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. Our Patreon backers can see the

Table of Stress Tensors I made for the podcast.

3. Other papers mentioned:

I found these papers useful for this program:

4. 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.

5. Related Shows:

8. Randy mentions Harry Reid's Advanced Aerospace Threat Identification Program (AATIP) program, a government UFO program funded from 2007 to 2014. It was run by Luis Elizondo, who Randy mentions in the podcast. Randy says he was directed to this topic by a discussion that Joe Rogan had with Thomas DeLonge who funds AATIP's private successor, To the Stars Academy. Although they focused on things that were out in left field (Harry Reid says he met his wife on a UFO, but no one believed him), you can see from

this list that they funded some good research as well (such as Ulf Leonhardt's (see above) and Maxim Tsoi's in spintronics). I didn't count, but it looked to be about a sixth solid research, a sixth reasonable research, as sixth fringy stuff, and a half

to EarthTech International.

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