originally published February 19, 2015

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:

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.

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