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 
asymetric radiation, which is obviously not reactionless, since 
an EM wave eith energy E carries momentum, and the emission of 
this wave reduces the rest mass of the apparatus by an equivalent 
amount E/c^2.

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.)