Bothe–Geiger coincidence experiment

Last updated

In the history of quantum mechanics, the Bothe-Geiger coincidence experiment was conducted by Walther Bothe and Hans Geiger from 1924 to 1925. The experiment explored x-ray scattering from electrons to determine the nature of the conservation of energy at microscopic scales, which was contested at that time. The experiment confirmed existence of photons, the conservation of energy and the Compton scattering theory.

Contents

At that time, quantum mechanics was still under development in what was known as the old quantum theory. Under this framework, the BKS theory by Niels Bohr, Hendrik Kramers, and John C. Slater proposed the possibility that energy conservation is only true for large statistical ensembles and could be violated for small quantum systems. BKS theory also argued against the quantum nature of light. The Bothe-Geiger experiments helped disprove BKS theory, marking an end to old quantum theory, and inspiring the re-interpretation of the theory in terms of matrix mechanics by Werner Heisenberg.

The experiment used for the first time a coincidence method, thanks to the coincidence circuit developed by Bothe. Bothe received the Nobel Prize in Physics in 1954 for this development and successive experiments using this method.

Motivation

Compton effect. Incident photon (with wavelenghth l) hits an electron in a target. This produces a scattered photon (with wavelenghth l'>l) and a recoil electron. Compton-scattering.svg
Compton effect. Incident photon (with wavelenghth λ) hits an electron in a target. This produces a scattered photon (with wavelenghth λ'>λ) and a recoil electron.

In 1923, Arthur Compton had shown experimentally that x-rays were scattered elastically by free electrons, in accordance to the conservation of energy. [1] The scattered photon had a lower frequency than the incoming photon, according to the Planck–Einstein relation for the energy E=ℏω ( is Planck constant and ω is the angular frequency), while the remaining energy was transmitted to the recoil electron. [1] [2]

This discovery started a debate between those that believed that the energy was always conserved like Compton, Albert Einstein and Wolfgang Pauli, [1] and those who believed it was only statistically valid. Bohr, Kramers and Slater published their BKS theory in February 1924 in Zeitschift fur Physik, arguing against energy conservation in individual atomic scattering events. [1] They also considered that light could be treated classically without the need of the light quanta hypothesis of Einstein. [3]

After finishing his doctoral degree under the supervision of Max Planck in 1913, Walther Bothe joined the radioactivity group in the Physikalisch-Technische Reichsanstalt in Charlottenburg, Berlin, to work with Hans Geiger, at that time head of the lab. [1] Bothe studied Compton scattering with x-rays using a cloud chamber filled with hydrogen. [3]

Shortly after the publication of the BKS theory, Hans and Geiger announced in the same journal an experiment proposal to test BKS theory. [1] [4]

Werner Heisenberg remained agnostic with respect to BKS theory. In a letter to Arnold Sommerfeld, he wrote: [5]

For the rest I believe more and more that the question 'photons or correspondence principle' is a question of semantics. All effects in quantum theory must after all have a classical counterpart, for the classical theory is almost correct; thus all effects must have two names, a classical and a quantum [name]. Which one prefers is really a matter of taste. Perhaps the Bohr radiation theory is a very happy description of this dualism; I am anxiously awaiting the results of the Bothe–Geiger experiment.

Experiment

According to Compton scattering, if an incident photon with energy given by hits an electron, the recoil electron and the scattered photon would fly in opposite directions in the direction perpendicular to the trajectory of the incident photon. [2]

For the experiment, a collimated x-ray beam is directed to a scattering material in a gap between two counters. [2] [3] The counters are placed in the line perpendicular to the beam. The two counters consist of an electron counter and a photon counter that are placed in opposite sides from the beam. Due to the minimal energy of the recoil electron, the electron detection essentially occurs at their scattering site. Thus the scattering volume must be situated within the electron counter. [2] The whole setup was enclosed in a glass sphere filled with hydrogen at atmospheric pressure. [3]

In Bothe–Geiger experiment, Geiger needle counters covered with thin platinum foil were used to detect scattered photons. A fraction of the photons produced a measurable electric current due to the photoelectric effect. [2] [3] The count detections were recorded photographically using silver bromide film, [1] by the means of a string electrometers. The efficiency of the coincidence counting was of the order of 1 for 10 events. [2] Bothe and Geiger observed 66 coincidences in 5 hours, of which 46 were attributed to false counts, with a statistical fluctuation of 1 in 400,000. [2]

The measurements and data treatment took over a year. [1] The overall experiment produced more than three kilometers of the just 1.5 centimeter-wide film that had to be analyzed manually. [1] According to Bothe, the "film consumption however was so enormous that our laboratory with the film strips strung up for drying sometimes resembled an industrial laundry". [3] [6]

Any delay between the detection of the photon and the electron would be a hint of a violation of the conservation of energy. However a simultaneous detection indicated a confirmation of Compton's theory. [1]

Results, reception and legacy

In April 1925, [7] [8] Bothe and Geiger reported that the photon and electron counters responded simultaneously, with a time resolution of 1 millisecond. [1] Their result confirmed the quantum nature of light and was the first evidence against BKS theory. They argued "Our results are not in accord with Bohr's interpretation of the Compton effect ... it is recommended therefore to retain until further notice the picture of Compton and [Peter] Debye.... One must therefore probably assume that the light quantum concept possesses a high degree of validity as assumed in that theory." [5]

Published in September of the same year, an experiment carried in parallel by Compton and Alfred W. Simon using a different technique, reached similar conclusions. [5] [9] The Compton–Simon experiment used cloud chamber techniques to track two different types of tracks: tracks of the recoil electron and tracks of the photoelectrons. Compton and Simon confirmed the relative angles between the tracks predicted by Compton scattering. [5] Compton and Simon write: "the results do not appear to be reconcilable with the view of the statistical production of recoil and photo-electrons by Bohr, Kramers and Slater. They are, on the other hand, in direct support of the view that energy and momentum are conserved during the interaction between radiation and individual electrons." [10]

The Bothe–Geiger experiment and the Compton–Simon experiment marked an end to the BKS theory. [8] Kramers was skeptic at the beginning. In a letter to Bohr, Kramers said "I can unfortunately not survey how convincing the experiments of Bothe and Geiger actually are for the case of the Compton effect". [5] Bohr however finished by accepting the results, in a letter to Ralph H. Fowler he wrote: "there is nothing else to do than to give our revolutionary efforts as honourable a funeral as possible". [7]

Compton congratulated Bothe and Geiger for their results. Max von Laue said that "Physics was saved from being led astray". [1] Science philosopher Karl Popper catalogued the result as an experimentum crucis . [7]

In 1925 after the experiment, Bothe succeeded Geiger as the director of the lab. [3]

The same year, Heisenberg would start to develop a new reinterpretation of quantum mechanics, based on matrix mechanics. In his 1927 paper on the uncertainty principle, he opposes the statistical interpretation of quantum mechanics, citing the Bothe–Geiger paper. [11] Heisenberg writes to Pauli: "I argue with Bohr over the extent to which the relation p1q1~h has its origin in the wave-or the discontinuity aspect of quantum mechanics. Bohr emphasizes that in the gamma-ray microscope the diffraction of the waves is essential; I emphasize that the theory of light quanta and even the Geiger-Bothe experiments are essential." [11]

Almost a decade later, Robert S. Shankland performed an experiment that allegedly showed some inconsistencies with photon scattering, resurfacing the idea of BKS theory. [12] However it was later disproved by Robert Hofstadter and John A. Mcintyre with an experiment similar to the Bothe–Geiger experiment reducing the time resolution to 15 nanoseconds. [5] [10] [13]

Further experiments were carried out by Bothe using his coincidence method. Geiger and Walther Müller further developed the Geiger–Müller tubes, that were used by Bothe and Werner Kolhörster experiment in 1929 to show that fast electrons detected in cloud chambers came from cosmic rays. [14] In 1954, the Nobel Prize in Physics was split in two, half for Max Born for "for his fundamental research in quantum mechanics, especially for his statistical interpretation of the wavefunction"" and the other half for Bothe for his "for the coincidence method and his discoveries made therewith". [6] Geiger had already died in 1945 so he was not eligible for a share of the prize. [1]

Related Research Articles

<span class="mw-page-title-main">Niels Bohr</span> Danish physicist (1885–1962)

Niels Henrik David Bohr was a Danish physicist who made foundational contributions to understanding atomic structure and quantum theory, for which he received the Nobel Prize in Physics in 1922. Bohr was also a philosopher and a promoter of scientific research.

A photon is an elementary particle that is a quantum of the electromagnetic field, including electromagnetic radiation such as light and radio waves, and the force carrier for the electromagnetic force. Photons are massless particles that always move at the speed of light measured in vacuum. The photon belongs to the class of boson particles.

Wave-particle duality is the concept in quantum mechanics that quantum entities exhibit particle or wave properties according to the experimental circumstances. It expresses the inability of the classical concepts such as particle or wave to fully describe the behavior of quantum objects. During the 19th and early 20th centuries, light was found to behave as a wave then later discovered to have a particulate behavior, whereas electrons behaved like particles in early experiments then later discovered to have wavelike behavior. The concept of duality arose to name these seeming contradictions.

<span class="mw-page-title-main">Compton scattering</span> Scattering of photons off charged particles

Compton scattering is the quantum theory of high frequency photons scattering following an interaction with a charged particle, usually an electron. Specifically, when the photon hits electrons, it releases loosely bound electrons from the outer valence shells of atoms or molecules.

A timeline of atomic and subatomic physics.

In physics, a correspondence principle is any one of several premises or assertions about the relationship between classical and quantum mechanics. The physicist Niels Bohr coined the term in 1920 during the early development of quantum theory; he used it to explain how quantized classical orbitals connect to quantum radiation. Modern sources often use the term for the idea that the behavior of systems described by quantum theory reproduces classical physics in the limit of large quantum numbers: for large orbits and for large energies, quantum calculations must agree with classical calculations. A "generalized" correspondence principle refers to the requirement for a broad set of connections between any old and new theory.

<span class="mw-page-title-main">Hans Geiger</span> German physicist (1882–1945)

Johannes Wilhelm "Hans" Geiger was a German physicist. He is best known as the co-inventor of the detector component of the Geiger counter and for the Geiger–Marsden experiment which discovered the atomic nucleus. He also carried the Bothe–Geiger coincidence experiment that confirmed the conservation of energy in light-particle interactions.

In physics and electrical engineering, a coincidence circuit or coincidence gate is an electronic device with one output and two inputs. The output activates only when the circuit receives signals within a time window accepted as at the same time and in parallel at both inputs. Coincidence circuits are widely used in particle detectors and in other areas of science and technology.

<span class="mw-page-title-main">Walther Bothe</span> German nuclear physicist and Nobel Prize shared with Max Born (1891–1957)

Walther Wilhelm Georg Bothe was a German nuclear physicist known for the development of coincidence methods to study particle physics.

<span class="mw-page-title-main">Bohr–Einstein debates</span> Series of public disputes between physicists Niels Bohr and Albert Einstein

The Bohr–Einstein debates were a series of public disputes about quantum mechanics between Albert Einstein and Niels Bohr. Their debates are remembered because of their importance to the philosophy of science, insofar as the disagreements—and the outcome of Bohr's version of quantum mechanics becoming the prevalent view—form the root of the modern understanding of physics. Most of Bohr's version of the events held in the Solvay Conference in 1927 and other places was first written by Bohr decades later in an article titled, "Discussions with Einstein on Epistemological Problems in Atomic Physics". Based on the article, the philosophical issue of the debate was whether Bohr's Copenhagen interpretation of quantum mechanics, which centered on his belief of complementarity, was valid in explaining nature. Despite their differences of opinion and the succeeding discoveries that helped solidify quantum mechanics, Bohr and Einstein maintained a mutual admiration that was to last the rest of their lives.

In physics, complementarity is a conceptual aspect of quantum mechanics that Niels Bohr regarded as an essential feature of the theory. The complementarity principle holds that certain pairs of complementary properties cannot all be observed or measured simultaneously. For example, position and momentum or wave and particle properties. In contemporary terms, complementarity encompasses both the uncertainty principle and wave-particle duality.

<span class="mw-page-title-main">Davisson–Germer experiment</span> Experiment contributing to the confirmation of wave-particle duality of matter

The Davisson–Germer experiment was a 1923-27 experiment by Clinton Davisson and Lester Germer at Western Electric, in which electrons, scattered by the surface of a crystal of nickel metal, displayed a diffraction pattern. This confirmed the hypothesis, advanced by Louis de Broglie in 1924, of wave-particle duality, and also the wave mechanics approach of the Schrödinger equation. It was an experimental milestone in the creation of quantum mechanics.

Quantum mechanics is the study of matter and its interactions with energy on the scale of atomic and subatomic particles. By contrast, classical physics explains matter and energy only on a scale familiar to human experience, including the behavior of astronomical bodies such as the moon. Classical physics is still used in much of modern science and technology. However, towards the end of the 19th century, scientists discovered phenomena in both the large (macro) and the small (micro) worlds that classical physics could not explain. The desire to resolve inconsistencies between observed phenomena and classical theory led to a revolution in physics, a shift in the original scientific paradigm: the development of quantum mechanics.

Heisenberg's microscope is a thought experiment proposed by Werner Heisenberg that has served as the nucleus of some commonly held ideas about quantum mechanics. In particular, it provides an argument for the uncertainty principle on the basis of the principles of classical optics.

The history of quantum mechanics is a fundamental part of the history of modern physics. The major chapters of this history begin with the emergence of quantum ideas to explain individual phenomena—blackbody radiation, the photoelectric effect, solar emission spectra—an era called the Old or Older quantum theories. Building on the technology developed in classical mechanics, the invention of wave mechanics by Erwin Schrödinger and expansion by many others triggers the "modern" era beginning around 1925. Paul Dirac's relativistic quantum theory work lead him to explore quantum theories of radiation, culminating in quantum electrodynamics, the first quantum field theory. The history of quantum mechanics continues in the history of quantum field theory. The history of quantum chemistry, theoretical basis of chemical structure, reactivity, and bonding, interlaces with the events discussed in this article.

In the history of quantum mechanics, the Bohr–Kramers–Slater (BKS) theory was perhaps the final attempt at understanding the interaction of matter and electromagnetic radiation on the basis of the so-called old quantum theory, in which quantum phenomena are treated by imposing quantum restrictions on classically describable behaviour. It was advanced in 1924, and sticks to a classical wave description of the electromagnetic field. It was perhaps more a research program than a full physical theory, the ideas that are developed not being worked out in a quantitative way. The purpose of BKS theory was to disprove Einstein's hypothesis of the light quantum.

The timeline of quantum mechanics is a list of key events in the history of quantum mechanics, quantum field theories and quantum chemistry.

In 1923, American physicist William Duane presented a discrete momentum-exchange model of the reflection of X-ray photons by a crystal lattice. Duane showed that such a model gives the same scattering angles as the ones calculated via a wave diffraction model, see Bragg's Law.

<span class="mw-page-title-main">Discovery of the neutron</span> Scientific background leading to the discovery of subatomic particles

The discovery of the neutron and its properties was central to the extraordinary developments in atomic physics in the first half of the 20th century. Early in the century, Ernest Rutherford developed a crude model of the atom, based on the gold foil experiment of Hans Geiger and Ernest Marsden. In this model, atoms had their mass and positive electric charge concentrated in a very small nucleus. By 1920, isotopes of chemical elements had been discovered, the atomic masses had been determined to be (approximately) integer multiples of the mass of the hydrogen atom, and the atomic number had been identified as the charge on the nucleus. Throughout the 1920s, the nucleus was viewed as composed of combinations of protons and electrons, the two elementary particles known at the time, but that model presented several experimental and theoretical contradictions.

A hallmark of Albert Einstein's career was his use of visualized thought experiments as a fundamental tool for understanding physical issues and for elucidating his concepts to others. Einstein's thought experiments took diverse forms. In his youth, he mentally chased beams of light. For special relativity, he employed moving trains and flashes of lightning to explain his most penetrating insights. For general relativity, he considered a person falling off a roof, accelerating elevators, blind beetles crawling on curved surfaces and the like. In his debates with Niels Bohr on the nature of reality, he proposed imaginary devices that attempted to show, at least in concept, how the Heisenberg uncertainty principle might be evaded. In a profound contribution to the literature on quantum mechanics, Einstein considered two particles briefly interacting and then flying apart so that their states are correlated, anticipating the phenomenon known as quantum entanglement.

References

  1. 1 2 3 4 5 6 7 8 9 10 11 12 13 Maier, Elke (2011). "Flashback: Particle Billiards, Captured on Film". MaxPlanckResearch. 3: 92–93.
  2. 1 2 3 4 5 6 7 Burcham, W. E.; Lewis, W. B. (1936). "A repetition of the Bothe-Geiger experiment". Mathematical Proceedings of the Cambridge Philosophical Society. 32 (4): 637–642. doi:10.1017/S0305004100019368. ISSN   0305-0041. S2CID   123475921.
  3. 1 2 3 4 5 6 7 Bonolis, Luisa (2011-10-18). "Walther Bothe and Bruno Rossi: The birth and development of coincidence methods in cosmic-ray physics". American Journal of Physics. 79 (11): 1133–1150. arXiv: 1106.1365 . doi:10.1119/1.3619808. ISSN   0002-9505. S2CID   15586282.
  4. Bothe, W.; Geiger, H. (1924). "Ein Weg zur experimentellen Nachprüfung der Theorie von Bohr, Kramers und Slater". Zeitschrift für Physik (in German). 26 (1): 44. doi:10.1007/BF01327309. ISSN   1434-6001. S2CID   121807162.
  5. 1 2 3 4 5 6 Dresden, M. (1987). H.A. Kramers Between Tradition and Revolution. New York, NY: Springer New York. doi:10.1007/978-1-4612-4622-0. ISBN   978-1-4612-9087-2.
  6. 1 2 "The Nobel Prize in Physics 1954". NobelPrize.org. Retrieved 2024-02-19.
  7. 1 2 3 Kragh, Helge (2009), Greenberger, Daniel; Hentschel, Klaus; Weinert, Friedel (eds.), "Bohr—Kramers—Slater Theory", Compendium of Quantum Physics, Berlin, Heidelberg: Springer Berlin Heidelberg, pp. 62–64, doi:10.1007/978-3-540-70626-7_19, ISBN   978-3-540-70622-9 , retrieved 2024-02-21
  8. 1 2 Bothe, W.; Geiger, H. (1925). "Über das Wesen des Comptoneffekts; ein experimenteller Beitrag zur Theorie der Strahlung". Zeitschrift für Physik (in German). 32 (1): 639–663. doi:10.1007/BF01331702. ISSN   1434-6001. S2CID   120858711.
  9. Compton, Arthur H.; Simon, Alfred W. (1925-09-01). "Directed Quanta of Scattered X-Rays". Physical Review. 26 (3): 289–299. doi:10.1103/PhysRev.26.289. ISSN   0031-899X.
  10. 1 2 Jammer, Max (1966). The Conceptual Development of Quantum Mechanics. McGraw-Hill.
  11. 1 2 Beller, Mara (1999). Quantum Dialogue: The Making of a Revolution. University of Chicago Press. ISBN   978-0-226-04182-7.
  12. Shankland, Robert S. (1936-01-01). "An Apparent Failure of the Photon Theory of Scattering". Physical Review. 49 (1): 8–13. doi:10.1103/PhysRev.49.8. ISSN   0031-899X.
  13. Hofstadter, Robert; Mcintyre, John A. (1950-04-01). "Simultaneity in the Compton Effect". Physical Review. 78 (1): 24–28. doi:10.1103/PhysRev.78.24. ISSN   0031-899X.
  14. Pfotzer, Georg (1985), Sekido, Yataro; Elliot, Harry (eds.), "Early Evolution of Coincidence Counting a Fundamental Method in Cosmic Ray Physics", Early History of Cosmic Ray Studies, Astrophysics and Space Science Library, vol. 118, Dordrecht: Springer Netherlands, pp. 39–44, doi:10.1007/978-94-009-5434-2_5, ISBN   978-94-010-8899-2 , retrieved 2024-02-21