Colloquium: Momentum of an electromagnetic wave in dielectric media

Almost $100\text{years}$ ago, two different expressions were proposed for the energy-momentum tensor of an electromagnetic wave in a dielectric. Minkowski’s tensor predicted an increase in the linear momentum of the wave on entering a dielectric medium, whereas Abraham’s tensor predicted its decrease. Theoretical arguments were advanced in favor of both sides, and experiments proved incapable of distinguishing between the two. Yet more forms were proposed, each with their advocates who considered the form that they were proposing to be the one true tensor. This paper reviews the debate and its eventual conclusion: that no electromagnetic wave energy-momentum tensor is complete on its own. When the appropriate accompanying energy-momentum tensor for the material medium is also considered, experimental predictions of all various proposed tensors will always be the same, and the preferred form is therefore effectively a matter of personal choice.

Figure 1

The suspension and its container. $A$, screws to tauten suspension; $B$, brass draft cover; $C$, phosphor bronze strip $0.005\mathrm{cm}$ thick; $D$, Johnson Matthey gold alloy suspension $0.005\times 0.0005{\mathrm{cm}}^2$; $E$, brass tube $0.8\mathrm{cm}$ internal diameter; $F$, magnet $0.2\mathrm{cm}$ long; $G$, electromagnet; $H$, 48 Standard Wire Gauge copper wire; $I$, liquid levels; $J$, screwed brass ring and lead washers; $K$, support for mirrors; $L$, lead washer; $M$, silvered glass mirror $0.2\times 0.5\times 0.02{\mathrm{cm}}^3$; $N$, brass swivel joint; $O$, brass nut and washers; $P$, copper-glass seal; $G\left[\mathrm{sic}\right]$, glass tube; $R$, cotton-wool plug; $S$, triangular cast iron base; $V$, rhodium-plated silver vane $0.2\times 0.5\times 0.01{\mathrm{cm}}^3$; and $W$, circular glass window $0.1\mathrm{cm}$ thick. From 53. Published by The Royal Society.

Figure 2

Basic apparatus: $A$, beam shapes for low power (solid curve) and high power (dashed curve) for positive surface lens; $B$, shapes (for low and high power) for a negative surface lens. For $A$ and $B$ the beam is incident from above. $C$, beam shapes for low and high power for a positive surface lens with the beam incident from below. $F$ is a $2–4\mu \mathrm{m}$ glass fiber used to identify the surface of the water under the microscope. A beam attenuator was placed either in position (1) or (2) depending on the power level desired within the glass cell. From 8.

Figure 3

Diagram of the experimental apparatus. From 98.