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Walther Bothe
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Free Will
Mental Causation
James Symposium
Walther Bothe

Walther Bothe shared the Nobel prize in 1954 with Max Born for his experimental confirmation of Albert Einstein's theory of light quanta, and his proof that the energy was conserved for each Compton electron-photon scattering event. This disproved the 1924 Bohr-Kramers-Slater theory that light was sometimes a wave, at other times a particle, and that energy was only conserved statistically over large numbers of events.

Einstein asked that this work be done and he was pleased that his theory of light quanta was perfectly confirmed. Until the early 1920's, Einstein was alone in his belief (since 1905) that light consisted of quanta (later called photons) and that wave properties were the result of averaging over large numbers of light particles. Einstein suggested (but never published) the idea that the waves provided what he called a "ghost-field" that guided the particles' motions. This became the deBroglie-Bohm "pilot-wave" theory of quantum mechanics.

The standard interpretation of the quantum-mechanical wave function that evolves deterministically according to the Schrödinger equation is that it is the probability of finding a quantum particle in a given state. Einstein wanted the wave to determine the location of the particle. He was bothered to the end of his life that quantum mechanics was only a statistical theory and that it involved indeterministic chance. That was a "weakness in the theory," he said. Bothe confirmed an important aspect of the theory.

Until the work of Compton and Bothe, virtually no one but Einstein believed in the reality of light quanta, and that they displayed irreducible chance in the timing and direction of their emission.

Nobel Lecture (excerpt)
It was in 1924 that I came across the theoretical paper by Bohr, Kramers, and Slater, which had just been published and which suggested a possible interpretation of the wave-particle dualism in the accepted description of the properties of light. This must be understood to mean the experimental fact that light of all wavelengths behaves as a wave process (interference) with pure propagation, but behaves as particles (light quanta: photo-effect, Compton effect) on conversion into other types of energy. The new idea consisted in denying strict validity to the energy-impulse law. In the individual or elementary process, so long as only a single act of emission was involved, the laws of conservation were held to be statistically satisfied only, to become valid for a macroscopic totality of a very large number of elementary processes only, so that there was no conflict with the available empirical evidence. It was immediately obvious that this question would have to be decided experimentally, before definite progress could be made. That such a decision was possible, Geiger and I agreed immediately, when I discussed the paper by Bohr, Kramers, and Slater with Geiger.

The experimental problem offered several means of attack. We decided in favour of an experiment with the effect discovered a short time previously by A.H. Compton, i.e. the scattering of light on practically free electrons. Apart from the scattered light, there occur the "recoil electrons" which had been observed and interpreted by C.T.R. Wilson in the cloud chamber, and by me both in the cloud chamber and by an ionization method. The "question to Nature" which the experiment was designed to answer could therefore be formulated as follows: is it exactly a scatter quantum and a recoil electron that are simultaneously emitted in the elementary process, or is there merely a statistical relationship between the two?

Meanwhile, Geiger had developed the so-called needle counter which has the advantage of responding not only to heavy particles but also to electrons, and therefore to light quanta of sufficiently high energy capable of releasing electrons within the counter.

Our arrangement therefore consisted of two needle counters, past the common front wall of which, without touching it, swept a beam of X-rays. The X-ray beam travelled in a hydrogen atmosphere; the Compton processes occurred in the one counter which indicated the recoil electrons, whereas only the scatter quanta were able to penetrate into the other counter and actuated it by electron release with very much lower probability. The readings of both counters were recorded side by side on a moving paper chart. In this way we succeeded after a few failures to establish the accuracy of any temporal "coincidence" between the two pointer readings as being 10-4 sec. Film consumption however was so enormous that our laboratory with the film strips strung up for drying sometimes resembled an industrial laundry.

The final result we obtained was that systematic coincidences do indeed occur with the frequency that could be estimated from the experimental geometry and the response probabilities of the counters on the assumption that, in each elementary Compton process, a scatter quantum and a recoil electron are generated simultaneously. The strict validity of the law of the conservation of energy even in the elementary process had been demonstrated, and the ingenious way out of the wave-particle problem discussed by Bohr, Kramers, and Slater was shown to be a blind alley.

This result was confirmed by different researchers using various experimental arrangements. When, more than ten years later, some doubts as to the correctness of this result were voiced, I tried with my then assistant, H. Maier-Leibnitz, to supplement and improve the original experiment in one point: the object was to demonstrate both simultaneity and uniformity of direction of scatter quantum and recoil electron, as was to be expected according to Compton's theory, i.e. according to the laws of elastic impact between two bodies. On this occasion, we employed the energy-rich gamma radiation of a radiothorium preparation. Again, the result was clearly positive. This demonstrated both the conservation of energy and the conservation of the impulse.

The possibility of the purely statistical validity of the conservation theorems discussed by Bohr, Kramers, and Slater appeared sufficiently important to be tested in yet another case. A spherical wave is emitted in the elementary process of light emission. The problem was: can this spherical wave initiate an absorption act in one direction of emission only, as the energy theorem postulates, or can it do so also statistically independently in several directions, as is to be expected according to Bohr, Kramers, and Slater? It must be borne in mind in an experiment of this kind, that, by contrast with the Compton effect, the probability of demonstrating an absorption act may not be of an order of magnitude much below unity, because otherwise any systematic coincidences that might occur would be submerged in the inevitable accidental coincidences. This was achieved by harmonizing the radiation source (iron or copper-K-fluorescence radiation) and the gas charge of the needle counters (argon) erected on either side so that the absorption probability in the gas charge was as close as possible to unity. Besides, the solid angles which the two counters offered to the radiation source had to amount as far as possible to 2 p. The result of this experiment (1926) was that no systematic coincidences occurred, at least not with the frequency to be expected according to Bohr, Kramers, and Slater. Strict conservation of energy in the elementary process had thus been confirmed also by a negative experiment. The wave-particle problem was destined to remain open for a short time only. During this time I had the singular good fortune of being able to discuss the problem constantly with Einstein. Some experiments done at Einstein's suggestion yielded no decisively new result. The (at least formal) solution was provided by wave mechanics; it is contained simply in the assumption that the Schrödinger wave of a system consisting of n particles is a wave in the 3n-dimensional "configuration space".

Historical Significance of the Bothe-Geiger Experiment
It is little-known that during the birth of quantum mechanics Walther Bothe (1891-1957) published partly together with Hans Geiger (1882-1945) from 1923 to 1927 as much as twenty papers which all deal with photons (light quanta). About half of the publications are of experimental nature; the other deal with theoretical problems. Among the latter there is theoretical work on the photo effect, the interaction of light with free electrons and on the particle-wave dualism. In his final publication within this field Bothe found in 1927 the correct interpretation of Einstein’s results for the energy fluctuations of black body radiation.1,2 In his Nobel lecture (Nobel prize 1954, together with Max Born) Bothe mentioned “that during this time I had the singular fortune of being able to discuss the [wave particle] problem constantly with Einstein”.

Walther Bothe was an exceptional scientist, with likewise outstanding skills in theoretical and experimental physics. He studied mathematics, physics and chemistry in Berlin and entered the radiation laboratory of the Physikalisch Technische Reichsanstalt (PTR) in 1913. After participation in the First World War he returned to Berlin in 1920 to resume work at the PTR. Bothe was known all over his life to be able to work extremely self-concentrated.

Briefly after his return to the PTR Einstein proposed an experiment to prove his light quantum hypothesis for the light emitted by canal rays. Geiger and Bothe performed the experiment immediately and showed that the light emitted by moving atoms/ions will not be deflected in dispersing medias, in accordance with Einstein’s prediction for light quanta. But subsequent discussions led Einstein to the result, that both, the light quantum picture and the light wave picture would finally yield the same results. Nevertheless it is a pity, that the experiment itself was never published, since it was for the first time, that the particle-wave dualism became apparent in a thorough discussion of an experiment.

In this period Bothe became interested in the interaction of X-rays with matter. After extended experiments on the pressure dependence of the ionization probability due to the secondary ß-radiation he interpreted his results in fall 1923 correctly as due to Compton scattering of photons on electrons.3 From this we may convey, that at the end of 1923 Bothe himself had accepted the particle picture of light, at least for elementary processes. Thus he was well prepared when at the beginning of 1924, N. Bohr, H.A.Kramers and J.C.Slater postulated that in atomic processes causality, momentum and energy conservation ought to be valid only statistically, in order to keep at any instances the continuous wave description of light if interacting with matter.4 To prove or disprove this claim experimentally,

Bothe and Geiger firstly built up a coincidence experiment and showed with quite some experimental effort that in Compton scattering of X-rays on hydrogen the scattered protons and the scattered X-ray quanta reach the detectors within a time delay of only 0,1ms or less.5 This was historically the very first coincidence experiment with high time resolution. Soon afterwards Compton and Simon6 found in the scattering of X-rays on electrons that energy and momentum is conserved as well.

Even though the consequences of the Bothe–Geiger experiment are frequently discussed,7 little is present in historical debates about its “courageous” performance. In this context it is a pity that the notebook of this experiment does not exist in Bothe’s legacy at the Archive of the Max Planck Gesellschaft in Berlin. But, luckily enough, a notebook (Nr.7) exists for Bothe’s second experiment in the spirit of the Compton scattering experiment, which Bothe then performed alone.8 In this experiment Bothe used again two counters in coincidence and in opposite position (1800), but both were now able to detect scattered X-rays. The idea was, that he will observe no coincidences if the scattered X-rays consist of light quanta (Nadelstrahlung) and coincidences if the fluorescence light is to be described by continuous electromagnetic waves. The negative outcome (no coincidences) proved Einstein’s light quantum hypothesis once more. It was a null experiment, much harder to be performed and analyzed than the Compton scattering experiments with their finite signals.

Nevertheless, this experiment was in general never highly ranked in the past nor today. But Bothe himself considered it e.g. in a letter to a publishing company dated from 1949 as one of the most important ones he ever performed.9 This view was at least shared by Compton10 and enthusiastically by Einstein, since the outcome of Bothe’s fluorescence experiment was exactly what he was after when proposing the canal ray experiment.

From his publications and additionally from the notebook we can infer how Bothe performed experiments: caring of any detail and listing it, crosschecking the essential experimental steps, being very critical in respect to himself and in particular not being biased at all by theoretical expectations or predictions in assessing his own experimental results.

We finish with the remark that Einstein wrote in support of a proposal of von Laue to award the 1954 Nobel price to Bothe, referring to the Bothe–Geiger experiment. Thus finally Bothe’s seminal experimental and theoretical contributions to enlighten the wave-particle dualism were honored shortly before his death with this prestigious prize.

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