BKS theory
Encyclopedia
The Bohr-Kramers-Slater 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 program than a full physical theory, the ideas that are developed not being worked out in a quantitative way.
One aspect, the idea of modelling atomic behaviour under incident electromagnetic radiation using "virtual oscillators" at the absorption and emission frequencies, rather than the (different) apparent frequencies of the Bohr orbits, significantly led Born
, Heisenberg and Kramers to explore mathematics that strongly inspired the subsequent development of matrix mechanics
, the first form of modern quantum mechanics
. The provocativeness of the theory also generated great discussion and renewed attention to the difficulties in the foundations of the old quantum theory. However, physically the most provocative element of the theory, that momentum and energy would not necessarily be conserved in each interaction but only overall, statistically, was soon shown to be in conflict with experiment.
, who proposed to Bohr
and Kramers
the following elements of a theory of emission and absorption of radiation by atoms, to be developed during his stay in Copenhagen:
. He may have had good hopes that his idea with respect to oscillators vibrating at the differences of the frequencies of electron rotations (rather than at the rotation frequencies themselves) might be attractive to Bohr because it solved a problem of the latter's atomic model, even though the physical meaning of these oscillators was far from clear. Nevertheless, Bohr and Kramers had two objections to Slater's proposal:
As Jammer puts it, this refocussed the theory "to harmonize the physical picture of the continuous electromagnetic field with the physical picture, not as Slater had proposed of light quanta, but of the discontinuous quantum transitions in the atom." Bohr and Kramers hoped to be able to evade the photon hypothesis on the basis of ongoing work by Kramers to describe "dispersion" (in present-day terms inelastic scattering
) of light by means of a classical theory of interaction of radiation and matter. But abandoning the concept of the photon, they instead chose to squarely accept the possibility of non-conservation of energy, and momentum.
of free electrons, where "each of the electrons contributes through the emission of coherent secondary wavelets". Although Compton had already given an attractive account of his experiment on the basis of the photon picture (including conservation of energy and momentum in individual scattering processes), is it stated in the BKS paper that "it seems at the present state of science hardly justifiable to reject a formal interpretation as that under consideration [i.e. the weaker assumption of statistical conservation] as inadequate". This statement may have prompted experimental physicists to improve `the present state of science' by testing the hypothesis of `statistical energy and momentum conservation'. In any case, already after one year the BKS theory was disproved by experiments studying correlations between the directions into which the emitted radiation and the recoil electron are emitted in individual scattering processes. Such experiments were independently performed by Bothe and Geiger, as well as by Compton
and Simon. They provided experimental evidence pointing in the direction of energy and momentum conservation in individual scattering processes (at least, it was shown that the BKS theory was not able to explain the experimental results). More accurate experiments, performed much later, have also confirmed these results..
As suggested by a letter to Born
, for Einstein the corroboration of energy and momentum conservation was probably even more important than his photon hypothesis: "Bohr's opinion of radiation interests me very much. But I don't want to let myself be driven to a renunciation of strict causality before there has been a much stronger resistance against it than up to now. I cannot bear the thought that an electron exposed to a ray should by its own free decision choose the moment and the direction in which it wants to jump away. If so, I'd rather be a cobbler or even an employee in a gambling house than a physicist. It is true that my attempts to give the quanta palpable shape have failed again and again, but I'm not going to give up hope for a long time yet."
Bohr's reaction, too, was not primarily related to the photon hypothesis. According to Heisenberg
, Bohr remarked: "Even if Einstein sends me a cable that an irrevocable proof of the physical existence of light-quanta has now been found, the message cannot reach me, because it has to be transmitted by electromagnetic waves." For Bohr the lesson to be learned from the disproof of the BKS theory was not that photons do exist, but rather that the applicability of classical space-time pictures in understanding phenomena within the quantum domain is limited. This theme would become particularly important a few years later in developing the notion of complementarity
. According to Heisenberg, Born's statistical interpretation also had its ultimate roots in the BKS theory. Hence, despite its failure the BKS theory still provided an important contribution to the revolutionary transition from classical mechanics to quantum mechanics
.
Old quantum theory
The old quantum theory was a collection of results from the years 1900–1925 which predate modern quantum mechanics. The theory was never complete or self-consistent, but was a collection of heuristic prescriptions which are now understood to be the first quantum corrections to classical mechanics...
, 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 program than a full physical theory, the ideas that are developed not being worked out in a quantitative way.
One aspect, the idea of modelling atomic behaviour under incident electromagnetic radiation using "virtual oscillators" at the absorption and emission frequencies, rather than the (different) apparent frequencies of the Bohr orbits, significantly led Born
Max Born
Max Born was a German-born physicist and mathematician who was instrumental in the development of quantum mechanics. He also made contributions to solid-state physics and optics and supervised the work of a number of notable physicists in the 1920s and 30s...
, Heisenberg and Kramers to explore mathematics that strongly inspired the subsequent development of matrix mechanics
Matrix mechanics
Matrix mechanics is a formulation of quantum mechanics created by Werner Heisenberg, Max Born, and Pascual Jordan in 1925.Matrix mechanics was the first conceptually autonomous and logically consistent formulation of quantum mechanics. It extended the Bohr Model by describing how the quantum jumps...
, the first form of modern quantum mechanics
Quantum mechanics
Quantum mechanics, also known as quantum physics or quantum theory, is a branch of physics providing a mathematical description of much of the dual particle-like and wave-like behavior and interactions of energy and matter. It departs from classical mechanics primarily at the atomic and subatomic...
. The provocativeness of the theory also generated great discussion and renewed attention to the difficulties in the foundations of the old quantum theory. However, physically the most provocative element of the theory, that momentum and energy would not necessarily be conserved in each interaction but only overall, statistically, was soon shown to be in conflict with experiment.
Origins
The initial idea of the BKS theory originated with SlaterJohn C. Slater
John Clarke Slater was a noted American physicist who made major contributions to the theory of the electronic structure of atoms, molecules and solids. This work is of ongoing importance in chemistry, as well as in many areas of physics. He also made major contributions to microwave electronics....
, who proposed to Bohr
Niels Bohr
Niels Henrik David Bohr was a Danish physicist who made foundational contributions to understanding atomic structure and quantum mechanics, for which he received the Nobel Prize in Physics in 1922. Bohr mentored and collaborated with many of the top physicists of the century at his institute in...
and Kramers
Hendrik Anthony Kramers
Hendrik Anthony "Hans" Kramers was a Dutch physicist.-Background and education:...
the following elements of a theory of emission and absorption of radiation by atoms, to be developed during his stay in Copenhagen:
- Emission and absorption of electromagnetic radiation by matter is realized in agreement with Einstein's photonPhotonIn physics, a photon is an elementary particle, the quantum of the electromagnetic interaction and the basic unit of light and all other forms of electromagnetic radiation. It is also the force carrier for the electromagnetic force...
concept; - A photon emitted by an atom is guided by a classical electromagnetic field (compare de Broglie's ideas published September 1923 ) consisting of spherical waves, thus enabling to explain interference;
- Even when there are no transitions there exists a classical field to which all atoms contribute; this field contains all frequencies at which an atom can emit or absorb a photon, the probabilityProbabilityProbability is ordinarily used to describe an attitude of mind towards some proposition of whose truth we arenot certain. The proposition of interest is usually of the form "Will a specific event occur?" The attitude of mind is of the form "How certain are we that the event will occur?" The...
of such an emission being determined by the amplitude of the corresponding Fourier component of the field; the probabilistic aspect is provisional, to be eliminated when the dynamics of the inside of atoms are better known; - The classical field is not produced by the actual motions of the electrons but by `motions with the frequencies of possible emission and absorption linesSpectral lineA spectral line is a dark or bright line in an otherwise uniform and continuous spectrum, resulting from a deficiency or excess of photons in a narrow frequency range, compared with the nearby frequencies.- Types of line spectra :...
' (to be called `virtual oscillators', creating a field to be referred to as `virtual' as well).
Development with Bohr and Kramers
Slater's main intention seems to have been to reconcile the two conflicting models of radiation, viz. the wave and particle modelsWave–particle duality
Wave–particle duality postulates that all particles exhibit both wave and particle properties. A central concept of quantum mechanics, this duality addresses the inability of classical concepts like "particle" and "wave" to fully describe the behavior of quantum-scale objects...
. He may have had good hopes that his idea with respect to oscillators vibrating at the differences of the frequencies of electron rotations (rather than at the rotation frequencies themselves) might be attractive to Bohr because it solved a problem of the latter's atomic model, even though the physical meaning of these oscillators was far from clear. Nevertheless, Bohr and Kramers had two objections to Slater's proposal:
- The assumption that photons exist. Even though Einstein's photon hypothesis could explain in a simple way the photoelectric effectPhotoelectric effectIn the photoelectric effect, electrons are emitted from matter as a consequence of their absorption of energy from electromagnetic radiation of very short wavelength, such as visible or ultraviolet light. Electrons emitted in this manner may be referred to as photoelectrons...
, as well as conservation of energyConservation of energyThe nineteenth century law of conservation of energy is a law of physics. It states that the total amount of energy in an isolated system remains constant over time. The total energy is said to be conserved over time...
in processes of de-excitationExcited stateExcitation is an elevation in energy level above an arbitrary baseline energy state. In physics there is a specific technical definition for energy level which is often associated with an atom being excited to an excited state....
of an atom followed by excitation of a neighboring one, Bohr had always been reluctant to accept the reality of photons, his main argument being the problem of reconciling the existence of photons with the phenomenon of interference; - The impossibility to account for conservation of energyConservation of energyThe nineteenth century law of conservation of energy is a law of physics. It states that the total amount of energy in an isolated system remains constant over time. The total energy is said to be conserved over time...
in a process of de-excitation of an atom followed by excitation of a neighboring one. This impossibility followed from Slater's probabilistic assumption, which did not imply any correlationCorrelationIn statistics, dependence refers to any statistical relationship between two random variables or two sets of data. Correlation refers to any of a broad class of statistical relationships involving dependence....
between processes going on in different atoms.
As Jammer puts it, this refocussed the theory "to harmonize the physical picture of the continuous electromagnetic field with the physical picture, not as Slater had proposed of light quanta, but of the discontinuous quantum transitions in the atom." Bohr and Kramers hoped to be able to evade the photon hypothesis on the basis of ongoing work by Kramers to describe "dispersion" (in present-day terms inelastic scattering
Inelastic scattering
In particle physics and chemistry, inelastic scattering is a fundamental scattering process in which the kinetic energy of an incident particle is not conserved . In an inelastic scattering process, some of the energy of the incident particle is lost or gained...
) of light by means of a classical theory of interaction of radiation and matter. But abandoning the concept of the photon, they instead chose to squarely accept the possibility of non-conservation of energy, and momentum.
Experimental counter-evidence
In the BKS paper the Compton effect was discussed as an application of the idea of "statistical conservation of energy and momentum" in a continuous process of scattering of radiation by a sampleSample (material)
In general, a sample is a limited quantity of something which is intended to be similar to and represent a larger amount of that thing. The things could be countable objects such as individual items available as units for sale, or a material not countable as individual items. Samples of countable...
of free electrons, where "each of the electrons contributes through the emission of coherent secondary wavelets". Although Compton had already given an attractive account of his experiment on the basis of the photon picture (including conservation of energy and momentum in individual scattering processes), is it stated in the BKS paper that "it seems at the present state of science hardly justifiable to reject a formal interpretation as that under consideration [i.e. the weaker assumption of statistical conservation] as inadequate". This statement may have prompted experimental physicists to improve `the present state of science' by testing the hypothesis of `statistical energy and momentum conservation'. In any case, already after one year the BKS theory was disproved by experiments studying correlations between the directions into which the emitted radiation and the recoil electron are emitted in individual scattering processes. Such experiments were independently performed by Bothe and Geiger, as well as by Compton
Arthur Compton
Arthur Holly Compton was an American physicist and Nobel laureate in physics for his discovery of the Compton effect. He served as Chancellor of Washington University in St. Louis from 1945 to 1953.-Early years:...
and Simon. They provided experimental evidence pointing in the direction of energy and momentum conservation in individual scattering processes (at least, it was shown that the BKS theory was not able to explain the experimental results). More accurate experiments, performed much later, have also confirmed these results..
As suggested by a letter to Born
Max Born
Max Born was a German-born physicist and mathematician who was instrumental in the development of quantum mechanics. He also made contributions to solid-state physics and optics and supervised the work of a number of notable physicists in the 1920s and 30s...
, for Einstein the corroboration of energy and momentum conservation was probably even more important than his photon hypothesis: "Bohr's opinion of radiation interests me very much. But I don't want to let myself be driven to a renunciation of strict causality before there has been a much stronger resistance against it than up to now. I cannot bear the thought that an electron exposed to a ray should by its own free decision choose the moment and the direction in which it wants to jump away. If so, I'd rather be a cobbler or even an employee in a gambling house than a physicist. It is true that my attempts to give the quanta palpable shape have failed again and again, but I'm not going to give up hope for a long time yet."
Bohr's reaction, too, was not primarily related to the photon hypothesis. According to Heisenberg
Werner Heisenberg
Werner Karl Heisenberg was a German theoretical physicist who made foundational contributions to quantum mechanics and is best known for asserting the uncertainty principle of quantum theory...
, Bohr remarked: "Even if Einstein sends me a cable that an irrevocable proof of the physical existence of light-quanta has now been found, the message cannot reach me, because it has to be transmitted by electromagnetic waves." For Bohr the lesson to be learned from the disproof of the BKS theory was not that photons do exist, but rather that the applicability of classical space-time pictures in understanding phenomena within the quantum domain is limited. This theme would become particularly important a few years later in developing the notion of complementarity
Complementarity (physics)
In physics, complementarity is a basic principle of quantum theory proposed by Niels Bohr, closely identified with the Copenhagen interpretation, and refers to effects such as the wave–particle duality...
. According to Heisenberg, Born's statistical interpretation also had its ultimate roots in the BKS theory. Hence, despite its failure the BKS theory still provided an important contribution to the revolutionary transition from classical mechanics to quantum mechanics
Quantum mechanics
Quantum mechanics, also known as quantum physics or quantum theory, is a branch of physics providing a mathematical description of much of the dual particle-like and wave-like behavior and interactions of energy and matter. It departs from classical mechanics primarily at the atomic and subatomic...
.