I stumbled over an article yesterday that I found again today in my newsfeed that finally causes me to be willing to spend time writing about something. The article is here.

This article is about a sketchy physics topic that the popular media loves itself something fierce. Namely, the EmDrive.

This device is supposed to be a form of engine that can drive spacecraft faster and more efficiently than current technology otherwise allows. The creator of the EmDrive loves to claim that the device can solve all the world’s ills, from the energy crisis and global warming to the drip under your sink. Never mind that the excessive claims should set everybody’s danger sense a-tingling, it is a device that has persisted past it’s creator’s obvious lack of background in the basic science of physics.

Here’s a description of how the EmDrive is supposed to work as quoted from the article:

How the EmDrive works

The EmDrive is the invention of British scientist Roger Shawyer, who proposed in 1999 that based on the theory of special relativity, electricity converted into microwaves and fired within a closed cone-shaped cavity causes the microwave particles to exert more force on the flat surface at the large end of the cone (i.e. there is less combined particle momentum at the narrow end due to a reduction in group particle velocity), thereby generating thrust.

The general idea here is that you’re injecting microwaves into a hollow cone and allowing them to bounce around. Because the cavity is asymmetrical, the argument goes, they end up breaking symmetry on the pressure they’re exerting and push the cone only in one direction.

In a way, the set-up is almost an exact duplicate of the thought experiment that Einstein used to come up with the equation of E=mc^2, but beyond that, this is actually a flagrant violation of conservation of momentum. You can think about it this way: a guy standing inside a train car pushes against the wall of the train car… no matter what the shape of the inside of the car, the guy walking around never moves the center of mass of himself with the car –even if the car will actually move slightly as he walks back and forth, if the axles of the car and the rails are frictionless. The only way the car can continue to move is if the guy goes running along the car and jumps out the end, thus enabling his center of mass to be decoupled from the car… if he were to keep running, the center of mass of his system and the car would remain at rest, while he and the car must both be moving in order to conserve the net zero momentum they started with as a system. The analogy breaks down because the guy standing on the ground would be able to exert force to stop running. As Christopher Nolan wrote in Interstellar: the only way to go somewhere in space is to leave something behind. As a physicist’s aside, one has to put in a train car analogy at least once in this discussion because Einstein loved trains during his explanations of special relativity (I’m convinced that this is part of why Sheldon Cooper loves trains).

Breaking conservation of momentum is a pathological, ‘do not pass go’ fault that should immediately consign this whole EmDrive concept to the dumpster the same way Avagadro’s number kills Homeopathy. Despite that, the creator of the EmDrive has a ready response:

However, Shawyer claims that following fundamental physics involving the theory of special relativity, the EmDrive does in fact preserve the law of conservation of momentum and energy.

The author’s recourse is “Don’t worry about it, it’s hidden in special relativity!” Having dealt with special relativity and being aware that Einstein used this very thought experiment to prove E=mc^2, I can assure you that violating conservation of momentum is still completely fatal to an argument. Special Relativity isn’t exactly an impassable mountain that breaks conservation rules the way General Relativity does.

Despite all of that, various labs around the world have built EmDrives to test the idea. In the end, this is sort of like continuing to test whether or not autism is caused by vaccination, but okay, fine.

To everyone’s surprise, some of these labs, including Eagle Labs at NASA, have reported tiny tiny thrust. Something smaller than micronewtons IIRC, but still thrust.

And, of course, the cranks go wild! Here it is, the reactionless Cannae drive that will take us to Alpha Centuari by 2035 and Vulcan by 2150.

Now, the fact is that while these labs have reported thrust, we don’t know exactly why it did. Sure, it did, but we need a theory that sits within physics that explains why it did. Rest assured, the reasons given by the drive’s creator are completely bogus, so new explanations are needed. Is it Casimir vacuum pressure? Is it warped spacetime? Is it Calvin’s Universal Transmogrifier? We need to figure it out.

The Finnish physicist in the IBTimes is remarkably conciliatory even if his tacitly favorably worded response is actually just another huge nail into the EmDrive’s already well-built coffin. Here is this physicist’s explanation:

“The EmDrive is an engine like any other engine. It takes in fuel and produces exhaust. The fuel side is easy for everyone to grasp – microwaves are being fed in. The trouble is, we don’t see anything coming out, which is why people think it doesn’t work,” Annila told IBTimes UK.

“So how could something come out that you can’t detect? Well, the photons bounce back and forth inside the metal cavity, and some of them end up going together in the same direction with the same speed, but they are 180 degrees out of phase. Invariably, when travelling together in this out-of-phase configuration, they cancel each other’s electromagnetic field out completely.

“That’s the same as water waves travelling together so that the crest of one wave is exactly at the trough of the other and cancelling each other out. The water does not go away, it’s still there, in the same way the pairs of photons are still there and carrying momentum even though you can’t see them as light.

“If you don’t have electromagnetic properties on the waves as they have cancelled each other out, then they don’t reflect from the cavity walls anymore. Instead they leak out of the cavity. So we have an exhaust – the photons are leaking out pair-wise.”

Whatever else I might think about everything here, this is actually not a bad explanation. Photons have the quality where they can be superpositioned: if you pick two photons headed in the same direction, of the same polarization, with their E-fields 180 degrees out of phase, the Poynting’s vector still exists, allowing them to still carry momentum, but their field oscillations will cancel out. If they are introduced pair-wise in this manner, there’s not a reason to think that they can interact with matter any longer and they could simply slip straight through the confinement of the drive and off into empty space. So, the thrust from the drive would then be generated by the physical asymmetry of the cone allowing photons to pair up and escape easily in one direction, but not in another.

As a slight aside, I think I disagree with the Finnish physicist’s usage of water waves in the example above. The reason is that macroscopic waves in water are not discrete the way photons are. By effecting the continuum of material in water, the displacement of the wave crest from its resting state is what contains the energy of the wave: for small displacements, the momentum is perpendicular to the direction of travel. By adding a second oscillation 180 degrees out of phase, you completely cancel out the energy of the wave… and no wave remains after the fact. I’ve been thinking and I continue to think about whether or not the same is true with photons. I don’t think that it is mainly because photons are quantum mechanical particles and they have a quality of being discrete objects in the sense of their particle-wave duality. Photons contain linear momentum parallel to their direction of travel, while a water wave does not (the momentum is perpendicular to its direction of travel), and two photons caught traveling in the same direction must conserve momentum, regardless of their phase.

Now, I am granting here that there’s a physical explanation for why thrust is being generated, but we’ve slipped into explicable physics. If you stop and think about what we’re talking about, all we’re talking about is a very specialized form of microwave antenna. If you want thrust from momentum carried away by emitted microwaves, this process of pairing up photons so that they become invisible to the walls of the device (and sensors behind the device) is sort of beside the point. Granted, it would not torch anything behind it, this device is not the most efficient way to produce photons in the form of thrust. A flashlight or a laser would be much more efficient at converting power into thrust by doing essentially the same thing.

You could presumbly do an experiment like this one with a lasing cavity using optical light. I would partially-silver the surface of one mirror with a coating that is about a quarter wavelength thick before you hit the actual mirror. It’d be technically challenging since you’re talking about 1/4 micron thicknesses that are the tolerance of the lasing mode, but that’s something that can be attempted. Provided you stay at a condition of optical gain in the cavity modes (not all the photons are canceling) you should be able to test whether the recoil of the laser body due to the emitted radiation is the same as the recoil at the laser light spot. You could probably just set it up as an interferometer with adjustable arms and forget the coating. Again, this would depend on polarizing the emitted light.

Just thinking about it, I can imagine several more ways to test this in an optical setting. Some of them could be quite cheap to do.

(Edit 2-27-20: Looking back at this, I think that my proposed experiments are probably sort of unnecessary. Light pressure and light momentum are very well understood. There aren’t really any experiments needed. Laser drives have been an idea for a very long time and the notion of what pressure would be generated by what radiation source is really pretty trivial.)

Point is that there’s nothing magic about this.

Again, the problem with the EmDrive is that it’s exploiting physics to not do the most efficient thing it could do at its supposed task. If you start tabulating the amounts of power needed to generate thrust that is appreciable by these methods, you’re going to start tripping over conservation of energy somewhere. This not being magical, the amounts of energy needed to do anything are also not magical and will turn into eyepopping numbers when you start demanding that the thrusts the engine can produce are big enough to move masses humans might want to move with it.

I’ve been quite generous here. This is supposing that the explanation the Finnish physicist has supplied is useful over the other potential sources of noise in the experiment –the micronewtons or nanonewtons Eagle labs reported is so tiny that somebody’s breath could have been hitting the side of the experiment.

Scaling this thing up in force is crazily hopeful and would require you to jettison basically the whole design and go with something that does better what this device is actually doing. At some point, it will be time to forget about this EmDrive and relegate it to the wide-eyed, hopeful crankery that it is.

Published by foolish physicist

Low level academic enthralled with learning how things work.

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