I think that aero solved all our problems gentlemen (with his last remark above ), but maybe not exactly the way he described it . We could consider positron channeling in crystals.. So we have an experimental setup where after the pair production event, the electron transfers some momentum to the nucleus, and the positron will channel through the crystal, thus increasing its momentum. No pair production - annihilation chain reaction, all laws of conservation of energy and momentum are valid, and it explains the enhanced momentum transfer. Bingo. I think that we are on the right track here.

Where we disagree is related to whether momentum transfer with the electron as the mediator is more efficient than a photonic drive, where momentum is transferred directly, with the photon as the mediator. For a single event, you are correct meberbs, the momentum transferred to the nucleus is smaller than the initial momentum of the photon. Now we get into the hairy part, the chain reaction.

We are on a reference frame tied to the mirror, in particular, to the nucleus.

The electron - positron pair is created. The electron transfers momentum to the nucleus. The positron is repelled by the Coulomb field of the nucleus, and annihilates with the electron of another atom. Two gamma photons are created (at or slightly above the total threshold energy 2mc^2 , where m is the rest mass of the electron ). At about 60% of light speed, due to the relativistic Doppler effect, an observer on the mirror will see the frequency of the incoming gamma photon doubled (when moving straight towards the photon, all the possible geometrical configurations have to be considered, this is just a special case ).

5. If this chain reaction is impossible, why is that the case? Can you prove that this chain reaction is not possible?

By the way, QFT (in particular QED) is need, in order to calculate the probability of these types of events, in order to see which are the dominating ones. There is no going around that, and the calculations are not pretty. This is actually the heart of the problem. Speculating based on the mathematics of relativity, and intuition, is not enough.

The "engine" does not emit anything. For each pair production event, momentum is transferred to the mirror, due to the laws of conservation of energy and momentum. The problem is trying to prove that the total momentum transferred makes this "engine" more efficient that a straight photon drive. I tried it with my chain reaction model (described above), but surely I am missing something.

Quote from: cristian on 02/05/2017 04:39 PMI think that aero solved all our problems gentlemen (with his last remark above ), but maybe not exactly the way he described it . We could consider positron channeling in crystals.. So we have an experimental setup where after the pair production event, the electron transfers some momentum to the nucleus, and the positron will channel through the crystal, thus increasing its momentum. No pair production - annihilation chain reaction, all laws of conservation of energy and momentum are valid, and it explains the enhanced momentum transfer. Bingo. I think that we are on the right track here.So based on what you've said - what is the way to optimize the effect of "enhanced momentum transfer"? Is there some kind of "mean free path" metric that needs to be increased? Is it the case that the longer a produced pair persists before anihilation, then the more momentum transfer happens? Is there some travel requirement that has to be maximized for a produced pair?

.......But, once there are electrons and positrons inside the cavity, I'm led to believe that they will be accelerated along the energy gradient within the cavity ......Just some thoughts.

Note that the "battery" energy (the energy required to set up the system), is only used at stage 1 and stage 2. Stage 3 is all about the energy stored in the Coulomb fields of the nuclei of the atoms in the metal (the crystal lattice that will accelerate the positrons generated at stage 2). This is what makes the difference, and what makes this superior to a pure photonic drive.

So that's it. The system will eject high velocity positrons, and will gain an enhanced thrust, as compared to a purely photonic drive or anything else. All laws of conservation of energy and momentum are valid, and no weird physics necessary. This is so far from the original design of the EM drive that I will not even try a comparison, or ask why the original design works the way it does. This is a completely different system, and no fuel necessary. Pair production is essential. Alpha Centauri, here we come!

The energy stored in the Coulomb fields of the nuclei of the atoms of the crystal lattice that channels the particles is quite large.

Compared to the way relativistic momentum increases with velocity, that is a small price to pay (you can do the math ). The efficiency will still be higher than anything currently possible, including the photonic drive. I am glad that you are paying attention.

The relativistic momentum increase of the channeled particles is what generates the thrust. Could be much more efficient than a photon drive. I hope you agree.

Quote from: cristian on 02/07/2017 04:03 PMThe relativistic momentum increase of the channeled particles is what generates the thrust. Could be much more efficient than a photon drive. I hope you agree.See, that's what makes me wonder about Laser Wakefield acceleration - because it provides such a high accelerative gradient to achieve relativistic velocities for electrons, that you can get extra action-reaction from that via relativistic momentum increase. Of course, the duty cycle on a Laser Wakefield accelerator is low, but it's still something to think about.

Thank you meberbs for keeping me on my toes. I have to put my thinking cap back on. The relativistic energy - momentum relation is perfectly valid, but you omit the phenomenon of self-oscillation, when the energy losses in the oscillating system are small. In this case, in order to sustain self-oscillations, the quantity of energy entering the system is very small in comparison with the total energy within the oscillating system....

Well, together we reached an interesting conclusion. The principle of operation of the EM drive has something to do with electron channeling in a crystal lattice. The thrust is connected to the relativistic momentum increase of the channeled particle.