> If you violate momentum conservation by different amounts, you violate energy conservation, too; energy is not only not conserved, it’s not conserved by different amounts in different reference frames. The most sacred law of particle physics — one that has been observed to apply to every system and every interaction set in history — would be busted.

But we've known since the 1920s, when we started figuring out that spacetime changes, that energy is not conserved.

Sean Carroll has a good article explaining this [1]. Some quotes:

> It’s clear that cosmologists have not done a very good job of spreading the word about something that’s been well-understood since at least the 1920’s: energy is not conserved in general relativity. (With caveats to be explained below.)

> The point is pretty simple: back when you thought energy was conserved, there was a reason why you thought that, namely time-translation invariance. A fancy way of saying “the background on which particles and forces evolve, as well as the dynamical rules governing their motions, are fixed, not changing with time.” But in general relativity that’s simply no longer true. Einstein tells us that space and time are dynamical, and in particular that they can evolve with time. When the space through which particles move is changing, the total energy of those particles is not conserved.

(skipping some elaboration and examples he gives)

It is possible to interpret GR in a way that lets you still say that energy is conserved but it is kind of a hack:

> Having said all that, it would be irresponsible of me not to mention that plenty of experts in cosmology or GR would not put it in these terms. We all agree on the science; there are just divergent views on what words to attach to the science. In particular, a lot of folks would want to say “energy is conserved in general relativity, it’s just that you have to include the energy of the gravitational field along with the energy of matter and radiation and so on.” Which seems pretty sensible at face value.

> There’s nothing incorrect about that way of thinking about it; it’s a choice that one can make or not, as long as you’re clear on what your definitions are. I personally think it’s better to forget about the so-called “energy of the gravitational field” and just admit that energy is not conserved, for two reasons.

> First, unlike with ordinary matter fields, there is no such thing as the density of gravitational energy. The thing you would like to define as the energy associated with the curvature of spacetime is not uniquely defined at every point in space. So the best you can rigorously do is define the energy of the whole universe all at once, rather than talking about the energy of each separate piece. (You can sometimes talk approximately about the energy of different pieces, by imagining that they are isolated from the rest of the universe.) Even if you can define such a quantity, it’s much less useful than the notion of energy we have for matter fields.

> The second reason is that the entire point of this exercise is to explain what’s going on in GR to people who aren’t familiar with the mathematical details of the theory. All of the experts agree on what’s happening; this is an issue of translation, not of physics. And in my experience, saying “there’s energy in the gravitational field, but it’s negative, so it exactly cancels the energy you think is being gained in the matter fields” does not actually increase anyone’s understanding — it just quiets them down. Whereas if you say “in general relativity spacetime can give energy to matter, or absorb it from matter, so that the total energy simply isn’t conserved,” they might be surprised but I think most people do actually gain some understanding thereby.

> Energy isn’t conserved; it changes because spacetime does. See, that wasn’t so hard, was it?

So, getting back to the Emdrive, if it works it won't be it not obeying conservation laws that surprises me. It will be how simple it is.

From Noether's theorem, we know that conservation laws are equivalent to various symmetries in the laws of physics. Translation invariance gives conservation of linear momentum. Rotational invariance gives conservation of angular momentum. Time invariance gives conservation of energy.

The universe looks pretty much the same in every direction from our point of view, and when we look into the past (by looking at things farther away), it looks like the laws of physics are the same. If we do NOT have translation, rotation, or time invariance, the variation appears to be very small. Thus, I'd expect actually exploiting any such variation to require something very very big, probably galaxy cluster size at least.

[1] http://www.preposterousuniverse.com/blog/2010/02/22/energy-i...