Reactionless Propulsion (Not)

Here's a common fallacy that sometimes leads people to think it's possible to create a reactionless propulsion system. First, consider two positively charged particles, held a fixed distance D apart by some framework. The particles exert equal and opposite forces on each other, and they transmit these forces to the framework, so there is a net zero force on the framework. Now, people sometimes imagine that is should be possible to somehow "turn off" the charge of one of the particles, so that it is no longer subject to any electro- magnetic force. In addition, they suppose that the other particle will continue to experience a net repulsive force for a period of time equal to D/c, reasoning that it will take this long for the effects of turning off one charge to reach the other (at the speed of EM wave propagation).

It's easy to dispose of this idea, simply by noting that charge is conserved, and we cannot simply "turn off" the charge of a particle. When this is pointed out, the proponent of reactionless propulsion will sometimes change the scenario, so that instead of considering two charged particles, we have two electro-magnets, repelling each other. It's certainly possible to "turn off" an electro-magnet, so it might seem that this provides a means of achieving reactionless propulsion. This would be true if the force on the de-powered coil instantly becomes zero when the circuit is opened, and if the full force continues to be exerted on the powered coil until the effect of turning off the first coil has time to propagate across the distance between the two coils.

However, the field surrounding an electromagnet doesn't just vanish when we open the circuit, because a changing electric field induces a magnetic field, and vice versa. As a result, there will be significant transient effects when we "turn off" one of the electro- magnets. These transients will also affect the other coil and its field, because the two coils are inductively coupled. As Faraday would have said, the "lines of force" linking the two coils will collapse. It isn't correct to view this as two superimposed static fields, one of which can simply be instantaneously deleted at will. In a sense, the fallacy with this idea is the same as with the idea of just "un-charging" a particle, i.e., it is the failure to take account of the conservation laws of electro-dynamics, which automatically ensure that momentum is conserved.

Of course, another consequence of the abrupt change in the combined field of the two coils is that some energy would be radiated away in the form of an EM wave. (You've probably heard a "click" on a nearby AM radio when you de-power any kind of inductive coil.)  Since our setup is non-symmetrical, the radiated wave would be non-symmetrical too, so it could carry away a net momentum in some particular direction. In this sense, we certainly can achieve a propulsive effect - but it isn't reactionless. It is reacting against the momentum of electro-magnetic radiation.

In a sense, the conservation of momentum (which is built into the basic laws of electrodynamics) is what prevents an EM field from simply disappearing instantly. When we de-power one coil, we are basically just changing the boundary conditions, and as a result the field reconfigures, in accord with Maxwell's laws (inducing transients in the coils themselves), to reach a new steady-state configuration. True, one of the constraints on this dynamical reconfiguration of the field is that changes propagate at the speed c, but another constraint is that momentum is conserved. The latter is a property of Maxwell's equations, just as it is of Newton's laws. The only net propulsive force will be due to asymmetric radiation, which is obviously not reactionless, since an EM wave with energy E carries momentum, and the emission of this wave reduces the rest mass of the apparatus by an equivalent amount E/c².

Now, it might seem possible to create reactionless propulsion just by means of EM transmitters and receivers, taking into account the time delay between transmission and reception, but this doesn't work either. To visualize this, we can think in terms of little momentum-carrying particles being exchanged between two mutually repelling electromagnetic coils, which are being held a fixed distance apart, say, at the front and back of a spaceship. Imagine a steady stream of these tiny particles being emitted by each coil and absorbed by the other coil. The force on each coil consists of two equal parts: (1) the "recoil" from the particles it is emitting, and (2) the momentum it absorbs from the particles it is receiving (from the other coil). In this condition the net force on the ship is zero, because the coils are exerting equal and opposite repulsive forces on each other.

Now we make the coil at the back of the spaceship stop emitting particles, so it is no longer subject to a recoil from an emitting stream. Hence the rear-ward force on this coil is cut in half (the remaining half being due to the stream of particles it is still receiving from the front coil). However, for some period of time D/v (where D is the length of the ship and v is the speed of the momentum-carrying particles) the coil at the front of the spaceship is still absorbing a stream of particles as well as transmitting a stream, so it is still subject to the full forward force - until the last particle emitted by the rear coil has arrived.

During this period of imbalance, particles have been accumulating at the back of the ship (because it's receiving but not emitting), and there has been a net forward force on the ship. At some point the last of the forward-going particles reaches the front coil, and at this time both coils are again subject to equal and opposite forces, because now the front coil is just transmitting, and the rear coil is just receiving. 

The ship will continue to move at the constant speed that it acquired during the period of imbalance, until eventually the front coil runs out of particles, so it stops transmitting, and is no longer subject to any force at all. Then, for some length of time (D/v) the rear coil will continue to receive particles, so the ship will have a net rear-ward force, of the same magnitude and duration as the previous forward imbalance. As a result, the ship will be brought to rest again (relative to the reference frame in which it started). 

This overall process has moved a number of particles from the front to the back of the ship, and the geometric center of the ship has moved forward (slightly), so that the center of mass has remained constant. This is the key point to keep in mind: all the processes involved in these exchanges of momentum obey the law of conservation of momentum, so as long as no momentum-carrying particle leaves the ship, the center of mass of the ship can't move. (This is true even if the momentum-carrying particles are massless photons, because the masses of the coils will increase and decrease in proportion to the energy absorbed and emitted, regardless of the form.)

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