Scientific Method / Science & Exploration

Generating thrust without fuel relies on missing details

A system called the EmDrive requires an exquisite balancing of forces.

Yang Juan

A new system called the EmDrive, a way of using electricity to generate thrust without the need for fuel, is one of those ideas that will generate a lot of heat and noise, but probably not a lot of thrust for many years to come. I had never heard of the idea until today, and the latest paper, a translation, doesn't throw a lot of light on the physics itself. So brace yourself and let's see what we can figure out from a grainy line drawing in the translation.

The idea is based on a standing wave cavity: two mirrors—in this case, microwave mirrors—facing each other so that microwaves travel back and forth between them. In one picture, two waves are travelling in opposite directions between two mirrors. If you look at both waves simultaneously, however, you get another picture: a standing wave, like the vibration on a violin string. The key thing about this system is that these two pictures must be self-consistent. We will use that to examine the EmDrive's potential for thrust.

In our simple picture of two mirrors facing each other, the mirrors are subject to equal and opposite forces. Essentially, the photons reflect from each mirror, exerting a force in doing so. Because this is symmetric, the cavity cannot have a net force. Even if we were to make the light very focused at one end and very diffuse at the other, we are simply distributing the same number of photons differently at each end, so the total force remains the same.

The key claim to the EmDrive is that it breaks this symmetry, allowing a net force to exist.

We can consider the EmDrive as having three mirrors. One is large and facing the other two. The other two are arranged at 45 degrees, so light from the big mirror hits these mirrors at 45 degrees. In this arrangement, the force imparted by the photons is divided up. Only half the force generated at the small mirrors is directed opposite to the large mirror, so it doesn't balance the force exerted by the photons hitting the large mirror. As a result, it seems that we should have thrust. In the standing wave picture, then, things look good.

Except that the photons reflected by the small mirrors don't return directly to the main mirror—they need to bounce off the other angled mirror before they can do so. So each photon applies half the force twice, which should balance that from the main mirror. This simple picture is why, on first glance, it appears that this will never generate a net force.

Put in a more general context, my feeling is that any stable optical resonator cannot exert a net force because it requires certain symmetries. But an unstable resonator certainly can. This is important, because the second part of the claim—though it's not made in the article—is that one can start to generate thrust by making the resonator better and better. Essentially, the longer the photon circulates in the cavity, the more net force it imparts.

You can think of it like this: if a resonator allows a photon to circulate a thousand times before it escapes and you attach a one Watt microwave source to the resonator, for each Watt that leaves the resonator, one thousand Watts are stored in it. It would seem that if we increase the quality of the resonator enough, every photon will contribute multiple times to generating the force, and we would be on to a winner.

But there's a problem here, in that some combination of two things must be happening to destabilize the resonator: each time a photon imparts a force to a mirror, the frequency of the light has to drop (the reflected light is ever so slightly red-shifted compared to the incoming light); alternately, the photon is absorbed by a mirror. If the quality of the resonator is high, then as soon as the photon shifts in frequency even a bit, it will get thrown out of the resonator. And if the photons are absorbed by the mirror, the quality is necessarily low. In either case, if the resonator is unstable, the photons don't stay in there for very long.

In the end, there is a limit to how much force this can impart. Each photon carries only so much energy, which can only exert so much force. Since a resonator is an energy storage device, when you use that energy to exert a force, you reduce the storage capability of the resonator. You cannot both exert a lot of force and store a lot of energy. Yet this is exactly what appears to be required.

What about the measurements in the paper? The measurements appear to back the claim up. Unfortunately, the work involves throwing around up to 2.5kW of power to measure less than a Newton of net force. In those conditions, little things like anisotropic thermal expansion become absolutely critical to the measurement. Quite simply, there isn't enough detail in the experimental setup and not enough tests against possible problems to trust the data yet.

There is also a further missing point: the quality of the resonator is measurable, and the mode—think of modes as the path the radiation takes inside the resonator—can be calculated. The measurements in the paper could and should have been compared to a calculation.

My opinion is that this is unlikely to ever work as intended, especially not in a challenging environment like space. I believe that if the microwave resonator is unstable, a net force can be produced, but in a stable cavity no net force can exist. Certainly, the idea that a high quality resonator can impart more force than a low quality resonator cannot be true—at least not if we also want to conserve energy.

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