical Transformation Theory (Chapter 6)." In Max Jammer (ed.), The Conceptual Developement of Quantum Mechanics. 2nd ed. New York [u.a.]: McGraw-Hill, 299-342.
19.03.2008, 10 a.m., MPIWG: Talk on Pascual Jordan (Harald Schumacher)
12.03.2008, 10 a.m., MPIWG: Beginnings of Quantum Field Theory II
The background of the treatment of quantum field theory in the "Dreimännerarbeit":
Einstein, Albert. 1909. "Zum gegenwärtigen Stand des Strahlungsproblems." Physikalische Zeitschrift 10: 185-193.
Einstein, Albert. 1909. "Über die Entwicklung unserer Anschauungen über das Wesen und die Konstitution der Strahlung." Deutsche Physikalische Gesellschaft, Verhandlungen 7: 482-500.
Debye, Peter. 1910. "Der Wahrscheinlichkeitsbegriff in der Theorie der Strahlung." Annalen der Physik 33: 1427-1434.
Ehrenfest, Paul. 1925. "Energieschwankungen im Strahlungsfeld oder Kristallgitter bei Superposition quantisierter Eigenschwingungen." Zeitschrift für Physik 34: 362-373.
Bothe, Walter. 1927. "Zur Statistik der Hohlraumstrahlung." Zeitschrift für Physik 41: 345-351.
Secondary literature:
Relevant parts of
Klein, Martin J. 1964. "Einstein and the Wave-Particle Duality." The Natural Philosopher 3: 3-49.
Bach, Alexander. 1989. "Eine Fehlinterpretation mit Folgen: Albert Einstein und der Welle-Teilchen Dualismus." Archive for History of Exact Sciences 40: 173-206.
27.02.2008, 10 a.m., MPIWG: Beginnings of Quantum Field Theory
We will look at the beginnings of quantum field theory in the "Dreimännerarbeit":
Born, Max, Heisenberg, Werner and Jordan, Pascual. 1926. "Zur Quantenmechanik II." Zeitschrift für Physik 35: 557-615.
Secondary literature:
Relevant parts of
Darrigol, Olivier. 1986. "The Origin of Quantized Matter Waves." Historical Studies in the Physical and Biological Sciences 16: 197-253.
and
Duncan, Anthony and Jannsen, Michel. 2007. "Pascual Jordan's resolution of the Condrum of the Wave-Particle Duality of Light." HQ1-Proceedings.
30.01.2008, 10 a.m., MPIWG: Pauli's Exclusion Principle
We will discuss the paper in which Wolfgang Pauli proposed the exclusion principle:
[1] Pauli, Wolfgang. 1925. "Über den Zusammenhang des Abschlusses von Elektronengruppen im Atom mit der Komplexstruktur der Felder." Zeitschrift für Physik 31: 765-783.
The paper was chosen because it constitutes a premise to the development of Fermi-Dirac statistics, which we have often discussed in the last meetings together with the Bose-Einstein one.
One of the questions we plan to address is the relationship between Pauli's new principle and previous interpretations of atomic
spectroscopy, as for example Bohr's model. There is a vast amount of literature on Pauli's exclusion principle. A short
discussion of the 1925 paper by Pauli and of those which closely preceded (and followed) it can be found in:
[2] Van der Waerden, Bartel L. 1960. "Exclusion Principle and Spin." In M. Fierz and V. Weisskopf (ed.), Theoretical Physics in the Twentieth Century. New York: lnterscience, 199-244.
16.01.2008, 10 a.m., MPIWG: P.A.M. Dirac, On the Theory of Quantum Mechanics (3)
Our reading group will come back to the indistiguishability problem. Dirac's 1926 paper "On the Theory of Quantum Mechanics" [1] will be discussed again, along with Heisenberg's related 1926 paper "Mehrkörperproblem und Resonanz in der Quantenmechanik" [2] which is slightly earlier and was quoted by Dirac in a note added in proof.
In his paper, Heisenberg reached the same results as Dirac regarding the necessity of symmetrizing or anti-symmetrizing many-particle wavefunctions and regarding the relationship between (anti-)symmetrization and statistical behavior of particles. It appears worthwhile to compare the different approaches of the two authors: Where Dirac brought forward formal and rather generic arguments on identical particles, Heisenberg focussed on explaining the structure of the Helium spectrum, making use of matrix mechanics to interpret it in terms of a physical "resonance" between particles which are equivalent ("gleich", "gleichberechtigt").
Main texts:
[1] Dirac, Paul Adrien Maurice. 1926. "On the Theory of Quantum Mechanics." Proceedings of the Royal Society, Series A 112: 661-677.
[2] Heisenberg, Werner. 1926. "Mehrkörperproblem und Resonanz in der Quantenmechanik." Zeitschrift für Physik 38: 411-426.
Supplementary literature:
Carson, Cathryn. 1996. "The Peculiar Notion of Exchange Forces - I: Origins in Quantum Mechanics, 1926-1928." Studies in History and Philosophy of Modern Physics 27: 23-45.
19.12.2007, 10 a.m., MPIWG: P.A.M. Dirac, On the Theory of Quantum Mechanics (2)
Our reading group will continue along the lines of the Dec. 5 session and focus on paragraphs 2 and 5 of Dirac's paper "On the theory of Quantum mechanics" [1]. §2 presents Dirac's reading of Schrödinger's theory and offers a comparison between matrix and wave mechanics, which we would like to compare to Schrödinger's own [2]. §5, entitled "Theory of Arbitrary Perturbations" is devoted to a perturbative derivation of the Einstein coefficients (for absorption and stimulated emission) on the basis of wave mechanics (see Einstein 1916 [3]). In a sense, the last paragraph is thus very much related to the probabilistic interpretation. We therefore propose Born 1926 as further suggested reading [4] (for convenience, we also included the second paper by Born on the subject [5] for those who are interested).
It is our feeling that there is still some need for discussion of the indistinguishability problem. We will, however, defer this discussion to the first meeting in 2008, because some of the main contributors to the discussion will not be present next week.
Main texts:
[1] Dirac, Paul Adrien Maurice. 1926. "On the Theory of Quantum Mechanics." Proceedings of the Royal Society, Series A 112: 661-677.
Supplementary literature:
[2] Schrödinger, Erwin. 1926. "Über das Verhältnis der Heisenberg-Born-Jordanschen Quantenmechanik zu der meinen." Annalen der Physik 79: 143-165.
[3] Einstein, Albert. 1916. "Strahlungs-emission und -absorption nach der Quantentheorie." Deutsche Physikalische Gesellschaft, Verhandlungen 18: 318-323.
[4] Born, Max. 1926. "Zur Quantentheorie der Stossvorgänge." Zeitschrift für Physik 37: 863-867.
[5] Born, Max. 1926. "Quantenmechanik der Stossvorgänge." Zeitschrift für Physik 38: 803-27.
05.12.2007, 10 a.m., MPIWG: P.A.M. Dirac, On the Theory of Quantum Mechanics (1)
An early reaction to Schrödinger’s wave mechanics, this paper has a quite composite structure, consisting of four parts dealing with: (1) general formulation of quantum mechanics; (2) systems of similar particles; (3) [Fermi]-Dirac statistics; (4) perturbation theory. Discussions on any of these themes are encouraged. However, some of us would particularly welcome a discussion of sections 2 and 3, for example on Dirac’s operationalization of the concepts of “similar” and “indistinguishable” particles or states; his choices in defining and counting atomic states in terms of electronic quantum numbers (Daniela Monaldi); his procedures of (anti)-symmetrization of wave functions with their implicit assumptions and consequences and their connection to Bose-Einstein statistics and Pauli’s exclusion principle (Arianna Borrelli).
Main texts:
Dirac, Paul Adrien Maurice. 1926. "On the Theory of Quantum Mechanics." Proceedings of the Royal Society, Series A 112: 661-677.
Supplementary literature:
Dirac, Paul Adrien Maurice. 1995. "Symmetrical and antisymmetrical states." In The Principles of Quantum Mechanics. Oxford: Clarendon Press, 206-211.
Heisenberg, Werner. 1958. "Der Mathematische Apparat der Quantentheorie." In Physikalische Prinzipien der Quantentheorie: Hochschultaschenbücher-Verlag, 92-97.
Heisenberg, Werner. 1930. "Mathematical Apparatus." In Werner Heisenberg (ed.), The physical principles of the quantum theory: Dover Publications Inc., 152-157.
22.11.2007, 10 a.m., MPIWG: Hilbert on Quantum Mechanics
Main texts:
Hilbert, David. 1926/1927. "Introduction to the lecture course: 'Mathematical Methods of Quantum Theory'.".
Hilbert, David. 1926/1927. "Transcription to lecture course: 'Mathematical Methods of Quantum Theory'." 131-156.
Supplementary literature:
Hilbert, David, Neumann, Johann von and Nordheim, Lothar. 1928. "Über die Grundlagen der Quantenmechanik." Mathematische Annalen 98: 1-30.
Schirrmacher, Arne. 2003. "Planting in his Neighbor's Garden: Daivd Hilbert and Early Göttingen Quantum Physics." Physics in Perspective 5: 4-20.
8.11.2007, 10 a.m., MPIWG: Lanczos and Schrödinger on the Continuous Representation of Quantum Mechanics
Main texts:
Lanczos, Cornelius. 1926. "Über eine feldmäßige Darstellung der neuen Quantenmechanik." Zeitschrift für Physik 35: 812-830.
Schrödinger, Erwin. 1926. "Über das Verhältnis der Heisenberg-Born-Jordanschen Quantenmechanik zu der meinen." Annalen der Physik 79: 143-165.
W. Pauli, Letter to P. Jordan, 12.4.1926
Supplementary literature:
Waerden, B. L. van der . 1997. "From Matrix Mechanics and Wave Mechanics to Unified Quantum Mechanics." Notices of the AMS 44: 323-328.
25.10.2007, 10 a.m., MPIWG: Born and Wiener: Operators in Matrix Mechanics
Main texts:
Born, Max and Wiener, Norbert. 1926. "A New Formulation of the Laws of Quantization of Periodic and Aperiodic Phenomena." J. Math. and Phys 5: 84-98.(English)
Born, Max and Wiener, Norbert. 1926. "Eine neue Formulierung der Quantengesetze für periodische und nicht periodische Vorgänge." Zeitschrift für Physik 35: 174-187. (German)
Supplementary literature:
Wiener, Norbert. 1926. "The Operator Calculus." Mathematische Annalen 95: 557-584.
27.09.2007, 10 a.m., MPIWG: Paul Dirac
Main texts:
Dirac, Paul Adrien Maurice. 1925. "The Fundamental Equations of Quantum Mechanics." Proceedings of the Royal Society, Series A 109: 642-653.
Supplementary literature:
(1) McCubbin, Norman. 2004. "Beauty in Physics: the Legacy of Paul Dirac." Contemporary Physics 45: 319-333.
(2) Darrigol, Olivier. 1992. "Queer Numbers." In From "c"-numbers to "q"-numbers: The Classical Analogy in the History of Quantum Theory. Berkeley: Univ.of California Press, 319-333.
13.09.2007, 10 a.m., MPIWG: Matrix Mechanics 2
Supplementary literature:
(1) Cassidy, David. 1992. "Principles and Politics (Ch. 9) and Quantum Multiplying (Ch. 10)." In Uncertainty: The Life and Science of Werner Heisenberg. New York: Freeman, 155-203.
(2) Darrigol, Olivier. 2003. "Quantum Theory and Atomic Structure, 1900-1927." In Mary Jo Nye (ed.), The Modern Physical. Cambridge: Cambridge University Press, 331-349.
(3) Duncan, Anthony and Michel Janssen. 2007. "On the verge of Umdeutung in Minnesota: Van Vleck and the correspondence principle (Part One)."
(4) Duncan, Anthony and Michel Janssen. 2007. "On the verge of Umdeutung in Minnesota: Van Vleck and the correspondence principle (Part Two)."
(5) Hilbert, David. 1922/23. Mathematische Grundlagen der Quantentheorie, Vorlesung WS 1922/23, ausgearbeitet von Lothar Nordheim und Gustav Heckmenn (Mathematisches Institut Göttingen; AHQP Mf. 17 Sec. 2; NL Born 1920), S. 82-87.
30.08.2007, 10 a.m., MPIWG: Matrix Mechanics
Main texts:
(1) Heisenberg, Werner. 1925. "Über die quantentheoretische Umdeutung kinematischer und mechanischer Beziehungen." Zeitschrift für Physik 33: 879-893.
(2) Born, Max and Jordan, Pascual. 1925. "Zur Quantenmechanik." Zeitschrift für Physik 34: 858-888.
(3) Born, Max, Heisenberg, Werner and Jordan, Pascual. 1926. "Zur Quantenmechanik II." Zeitschrift für Physik 35: 557-615.
Supplementary material:
(4) Kramers, Hendrik A. and Werner Heisenberg. 1924. "Über die Strueuung von Strahlung durch Atome." Zeitschrift für Physik 31: 681-708.
(5) Kramers, Hendrik A. 1924. "The Quantum Theory of Dispersion." Nature 114: 310-311.
(6) Kramers, Hendrik A. 1924. "The Law of Dispersion and Bohr's Theory of Spectra." Nature 133: 673-676.
(7) Heisenberg, Werner. 1926. "Über quantentheoretische Kinematik und Mechanik." Mathematische Annalen 95: 683-705.
02.08.2007, 10 a.m., MPIWG:
Talk Adrian Wuethrich
Feynman Diagrams
Supplementary material:
(1) Euler, Hans. 1936. "Über die Streuung von Licht an Licht nach der Diracschen Theorie." Annalen der Physik: 398-448.
(2) Koba, Ziro and Fakeda, Gyo. 1949. "Radiation Reaction in Collision Process III1. First Radiative Correction for an Arbitrary Process Including Electrons, Positrons, and Light Quanta." Progress of Theoretical Physics 4: 60-70.
(3) Koba, Ziro and Fakeda, Gyo. 1949. "Radiation Reaction in Collision Process III2. First Radiative Correction for an Arbitrary Process Including Electrons, Positrons, and Light Quanta." Progress of Theoretical Physics 4: 130-141.
(4) Weinberg, Steven. 1977. "The Search for Unity: Notes for a History of Quantum Field Theory." Daedalus 106: 17-35.
21.06.2007, 10 Uhr, MPIWG: Wave Mechanics 2
(1) Summary of reading group questions on wave mechanics
(2) Schrödinger, Erwin. 1926. "Der stetige Übergang von der Mikro- zur Makromechanik." Die Naturwissenschaften 14: 664-666.
(3) Schrödinger, Erwin. 1926. "Über das Verhältnis der Heisenberg-Born-Jordanschen Quantenmechanik zu der meinen." Annalen der Physik 79: 143-165.
(4) Hanle, Paul A. 1977. "Erwin Schrodinger's Reaction to Louis de Broglie's Thesis on the Quantum Theory." Isis 68: 606-609.
(5) Hanle, Paul A. 1971. "The Coming of Age of Erwin Schrodinger: His Quantum Statistics of Ideal Gases." Archive for History of Exact Sciences 17: 165-192.
(6) Kragh, Helge. 1982. "Erwin Schrödinger and the Wave Equation: The Crucial Phase." Centaurus 26: 154-197.
(7) Klein, Martin J. 1964. "Einstein and the Wave-Particle Duality." The Natural Philosopher 3: 3-49.
(8) Raman, Varadaraja V. and Forman, Paul. 1969. "Why Was It Schrödinger Who Developed De Broglie's Ideas?." Historical Studies in the Physical Sciences 1: 291-314.
(9) Wessels, Linda A. 1979. "Schrödinger's Route to Wave Mechanics." Studies in History and Philosophy of Science 10: 311-340.
07.06.2007, 10 a.m., MPIWG: Wave Mechanics
(1) Schrödinger, Erwin. 1926. "Quantisierung als Eigenwertproblem (Erste Mitteilung)." Annalen der Physik 79: 361-376.
(2) Schrödinger, Erwin. 1926. "Quantisierung als Eigenwertproblem (Zweite Mitteilung)." Annalen der Physik 79: 486-527.
24.05.2007, 10 a.m., MPIWG: Schlick and Reichenbach
Continuation of the talk by Olaf Engler
(1) Heisenberg, Werner. 1926. "Quantenmechanik." Die Naturwissenschaften 14: 989-994.
(2) Reichenbach, Hans. 1920. "Philosophische Kritik der Wahrscheinlichkeitsrechnung ." Die Naturwissenschaften 8: 146-153.
(3) Schlick, Moritz. 1920. "Naturphilosophische Betrachtungen über das Kausalprinzip." Die Naturwissenschaften 8: 461-474.
10.05.2007, 10 Uhr, MPIWG: Schlick und Reichenbach
Vortrag Olaf Engler
Wissenschaftliche Philosophie und moderne Physik um 1920
Abstract
Als Moritz Schlick am Vormittag des 18. September 1922 in der überfüllten Alberthalle des Krystallpalastes zu Leipzig im Eröffnungsvortrag anläßlich der Einhundertjahrfeier der Gesellschaft deutscher Naturforscher und Ärzte seinen Empirismus zum Sieger in der wissenschaftphilosophischen Auseinandersetzung um die moderen Physik erklärt, sind Werner Heisenberg und Wolfgang Pauli unter den Zuhörern. Schlick hatte in den Jahren zuvor mit freundschaftlicher Unterstützung Einsteins intensive Debatten mit Vertretern kantischer, neukantischer und sensualistisch-positivistischer Auffassungen geführt und sich schließlich mit seiner Position behauptet. Auf der Grundlage von veröffentlichten Texten und unveröffentlichtem Materialien wird der Vortrag einen Überblick der um das Jahr 1920 geführten wissenschaftsphilosophischen Debatten unter besonderer Berücksichtigung der Auseinandersetzungen zwischen Schlick, Reichenbach und Cassirer geben und ausführen, weshalb sich Schlick mit seinen Argumenten durchsetzen konnte. Schlicks Position, die man präzise als Empirismus mit gegenstandskonstitutiven Prinzipien
bezeichnen sollte, erweist sich dabei nicht nur als am besten vereinbar mit der Relativitätstheorie Einsteins, sondern ist daneben attraktiv genug, um von der aufstrebenden Generation junger Quantenphysiker als philosophische Leitidee für die Konstruktion ihrer Theorien akzeptiert zu werden.
26.04.2007, 10 Uhr, MPIWG: Bose-Einstein Statistics
(1) Wolfke, M. 1921. "Einsteinsche Lichtquanten und räumliche Struktur der Strahlung." Physikalische Zeitschrift 22: 375-379.
(2) Broglie, Louis de. 1922. "Sur les interférences et la théorie des quanta de lumière." Comptes Rendus 175: 811-813.
(3) Bose, Satyendranath. 1924. "Plancks Gesetz und Lichtquantenhypothese." Zeitschrift für Physik 26: 178–181.
(4) Einstein, Albert. 1924. "Quantentheorie des einatomigen idealen Gases." Sitzungsberichte der Preussischen Akademie der Wissenschaften. Physikalisch-Mathematische Klasse: 261-267.
(5) Einstein, Albert. 1925. "Quantentheorie des einatomigen idealen Gases. Zweite Abhandlung." Sitzungsberichte der Preussischen Akademie der Wissenschaften. Physikalisch-Mathematische Klasse: 3-14.
(6) Schrödinger, Erwin. 1926. "Zur Einsteinschen Gastheorie." Physikalische Zeitschrift 27: 95-101.
12.04.2007, 10 a.m., MPIWG: Louis de Broglie
(1) Broglie, Louis de. 1923. "Les quanta, la théorie cinétique des gaz et le principe de Fermat." Comptes Rendus des Seances de L´Academie des Sciences (Paris) 177: 630-632.
(2) Broglie, Louis de. 1923. "Ondes et quanta." Comptes Rendus des Seances de L´Academie des Sciences (Paris) 177: 507–510.
(3) Broglie, Louis de. 1923. "Quanta de lumière, diffraction et interférences." Comptes rendus 177: 548-450.
(4) Broglie, Louis de. 1924. "A Tentative Theory of Light Quanta." Philosophical Magazine 177: 446-458.
(see also: Broglie, Louis de. 1927. Untersuchungen zur Quantentheorie. Leipzig: Akademische Verlagsgesellschaft.)
13.03.2007, 16 a.m., MPIWG: Einstein's Emission Theory
Einstein, Albert. 1916. "Strahlungs-Emission und -Absorption nach der Quantentheorie." Deutsche Physikalische Gesellschaft, Verhandlungen 18: 318-323.
Einstein, Albert. 1916. "Zur Quantentheorie der Strahlung." Physikalische Gesellschaft, Mitteilungen (Zürich) 16: 47-62.
22.02.2007, 10 a.m., MPIWG: Quantentheorie von Planck und Einstein
Büttner, Jochen and Olivier Darrigol and Dieter Hoffmann. 2000. "Revisiting the Quantum Discontinuity." MPIWG-preprint.
Einstein, Albert. 1905. "Über eine die Erzeugung und die Verwandlung des Lichtes betreffenden heuristischen Gesichtspunkts." Annalen der Physik 17: 132-148.
Planck, Max. 1900. "Zur Theorie des Gesetzes der Energievertheilung im Normalspektrum." Deutsche Physikalische Gesellschaft, Verhandlungen 2: 237-245.