Any useful comments will be appreciated. Note that no new physics is required in this model, and all the laws of conservation (energy and momentum) are valid.

The ratio momentum over energy for a non relativistic electron is 2/v , where v is the velocity of the electron. This is orders of magnitude higher than 1/c, in the photon case. The chain reaction involving pair creation and annihilation, facilitated by the relativistic Doppler shift, where momentum is trasferred by the electron for each pair creation step, more than compensates for the energy required for the creation of the electron - positron pair. Your assumption that having the photon as the mediator of momentum transfer is the best you can do, is incorrect. Have you ever had a look at QFT mathematics? There are tomes of dense mathematics, just to understand the basics, and this is what we are talking about. Any attempt to dive into that on these posts would be a joke.

Answer for sanmanI don't know the answer to this one. We are still struggling with pair production (as you can see). I mentioned the Schwinger effect as an interesting venue of research related to all this, but as you can see from these discussions, we cannot handle even much simpler events.

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.

Energy and momentum conservation show that photons thrust is the best you can do if you start with pure energy. Generating particles to emit as reaction mass consumes energy and reduces the thrust per input power. I can just look at the initial and final conditions of your claimed setup and tell that you are violating energy or momentum conservation. This means you are making a mistake in the middle somewhere. There is plenty of room for you to post your math here, and then someone (me if I have time) can help you find your mistake.

III. THEORY OF ACCELERATED LIGHT AND OTHER SOURCESIf one searches for the term “waveguide” in the book, “Theory of Photon Acceleration” by J T Mendonca2 it discussed how the eﬀective mass of a photon can change in a waveguide that approaches cutoﬀ wavelength, as well as a plasma. Another source was found discussing a change in the eﬀective mass of light in a waveguide approaching cutoﬀ wavelength titled, “Alternative perspective on photonic tunneling” by Zhi-Yong Wang1, Cai-Dong Xiong, Bing He5. It appears they show how a photon in a narrow waveguide may appear to change in mass and how it relates to evanescent waves. The author suspects how photons in the vacuum can excite electron positron (ep) pairs and those pairs when they annihilate can create photon pairs suggest that photons may them selves be low level excitations of overlapping ep pairs. If our quantum vacuum is made up of hidden ep pairs, then an acceleration of light may directly be a form of accelerating the quantum vacuum. This may parallel to locally accelerating a frame as happens when light enters a gravitational ﬁeld.

Quote from: meberbs on 02/03/2017 04:34 PMEnergy and momentum conservation show that photons thrust is the best you can do if you start with pure energy. Generating particles to emit as reaction mass consumes energy and reduces the thrust per input power. I can just look at the initial and final conditions of your claimed setup and tell that you are violating energy or momentum conservation. This means you are making a mistake in the middle somewhere. There is plenty of room for you to post your math here, and then someone (me if I have time) can help you find your mistake.The photon recycling thruster immediately disproves the assumption that the best thrust you can get is that of collimated light. The thrust achievable with photon recycling thrusters is larger.

Quote from: dustinthewind on 02/15/2017 03:12 AMThe photon recycling thruster immediately disproves the assumption that the best thrust you can get is that of collimated light. The thrust achievable with photon recycling thrusters is larger.Yes, and the reason for this has been explained many times. It has nothing at all to do with propellantless thrust.

The photon recycling thruster immediately disproves the assumption that the best thrust you can get is that of collimated light. The thrust achievable with photon recycling thrusters is larger.

Quote from: as58 on 02/15/2017 06:35 AMQuote from: dustinthewind on 02/15/2017 03:12 AMThe photon recycling thruster immediately disproves the assumption that the best thrust you can get is that of collimated light. The thrust achievable with photon recycling thrusters is larger.Yes, and the reason for this has been explained many times. It has nothing at all to do with propellantless thrust.You're right that the Recycling Thruster has nothing to do with the Quantum Vacuum and Propellantless Propulsion. However, it does demonstrate that Resonance can milk more juice out of photons to obtain more momentum transfer than is possible from an ordinary Photon Rocket like a flashlight-in-space.Unlike Prof Bae's Recycling Thruster, the EMdrive concept seeks to do the Propellantless Propulsion, but it seeks to exploit the Resonance to help it do so in a meaningful way - ie. achieve a more meaningful amount of thrust than would otherwise be possible without the resonance.

Could the Rocket Bell in conventional chemical rockets provide a useful analogy?Whether or not you have the Rocket Bell there, you are still spewing the same hot gas out of your combustion chamber.But having the Rocket Bell there allows you to extract more useful energy from the exhaust gas than would otherwise be possible.

I want to emphasize a few points related to this issue. I will assume that the thrust experimentally observed, as related to the EM drive, is a real phenomenon, and I will try to explain it. I will mention the following interconnected effects, the dynamical Casimir effect, Unruh radiation of accelerated mirrors, and the Schwinger effect.