From time to time peculiar claims about machines that defy basic physics pop into view. One that caught my attention recently is a radiation-based rocket engine. Called the Emdrive, this privately-developed device has been adopted by the Chinese government as an experimental alternative to the low-thrust ion drives now in use on many satellites and interplanetary probes. The Emdrive uses microwaves as the source of its thrust. The advantage of using microwaves over ions is that the spacecraft does not need to carry a propellant; the device can run indefinitely on the power collected from the Sun.
The idea that radiation can accelerate a rocket is certainly not new; light carries both energy and momentum. Because momentum is conserved when a rocket fires its engine, the amount of momentum a rocket acquires when it emits light is the precise opposite of the total momentum carried by the light. This is the basis of a simple test problem in special relativity that I once had to solve. The problem asked how long an astronaut would need to shine a flashlight of a certain wattage in one direction to accelerate to half the speed of light. For a 100 kilogram astronaut with a 10 watt flashlight, it would take about 16 billion years, which is the maximum age of the universe. This answer shows why light is not generally a good propellant for a rocket engine. Light as a propellant requires too much energy to generate a useable amount of acceleration.
This brings us to the Emdrive. When I first heard about it, I assumed that it created a force by driving an intense beam of microwaves out of the engine. In fact, while the design makes use of radiation pressure, it does so in a very peculiar way. The Emdrive emits microwaves into a closed box, where they are trapped. Roger Shawyer, the designer of the engine, claims that the shape of the box causes the microwaves to exert more pressure at one end of the box than at the other, so that a net force is exerted in one direction by the microwaves. The designer claims that because the microwaves oscillate back and forth many times before being absorbed by the walls of the box, the device produces a strong force that can accelerate a spacecraft. The problem with this analysis is that it violates the conservation of momentum, because this device gives a rocket momentum without emitting microwaves of opposite momentum. The very equations that are used by the designer to calculate a force exerted by the Emdrive—Maxwell's equations, which describe the interaction of electromagnetic fields with matter—explicitly conserve both energy and momentum; most physicists would use conservation of momentum as a test for whether they had correctly solved the problem of the interaction of microwaves within a box. When a paper describing the Emdrive was published by New Scientist a couple of years ago, the unphysical nature of the device provoked a storm of complaints from the physics community.
What is interesting about the articles describing the Emdrive is that the writers explain the workings of the engine with jargon-laden descriptions of esoteric and new physics. In the article on the Emdrive in New Scientist, for instance, the writer, apparently paraphrasing an explanation from Shawyer, tries to explain the force without thrust in the following way:
How can photons confined inside a cavity make the cavity move? This is where relativity and the strange nature of light come in. Since the microwave photons in the waveguide are travelling close to the speed of light, any attempt to resolve the forces they generate must take account of Einstein's special theory of relativity. This says that the microwaves move in their own frame of reference. In other words they move independently of the cavity—as if they are outside it. As a result, the microwaves themselves exert a push on the cavity.
This little explanation makes no sense. One does not need to explicitly include special relativity to calculate the force, because special relativity is implicitly contained in Maxwell's equations; by using Maxwell's equation to solve a problem, one automatically taking special relativity into account. The bit about “microwaves move in their own frame of reference” is meaningless; under special relativity, the reference frame is simple the coordinate system used to solve the problem, and the claim that all reference frames are the same is simply the statement that I can choose any non-accelerating coordinate system that is convenient without worrying that the answer differs from that found using any other coordinate system. For instance, if I solve Maxwell's equations in the laboratory where the device is fixed, and I solve the equations in a reference frame where the device is moving at half the speed of light, I will get the same answer. One answer I will get in either reference frame is that momentum is conserved. The resort to special relativity and a claim of “the strange nature of light” serve more to awe than to enlighten the reader.
But the explanation provided in the New Scientist article is mundane compared to the explanation given in an article from Eureka magazine cited on the Emdrive web site. In the article, the author writes this:
The crucial part, as he explained, is that it is a relativistic effect that arises because the waves being reflected at the two ends of the conical cavity into which the microwaves are injected have different effective velocities, and thus different frames of reference, and that a closed microwave wave guide is an ‘open system’ in terms of relativity. According to Einstein, all moving frames of reference are equivalent. Why this should be so, whether one is standing still or going at half the speed of light, nobody knows, and in effect Shawyer's engine could be chucking Dark Energy out of the back of it and functioning as a conventional rocket. On the other hand, here may be no such thing as Dark Energy, and Shawyer may have stumbled on what is really driving the galaxies apart.
I can guarantee that the Emdrive is not chucking Dark Energy or anything else out its back, because these things have nothing to do with special relativity, which is simply a property of space and time that is contained within Maxwell's equations for electricity and magnetism.
A prototype of the device has been built, and Shawyer claims that the test results confirm his calculations. Whatever force he are measuring, it cannot be arising through the mechanism he invokes; on a spacecraft in space, the device should exert no force. I'm just glad the Chinese government is paying for the Emdrive rather than the U.S. government. My tax dollars support too many shady projects and bailouts of bad public policy as it is.