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Recorded: 5/26/2018 Released: 10/14/2018

Randy tells Jim about advances in the stress-momentum tensor of electrodynamics. This tensor can be integrated over the boundary of an object to describe the force on it from the magnetic field. It is closely related to the momentum carried in the electromagnetic field, and its proper formulation in materials has been the subject of debate for over a hundred years.

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Notes:

1. The papers we read for this program:

- Wang, S., J. Ng, C.T. Chan, "Electromagnetic Stress at the Boundary: Photon Pressure or Tension?"
*Science Advances***2**, e1501485 (2016). [arXiv] - Wang, N., S. Wang, J. Ng, "Electromagnetic Stress Tensor for Amorphous Metamaterial Medium."
*Phys Rev A***97**, 033839 (2018). 1745-1749. [arXiv]

2. Other papers mentioned:

I found these papers useful for this program:

- Brevik, I., "Expriments in Phenomenological Electrodynamics and the Electromagnetic Energy-Momentum Tensor."
*Phys Rep***52**133(1979). [CiteSeerX] - Barnett, S.M., and R. Loudon, "The Enigma of Optical Momentum in a Medium."
*Phil Trans R Soc A***368**927(2010)

3. Books mentioned in this podcast:

- J.D. Jackson's
*Classical Electromagnetism*, discusses the Maxwell stress tensor twice: in a discussion about of conservation laws in macroscopic media (pp 239-40) and then in a discussion about forces in special relativity (pp 602-607). Page numbers from my copy of the 2nd edition. - Landau & Lifshitz'
*Electrodynamics of Continuous Media*goes into more depth on how the stress tensor is derived. Beyond being one of my favorite books in grad school, the entire series is classic. - M. Schwartz'
*Principles of Electrodynamics*(available from Dover, probably because of Schwartz' Nobel Prize, not because its great exposition (which it has)) uses the electromagnetic stress tensor repeatedly in different contexts and problems that gives you a good idea of what it actually means. - U. Leonhardt and T. Philbin's
*Geometry and Light: The Science of Invisbility*is an excellent technical book of the use of the mathematics of general relativity in optics. This includes the optical analogue of black holes and the photonic Aharonov-Bohm effect.

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