Could you? How? Perpetual motion machines must put out at least as much energy as they take in. AIUI the EmDrive requires external power (such as solar panels) and produces a rather tiny amount of force. This does not sound to me like it's anywhere even remotely close to putting out as much energy as it takes in.

It's because there's no such thing as absolute velocity, so your thrust can't vary with velocity, it has to be a constant for given input energy. Kinetic energy is the square of velocity, so as you keep accelerating at a constant rate, you'll eventually get to some velocity at which the energy you get out is higher than the energy you put in, assuming your reactionless drive is more efficient than a photon rocket.

Not that it matters. If it works, it already violates conservation of momentum as we currently understand it. That's just as fundamental as conservation of energy.

Hmm, relativistic velocity under constant acceleration is

    v(t) = a t / sqrt(1 + a^2 t^2)

and relativistic kinetic energy is

    Ek = m c^2 / sqrt(1 - v^2/c^2) - m c^2

Leave out the constant -mc^ and for simplicity put m=1, v=1, c=1, and we get

    Ek = (1 - t^2/(1+t^2))^(-1/2)

which is linear in larger values of t, not square.

Proof:

    d/dt Ek = t sqrt(1 / (1 + t^2))
            = sqrt(t^2 / (1 + t^2))

which is always < 1.

So at the extreme efficiencies Shawyer claimed, overunity was at decidedly nonrelativistic velocity. It'd be interesting to calculate a maximum drive efficiency before you get overunity.

I've seen claims that the max is the efficiency of a photon rocket, but I haven't seen it backed up with math.

This is violating conservation of momentum, not conservation of energy. You cannot build a perpetual motion machine using it. But even if you could, that is not a reasonable argument. Reality is what it is.

"But even if you could, that is not a reasonable argument"

It may not be a reasonable argument to claim that it is impossible, but it is a totally fine argument to make that it is insanely unlikely and needs a mountain of evidence before we take the conclusions seriously.

That's an argument about priors. In the face of actual evidence of its reality, priors establish significance not believability.

No... priors are precisely about believability.

Any evidence can be explained either by the effect or by experimental error. Your prior is how relatively likely these two possibilities are.

If something is "significant" then it is surprising and requires stronger evidence.

Or your premises are wrong. Before calling it not real let's allow the testing to continue to see wether our understanding of physics is not enough to explain how it's working, or if there's something that has escaped every study and reproduction of the system.

It's certainly not going to take too long before someone puts an EM drive to space to see if it works there too, it's not that expensive to do so when put into context.

How would you build that?

They're putting in a fair amount of energy to make this happen.