# Does a circularly polarized electromagnetic wave transfer angular momentum from the transmitter to a receiving antennae?

This question is about the rotation of macroscopic objects and looks at the magnetic vector of an electromagnetic wave.

As basis for comparison, we consider an induction motor. The stator induces a magnetic field in the rotor. The field in the rotor follows the magnetization of successive stator poles and causes its rotation.

In this question, we replace the stator field by a circularly polarized electromagnetic wave. We replace the rotor with a small iron sphere (ball-bearing or similar) in weightless in empty space. We consider the magnetic vector that appears to be rotating.

This should induce a current and then a magnetic field in the sphere. This field would tend to follow the rotation of the magnetic vector of the wave and put the ball in rotation. Any momentum not captured would continue to be later intercepted by other conducting objects or even never.

For example, a LW transmission at 16 kHz would trigger a rotational speed of 960 000 rpm, speed attained by some electric motors.

According the law of conservation of angular momentum, the transmitter should undergo an equal and opposite momentum change.

According to the principle of reversibility: If you turn off the transmitter, the rotating magnetized sphere should behave as a transmitter.

If all this were to be true, there should be existing applications such as stabilization of spacecraft or transponders without active components.

This does not seem to be the case.

Why not?

Edit, following comment: There may be a SETI application in which an object on the scale of one gramme would need to become detectable over long periods. nature.com/SETI-detection-by-data-carrying-objects Thus it could spin up reacting to natural radio background over a timescale of 10^8 years. If superconducting, magnetized and rotating near 1 000 000 RPM, would it generate a significant radio signal detectable from short distances ?

• Yes, there is an angular momentum transfer, but it is tiny and very hard to measure (which makes it technologically irrelevant). The speed of rotation would not be determined by the frequency of the wave but by the friction and moments of inertia of the system that experiences the torque, so it's unlikely that anything but atomic and molecular systems can be "spun up" to the classical rotation frequencies. Jun 13 '16 at 18:16
• thanks. One application would be SETI inscribed matter <nature.com/nature/journal/v431/n7004/full/nature02884.html>. example: one-gramme mass free-floating in space to be spun-up over 10^8 years. I Will edit my question. Jun 13 '16 at 18:49
• @CuriousOne You can spin up a bunch of particles that are at least microscopic (i.e. ~1 micron) in size. I'm not sure it goes as far as "anything you can put in optical tweezers", but it's definitely way past atomic and molecular systems. Jun 13 '16 at 19:20
• @EmilioPisanty: Sorry for the misunderstanding, I was talking about reaching the frequency of the light. Optical tweezers aren't spinning things up to $10^{15} Hz$. I think molecular rotation is as far as one can get, and that's in the far IR, if I remember correctly. I agree, one can, of course, move things that are much larger, just not as fast as the OP has in mind. It's an interesting question if e.g. an electric motor can be thought of as transferring macroscopic angular momentum trough the near field of the electromagnets? Jun 13 '16 at 19:49
• @CuriousOne Oh, in that case, then yes. Jun 14 '16 at 0:03

All of your claims are essentially true. The angular momentum of light, in both its orbital and spin varieties, is indeed angular momentum that can be transferred to matter to make it spin and give it the garden variety of mechanical angular momentum. This is well explained in the relevant Wikipedia section, with good references for experiments that show it. If you want something more tangible, this video is a good starting point, showing particles spinning under the action of circularly polarized light.

Where you fail, however, is in your estimation:

If all this were to be true, there should be existing applications such as stabilization of spacecraft or transponders without active components.

The effect is definitely present, but that doesn't mean that it's present in a sufficiently strong capacity to be technologically useful. In particular, each photon of light carries a spin angular momentum of $\hbar$, and an energy of $\hbar \omega$, and from here it follows that the ratio of torque to power carried by a monochromatic beam is fixed at $$\frac{\mathrm{torque}}{\mathrm{power}} = \frac{\mathrm{SAM}/\Delta t}{\mathrm{energy}/\Delta t} =\frac{\hbar}{\hbar\omega}=\frac{1}{\omega}.$$ If you have a wave at $\nu=16\:\mathrm{kHz}$, that means that for every watt of power you get a torque of $$\tau=\frac{P}{\omega}=\frac{1\:\mathrm{W}}{2\pi\times 16\:\mathrm{kHz}} \approx 9.95\times 10^{-6}\:\mathrm{N\:m}.$$ Or put another way, if you want to stabilize a spacecraft, using torques of several hundred newton meters, you'd have to arrange for the spacecraft to interact with (i.e. absorb, or ideally completely reflect, though of course even a 99% reflectance will mean a lot of absorbed power) something like a megawatt of power in the beam. Whilst possible in principle, this is not a reasonable technological solution compared to all the other ways to impart torque to objects.

• I didn"t make it clear that the transmitter would be onboard the spacecraft (using counter-rotation)and the power needed would be proportional to speed of acccumulation of rotation to be countered. I will take my time to use your formuea as I'm not in physics. I will also work through the first part of your answer for the SETI application that I edited into my question to answer the comment from CuriousOne. Thanks for now. Jun 13 '16 at 21:23
• Either way, the torque to power ratio is simply too small to be useful. You've got a MW power source in board? There's a gazillion better ways to use it. "Proportional" only works when the constant of proportionality doesn't have six more zeros than you need. Jun 14 '16 at 0:01

You want to read the classic paper by Richard Beth, Mechanical detection and measurement of the angular momentum of Light, Physical Review 50 115 (1936). Beth used bright circularly polarized light to drive a torsion pendulum in a vacuum chamber, and was able to observe torques due to circular polarization of order $10^{-16}\rm\,N\,m$. This was with a clever arrangement of quarter- and half-wave plates which transferred angular momentum $4\hbar$ from each photon to the torsion pendulum.

So, yes! Absolutely! Circularly polarized electromagnetic radiation does transmit angular momentum from the source to the receiver. I would never expect to detect this using a radio antenna, however.