She cannae do it, Captain! — Why the Cannae Drive, EmDrive, and other proposed microwave-powered spacecraft engines are a lot of nonsense — Part One

Posted: April 12, 2015 in Uncategorized

We live in the golden age of pseudoscience.  Thanks to the internet, the public now has enough science knowledge that the average person feels reasonably comfortable discussing science concepts and science news stories.  However, that knowledge hasn’t really gotten to the point where the average person can critically evaluate scientific statements.  The result is that hucksters can come forward with unsubstantiated claims and half-baked ideas, and have those claims and ideas virulently propagated throughout the popular consciousness.  I believe that this phenomenon is retarding the advancement of human culture.  And so, in the spirit of public service, I would like to do my best to debunk a recent pseudoscientific sham that’s cropped up in the field of spacecraft propulsion.

It started in 2006, when New Scientist ran a cover story on Roger Shawyer’s “EmDrive”.  The EmDrive is essentially nothing more than a microwave resonance cavity — an enclosed metal container that has microwaves bouncing around inside.  Shawyer claimed that the geometry of his cavity was such that the microwaves would produce a net force on the enclosure.  If the device worked as he claimed, Shawyer would be revolutionizing not just space travel but virtually all of human science and engineering.  The ability to convert electricity directly into momentum, without any reaction mass, would mean that spaceships no longer need to carry propulsion fuel of any kind.  They would only need an electrical generator, like the nuclear thermoelectric and solar ones that NASA’s space probes currently use to operate their science instruments and communicate with Earth.

The EmDrive.

The EmDrive.

The problem is that such a device, as far as anyone can tell, would violate one of the most fundamental laws of physics — the law of conservation of momentum.  Conservation of momentum is a modern reformulation of Isaac Newton’s first law of motion.  In his treatise Principia Mathematica, published in 1687, Newton wrote:

When viewed in an inertial reference frame, an object either remains at rest or continues to move at a constant velocity, unless acted upon by an external force.

This means an an object — say, a spacecraft — cannot spontaneously accelerate until some external object or force acts on it.  For a rocket, this force takes the form of high-temperature gasses pressing against the inside of the combustion chamber and rocket nozzle.  What happens to those gasses?  Newton summed that up with his third law of motion:

When one body exerts a force on a second body, the second body simultaneously exerts a force equal in magnitude and opposite in direction on the first body.

Which means whatever direction the rocket accelerates in, the gasses are accelerated in the opposite direction.  If we consider the situation from the perspective of a “stationary” observer, it would look like this:

Apollo at rest

Apollo firing

In order for the spacecraft to move to the left, it has to bounce off of something else, and send that something else moving to the right.  In the first picture, the total momentum is zero, because nothing is moving.  In the second picture, the total momentum is still zero, because the momentum of the spacecraft is equal and opposite to the momentum of the exhaust.

Conservation of momentum doesn’t just apply to macroscale objects bouncing off each other.  It applies to fundamental particles as well.  Quantum electrodynamics is the branch of quantum theory that deals with electromagnetic interactions.  This subject was pioneered by Richard Feynman, who invented a tool for understanding the interactions between photons, electrons, and other fundamental particles — the Feynman Diagram:

From Feynman's QED: The Strange Theory of Light and Matter

From Feynman’s QED: The Strange Theory of Light and Matter

These diagrams are still used by physicists to figure out the probabilities of different types of interactions occurring.  Here’s an example of a Feynman diagram showing the Higgs Boson being created and destroyed:

Two gluons produce six quarks and two leptons, with intermediate help from the elusive Higgs boson.

Two gluons produce six quarks and two leptons, with intermediate help from the elusive Higgs boson.

The horizontal axis is not time.  These interactions occur so quickly that we cannot assign a timescale to them.  The vertical axis is not space.  The interactions occur within such a small space that we have no way of determining the relative locations of the particles at the time of the interaction.  The arrows do not represent direction of travel of the particles.  Quantum theory is agnostic about the direction of causality, and the interactions are considered equally valid going from left to right or right to left.  Aside from the rules about what kind of particles can interact with which other ones (for instance, photons can only interact with particles that have charge), just about the only thing we DO know about these interactions is that momentum and energy are conserved.  Without those assumptions, we simply wouldn’t have a physics anymore.  We’d have to start from the beginning.

Of course, we have no reason to.  The law of conservation is called a “law” because the amount of evidence supporting it is overwhelming.  In the 1920s, physicists almost threw out conservation of energy and momentum, because there seemed to be energy and momentum disappearing during beta decay — when a neutron decays into a proton and electron.  Then Wolfgang Pauli proposed the existence of a new, hard-to-detect particle that (he theorized) was also being produced during beta decay — the “neutrino”.  It was a move of desperation and seemed like a stretch at the time, but subsequent experiments showed that the neutrino does in fact exist.  So the conservation laws are not only supported by the evidence, but they have actually driven discovery over the last century.

Now, back to Roger Shawyer and the EmDrive.  Shawyer denies that the EmDrive violates any known physical laws.  The following appears on his website:

Q. Why does the EmDrive not contravene the conservation of momentum when it operates in free space?
A. The EmDrive cannot violate the conservation of momentum. The electromagnetic wave momentum is built up in the resonating cavity, and is transferred to the end walls upon reflection. The momentum gained by the EmDrive plus the momentum lost by the electromagnetic wave equals zero. The direction and acceleration that is measured, when the EmDrive is tested on a dynamic test rig, comply with Newtons laws and confirm that the law of conservation of momentum is satisfied.

I have bolded the phrase to focus on.  He says that the momentum is built up inside the cavity, and only then is it transferred to the enclosure.  This is identical to saying that the device, with no external influence, goes from a state of net zero momentum, to one of net non-zero momentum.  Given that Shawyer is an aerospace engineer, and his paper on the EmDrive seems to demonstrate a facility with mathematics, my assessment is that he is intentionally producing pseudoscientific nonsense in an attempt to fool everyone who isn’t fluent in physics.  Here is the diagram of the device that appears in his paper:

From "A Theory of Microwave Propulsion for Spacecraft" by Roger Shawyer

From “A Theory of Microwave Propulsion for Spacecraft” by Roger Shawyer

The microwaves are created by the magnetron and enter the resonance chamber via the waveguide.  Since the microwaves carry momentum, they exert a backward pressure on the source:

Microwave momentumAssuming the entire apparatus is hanging in empty space, this means that it will accelerate in the direction of the blue arrow… but only during the time the microwaves are traveling through empty space.  Since microwaves travel at the speed of light, they will reach every portion of the cavity in a few nanoseconds.  As the microwaves reflect off each surface, they will transfer momentum to those surfaces.  And because the microwaves have nowhere to escape to, all of their momentum will transfer to the enclosure, cancelling out any net momentum.  If, instead of a magnetron, this were a machine gun, then you would be able to see the device vibrate as the bullets struck various surfaces.  If it were a cannon firing a single cannon ball, and the enclosure were the size of a room, you might see the entire enclosure move and change direction a few times.  However, it would eventually stop moving, and the center of mass of the entire device would be in the exact same spot where it started.

This brings us the central claim of Sawyer’s paper:

The group velocity of the electromagnetic wave at the end plate of the larger section is higher than the group velocity at the end plate of the smaller section. Thus the radiation pressure at the larger end plate is higher that that at the smaller end plate.

By group velocity, he means the speed at which the waveform travels along the length of the device.  Inside a waveguide, the microwaves bounce back and forth, and therefore the waveform will move more quickly in the axial direction the more narrow the chamber is.  This is called the group velocity, and (for reasons I won’t get into) it is the rate that energy is transferred down the length of the waveguide.  But the device that we’re talking about isn’t a waveguide, it’s a resonant cavity.  Inside a cavity at resonance frequency, the reflected waves combine together to form standing waves.  Depending on the geometry of the cavity, there will be some number of stationary nodes where the electromagnetic field is always zero.  Between the nodes will be points where the field oscillates between maximum and minimum values of the electric and magnetic fields.  It’ll look something like this:

From University of Liverpool course notes for Physics 370, Advanced Electromagnetism

From University of Liverpool course notes for Physics 370, Advanced Electromagnetism

If the enclosure is made from a perfectly conductive material, then the radiation is perfectly reflected from the walls.  For the case of a traveling wave, this would mean that twice the momentum of the wave is transferred to the material.  For a standing wave, however, there is no momentum transfer.  This is because a standing wave is a superposition of a wave moving toward the wall, and one moving away from the wall, simultaneously.  In a waveguide, there is no radiation pressure on the transverse walls.  In a resonant cavity, all the walls are transverse.  The electric field is perpendicular to the boundary at every point, and the magnetic field is parallel to it at every point.  The direction of energy (and momentum) transport is given by the Poynting vector, which is the cross product of the electric and magnetic fields.  Therefore, energy can only flow along the surface, not into it.    Moreover, in a traveling wave, the electric and magnetic fields are in phase.  In a standing wave, they are 90 degrees out of phase, so the Poynting vector switches direction twice every cycle.  This means that energy is sloshing back and forth.  In the resonant mode depicted above, the peak energy density moves from the center toward the outer surface and back again.

It may seem odd that the energy within the cavity can move around without exerting pressure on the walls on the enclosure.  In truth, there is energy transfer occurring, but it takes a different form.  The electromagnetic field is causing the electrons in the enclosure to slosh around.  If it truly were a perfect conductor (“superconductor”), and the interior of the cavity a vacuum, the field and electrons could oscillate forever, without any energy input.  If the cavity is constructed of copper (like the EmDrive), then resistive heating will occur in the metal.  The energy radiated as heat would have to be continually replaced by the magnetron.

Getting back to the subject at hand, I have shown that Sawyer’s central claim is nonsense.  However, there’s more.  After making his declaration about the group velocity, he seems to segue into an entirely different justification for the same supposed effect:

"Assume that the waveguide is now tape red as shown.  In this case the group  velocity is higher at the wide end than at  the narrow end. Thus re solution of the forces  shows F1 is greater than F2, whereas th e sidewall force Fs2 is higher than Fs1. "
“Assume that the waveguide is now tapered as shown. In this case the group velocity is higher at the wide end than at the narrow end. Thus resolution of the forces shows F1 is greater than F2, whereas the sidewall force Fs2 is higher than Fs1. “

He is now making an argument about force vectors, and putting his foot directly in his mouth as a result.  The gist of this seems to be that because the right endcap is a smaller target, it gets less pressure applied than the left endcap.  Well, *if* the radiation were actually applying pressure (uniformly, let’s say), then it would be applying horizontal pressure to the sloped portion as well.  Sawyer seems to have intentionally left that contribution out of the free body diagram in the lower right.  He specifically addresses this complaint on his website:

Q. Why does the net force not get balanced out by the axial component of the sidewall force?
A. The net force is not balanced out by the axial component of the sidewall force because there is a highly non linear relationship between waveguide diameter and group velocity. (e.g. at cut off diameter, the group velocity is zero, the guide wavelength is infinity, but the diameter is clearly not zero.) The design of the cavity is such that the ratio of end wall forces is maximised, whilst the axial component of the sidewall force is reduced to a negligible value.

This is simply gibberish.  It’s true that there is a nonlinear relationship between the diameter of a waveguide and the group velocity, but as discussed above, group velocity just isn’t relevant here.  Moving along in the paper, Sawyer states:

As with any microwave cavity, if the axial path length is a multiple of half the mean guide wavelength, at the frequency of operation, then the waveguide will form a resonant cavity.

“Axial path length” and “mean guide wavelength” are both characteristics of the geometry of the cavity, and do not depend on the “frequency of operation”.  A “waveguide” will not form a “resonant cavity”, unless you put end caps on it so that it’s not a “waveguide” anymore.  It’s like he doesn’t even understand the basics of his own device.

The electrical and magnetic fields at each end plate will add in phase, to give instantaneous powers equal to Q times the transmitted power.

Nope.  The fields are 90 degrees out of phase in a resonant cavity, and there is no calculation in physics that involves adding the electric and magnetic fields.

In the remainder of this paper, Sawyer reasons in circles, butchers special relativity, and comes to the conclusion that the thrust of his device is velocity-dependent.  Finally, he vaguely describes his test program, without any data, though he does say he achieved a “specific thrust” of 214 milinewtons per kilowatt.  Given that “specific thrust” is the ratio of thrust to the rate of air flow through an engine, it’s impossible to tell whether he just got his units confused, or he actually had air rushing through his resonant microwave cavity.  That would certainly explain any forces that showed up.

OK, that’s it for the EmDrive.  I hope we can now dump it into the wastebin of history.  In part two, I’ll take a look at the recent controversy over the Cannae drive.

I hope you enjoyed my analysis!  If you believe I have made any mistake, or you just want to contribute to the discussion, please comment below.

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Comments
  1. Mike says:

    Waving you bible and extorting the blasphemers, “the world is flat and that’s that!” sound familiar?

  2. Mich Sausa says:

    Here is a better idea of the EM drive resonant cavity. http://postimg.org/image/5v2cjhvy5/d5329df9/

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