QUADERNIDISTORIADELLAFISICA N.0-June2008 The Rise of Quantum Mechanics Sigfrido Boffi Dipartimento di Fisica Nucleare e Teorica, Universit`adegli Studi di Pavia 1. Introduction cal physics was well organized in differ- ent sectors. Within each sector a closed and coherent system of concepts and laws “The discovery and development of was able to satisfactorily account for the quantum theory in the twentieth century corresponding phenomenology. Some re- is an epic story and demands appropri- markable syntheses, such as the unifica- ate telling. This story cannot be told in tion of electric and magnetic phenomena the fullness of its glory without analyz- or the kinetic theory of matter, were sug- ing in some detail the multitude of prob- gesting that mechanics, thermodynam- lems which together came to constitute ics, electromagnetism were only different the fabric of quantum theory. Much more branches of physics on the road towards a than the relativity theories, both special global unified description of physical phe- and general, which completed the edifice nomena. Analytical mechanics would in of classical mechanics, the quantum the- any case play a privileged role because ory is unique in the history of science and the three Newton’s laws were at the ori- intellectual history of man: in its con- gin of the scientific paradigm of an objec- ceptions it made a complete break with tive world governed by the causality law, the past and fashioned a new worldview where the global behaviour can be lead about the structure of matter and radia- back to the knowledge of the mutual in- tion and many of the fundamental forces teraction of constituents. of nature.” With such emphatic words With the advent of quantum mechan- Jagdish Mehra starts a cyclopical enter- ics as a result of accounting for new prise together with Helmuth Rechenberg facts and discoveries, this paradigm was arXiv:0806.4515v1 [physics.hist-ph] 27 Jun 2008 describing the historical development of turned over. Objectivity, determinism quantum theory [1]. and locality were substituted by a pic- In fact, quantum mechanics has com- ture where the observer plays an essential pletely reoriented the way of looking at role in determining the phenomenon, the physical phenomena that emerged af- description of phenomena can only be ac- ter more than three centuries of intense complished in terms of probability of oc- investigation of nature. Around the currence, and non-locality effects have to year 1900 the nowadays so-called classi- be considered. 2 Sigfrido Boffi Fig. 1. – In the first quarter of the twentieth century the crisis produced when trying to unify the different sectors of physics, such as macrophysics (described in terms of temperature T and entropy S), mechanics (with its Lagrangian L and Hamiltonian H) and electromagnetism (with its electric and magnetic fields E~ and B~ , respectively), was overcome by introducing new concepts and a new way of thinking of reality as a consequence of the development of relativity theory (with its equivalence between energy E and mass m and the invariance of the light velocity c) and quantum mechanics (that associates, through the Planck’s constant h, a wave with wavelength λ and frequency ν to the motion of a particle with momentum p and energy E, respectively). This was achieved in the first quarter a scheme suffered a big attack when of the twentieth century, especially be- physicists realized that the mechanical tween June 1925 and October 1927, as a equations of motions are not compatible consequence of an extraordinary develop- with the Maxwell’s equations for the elec- ment of new data, ideas, formalisms, in- tromagnetic phenomena. The solution terpretations, within a polyphonic frame- found in 1905 by Albert Einstein (1879– work where very young researchers and 1955) with his revision of the concept more experienced scientists were chal- of simultaneity and the space-time struc- lenging each other in a cooperative and ture made it possible to reconcile me- unique effort. chanics and electromagnetism in a unified and objective picture. Thus, though rev- olutionary, relativity theory, even with 2. Crisis towards unification its extension to general relativity, still obeys the principle of objectivity and In analytical mechanics observers are lives within the paradigm of classical simulated by inertial frames of reference physics. and time is assumed to be an abso- lute evolution parameter. Then the ob- In contrast, in the attempt to es- jective description of phenomena means tablish a connection between the macro- that any physical law is translated into scopic behaviour of a complex system and one and the same equation when pass- the microscopic motion of its constituent ing from one observer to another. Such particles or to account for the thermody- The Rise of Quantum Mechanics 3 namic effects of radiation, one meets dif- On a different side, the discoveries of ficulties that are unsurmountable within radioactivity by Wilhelm Conrad R¨ont- the classical framework (Fig. 1). For ex- gen (1845–1923) and of the electron in ample, the frequency distribution of the the study of cathode rays by Joseph radiation energy density cannot be pre- John Thomson (1856–1940) added im- dicted invoking the classical thermody- portant insights into the constitution of namics of radiation. The formula pro- matter. In atomic physics by the end of posed on heuristic arguments by Max the 19th century a large amount of ac- Planck (1858–1947) in 1900 could only cumulating data on the line spectra were be explained by Einstein under the as- organized according to the combination sumption that the energy of the har- principle emerging from the studies of monic oscillator associated to each fre- Johann Jakob Balmer (1858–1898), Jo- quency takes discrete values or, alterna- hannes Robert Rydberg (1854–1919) and tively, the action corresponding to a com- Walther Ritz (1878–1909). In the case of plete oscillation is an integer multiple of the hydrogen atom, for example, in the an elementary value h, the Planck’s con- Balmer’s formula the inverse wavelength stant. Similarly, the temperature depen- of every spectral line could be expressed dence of specific heat of solids cannot be as the difference of two terms, each of explained assuming a classical motion of which depending on an integer number. atoms within the solid and violates the The discrete nature of the line spectra is classical equipartition principle of energy, incompatible with the stable atom gov- unless again one assumes with Einstein erned by the laws of classical physics, and and Peter Debye (1884–1966) the possi- their classification in terms of the inter- bility of a discrete energy spectrum for nal atomic dynamics was a big puzzle. the oscillating atoms in solids. The discovery of the effect of a mag- The discrete nature of the electro- netic field on the spectral lines by Pieter magnetic field interacting with matter Zeeman (1865–1943) and its explana- and Einstein’s idea of a light quantum tion by Hendrik Antoon Lorentz (1853– with energy hν and momentum hν/c 1928) and Joseph Larmor (1857–1942) were not accepted by the physics commu- were a great success of the electron the- nity without a long discussion. Even af- ory of matter. However, in some cases ter the successful test of Einstein’s equa- an anomalous line splitting was observed tion for the photoelectric effect predict- such as that occurring for the two sodium ing a linear relation between the maxi- D-lines, with the D1-line splitting into mal kinetic energy of the ejected photo- a quartet and the D2-line into a sextet. electron and the frequency ν of the inci- Within the classical theory one could not dent radiation, Robert Andrews Millikan explain such an anomalous Zeeman ef- (1868–1953) remarked that “the semi- fect. corpuscolar theory by which Einstein ar- According to the model put forward rived at this equation seems at present to in 1911 by Ernest Rutherford of Nelson be wholly untenable” [2]. It took other (1871–1937) electrons revolving about ten years to look at the light quantum the positively charged atomic nucleus fol- as the “photon” responsible, e.g., of the low a periodic motion. Quantization Compton effect [3]. rules for such periodic systems were pro- 4 Sigfrido Boffi posed in 1913 by Niels Hendrik David could also provide the necessary founda- Bohr (1885–1962) and implemented in tion for atomic mechanics. 1916 by Arnold Sommerfeld (1868–1951). The Bohr-Sommerfeld rules were With such rules one defines azimuthal soon applied to a variety of problems and radial quantum numbers describ- such as quantum theory of radiation, ing the Kepler’s orbit of the electron in atoms with one electron and with sev- a plane, and the Balmer’s formula for eral electrons, quantum theory of solids spectral lines can be easily recovered. and gases, atomic magnetism. They were Also the normal Zeeman effect could be so successful describing the constitution described by Sommerfeld introducing a of atoms and the periodic table of ele- third quantum number, whose values de- ments that the predicted element with termine the discrete positions of the elec- atomic number 72 was just discovered by tron orbit with respect to the external Dirk Coster (1889–1950) and George de magnetic field. Hevesy (1985–1966) in Bohr’s Institute in The Bohr-Sommerfeld rules are de- Copenhagen and called hafnium after the rived from two postulates, i.e. the ex- Latin name of Copenhagen (Hafnia), in istence of stable stationary states of the time for Bohr to mention it in his Nobel atom and the definition of the emitted or lecture in 1922. absorbed radiation frequency in terms of However, there were also some fail- the energy difference between initial and ures, such as the calculation of the en- final stationary states.