The Cannae Drive Impossibility Proofs

I teach a modern physics class to high school students, which includes a unit on special relativity.  I gave them this as a bonus exam problem, and I’m pleased to say they all got it right.  It’s not hard to prove that, whether the proposed virtual particle radiation is massless or massive, it is not feasible.  For massless particles (photons), the drive would have to use 600 times more power than is reported.  For massive particles, (like electrons and positrons), the particles would have to be moving at 600 times the speed of light to produce the reported force at the reported power.

See this PDF for the proof.


“Family Demons” free until Wednesday!

Get it here.

New Novella, “Family Demons,” Now Available on Amazon!

Spook is a sorcerer for hire in downtown Atlanta. He’s also the youngest son in a megachurch dynasty, estranged for years until his eldest brother tracks him down. Their dying father needs him, and not for deathbed reconciliation. In this novella, Spook’s return home will put his skills to the test as he unlocks his family’s secrets and learns that one of their demons is real.

Find it here.

New Story: Shutterblind

Sometimes you can’t see the forest for the trees, and sometimes you can’t see your life for the stories that you’re weaving through it.

Shutterblind“, in SQ Mag.

New Story: “Quorum”

I have a new story up in Perihelion!  Science fiction/horror.

Happy October!

Keeping up the momentum

I almost certainly won’t keep up this momentum.  The last post garnered 100 times the total number of views I had previously.  I doubt this one will keep up, but I shall press onward.

Now: About rockets.

A conventional rocket works by throwing stuff backwards. If stuff is thrown backwards, other stuff must be thrown forward, just like a rifle kicks backward when the bullet flies forward.  We call this the conservation of momentum.

For a rocket, the fuel that is burned doubles as “reaction mass”, mass that gets thrown backward to fling the rocket forward.  The combustion supplies the energy (something all propulsion mechanisms must have), and the exhaust provides the push.

A drive that wouldn’t have to carry its own reaction mass would be very handy.  First, you don’t have to carry dead weight into space, which is incredibly expensive.  Second, without a limit to the reaction mass you can access, there is not nearly as much of a limit on how long you can provide a thrust. (Specifically, the limit is only the available energy).

How do we know the Law of Conservation of Momentum is true?  Could the Cannae drive disprove it?   This is the law that some say the Cannae drive violates.  You can’t have an object sitting in space (or in a vacuum chamber, or whatever), and then suddenly move to the left. Something else had to use a force to move that object, and that something must experience a force to the right in the process.

The conservation of momentum is ingrained in physics — if it isn’t true, then we have a lot to redo. Like, the past 300 years. Fortunately, we have at least two good proofs1 of conservation of momentum: Newton’s 3rd Law and Noether’s Theorem

 Newton’s 3rd Law

You know this by heart, right? “For every action, there is an equal and opposite reaction.”  But what does that mean?  I usually find that people can quote Newton’s 3rd Law (after you remind them which one it is), but they have trouble applying it.

What Newton’s 3rd Law means is that every force occurs between a pair of physical bodies2 and that every force has a friend.  Say you’re standing facing a buddy, separated about about a foot.  Each of you keep your feet together. Now, you put your hands on your buddy’s shoulders and push.  What happens? You both fall over.  Why? You pushed your buddy, right?  Well, Sir Isaac says that when you pushed on your buddy, your buddy automatically, simultaneously pushed back on you, just as hard, in the opposite direction, without lifting a hand.  In this case, the pushing occurs between the surface of your hands and your pal’s shoulders.

This happens for every force.  The floor is holding you up, and you’re pushing down on the floor 3.  The Earth is pulling you down with gravity, and you’re pulling up on the Earth with gravity, too, just as much 4.

What do forces do?  They change the momentum of objects over time, as encapsulated in Newton’s famous 2nd law (in a less famous form), F = change in momentum / change in time.

Back to the rockets.  By Newton’s 3rd Law, the stuff pushes back, and the rocket goes forward.  That very simple idea is easy to get confused once you add more to it.  My favorite example is a January 13th, 1920 science editorial in the  New York Times about Robert Goddard’s rocket research.  I read this to my students with the most sniveling voice possible:

“That professor Goddard, with his “chair” in Clark College and the countenancing of the Smithsonian Institution, does not know the relation of action to reaction; and of the need to have something better than a vacuum against which to react – to say that would be absurd. Of course, he only seems to lack the knowledge ladled out daily in high schools.”

This is hilarious, because the author is making fun of Goddard for misunderstanding the Newton’s 3rd Law while completely failing to understand it himself.  The atmosphere isn’t needed, because the exhaust itself provides the reaction force.

Newton’s 3rd Law, if you integrate over time, gives you the Law of Conservation of Momentum.

Let’s go back to you and your friend.  You push your friend and change their momentum in your forward (their backward) direction.  Newton’s 3rd says that your friend automatically pushes back on you just as much (without raising a hand), changing your momentum in your backward direction.  If the forces are equal magnitude, and the amount of time the forces are applied is equal, the the magnitude of momentum change is the same for each of you — only one is your forward direction and one is your backward direction.  Therefore, the total momentum of you and your friend added together is the same before and after5. That is, momentum is conserved!


Noether’s Theorem

I advise you to just go and read everything you can about Noether’s Theorem6.  It has been called the most beautiful result in physics, and I’d have a hard time disagreeing.  But it’s a little more involved than Newton’s 3rd law. I’ll state it first, and then explain a simplified example: For every continuously differential symmetry of the system, there is a conserved quantity.

What the heck does that mean?

First of all, we’ve already shown that between particles, the total momentum is conserved, by Newton’s 3rd law.  So, let’s focus on a specific particle and see what happens (arguably, this is closer to an analogy than an example).

If you’ve got a particle sitting in space (we’ll start in the frame of reference in which the particle is initially at rest), then it’s only going to move if a spot right next to it has lower energy, right?  Like a particle resting on the slope of a bowl.  It will experience a force toward the bottom of the bowl, and that’s because that direction has a lower (gravitational potential energy).  We can think of the environment causing forces on objects by the shape of the energy profile: the forces go from higher energies to (nearby) lower energies.

Well, if there is a force applied to that particle, its momentum changes, right?  So the momentum would not be conserved.

For momentum of the particle to be conserved, there would have to be no slope: the energy would have to be the same everywhere near the particle (this is translational symmetry).  Then, whether the particle is initially rolling or initially staying still, it’ll keep on going with constant momentum.

That energy being the same everywhere nearby the particle? That’s the continuous symmetry.  In this case, if there is a continuous spatial symmetry, then momentum is conserved.

But I cheated!  The bowl is also a physical body!  This really belongs to the Newton’s 3rd Law example!

So, we have to consider all particles in the universe to be, together, our “particle” here, and we’re comparing it to the energy due to the shape/geometry/etc of the Universe7.  That is, as long as physics is exactly the same if you pick up all the particles in the Universe, scoot it all over by a smidge, put it back down, and everything (forces, energy, particle motions, etc) acts exactly the same as before, then momentum is conserved in such a Universe!

Similarly, if you cut and paste all the matter in the Universe from one time to another, and everything is the same, then energy is conserved8!

There are others, too.  The symmetry of nature imposes these conservation laws, which is pretty sweet. The proofs are incredibly easy with the right mathematical framework, so if you are a physics student and have seen Lagrangian mechanics, you should really look it up.


What this means

Essentially, one of three things must be happening in the Cannae experiment:

1) It’s wrong.

2) It’s right, and momentum is not conserved.  (In which case, I’m out of a job, because physics is broken).

3) It’s right, momentum is conserved, and something is carrying away the unmeasured momentum.

Let’s focus on (3).  This something must be particles or radiation, both of which are, in principle, detectable.  A falsifiable prediction! If the Brady et al group is right, then we should be able to detect these particles.

Now, why are physicists so skeptical that (3) is possible?  The claim by the Brady group is (if one is a little generous in rephrasing it for them into something meaningful) that virtual particles in the vacuum are being given energy and promoted to real particles, and these real particles are carrying away momentum.   What’s wrong with that (and/or, what does that mean)?

Find out next time…



1. Insofar as you prove things in science, right?  Everything is conditioned upon further evidence.  But you can prove things in math, and these proofs are mathematically solid. All that could be questioned is whether the model behind the math is supported by evidence in the real world, which it hella is.

2. Things get a little uglier in a field theory, where one considers the agent to be the field itself, but conservation of momentum still works out in the end.

3.  This is not gravity, by the way.  It’s just a contact force, which we call the normal force (normal in the math sense of perpendicular).  The action/reaction pair of forces must always be the same type of force.  The floor isn’t pushing up on you with gravity, is it?

4. But the Earth is way bigger than you, so the same amount of force doesn’t matter as much to it as it does to you.

5. Momentum is what we call a vector quantity — it has magnitude and direction.  Some amount of forward momentum, plus the same measure of backward momentum add up to zero.

6. Did I really just link Wikipedia?  As if my dear reader wouldn’t search there first, anyway?  Yes.  Yes, I did.

7.  I’m sorry, but my analogy is getting gradually less precise, though I think the conceptual idea is adequate for most people.  More technically, what we’re really doing is looking at the Lagrangian and/or Hamiltonian of our system of particles.  The Lagrangian and Hamiltonian are both ways to account for the energy and motion of particles in the system. These are determined by the environment of our particles, i.e., everything that exists that isn’t our particles.  This is the Universe itself.

8.  This is probably not the best place to bring this up, but it turns out that energy is not absolutely conserved, because of expansion. However, for small volumes of space (say, our galaxy), or over small durations9, the energy is conserved.

9. But not too small, because then quantum particles can borrow energy for short periods of time, so long as energy is conserved on average.  More on this tomorrow.

The Infinite Impossibility Drive

There’s been a lot of chatter on these here intertubes about the “NASA”1 validation of a new propulsion mechanism called the Cannae drive, which wouldn’t need to carry reaction mass with it into space2. It supposedly works by pushing against the “quantum vacuum virtual plasma” which sounds like something Gene Roddenberry might have typed at 2:00 am on the day of filming. The original Wired UK article spurred reactions from the physics crowd, which led Wired to post a rebuttal to the objections.  I haven’t seen a lot of counter-rebuttals, and now that the (non-peer reviewed) conference paper is out3, we can finally start digging into what they did and did not see.

(Edit:  Here are some great G+ posts by John Baez (Link 1, Link 2), who lent his voice to the articles linked above, but also wrote his own fantastic pieces. Thanks /u/Saivo)

There are several things to unpack when talking about this experiment.

  • What does the paper actually show? Are the objections raised by physicists about the experiment valid?
  • What is conservation of momentum, and why does this cause physicists to doubt the Cannae drive measurements?
  • Is the authors’ explanation of how the drive works valid?  What is the “quantum vacuum virtual plasma”?

I’ll be writing a series of posts to answer these questions to the best of my ability.  Keep an eye out for updates.

Update!  The momentum article is up now!

Update! A short relativity proof that argues against the feasibility drive is up now!

But first, let’s talk about the experiment as laid out in the paper.

What was tested:

There were, in fact, three drives tested: two types of the Cannae drive and a tapered cavity.  Each Cannae drive looks from the outside like a deranged vase with a tube coming out both the top and the bottom.  The difference lies in the bulb of the vase — in one, suitably called the “slotted” device, slots were cut in only the bottom half.  Cannae himself hypothesized that this asymmetry would cause the driving force.  The other was identical except that slots were not cut.  This is the “null drive” referred to in the other articles.  It isn’t really a control; it only tests whether the slots are necessary.  You can see the side view diagrams, generated with my earth-shaking Inkscape skills, which show the three devices in the test chamber.

g3228 g3255 g3268

All of these have a resonance cavity in the center.  In a resonance cavity, the incoming radio waves from the source bounce back and forth a lot before leaving one side or the other, adding together as they do so — the sensor is there to allow adjustments to the power or frequency.  This alone shouldn’t produce any thrust.  There has to be a difference in something moving to the left or the right to produce a thrust.  That something could just be radio waves — if more radio waves bounced back to the right, there would be a thrust to the left — but that wouldn’t be anything more than a complicated solar sail4. A simple calculation5 shows that the maximum thrust the photon radiation pressure of the radio waves themselves could be is 0.2 micronewtons, much less than the reported force.

The assertion in the paper is that the electromagnetic field of the radio waves confined in the pipes adjacent to the resonator is stronger on the right side than the left, and this is somehow responsible for the thrust.

The only device control is in the form of a 50 ohm resistor. More on that later.

The test:

The total force delivered by these drives at low power is minute, so a very sensitive experiment is necessary. Fortunately, that’s what the team appears to regularly do.  The measurement device is called a torsion pendulum.  In essence, it is like a super-sensitive spring scale on vertical rods.  Just like a spring scale shows you how much force of bananas you’ve added by how far the spring stretches, if the rods of the torsion pendulum are twisted by a force, lasers measure how much they move. This is calibrated to give a force, measured in the physics-y units of Newtons.

One way to test whether it was the drive making the force, as opposed to a hiccup from the testing environment, is to flip the drive over and try it again.  If it’s legit, the force direction should flip, too, but the amount of force should be about the same.  The experimenters did just that, but only once for each drive.

The results:

In each case, between 20 – 30 Watts of power were used (enough power to run a fan or charge four cell phones simultaneously), and 50 micronewtons of force were generated (enough to levitate a couple of mosquitoes that weren’t already flying) in the expected directions.  The flip test also seemed alright, if under-sampled — the force was of similar strength in the opposite direction.

Is that a good amount of force?  Well, it isn’t great, but it’s not as bad as it might seem on the face of it.  First of all, 50 micronewtons doesn’t do anyone any good, but 20 Watts is an incredibly low power to drive a real system.  It could scale up with the application of more power.  For example, a shuttle’s engine, after the solid-fuel stage, burns at a rate of 30 billion Watts, a billion times more power than in the Cannae experiment.  However, that rocket also delivers a force of 5 meganewtons, one hundred billion times more force than the Cannae.

But, this drive isn’t meant to replace a rocket to get a satellite into space.  This is meant to replace the drive you’d use on something that was already in space.  A small force over a long period of time could have the same effect as a large force over a small period of time.  Without having to drag extra reaction mass around or burn out, it could work for much longer and achieve very high speeds in space.

The Control:

A… resistor? A 50 ohm  resistor? Not even inside a pipe like those attached to the resonant cavities of the Cannae drives.  I suppose this resistor matched the impedance of the resonant cavity/waveguide test objects, but it has nothing else in common. And I suppose this shows that the radio waves aren’t affecting the torsion pendulum of the measurement device, but it leaves something to be desired.  Generally, you’d like a control which is as close to your test objects as possible, but without the element you consider critical.  The “null” device was a decent control to the assertion that the slots would be necessary, but only if they can validate the force measurements generally.

 The Outcome

So far, the experiment seems reasonable, except for a poorly considered control.  Why all the hullabaloo?  Because the mechanism for generating the force is, let’s just say, uncertain.  As it stands, we must either question the experiment’s results, or we must question the Law of Conservation of Momentum and our understanding of the quantum vacuum.  We have a lot of evidence in support of those last two, the authors must present a lot more evidence in support of their results before they can gain much ground with the community at large.  That is, other labs (and not commercial ones, like EmDrive) must validate the results.  That’s science.

So, what about that Conservation of Momentum or the quantum vacuum dealy? What do we know about them, and what, if anything, do they have to do with this experiment?

You’ll just have to wait for my updates.

Update!  The momentum article is up now!

Edit: I’m commenting on a Reddit thread with my brand new account.  This is proof that /u/gildthetruth is me.

Edit 2: No, I’m not.  My account is too new. I’ve lurked for a couple of years without an account and made one today to comment. Anyway, just listen to /u/kleinergruenerkaktus.

1 It was a small team among NASA’s giant organization. While this is what they do for a living, they aren’t speaking for NASA.

2 It would still require energy. If they claimed it didn’t require energy, no one would be paying any attention at all. For more on how rockets use reaction mass to generate lift, see my upcoming article on conservation of momentum.

3 Though not public.  Since this is a federally funded agency, the research should be public eventually, as I understand it.

4 As long as the RF source remained external. For these drives, though, the source travels with the drive, which wouldn’t work as a solar sail any more than you can point a fan at the sail of your boat and hope to move.

5 They used about 30 Watts of power in the radio frequency signal. Each photon that hits a sail would impart an impulse of 2*p, where p is the magnitude of the momentum of the photon (assuming a single reflection isn’t enough to accelerate the sail much). The momentum of a photon is related to its energy by E = pc, where c is the speed of light. Since power P is energy over time, P = dE/dt = dp/dt *c = F*c, because F = dp/dt is the momentum form of Newton’s 2nd law. Thus F = 2*P/c = 2* 30W/3E8 m/s = 0.2 micronewtons.