B OHR’S STRUCTURAL REALISM AND ITS INFLUENCE ON THE HEURISTIC

3. B OHR’S STRUCTURAL REALISM AND ITS INFLUENCE ON THE HEURISTIC

OF HIS ATOMIC RESEARCH PROGRAMME

It seems to me that the most appropriate way of starting my reconstruction of the influence of Niels Bohr’s structural realism on the heuristic of his atomic

research programme is to quote the following letter by Bohr from June 19, 1912 to his brother Harald. Here Niels Bohr expresses his wish for immediate publi-

cation of an essay later known as the Rutherford Memorandum 17 , in which Bohr

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claims for the first time to reveal something of the real structure of the atoms. Niels Bohr writes:

Dear Harald, Perhaps I have found out a little about the structure of the atoms. Don’t talk about it to

anybody, for otherwise I couldn’t write to you about it so soon. If I should be right it wouldn’t be a suggestion of the nature of a possibility (i.e., an impossibility, as J.J.Thomson’s theory) but perhaps a little bit of reality. It has grown out of a little infor- mation I got from the absorption of

(the little theory I wrote about last time). You understand that I may yet be wrong, for it hasn’t been worked out fully yet (but I don’t

think so); also, I do not believe that Rutherford thinks that it is completely wild; he is a man of the right sort, and he would never say that he was convinced of something that

was not fully worked out. Believe me, I am eager to finish it in a hurry, and to do that I have taken off a couple of days from the laboratory (this is also a secret). This was intended only as a little greeting from

Your Niels 18 Back in the summer of 1912 when Bohr’s scientific breakthrough with respect to

the constitution and the structure of the atom took place, Bohr was in Manchester and especially concerned with the unsolved stability problem of the Rutherford atomic model that, however, successfully explained some experimental results

like the large angle scattering of This model, as it is well known and expressed by Bohr in the following words, “consists of a positive charge con- centrated in a point (in an extension that is very small compared with the dimen-

sions of the atoms) surrounded by a system of electrons, the total charge of which is equal to that of the positive ‘kernel’; the kernel is also assumed to be

the seat of the mass of the atom.” 19 Using mechanical and electro-dynamical concepts alone, Bohr was facing the problem that the stability of the Rutherford

atom could not be explained. Based on the constant motion of electrons around the atomic kernel, the classical theory predicts a radiative dissipation of energy

coupled by a steady contraction of the atom. Obviously, such an apparent insta- bility of the system of electrons does not occur in nature. Hence the alleged

stability of the atom could not be explained by the assumption of the classical theory alone.

Following Bohr’s account, it was in particular his attempt to determine a quantitative relation that allows one to limit the permissible number of radii of the electron-orbits or -rings around the kernel to a certain amount and thus to

avoid the stability problem. 20 In this respect Bohr defines the concept of the so- called ‘permanent’ or ‘stationary states’ of electrons where for each of them there exist definite values for the radius and the spectral frequencies. The latter

were in some way related to mechanical modes of vibration within the atom. That there must be definite values for these physical magnitudes was clear to

Bohr because of the existence of a vast number of sharp and discrete spectral lines and patterns charted for many of the chemical elements. Furthermore, Bohr had some numerical evidence at hand that only a number of electronic configu-

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rations in the atom are stable. After exceeding the number of seven electrons the instability of a ring begins where this seems to allow for an explanation of the

periodic properties of the chemical elements. 21 Bohr summarizes his considera- tion concerning the stability problem of the atom in the following passage of the Rutherford Memorandum:

In the investigation of the configuration of the electrons in the atoms we immediately meet with the difficulty (connected with the mentioned instability), that a ring, if only the strength of the central charge and the number of electrons in the ring are given, can rotate with an infinitely great number of different times of rotation, according to the assumed different radius of the ring; and there seems to be nothing (on account of the instability) to allow from mechanical considerations to discriminate between the different radii and times of vibration. 22

And Bohr goes on to express the aim of his further research:

In the further investigation we shall therefore introduce and make use of a hypothesis, from which we can determinate the quantities in question. This hypothesis is: that for any

stable ring (any occurring in the natural atoms) there will be a definite ratio between the kinetic energy of an electron in the ring and the time of rotation. This hypothesis, for

which there will be given no attempt of a mechanical foundation (as it seems hopeless), is chosen as the only one which seems to offer a possibility of an explanation of the whole

group of experimental results, which gather about and seem to confirm conceptions of the mechanism of radiation as the ones proposed by Planck and Einstein.

At that point, Bohr had not yet identified the exact relation required in order to define stationary states. But it should be emphasized, however, that at this stage

of his research Bohr was already – from a general point of view – aware of the fact that he could possibly gain some knowledge of the structure of the atom as indicated by his letter mentioned above. For this reason it seems plausible that Bohr was looking for a distinct relation so as to reveal something of the struc-

tural condition of the atom. With this lawful relation, Bohr was also hopeful that

he could explain the process of radiation. The problem of the explanation of the process of radiation did not appear on Bohrs agenda until February 1913. In a letter to Rutherford on 31 January 1913, Bohr, reflecting on his research, wrote: “I do not at all deal with the question of calculation of the frequencies corre- sponding to the lines in the visible spectrum. I have only tried, on the basis of the simple hypothesis which I used from the beginning, to discuss the constitution of

the atoms and molecules in their ‘permanent’ state.” 23 But the situation immedi- ately changed when H. M. Hanson, an expert on spectroscopy, arrived in Copen- hagen a few days later and asked Bohr for an explanation of the Balmer formula of the frequencies of the lines of the spectrum of the hydrogen atom. “As soon as

I saw Balmer’s formula”, Bohr from time to time stated in later years, “the whole thing was immediately clear to me.” 24 From this point it was just a few weeks until Bohr had finished the trilogy that would win him immortality in physics.

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Right at the beginning of Part I of the trilogy, Bohr has raised the stability problem again but during the course of his treatise he established the required quantitative relation characterising the permanent states that structures the atom explicit, using Planck’s elementary quantum of action, which is symbolized by h. As Max Jammer has already pointed out, by adopting Planck’s universal con- stant, Bohr did not intend to show the physical significance of the elementary quantum of action but rather to account quantitatively for the stability of the

atom. 25 “By the introduction of this quantity”, Bohr writes underlining this as- sumption, “the question of the stable configuration of the electrons in the atoms is essentially changed, as this constant is of such dimension and magnitude that it, together with the mass and charge of the particles, can be deemed a length of

the order of magnitude required.” 26 Thus, with the magnitude at his disposal that allows one to consider atomic dimensions, Bohr was now able to present the quantitative relation defining the permanent states of the atom. Furthermore Bohr accounted for hitherto unexplained empirical facts by deducing the law of the line spectrum of hydrogen (the Balmer formula) from the relation that structures the atom in the correct way. Without going here into greater detail regarding

Bohr’s formal derivation – which can be found elsewhere in the literature 27 –I will discuss Bohr’s general result as it relates to structural realism and the conse- quences for the heuristic of his research programme.

Bohr writes: “We shall now return to the main object of this paper – the discussion of the ‘permanent’ state of a system consisting of nuclei and bound electrons. For a system consisting of a nucleus and an electron rotating round it, this state is, according to the above, determined by the condition that the angular

momentum of the electron round the nucleus is equal to The connection between Bohr’s major result of the trilogy and his intention stated in the Ruther-

ford Memorandum can be seen as follows. Bohr explains this major assumption in the following manner: “If we therefore assume that the orbit of the electron in the stationary states is circular, the calculation on p. 5 can be expressed by this simple condition: that the angular momentum of the electron round the nucleus in a stationary state of the system is equal to an entire multiple of a universal

value, independent of the charge on the nucleus.” 29 The angular momentum M is defined by Bohr as

where W is the mean value of the kinetic energy and

is the frequency of the revolution of the electron around the nucleus (angular velocity). Furthermore, we have the simple condition that

where is the entire multiple of the universal value that is equal to . After some calculation we get the relation that can be found on page

5 in the original paper and that in an appropriate manner allows us to define the required “definite ratio between the kinetic energy of an electron in the ring and

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the time of rotation” expressed by Bohr above in the passage from the Ruther- ford Memorandum. From this expression Bohr proceeded to successfully deduce

the Balmer formula. We can thus conclude that Bohr’s invariant condition in the form of the con-

stancy of the angular momentum has to be regarded as the underlying quantita- tive relation for the structure of the atom. Finally, it is this invariant condition that enables Bohr to discover from the continuum of the manifold of allowable states the appropriate stationary states for the quantification of the atom. The general heuristic device Bohr has applied to investigate the atom thus reflects his philosophical idea that physicists should look for quantitative relations in order to reveal something of the structure of the reality. Subsequently it was Arnold

Sommerfeld who generalized Bohr’s theory of the hydrogen atom to the extent that the theory accounts for the fine structure of the hydrogen spectral lines. 30 Here Sommerfeld was decisively relying on the overall philosophy of Bohr’s atomic programme. In the following Sommerfeld describes his view that is

attributed to the idea that micro nature is structured as a network of permanent states:

F Ü r die allgemeine Auffassung des Naturgeschehens lernen wir aus der Schärfe der Spek- trallinien oder aus der ihr Rechnung tragenden Quantentheorie der Spektrallinien: Die stationären Bahnen der Elektronen im Atom (und weiterhin im Molekül) bilden kein Kon-

tinuum, sondern ein Netzwerk. Der Phasenraum, als Mannigfaltigkeit aller denkbaren, auch der nicht stationären Zustände, ist von den Bildkurven der stationären Bahnen

maschenartig durchzogen. Die Größe der Maschen ist durch das Plancksche h be- stimmt. 31

Sommerfeld’s search for a more general condition than Bohr’s invariant one that would enable him to know something of the supposed structure of the atom has

led him in the following to the well-known generalized quantum condition that “the phase integral for every coordinate is an integral multiple of the quantum of

action.“ 32 Subsequently Epstein and Schwarzschild showed that Sommerfeld’s theory, further generalized by more universal coordinates, successfully explains

the Stark effect. 33 Therefore, from a more general point of view, the underlying idea of the successful development of the older quantum theory was to uncover

in a more and more comprehensive manner the structural conditions of the atom that reasonably allow the definition of stationary states, thus solving the stability

problem and explaining the process of atomic radiation. In this way, the general idea of structural realism influenced the heuristic of the older quantum theory.