2. THE ABRAHAM-MINKOWSKI CONTROVERSY 2.1. Background "What happens to the momentum of a photon when it enters a dielectric medium? This seemingly innocuous question lies at the centre of a century-long debate. The answer is tied to the closely-related question, " What is the energy-momentum tensor of an electromagnetic wave traversing a dielectric material? The energy-momentum tensor describes the propagation of energy and momentum in a four-dimensional space-time. To derive the appropriate expression for an electromagnetic wave propagating in free space is relatively straightforward and the result is known as Maxwells tensor. Its derivation may be found in more advanced texts on electromagnetism or special relativity ,5 It is only within material media that uncertainty arises The first expression for the electromagnetic energy-momentum tensor in a dielectric medium was proposed by Minkowski in 1908., According to the Minkowski electromagnetic energy-momentum tensor, the momentum Aux density of an electromagnetic wave increases from p in free space to np in a material medium, where n is the refractive index of the medium, and the electromagnetic momentum density is given by d B. However, the tensor which Minkowski proposed came under heavy criticism on account of its lack of diagonal symmetry, a fact which was held incompatible with conservation of angular momentum. In response to this, first Einstein and Laub, 9 and later Abraham10, II developed symmetric energy-momentum tensors. However, under these tensors the momentum of an electromagnetic wave decreases on entering a dielectric medium from p to p/n, and the electromagnetic momentum density is given by(1/c)Ex H. The tensor of Einstein and Laub did not purport to be valid outside of the rest frame of the material medium, whereas that of abraham was rigorously developed in accordance with the principles of special relativity and hence rapidly gained favour. Numerous arguments and thought experiments were proposed attempting to discriminate between the two tensors(for example, Refs. 5, 12-15) though neither gained a convincing upper hand. In 1954, Jones and Richards performed an experiment 6 to measure the momentum transferred by a beam of light to a reflecting surface suspended within a dielectric medium, and demonstrated that the magnitude of the momentum transfer ras np, but Jones comments that this is consistent with both the Minkowski and the Abraham tensors, if one recognises that under the Abraham tensor, the electromagnetic wave is also accompanied by a disturbance within the dielectric medium carrying momentum In 1973, another significant experiment was performed by Ashkin and Dziedzicl? in response to a theoretical paper by Burt and Peierls, 8 in which they considered the behaviour of a liquid interface traversed by a laser beam. As the electromagnetic wave traversed the air-liquid interface it would either increase or decrease in momentum, and conservation of momentum required that an equal and opposite quantity of momentum be imparted to the fluid interface, which would then either bulge inwards or outwards accordingly. Burt and Peierls argued that the material disturbance in the medium in the Abraham case described above would propagate far lower than the electromagnetic radiation, and hence the initial response of the interface would depend upon the electromagnetic momentum alone. Ashkin and Dziedzic performed this experiment, and discovered that the interface bulged outward, into the medium of lower refractive index. However, they also recognised the then-unpublished work of Gordon19who performed a more detailed analysis and showed that the role of the material disturbance was not negligible and hat the predictions of the two tensors would be identical after all the gordon recognised that the disturbance in the dielectric medium arises as a result of interactions between medium and the electromagnetic wave. It is established by the leading edge of an electromagnetic pulse as it traverses the medium, and restored to normal by the trailing edge. The material disturbance therefore propagates at the speed of the electromagnetic wave, and not at the speed of sound in the medium, as previously supposed. Pressure effects arising from the edges of the beam were also found to play a significant role Gordon's work provided a very practical demonstration of the equivalence of the Abraham and Minkowski tensors but was confined to fuids with a dielectric constant e 1. It was later extended to elastic solids by2. THE ABRAHAM–MINKOWSKI CONTROVERSY 2.1. Background “What happens to the momentum of a photon when it enters a dielectric medium?” This seemingly innocuous question lies at the centre of a century-long debate. The answer is tied to the closely-related question, “What is the energy–momentum tensor of an electromagnetic wave traversing a dielectric material?” The energy–momentum tensor describes the propagation of energy and momentum in a four-dimensional space–time. To derive the appropriate expression for an electromagnetic wave propagating in free space is relatively straightforward and the result is known as Maxwell’s tensor. Its derivation may be found in more advanced texts on electromagnetism3 or special relativity.4, 5 It is only within material media that uncertainty arises. The first expression for the electromagnetic energy–momentum tensor in a dielectric medium was proposed by Minkowski in 1908.6, 7 According to the Minkowski electromagnetic energy–momentum tensor, the momentum flux density of an electromagnetic wave increases from p in free space to np in a material medium, where n is the refractive index of the medium, and the electromagnetic momentum density is given by D × B. However, the tensor which Minkowski proposed came under heavy criticism on account of its lack of diagonal symmetry, a fact which was held incompatible with conservation of angular momentum. In response to this, first Einstein and Laub8, 9 and later Abraham10, 11 developed symmetric energy–momentum tensors. However, under these tensors the momentum of an electromagnetic wave decreases on entering a dielectric medium from p to p/n, and the electromagnetic momentum density is given by (1/c) E × H. The tensor of Einstein and Laub did not purport to be valid outside of the rest frame of the material medium, whereas that of Abraham was rigorously developed in accordance with the principles of special relativity and hence rapidly gained favour. Numerous arguments and thought experiments were proposed, attempting to discriminate between the two tensors (for example, Refs. 5, 12–15) though neither gained a convincing upper hand. In 1954, Jones and Richards performed an experiment16 to measure the momentum transferred by a beam of light to a reflecting surface suspended within a dielectric medium, and demonstrated that the magnitude of the momentum transfer was np, but Jones comments that this is consistent with both the Minkowski and the Abraham tensors, if one recognises that under the Abraham tensor, the electromagnetic wave is also accompanied by a disturbance within the dielectric medium carrying momentum  n − 1 n  p. (1) In 1973, another significant experiment was performed by Ashkin and Dziedzic17 in response to a theoretical paper by Burt and Peierls,18 in which they considered the behaviour of a liquid interface traversed by a laser beam. As the electromagnetic wave traversed the air–liquid interface it would either increase or decrease in momentum, and conservation of momentum required that an equal and opposite quantity of momentum be imparted to the fluid interface, which would then either bulge inwards or outwards accordingly. Burt and Peierls argued that the material disturbance in the medium in the Abraham case described above would propagate far slower than the electromagnetic radiation, and hence the initial response of the interface would depend upon the electromagnetic momentum alone. Ashkin and Dziedzic performed this experiment, and discovered that the interface bulged outward, into the medium of lower refractive index. However, they also recognised the then-unpublished work of Gordon19 who performed a more detailed analysis and showed that the role of the material disturbance was not negligible and that the predictions of the two tensors would be identical after all. Gordon recognised that the disturbance in the dielectric medium arises as a result of interactions between the medium and the electromagnetic wave. It is established by the leading edge of an electromagnetic pulse as it traverses the medium, and restored to normal by the trailing edge. The material disturbance therefore propagates at the speed of the electromagnetic wave, and not at the speed of sound in the medium, as previously supposed. Pressure effects arising from the edges of the beam were also found to play a significant role. Gordon’s work provided a very practical demonstration of the equivalence of the Abraham and Minkowski tensors but was confined to fluids with a dielectric constant ε  1. It was later extended to elastic solids by