Fly by light
This week's New Scientist has a cover story entitled Fly by Light by Justin Mullins. This article describes a device invented by Roger Shawyer that is so obviously a "perpetual motion machine" that I am amazed that New Scientist had the cheek/ignorance to publish the article. In fact, the article is perfect source material for this Fact and Fiction blog.
Here is a quote from the article to start us off:
Take a standard copper waveguide and close off both ends. Now create microwaves using a magnetron, a device found in every microwave oven. If you inject these microwaves into the cavity, the microwaves will bounce from one end of the cavity to the other. According to the principles outlined by Maxwell, this will produce a tiny force on the end walls.
All is OK so far. But then the article goes on to say:
You might think that the forces on the end walls will cancel each other out, but Shawyer worked out that with a suitably shaped resonant cavity, wider at one end than the other, the radiation pressure exerted by the microwaves at the wide end would be higher than at the narrow one.
Shawyer calculates the microwaves striking the end wall at the narrow end of his cavity will transfer less momentum to the cavity than those striking the wider end [this is supported by a diagram showing a tapered cavity with sloping sides and parallel end walls]. The result is a net force that pushes the cavity in one direction. And that's it, Shawyer says.
This is backed up by a lot of pseudo-scientific hocus-pocus, and it also mentions how "relativity and the strange nature of light come in". You couldn't invent this stuff! Sorry, unfortunately someone has, and I am reading it.
Shawyer's calculation evidently omits contributions to the overall force on the cavity from microwaves striking the sloping side walls of the cavity, where the local contribution to the force is perpendicular to the local patch of side wall. Note that this perpendicularity assumption is a good approximation for the high-Q cavities discussed in the article, where the walls of the cavity act as mirrors. Overall, the net force due to striking the side walls points towards the tapered end of the cavity. If Shawyer had taken this into account then he would have found that the net force due to striking the side walls is equal and opposite to the net force due to striking the end walls.
This result does not depend on the detailed shape of the closed cavity; the forces always cancel out when they are all taken into account. That means that there is no net force on the cavity, so it will not accelerate off in one direction. You certainly won't be powering spaceships using this type of drive, as is suggested in the article's title "Fly by Light".
This "Fly by Light" article belongs in a 1st April edition of New Scientist.
Update: Roger Shawyer has now written a letter to New Scientist (see here) to defend his position against all of the criticism he has received following the publishing of the article discussed above. Here is a copy of his letter with my comments inserted in square brackets:
The momentum exchange is between the electromagnetic wave and the engine, which is attached to the spacecraft. As the engine accelerates, momentum is lost by the electromagnetic wave and gained by the spacecraft, thus satisfying the conservation of momentum. In this process, energy is lost within the resonator, thus satisfying the conservation of energy. [This is a correct description of energy and momentum conservation by the individual interactions between photons in the EM wave and electrons in the engine, but you can't build up the claimed acceleration in this way because there are interactions all over the inside wall of the engine, and these balance out on average.]
The emdrive concept is clearly difficult to comprehend without a rigorous study of the theory paper, which is available via emdrive. corn or the New Scientist website (http://tinyurl.com/npxv8). This paper, which has been subjected to a long and detailed review process by industry and government experts, derives two equations: the static thrust equation and the dynamic thrust equation. [The analysis in the cited paper is unnecessarily complicated, so one can't see the wood for the trees, which is why mistakes were made. The simplest way to see that the claims are false is to consider the energy/momentum conserving individual photon-electron interactions, as described in my comment immediately above. QED.]
The law of the conservation of momentum is the basis of the static thrust equation, the law of the conservation of energy is the basis of the dynamic thrust equation. Provided these two fundamental laws of physics are satisfied, there is no reason why the forces inside the resonator should sum to zero. [Force is built out of the impluses due to the momentum exchanges that occur during all of the individual photon-electron interactions, which are momentum conserving so that equal and opposite momenta are exchanged during each interaction. The system is closed, so the total force must be zero.]
The equations used to calculate the guide wavelengths in the static thrust equation are very nonlinear. This is exploited in the design of the resonator to maximise the ratio of end plate forces, while minimising the axial component of the side wall force. This results in a net force that produces motion in accordance with Newton's laws. [Non-linearity is irrelevant. Think in terms of the individual photon-electron interactions to avoid unnecessary complications.]
We are now in the process of negotiating a trial flight programme. [Good luck! You'll need it!]