Reactionless Drive

Lately I’ve been seeing a bunch of different ideas being bandied about for how it might be possible to have a science fictiony space drive that doesn’t need to obey the classic Newtonian laws of motion — drives that might produce action without reaction, by taking advantages of possible loopholes in the laws of relativity. Some might even open the possibility of moving faster than light. NASA has an office for investigating these exotic possibilities. Some of the ideas being talked up are:

• the Cannae Drive, or Quantum Vacuum Plasma Thruster: This gizmo is supposed to produce a net thrust out of a closed microwave resonator by using the virtual particles of the quantum vacuum as a sort of reaction medium. (It might produce an exhaust trail of real particles. In that case, it’s really just a difficult way of building something that would resemble a conventional ion drive.)
• the EmDrive: A simpler microwave resonator device which doesn’t claim to involve any quantum effects.
• the Woodward Effect: When a capacitor stores an electrical charge, that’s energy, so by E=MC² it’s slightly heavier, though it contains the same number of particles. So you charge it, pull it toward you, discharge it, and push it away, and there’s a slight difference of momentum for the opposite movements, resulting in net thrust in the pulling direction. James F. Woodward has a lab where he swears he’s measured a real force on delicate instruments. Woodward claims it isn’t really violating conservation of momentum due to “Mach’s Principle”, which he thinks allows it to exchange momentum with the universe as a whole.
• the Alcubierre Drive: This hypothetical idea is based on an allowed solution to the equations of general relativity, where you could put a compressive effect on one zone of spacetime and an expansive effect on another nearby, and the zone between them would be accelerated, dragging the whole mess along, and possibly creating a local redefinition of the speed of light, allowing the thing to appear faster than light from outside. There’s one catch: you’d essentially have to invent a negative form of gravity. The weird thing is, this somehow got written up as a real Nasa project, with news articles claiming that this could definitely be built someday.
• negative mass: If you had a positive mass and a negative mass, the gravitational attraction between them would become repulsion, but repulsion would act backwards on the negative mass, so — unless there’s a sign component of the laws of momentum that we don’t know about — both would move in the same direction. Now negative mass is a lot to ask for, but it’s not as instantly absurd as you might think, because a gravitational field is a real example of something that has negative energy, and a Casimir-effect device has negative energy in its central gap.

All of these ideas share a single fundamental problem. If they work, it would mean you could produce net momentum that isn’t conserved. Now it’s not such a mental stretch to imagine that maybe our idea of conservation of momentum is too narrow and needs revision. But how could such a revision allow the rest of physics to hang together?

Here’s a question that needs answering by anyone who claims we can rewrite conservation of momentum. If an object can move itself reactionlessly through space like Superman... what is its kinetic energy, and what kind of energy input is required to give it a particular change of speed? What is the relation between power consumption and thrust?

The answer is very awkward, because unlike momentum, the kinetic energy of the system, and the degree of change to that energy which arises from any change of velocity, depends on the frame of reference you measure it in. If something starts from a standstill and builds up a small velocity, that gives it a small kinetic energy. But if it’s already going fast and then it speeds up by that same small amount, the gain in its kinetic energy is greater than what it gained from a stop. And if it’s going fast the other way and slows itself down, it loses energy. The question of what power is required to give it thrust becomes unanswerable: from one viewpoint it takes a little, from another it takes a lot, and from a third the process gives energy back. But from the point of view of the moving object itself, it’s absurd to think that the power consumption of its engine depends on how fast it’s going relative to this or that randomly selected outside observer. There has to be a single noncontradictory criterion to go by. Which implies the power consumption ought to be more of a constant.

But if the power consumption is a finite constant, this means that, if it’s going fast enough relative to some observer, it’s possible from that observer’s viewpoint to produce more energy than you consume. Which means that if the flying object is caught on a big paddle wheel, you’ve obtained free energy. It can launch projectiles to itself that land with more energy than they took off with. Et voila, you’re the proud owner of a perpetual motion machine. Even Mach’s principle won’t get you out of that one, I don’t think.

Unless, that is, you postulate a preferred frame of reference which matches the net momentum of the entire universe, and then figure that the faster you go relative to that preferred frame, then the more power it takes to accelerate. The math them becomes the same as a plane flying through air, or for that matter a car on the ground. Then there’s no conservation violation — there’s only an unexplained mechanism by which you’re supposedly connecting to extremely distant other masses. And if it’s really the whole universe, that includes masses that are undetectable because they’re beyond your light cone. But if you avoid that, you’re hypothesizing a force which acts with a finite speed and range, so somebody light years away can reach out and grab you (very gently) to use as reaction mass, yet his strange influence might not reach your neighbor. And if there is no outside mass near the accelerating ship, then there might be a very long delay between when he opens the throttle and when he starts to move.

I don’t think most of the people who build these gadgets are thinking in those terms. EM drive enthusiasts, for instance, are throwing out speculative figures in “newtons per kilowatt”, and if that were a legitimate measure for the engine’s performance, it puts you right into perpetual-motion country. It seems to me that these weenies really are the same sort who in the past tried to make perpetual motion out of wheels and levers. They’re just fooling themselves into thinking that if they just make it tricky and complicated enough, somehow the books will fail to balance. Some people just don’t want to believe bad news — they really don’t want to listen if you tell them they can’t have what they want.

But it is fun to try to wrap your head around what the math would be for some of these hypothetical situations. Like, if an object really did have a negative mass, would pushing against it really move it toward you rather than away? If not, you’ve already got a contradictory result in terms of conservation of momentum and kinetic energy. But if it does... that may make sense in terms of applying a gravitational or electromagnetic force from a distance, but what on Earth happens if you’re in solid contact with it and just pushing with your hand? Does it stay fixed in place because every movement you make is blocked by a reverse motion? That seems absurd. Or would it allow you to push it away, but instead of resisting the movement it would suck your hand after it, yielding excess energy? That might be even worse.