The momentum of light in media the abraham-Minkowski controversy Peter Bowyer School of Physics Astronomy Southampton, UK January 2005
1 The momentum of light in media: the Abraham-Minkowski controversy Peter Bowyer School of Physics & Astronomy Southampton, UK January 2005
Abstract The controversy arises due to abrahams and minkowski's calculations disagreeing as to whether the momentum carried by an electromagnetic field is increased or decreased by the presence of a refractive medium. This paper starts by providing an overview of the life of Abraham and minkowski. The opinions on the century are considered, and the arguments they put forward to support her o> controversy, and solutions for the controversy proposed by physicists over the pa position are examined. Finally, some of the experiments undertaken are discussed, along with whether they have shed light on the controversy. The paper concludes by considering proposed future work on the topic
2 Abstract The controversy arises due to Abraham’s and Minkowski’s calculations disagreeing as to whether the momentum carried by an electromagnetic field is increased or decreased by the presence of a refractive medium. This paper starts by providing an overview of the life of Abraham and Minkowski. The opinions on the controversy, and solutions for the controversy proposed by physicists over the past century are considered, and the arguments they put forward to support their position are examined. Finally, some of the experiments undertaken are discussed, along with whether they have shed light on the controversy. The paper concludes by considering proposed future work on the topic
Table of contents Introduction Biographies…… 355 Abraham(1875-1922) Minkowski(1864-1909) Theory……… The abraham and minkowski tensors Radiation Pressure Momentum of light Poynting Vector Pseudomomentum 7788999 Tensors Einstein's box The proponents… 10 Alternative theories 15 Experimental Work 17 Early Experiments 17 17 Jones and richards Jones and lesli Ashkin and dziedzic 20 Walker Lahoz and Walker 20 The problem with experiments 21 uture Experimental work conc| usIon∴n 22 References:∴ Introduction For nearly 100 years physicists and mathematicians have been debating the correct form of the energy-momentum tensor required to describe the behaviour of The two main 'competing theories during this time have been those proposed b u light at the interface between two dielectric materials of different refractive indice Minkowski(1908)[1] and Abraham(1909)[2]. Put simply, the dilemma is whether the momentum of a photon in a medium is equal to nnk Minkowski) or nk/n (Abraham), where n is the refractive index of the material, h is Planck's constant divided by 2T, and k is the wavevector
3 Table of Contents Introduction...................................................................................3 Biographies...................................................................................5 Abraham (1875 –1922)................................................................................ 5 Minkowski (1864—1909) ............................................................................. 6 Theory............................................................................................7 The Abraham and Minkowski tensors.......................................................... 7 Radiation Pressure ...................................................................................... 8 Momentum of light ....................................................................................... 8 Poynting Vector ........................................................................................... 9 Pseudomomentum....................................................................................... 9 Tensors........................................................................................................ 9 Einstein’s box............................................................................................. 10 The proponents...........................................................................10 Alternative theories ....................................................................15 Experimental Work .....................................................................17 Early Experiments...................................................................................... 17 G. Barlow................................................................................................... 17 Jones and Richards ................................................................................... 18 Jones and Leslie........................................................................................ 19 Ashkin and Dziedzic .................................................................................. 20 Walker, Lahoz and Walker......................................................................... 20 The problem with experiments................................................................... 21 Future Experimental work.......................................................................... 22 Conclusion ..................................................................................22 References: .................................................................................23 Introduction For nearly 100 years physicists and mathematicians have been debating the correct form of the energy-momentum tensor required to describe the behaviour of light at the interface between two dielectric materials of different refractive indices. The two main ‘competing’ theories during this time have been those proposed by Minkowski (1908) [1] and Abraham (1909) [2]. Put simply, the dilemma is whether the momentum of a photon in a medium is equal to nħk (Minkowski) or ħk/n (Abraham), where n is the refractive index of the material, ħ is Planck’s constant divided by 2π, and k is the wavevector
While interest in the problem has waxed and waned over the years, it has never completely disappeared, and recently the topic has come back into vogue, with many papers published over the past 10 years and more due in the next year It is interesting to note how people s views have changed over the years Minkowski was originally thought to be correct, although whether this was due to the convincing nature of his proposal, or people s dislike of Abraham is unclear. In 1950 M.V. Laue [3] was quite conclusive that Minkowski had developed the correct tensorial solution, and his views continued to be held through to the early 1970s without questioning. At this time experiments were undertaken which proved the existence of the Abraham force, and the opinion began to swing in favour of Abrahams tensor as being the correct solution. Recently though views have changed again, towards understanding that both are correct but in different circumstances It appears Minkowski derived his energy-momentum tensor independent of any other work; however Abrahams was not formulated separately, but was an attempt to reformulate minkowski's tensor without the extra 'minkowski force term. his goal was to preserve the form from classical mechanics-a derivative with respect to time. In a previous paper Abraham had developed a system for the electrodynamics of objects in motion, which, while consistent with Maxwell and Hertz, also incorporated ideas by Lorentz and minkowski. While dealing with Minkowski's ponderomotive force, Abraham derived another ponderomotive force and stated that his satisfied relativity At first sight it seems strange that such a small problem from the early twentieth century is still of interest. the author believes there are two contributing factors 1. Physicists do not like unsolved problems. It spoils the 'neatness'(well whatever neatness we have left after Heisenberg and quantum theory! )of the subject. There must be one definite mathematical formula for a particular problem. a case like this is particularly annoying, where the two equations are equivalent sometimes, yet at other times only one will solve a problem 2. As optics becomes ever-increasingly important due to its use telecommunications etc, any area with unanswered questions is worth investigating. We cannot tell what future technological breakthroughs it may lead to Many physicists and mathematicians have proposed alternative tensors that they claim do not suffer the same problem and will describe all situations. The author is not mathematically accomplished enough to comment on the accuracy of their claims. However, most have gone un-noticed and unreferenced by other paper from which the author deduces that none have solved the problem completely rather they reformulate it, sometimes clarifying areas, other times providing yet another layer of complexity over the problem This paper will start by providing an overview of the life of Abraham and minkowski followed by background theory. Next the opinions of physicists over the past century will be considered and the arguments they put forward to support their position will be examined. Finally, some of the experiments undertaken will be
4 While interest in the problem has waxed and waned over the years, it has never completely disappeared, and recently the topic has come back into vogue, with many papers published over the past 10 years and more due in the next year. It is interesting to note how people’s views have changed over the years. Minkowski was originally thought to be correct, although whether this was due to the convincing nature of his proposal, or people’s dislike of Abraham is unclear. In 1950 M. V. Laue [3] was quite conclusive that Minkowski had developed the correct tensorial solution, and his views continued to be held through to the early 1970s without questioning. At this time experiments were undertaken which proved the existence of the Abraham force, and the opinion began to swing in favour of Abraham’s tensor as being the correct solution. Recently though views have changed again, towards understanding that both are correct but in different circumstances. It appears Minkowski derived his energy-momentum tensor independent of any other work; however Abraham’s was not formulated separately, but was an attempt to reformulate Minkowski’s tensor without the extra ‘Minkowski force’ term. His goal was to preserve the form from classical mechanics - a derivative with respect to time. In a previous paper Abraham had developed a system for the electrodynamics of objects in motion, which, while consistent with Maxwell and Hertz, also incorporated ideas by Lorentz and Minkowski. While dealing with Minkowski’s ponderomotive force, Abraham derived another ponderomotive force and stated that his satisfied relativity. At first sight it seems strange that such a small problem from the early twentieth century is still of interest. The author believes there are two contributing factors: 1. Physicists do not like unsolved problems. It spoils the ‘neatness’ (well, whatever neatness we have left after Heisenberg and quantum theory!) of the subject. There must be one definite mathematical formula for a particular problem. A case like this is particularly annoying, where the two equations are equivalent sometimes, yet at other times only one will solve a problem. 2. As optics becomes ever-increasingly important due to its use in telecommunications etc, any area with unanswered questions is worth investigating. We cannot tell what future technological breakthroughs it may lead to. Many physicists and mathematicians have proposed alternative tensors that they claim do not suffer the same problem and will describe all situations. The author is not mathematically accomplished enough to comment on the accuracy of their claims. However, most have gone un-noticed and unreferenced by other papers, from which the author deduces that none have solved the problem completely; rather they reformulate it, sometimes clarifying areas, other times providing yet another layer of complexity over the problem. This paper will start by providing an overview of the life of Abraham and Minkowski, followed by background theory. Next the opinions of physicists over the past century will be considered and the arguments they put forward to support their position will be examined. Finally, some of the experiments undertaken will be
discussed, along with whether they have given additional insight to the controversy. In this paper the problem will be both considered tensorially and using a simplified form. Both approaches have been considered widely in the literature on the subject, and the latter approach provides a more accessible route into the subject for those with less mathematical knowledge Biographies Abraham(1875-1922 Max abraham was born to a wealthy Jewish family and studied Physics at the University of Berlin under Planck. Abraham was appointed as a Privatdozent (an unpaid lecturer) at Gottingen in 1900, a position which lasted until 1909. The reason for his failure to obtain a permanent university position during this period was not due to any lack of ability but rather to his personality. Goldberg writes [4 he had no patience with what he considered to be silly or illogical argumentation. Abraham had a penchant for being critical and had no hesitation in publicly chastising his colleagues, regardless of their rank or position. His sharp wit was matched by an equally sharp tongue, and as a result he remained a Privatdozent at Gottingen for nine years. In 1909 Abraham accepted a post at the University of linois in the United States However, he disliked the atmosphere of Illinois, and returned within a few months to Gottingen. He then moved to ltaly at the invitation of Levi-Civita, where he became professor of rational mechanics at the University of Milan, a position he held until 1914. While he was here Abraham and Einstein disagreed strongly about the theory of relativity The onset of World War 1 forced abraham to return to germany, where he worked on the theory of radio transmission. After the war he was unable to return to milan and so he worked at Stuttgart until 1921, substituting for the professor of physics at the Technische Hochschule. He accepted a chair in Aachen but on the journey there he was taken ill and a brain tumour was diagnosed. He never recovered and died in agony six months later Almost all of Abraham s work was related to Maxwell's theory. His consistent use of vectors in his text on the subject was a significant factor in the rapid acceptance of vector notation in germany one of the most noteworthy features of his text was that in each new edition Abraham included not only the latest experimental wor but also the latest theoretical contributions even if these contributions were in dispute. For better or worse, he had no hesitation, after explaining both sides of a question, to use the book to argue his own point of view He developed a theory of the electron in 1902, but in 1904 Lorentz and Einstein produced a different theory. Abraham's study of the structure and nature of the electron led him to the idea of the electromagnetic nature of its mass, and
5 discussed, along with whether they have given additional insight to the controversy. In this paper the problem will be both considered tensorially and using a simplified form. Both approaches have been considered widely in the literature on the subject, and the latter approach provides a more accessible route into the subject for those with less mathematical knowledge. Biographies Abraham (1875 –1922) Max Abraham was born to a wealthy Jewish family and studied Physics at the University of Berlin under Planck. Abraham was appointed as a Privatdozent (an unpaid lecturer) at Göttingen in 1900, a position which lasted until 1909. The reason for his failure to obtain a permanent university position during this period was not due to any lack of ability but rather to his personality. Goldberg writes [4]: “...he had no patience with what he considered to be silly or illogical argumentation. Abraham had a penchant for being critical and had no hesitation in publicly chastising his colleagues, regardless of their rank or position. His sharp wit was matched by an equally sharp tongue, and as a result he remained a Privatdozent at Göttingen for nine years.” In 1909 Abraham accepted a post at the University of Illinois in the United States. However, he disliked the atmosphere of Illinois, and returned within a few months to Göttingen. He then moved to Italy at the invitation of Levi-Civita, where he became professor of rational mechanics at the University of Milan, a position he held until 1914. While he was here Abraham and Einstein disagreed strongly about the theory of relativity. The onset of World War 1 forced Abraham to return to Germany, where he worked on the theory of radio transmission. After the war he was unable to return to Milan and so he worked at Stuttgart until 1921, substituting for the professor of physics at the Technische Hochschule. He accepted a chair in Aachen but on the journey there he was taken ill and a brain tumour was diagnosed. He never recovered and died in agony six months later. Almost all of Abraham's work was related to Maxwell's theory. His consistent use of vectors in his text on the subject was a significant factor in the rapid acceptance of vector notation in Germany. One of the most noteworthy features of his text was that in each new edition Abraham included not only the latest experimental work but also the latest theoretical contributions, even if these contributions were in dispute. For better or worse, he had no hesitation, after explaining both sides of a question, to use the book to argue his own point of view. He developed a theory of the electron in 1902, but in 1904 Lorentz and Einstein produced a different theory. Abraham's study of the structure and nature of the electron led him to the idea of the electromagnetic nature of its mass, and