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Final Report Summary - BOHRREC (Reconsidering Niels Bohr's Interpretation of Quantum Physics)

Overview of results.

Following Ernst Cassirer’s functional interpretation of natural sciences, it was the fellow's primary aim to reconsider the conceptual evolution of Max Planck’s quantum of action (viz. Planck’s constant h) from 1900 onwards. In this regard, the fellow emphasized the importance of the quantum of action in the architectonic structure of the quantum theory, in the role of an element of fundamental continuity between the old quantum theory and quantum mechanics. In reconsidering the quantum of action as a “constant of nature” à la Cassirer, the fellow succeeded in setting the role of this constant in a complex structure of functions, in the passage from the old quantum theory (1900-1924) to quantum mechanics (1925-1932).
In his "Determinism and Indeterminism in Modern Physics" (1937), Cassirer, indeed, explicitly recognized the quantum of action as a “fact of science”. For this purpose, the fellow wanted to take as a starting point of his present reflection the following Cassirer’s insight into the Planck’s constant:

“The elementary quantum of action constitutes, as it were, the fixed frame, into which all statements of quantum theory are fixed; and the security and firmness of this frame alone ought to be sufficient to protect the indeterminism of the theory against those speculative interpretations to which it was exposed in the transition from physics to general conclusions concerning man’s Weltanschauung” (p. 122).

On the basis of this understanding of the Planck’s h, the fellow laid emphasis on the principle of quantization in the role of principle of coordination of the quantum theory, as a conceptual function, springing out from the original universal constant of the quantum of action. In this regard, the principle of coordination has been refashioned into an abstract relation (Zuordnung) between a concept and its object, according to Cassirer’s pre-Symbolic Forms approach (which preceded the completion of Cassirer’s Trilogy, The Philosophy of Symbolic Forms). The relation of coordination was thus purged of “intuitive”, “visualizable”, evidential content.
Furthermore, the principle of coordination served the purpose to explain the meaning and role of the general causality principle in terms of conformity to law.
In the wake of Cassirer’s teaching, the fellow ascribed to the well-known Planck-Einstein-de Broglie relation, E = hν, the role of principle of coordination of quantum theory, although the fellow pointed out that Cassirer remained obscure on defining the principle of quantization. In fact, in contemporary physics, the quantization principle should be considered in a wider sense, involving, so to speak, the whole process of transition from a classical understanding of phenomena to a new understanding, or from classical field theory to quantum field theory, by introducing a commutative relation between a particle’s position and momentum, in the case of transition from classical to quantum mechanics, or a commutative relation between canonical coordinates and canonical momentum, in the case of a transition from classical to quantum field theory. According to the fellow, the definition of quantization principle should be left open (also in view of further applications, modifications and extension of the functional-based approach to contemporary physics that the fellow will developed later on), as it seems to imply a general procedure for constructing quantum mechanics starting from classical mechanics, while maintaining the formal structure of the latter. This is an aspect that seems to emerge from Cassirer’s analysis of Heisenberg’s early contribution to quantum mechanics: in particular (Heisenberg 1925) and (Born-Heisenberg-Jordan 1925), in which Heisenberg devoted specific attention to the conservation laws.

Achievements and Conclusions.
The fellow succeeded in demonstrating that from the introduction of the Planck’s h (and the beginning of its transition into statement of law, already in 1900) there followed three stages of generalization along the principle of quantization: Einstein’s frequency condition, Einstein’s theory of the specific heats of solids, and the quantization of the hydrogen atom by Niels Bohr. To do that, the fellow studied and analyzed the following fundamental steps as indicative of the historical development of quantum theory: 1900 (the discovery of Planck’s constant and the first theory of radiation), 1906 (Einstein’s frequency condition), 1907 (Einstein’s theory of the specific heats of solids), 1910 (the quantization of rotational energy), 1912 (Planck’s second theory of radiation), 1913 (Bohr’s first atomic theory), 1916 (Einstein’s transitions probabilities and Sommerfeld’s quantization method), 1918 (early formulation of Bohr’s correspondence principle), 1922 (the crisis of the helium model), 1924 (Bohr-Kramers-Slater theory), and 1925 (Heisenberg’s reinterpretation paper and the basis of matrix mechanics).
First, the fellow applied Cassirer’s functional reading to the first quantum theory (1900-1912); then to the old quantum theory (1913-1924), with regard to which the fellow pointed out how the early formulation of the correspondence principle fitted with a Kantian interpretation. Finally, the fellow proposed a symbolic reading of Heisenberg’s reinterpretation paper, and of the sharpening of the correspondence principle, based on Cassirer’s approach and Hermann Helmholtz’s theory of signs (1896).
Specifically, on the one hand, the fellow demonstrated that the conception underlying Bohr’s correspondence principle (1917-1924) was still bound to the classical, Kantian, doctrine of space-time intuition. On the other hand, he showed that Helmholtz’s theory of signs anticipated one of the main aspects of the 1925-quantum mechanical revolution: the numerical quantities introduced in the new quantum theory did not link with mechanical orbits, so that this new approach undermined any visualizable models of the atom, which indeed recalled the Kantian doctrine of space-time intuition. In fact, Helmholtz’s sign theory laid emphasis on one of the fundamental aspects of the new quantum mechanics: the relation between signs and designatum. According to Helmholtz, via Cassirer’s reading, the description is never a direct copy of the designated thing, but it bears a purely symbolic character. Specifically, the sign retains the objective relations in which it stands to other signs like it.
Helmholtz’s doctrine brought me to reconsider a central feature of Cassirer’s epistemological reflection: the validity of a physical concept does not rest upon its capacity of representing “real elements of existence”, but in the validity of its connection with “the element of existence”. On that the fellow showed that this revolutionary move from “representation” to “relation” accounts for Heisenberg’s turn from the representational models of the atom to a conceptual model of the atom laid down in 1925 by Heisenberg in the "Reinterpretation paper", which is the starting point of the new quantum mechanics.

Impact and Dissemination Activities.
This is a cutting-edge project, because it proposed an original interpretation of the quantum theory through a reconsideration of Bohr's philosophy of physics in light of the functional-based approach suggested by Cassirer's reading. It is worth reminding that this approach was also suggested in the early 1950s by Julian Schwinger, the inventor of the procedure of "renormalisation" of quantum electrodynamics in particle physics, without Schwinger knowing a word of Cassirer's work. This project sought to underpin the philosophical foundation to that approach, by focusing on the first part of the quantum theory. The execution of this project involved an active engagement of the fellow in an international community of scholars and specialists in Kantian and neo-Kantian studies, who expressed a strong interest in the project results, which was, in fact, manifested during the numerous conferences and workshops, which the fellow participated in, and he also organized:
1) Talk given in June 2014 at the Department of History and Philosophy of Science at Paris 7.
2) Taken part in the international conference on Ernst Cassirer in June 2014 in Milwaukee. Where he created important collaborations with experts and specialists in the history of philosophy and philosophy of science.
3) Invited as a speaker at the Niels Bohr Institute in Copenhagen in December 2014, in the context of a seminar series in history of physics.
4) Speaker, chair, and commentator at the International Conference of The Nordic Network for Philosophy of Science, Pärnu (Estonia), 20-25 April 2016. Session Philosophy of Physics.
5) Invited discussant at the American Philosophical Association, Pacific Division, S. Francisco, 30 April – 3 May 16. Session “Post-Kantian Theories of Concepts”.
6) Selected speaker and chair at the international conference “The History of Science and Contemporary Scientific Realism”, Indiana University – Purdue University Indianapolis, 19-21 February 2016.
7) Speaker, organiser, and chair at “Journée d’étude doctorants-chercheurs SPHERE en histoire et philosophie de la physique”. Talk’s title: “Quantum postulates and functional concepts: setting the stage for a Cassirerean interpretation of Quantum Theory”. 4 November 2015, Université Paris Diderot.
8) Speaker at the “Workshop ‘Perspectives kantienne et néo-kantiennes sur la théorie quantique’”. Talk’s title: “From Bohr’s Correspondence principle to Heisenberg’s Matrix Mechanics: Kantian and Neo-Kantian perspectives on Quantum Theory”, 7 October 2015, Université Paris Diderot.
9) Invited discussant at the Fourth International Conference of History of Quantum Physics, San Sebastian, 16-18 July 2015.

Organization of conferences and workshops.
1) Journée d’étude doctorants-chercheurs SPHERE en histoire et philosophie de la physique, with the participation of scholars from Stanford University. 4 November 2015, Université Paris -Diderot.
2) Workshop “Perspectives kantienne et néo-kantiennes sur la théorie quantique”, 7 October 2015, Université Paris Diderot.
3) International Conference on Entanglement. 28-29 November 2014.

Furthermore, in the context of the Marie Curie Outreach Activities, the fellow started to collaborate with UNESCO within a project whose objective is enhancing scientific and technological literacy.

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