Strictly speaking, photons are massless, but there's more to momentum than just mass - relativistic equation for it gives you a mass-independent component of it.
This is a good point. Everyone knows the formula E=mc
2, but this only applies to massive particles which are at rest. The general formula is actually E
2 = p
2c
2+m
2c
4. Right away you can see that massless particles have energy E=pc as Herra showed. And for massive particles which are not moving, it simplifies to E=mc
2.
It also clears up things like Oberth effect, which are really darn hard to explain.
Actually no, the Oberth effect has nothing to do with this -- it is explained by classical mechanics without relativity. If you tried to explain it with relativistic effects, your prediction for its strength will be orders of magnitude too small. You really only need the definition of work to understand it, or definition of total energy (gravitational potential plus kinetic) if involving a gravitational field. To think about it, consider a rocket which is held stationary while burning. In this case, the work done on the rocket by the fuel is zero, by definition, since it is moving through zero distance. All of the work is done on the propellant -- the propellant gains all the energy from combustion. If the rocket is moving, then more work is done on it because it moves through a greater distance. This is at the cost of putting less energy into the propellant -- it is left behind with less kinetic energy.
@Herra: Great posts. I don't think it's likely that it has anything to do with dark matter (the properties of dark matter just don't really fit the bill), but dark energy might make sense, given that it's apparently a property of space-time pertaining to vacuum fields. If the quantum thruster works by interacting (somehow?) with the vacuum energy, then that's...
crazy.
I've also heard a lot of speculation that the drive might be operating via general relativistic effects, of the sort involved with Mach's Principle. Mach's principle is the notion that the local standard of "rest" (the locally inertial frame) is determined by fields produced by the large-scale distribution of matter and energy in the universe. Perhaps the drive is (somehow?) interacting with those fields, thereby exchanging momentum with matter "at a distance". Which reminds of quantum entanglement sort of, and I can't help but think it can't possibly work that way because of causality issues. Then again, this thing pretty much completely defies our understanding of basic physics... we haven't seen such a confounding experimental result since Michelson-Morley over 100 years ago.