Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Cambridge University Press eBooks

Guiding fields in 3-space

Guido Bacciagaluppi, Antony Valentini

Published Oct 22, 2009• 0 citations
Publisher

Abstract

In this chapter, we address proposals (by Einstein and by Bohr, Kramers and Slater) according to which quantum events are influenced by ‘guiding fields’ in 3-space. These ideas led to a predicted violation of energy-momentum conservation for single events, in contradiction with experiment. The contradiction was resolved only by the introduction of guiding fields in configuration space. All this took place before the fifth Solvay conference, but nevertheless forms an important background to some of the discussions that took place there. Einstein's early attempts to formulate a dynamical theory of light quanta Since the publication of his light-quantum hypothesis in 1905, Einstein had been engaged in a solitary struggle to construct a detailed theory of light quanta, and to understand the relationship between the quanta on the one hand and the electromagnetic field on the other. Einstein's efforts in this direction were never published. We know of them indirectly: they are mentioned in letters, and they are alluded to in Einstein's 1909 lecture in Salzburg. Einstein's published papers on light quanta continued for the most part in the same vein as his 1905 paper: using the theory of fluctuations to make deductions about the nature of radiation, without giving details of a substantial theory. Einstein was essentially alone in his dualistic view of light, in which localised energy fragments coexisted with extended waves, until the work of de Broglie in 1923 – which extended the dualism to all particles, and made considerable progress towards a real theory (see Chapter 2).

DOI
10.1017/cbo9781139194983.010

Related papers

Quanta, relativity and Einstein's dual vision of light

Christian Bracco

In the absence of any reliable document, from which Einsteins ideas on relativity prior to 1905 could uniquely be drawn, we are forced to make assumptions. If many historians (J. Norton, O. Darrigol, ) have privileged an electromagnetic origin, others like A. Miller have emphasized the role of light quanta. Ill come back on some evidences that the March quanta have played a role in the June and September 1905 relativity papers and reciprocally that the relativity principle may have influenced Einsteins reflexions on free moving quanta. From both a scientific and an historical perspective, the association of quanta and relativity is indeed natural if one has in mind Plancks work on the black body radiation and Poincarés contribution Lorentz theory and the reaction principle to the Lorentz Jubilee, which both occurred in mid-December 1900. As well known, the former introduced fixed energy quanta and the latter (quoted by Einstein in 1906) opened the way to a dynamical and relativistic (at first order in v/c) account of the electromagnetic field behaviour. But unknown, Poincarés paper also exhibited at this order the same transformation law for the energy and the frequency of an electromagnetic plane wave of finite length. If Einstein remarked this before 1906 (which is not proved), it may have encouraged his thinking of moving quanta. We would then meet the point of view expressed by R. Penrose in his preface of J. Stachels book Einsteins miraculous year, that it is virtually inconceivable that [Einstein] would have put forward two papers [March/June] in the same year which depended upon hypothetical views [particle/wave] of Nature that he felt were in contradiction with each other. March, June and September 1905 Einstein's papers would constitute a remarkable synthesis, in a fully original and new epistemological view, of Planck's 1900 work on the interaction between matter and radiation and Poincarés 1900 paper on the relativistic dynamics of charges and the electromagnetic field.

•Jul 21, 2013•0 citations

Waves and particles

Louis de Broglie

When in the spring of 1926 Erwin Schrödinger set out the form of the equation for wave propagation and drew important conclusions from it, in some very elegant work which appeared to develop the ideas which I had introduced in 1923–24 (de Broglie 1924), he really profoundly modified the ideas which had guided me two years earlier in my original research. For his idea was that although the ψ wave which he was introducing was still a true physical wave propagated in space and time, it would not have any single area of high field concentration which could be a particle; whereas in my original concept I assumed that the coexistence of waves and particles, perceived by Einstein in 1905 in respect of light in his theory of light quanta, should be extended to all types of particle in the form of the coexistence of a physical wave with a particle incorporated in it.

Physics Bulletin•Mar 1, 1971•0 citations

Preliminary concepts

P. C. W. Davies, David S. Betts

This chapter presents the basic physical ideas that underpin the quantum theory. Historians place the beginnings of the quantum theory at 1900. That year Max Planck published his famous formula for the distribution of energy as a function of frequency in black-body radiation. Curiously, although radiation theory gave birth to quantum mechanics, the interaction of matter and electromagnetic radiation is a rather advanced topic in quantum mechanics and it took almost fifty years for an acceptable formulation to be achieved. One reason for this is that photons are quanta of the electromagnetic field, and the quantum theory of fields requires a relativistic treatment to be entirely successful. The corpuscular nature of light was only half of the input that gave birth to quantum mechanics. The other half concerns matter. Given that the discreteness of photons manifests itself during the emission and absorption process, it is not surprising to find that quantum oddities afflict the behaviour of material particles too.

Routledge eBooks•Apr 27, 2018•0 citations

The Triumph of the Light Quantum Hypothesis

Malcolm S. Longair

Einstein never deviated from his belief in the reality of light quanta. In 1909, he published a remarkable paper in which he showed that fluctuations in the intensity of black-body radiation consisted of the statistical sum of the wave and particle properties of light. Following the 1911 Solvay conference, most of the participants were converted to the existence of light quanta. Bohr first applied the concepts of quanta to the structure of atoms. The experiment which finally convinced everyone of the light quantum hypothesis was Compton's demonstration of the energy change of X-rays in their scattering by electrons. This resulted in the concept of the wave-particle duality of light, one of the major foundation stones of quantum mechanics.

Cambridge University Press eBooks•Mar 30, 2020•0 citations

Experiments with Single Photons

Philippe Grangier

The birth of the light quanta- “licht quanten ” in their original version- is rightfully associated with the article [1] published by Albert Einstein in 1905, “An heuristic point of view about the production and transformation of light”. Interestingly, several points expressed in a very collegial style in this article were exposed again in a more direct, “einsteinian ” style, in a conference [2] that Einstein gave in Salzburg on september 21, 1909. This conference, entitled “The evolution of our conceptions about the nature and the constitution of radiation ” reveals, and to some extend completes, the way of thinking that lead Einstein to the 1905 papers on relativity and radiation. For instance, in 1909 Einstein gives again the list of open problems in the radiation theory, which briefly alluded to in the 1905 article. These problems were: 1. why does the appearance of a photochemical reaction depends only on the colour of light, and not on its intensity? 2. why is short wavelength radiation generally more active chemically than long wavelength radiation? 3. why is the kinetic energy of cathode rays (electrons) produced by the photoelectric effect independant on the light intensity?

Birkhäuser Basel eBooks•Jan 1, 2005•6 citations

Einstein and the quantum theory

A. Pais

This is an account of Einstein's work and thoughts on the quantum theory. The following topics will be discussed: The light-quantum hypothesis and its gradual evolution into the photon concept. Early history of the photoelectric effect. The theoretical and experimental reasons why the resistance to the photon was stronger and more protracted than for any other particle proposed to date. Einstein's position regarding the Bohr-Kramers-Slater suggestion, the last bastion of resistance to the photon. Einstein's analysis of fluctuations around thermal equilibrium and his proposal of a duality between particles and waves, in 1909 for electromagnetic radiation (the first time this duality was ever stated) and in January 1925 for matter (prior to quantum mechanics and for reasons independent of those given earlier by de Broglie). His demonstration that long-known specific heat anomalies are quantum effects. His role in the evolution of the third law of thermodynamics. His new derivation of Planck's law in 1917 which also marks the beginning of his concern with the failure of classical causality. His role as one of the founders of quantum statistics and his discovery of the first example of a phase transition derived by using purely statistical methods. His position as a critic of quantum mechanics. Initial doubts on the consistency of quantum mechanics (1926-1930). His view maintained from 1930 until the end of his life: quantum mechanics is logically consistent and quite successful but it is incomplete. His attitude toward success. His criterion of objective reality. Differences in the roles relativity and quantum theory played in Einstein's life. His vision regarding quantum theory in the context of a unified field theory. His last autobiographical sketch, written a few months before his death, concluding with a statement about the quantum theory, a subject to which (by his own account) he had given more thought than even to general relativity.

Reviews of Modern Physics•Oct 1, 1979•297 citations
In this chapter, we address proposals (by Einstein and by Bohr, Kramers and Slater) according to which quantum events are influenced by ‘guiding fields’ in 3-space. These ideas led to a predicted violation of energy-momentum conservation for single events, in contradiction with experiment. The contradiction was resolved only by the introduction of guiding fields in configuration space. All this took place before the fifth Solvay conference, but nevertheless forms an important background to some of the discussions that took place there. Einstein's early attempts to formulate a dynamical theory of light quanta Since the publication of his light-quantum hypothesis in 1905, Einstein had been engaged in a solitary struggle to construct a detailed theory of light quanta, and to understand the relationship between the quanta on the one hand and the electromagnetic field on the other. Einstein's efforts in this direction were never published. We know of them indirectly: they are mentioned in letters, and they are alluded to in Einstein's 1909 lecture in Salzburg. Einstein's published papers on light quanta continued for the most part in the same vein as his 1905 paper: using the theory of fluctuations to make deductions about the nature of radiation, without giving details of a substantial theory. Einstein was essentially alone in his dualistic view of light, in which localised energy fragments coexisted with extended waves, until the work of de Broglie in 1923 – which extended the dualism to all particles, and made considerable progress towards a real theory (see Chapter 2).
In the absence of any reliable document, from which Einsteins ideas on relativity prior to 1905 could uniquely be drawn, we are forced to make assumptions. If many historians (J. Norton, O. Darrigol, ) have privileged an electromagnetic origin, others like A. Miller have emphasized the role of light quanta. Ill come back on some evidences that the March quanta have played a role in the June and September 1905 relativity papers and reciprocally that the relativity principle may have influenced Einsteins reflexions on free moving quanta. From both a scientific and an historical perspective, the association of quanta and relativity is indeed natural if one has in mind Plancks work on the black body radiation and Poincarés contribution Lorentz theory and the reaction principle to the Lorentz Jubilee, which both occurred in mid-December 1900. As well known, the former introduced fixed energy quanta and the latter (quoted by Einstein in 1906) opened the way to a dynamical and relativistic (at first order in v/c) account of the electromagnetic field behaviour. But unknown, Poincarés paper also exhibited at this order the same transformation law for the energy and the frequency of an electromagnetic plane wave of finite length. If Einstein remarked this before 1906 (which is not proved), it may have encouraged his thinking of moving quanta. We would then meet the point of view expressed by R. Penrose in his preface of J. Stachels book Einsteins miraculous year, that it is virtually inconceivable that [Einstein] would have put forward two papers [March/June] in the same year which depended upon hypothetical views [particle/wave] of Nature that he felt were in contradiction with each other. March, June and September 1905 Einstein's papers would constitute a remarkable synthesis, in a fully original and new epistemological view, of Planck's 1900 work on the interaction between matter and radiation and Poincarés 1900 paper on the relativistic dynamics of charges and the electromagnetic field.
When in the spring of 1926 Erwin Schrödinger set out the form of the equation for wave propagation and drew important conclusions from it, in some very elegant work which appeared to develop the ideas which I had introduced in 1923–24 (de Broglie 1924), he really profoundly modified the ideas which had guided me two years earlier in my original research. For his idea was that although the ψ wave which he was introducing was still a true physical wave propagated in space and time, it would not have any single area of high field concentration which could be a particle; whereas in my original concept I assumed that the coexistence of waves and particles, perceived by Einstein in 1905 in respect of light in his theory of light quanta, should be extended to all types of particle in the form of the coexistence of a physical wave with a particle incorporated in it.
This chapter presents the basic physical ideas that underpin the quantum theory. Historians place the beginnings of the quantum theory at 1900. That year Max Planck published his famous formula for the distribution of energy as a function of frequency in black-body radiation. Curiously, although radiation theory gave birth to quantum mechanics, the interaction of matter and electromagnetic radiation is a rather advanced topic in quantum mechanics and it took almost fifty years for an acceptable formulation to be achieved. One reason for this is that photons are quanta of the electromagnetic field, and the quantum theory of fields requires a relativistic treatment to be entirely successful. The corpuscular nature of light was only half of the input that gave birth to quantum mechanics. The other half concerns matter. Given that the discreteness of photons manifests itself during the emission and absorption process, it is not surprising to find that quantum oddities afflict the behaviour of material particles too.
Einstein never deviated from his belief in the reality of light quanta. In 1909, he published a remarkable paper in which he showed that fluctuations in the intensity of black-body radiation consisted of the statistical sum of the wave and particle properties of light. Following the 1911 Solvay conference, most of the participants were converted to the existence of light quanta. Bohr first applied the concepts of quanta to the structure of atoms. The experiment which finally convinced everyone of the light quantum hypothesis was Compton's demonstration of the energy change of X-rays in their scattering by electrons. This resulted in the concept of the wave-particle duality of light, one of the major foundation stones of quantum mechanics.
The birth of the light quanta- “licht quanten ” in their original version- is rightfully associated with the article [1] published by Albert Einstein in 1905, “An heuristic point of view about the production and transformation of light”. Interestingly, several points expressed in a very collegial style in this article were exposed again in a more direct, “einsteinian ” style, in a conference [2] that Einstein gave in Salzburg on september 21, 1909. This conference, entitled “The evolution of our conceptions about the nature and the constitution of radiation ” reveals, and to some extend completes, the way of thinking that lead Einstein to the 1905 papers on relativity and radiation. For instance, in 1909 Einstein gives again the list of open problems in the radiation theory, which briefly alluded to in the 1905 article. These problems were: 1. why does the appearance of a photochemical reaction depends only on the colour of light, and not on its intensity? 2. why is short wavelength radiation generally more active chemically than long wavelength radiation? 3. why is the kinetic energy of cathode rays (electrons) produced by the photoelectric effect independant on the light intensity?
This is an account of Einstein's work and thoughts on the quantum theory. The following topics will be discussed: The light-quantum hypothesis and its gradual evolution into the photon concept. Early history of the photoelectric effect. The theoretical and experimental reasons why the resistance to the photon was stronger and more protracted than for any other particle proposed to date. Einstein's position regarding the Bohr-Kramers-Slater suggestion, the last bastion of resistance to the photon. Einstein's analysis of fluctuations around thermal equilibrium and his proposal of a duality between particles and waves, in 1909 for electromagnetic radiation (the first time this duality was ever stated) and in January 1925 for matter (prior to quantum mechanics and for reasons independent of those given earlier by de Broglie). His demonstration that long-known specific heat anomalies are quantum effects. His role in the evolution of the third law of thermodynamics. His new derivation of Planck's law in 1917 which also marks the beginning of his concern with the failure of classical causality. His role as one of the founders of quantum statistics and his discovery of the first example of a phase transition derived by using purely statistical methods. His position as a critic of quantum mechanics. Initial doubts on the consistency of quantum mechanics (1926-1930). His view maintained from 1930 until the end of his life: quantum mechanics is logically consistent and quite successful but it is incomplete. His attitude toward success. His criterion of objective reality. Differences in the roles relativity and quantum theory played in Einstein's life. His vision regarding quantum theory in the context of a unified field theory. His last autobiographical sketch, written a few months before his death, concluding with a statement about the quantum theory, a subject to which (by his own account) he had given more thought than even to general relativity.