...
Momentum is conserved and Energy is conserved.
Momentum is obviously not conserved. Start with an emDrive at rest, it has 0 momentum. Run it for a while, and then turn it off. It now has momentum, but nothing has left the cavity, and there is nothing inside the cavity moving the opposite direction. The only thing that could possible leave the cavity is IR radiation, but that would at best have the momentum of a photon thruster. Obviously nothing in the cavity is moving the opposite direction, because if it was it would soon hit the back of the cavity and make the cavity stop moving forward.
Heat has left the cavity, heat came from RF energy; and more Doppler down-shifted, lower frequency energy than up-shifted higher frequency energy; and the down-shifting happened at the apex where the up-shifting happens at the base (sidewalls too); and that means more radiation-reaction momentum was imparted in the forward direction whereas radiation-reaction momentum in the reverse wasn't imparted since it was absorbed then radiated as heat.
Imagine a hollow sphere, an isotropic laser in the center, one hemisphere is reflective, the opposite hemisphere has a high-Q frequency-selective absorbent dye over a reflective coating. Laser is tuned a hair down the dye's absorption spectral line. Accelerate the very light, rigid sphere at an unreal rate, so the Doppler downshifted radiation from the forward-moving hemisphere is now absorbed and radiated as heat.
The radiation pressure is then anisotropic, unsymmetrical for an accelerating cavity with unsymmetrical spectral absorption.
This trick only works in the Lorentz-invariant vacuum. Because, as the Sagnac Effect proves, you don't accelerate the spacetime inside a cavity. You accelerate the cavity shell through spacetime. You don't accelerate (Doppler shift) photons in a hollow cavity until they reflect off the cavity shell.
If you fill the waveguide with a material, then you must account for the Fresnel-Drag, and consider the Abraham-Minkowski stuff.
During continual acceleration, as KE increases, the energy to support increasing Work and KE is sourced from cavity energy, increasing energy loss per cycle, dropping Q and dropping N.
Why is this so hard to accept?
Because it makes no sense, it implies that an emdrive that has been accelerating for 10 minutes will produce less force than one that has been accelerating for 10 seconds, when there is nothing physically different between them. There is no mechanism by which it can tell the difference, the RF is from a co-moving source, so there will not be Doppler problems, and you have claimed that simply turning it back off and then back on will reset the magic tracking how long it was running for by some additional magic.
There is a physical difference between the drives accelerating for different times. You can tell the difference between them from the RF spectra. There is a Doppler "problem" in an accelerating drive with a co-moving source (frustrum injector antenna) though not in a constant velocity frustrum.
If this were not so, we'd have no Sagnac fiber-optic gyros.
There is a finite propogation delay in the frustrum, between the antenna, the sidewalls, and the end reflectors. If the frustrum accelerates, the frequency is Doppler shifted. Also the dissipation of the frustrum loss phase shifts and attenuates, and does so frequency-selectively according to tuning.
This all comes to steady state in comparable to the cavity fill time constant. After that it should stay constant, and there is no difference between 1 minute or 10 minutes of operation.
...
Momentum is conserved and Energy is conserved.
Momentum is obviously not conserved. Start with an emDrive at rest, it has 0 momentum. Run it for a while, and then turn it off. It now has momentum, but nothing has left the cavity, and there is nothing inside the cavity moving the opposite direction. The only thing that could possible leave the cavity is IR radiation, but that would at best have the momentum of a photon thruster. Obviously nothing in the cavity is moving the opposite direction, because if it was it would soon hit the back of the cavity and make the cavity stop moving forward.
Heat has left the cavity, heat came from RF energy; and more Doppler down-shifted, lower frequency energy than up-shifted higher frequency energy; and the down-shifting happened at the apex where the up-shifting happens at the base (sidewalls too); and that means more radiation-reaction momentum was imparted in the forward direction whereas radiation-reaction momentum in the reverse wasn't imparted since it was absorbed then radiated as heat.
What is "heat"? Radiated as heat means radiated as IR radiation, which I already stated. This has same energy/momentum relation as a photon rocket, because that is what it is. (worse actually, because it is not very directional.
Therefore momentum, really, truly not conserved whatsoever. There simply by definition is not enough energy dissipated to equal the momentum the cavity is supposed to gain, and if there was, you would just have a photon rocket.
Hello, I have a question. Excuse this layman example, but I'm new to EMdrive and the math behind it.
I understood there are issues with CoE and CoM. Lets imagine the following scenario:
1. "EMDrive" is enclosed in a box, blocking 100% of any energy from leaking out from inside of it.
2. There is a battery on board, 10kWh worth, enough for the engine to operate few minutes.
3. We have a race track, where the box can move freely, without any friction, from point A to B
4. At point B, we have a 100%-efficient kinetic energy recovery mechanism.
Now, assuming EMDrive somehow works, could it be that the 10kWh energy spent on the A-B travel, gets fully recovered (without any net) at point B, and the box arrives a little bit lighter at point B?
Yes, I'm saying there has been no exhaust at all, just a pure conversion of 10kWh from battery, into kinetic energy, does that break anything? Or is it the most plausible case (assuming it works)?
That being said, would that equal to a photon rocket? I mean, if we converted 10kWh energy into photons, shoot them out from the back of the box, would point B recover 10kWh?
Thank you.
Some of us have concluded or admitted that the EMDrive or Mega drive or any such propellent-less propulsion device would have to amount to and allow for an energy generation machine.
You say I don't understand them and am going off half (maybe all) cocked. Do you really think they would write all those papers if all they were saying is "Hey, here's an interesting way to make a propellent-less propulsion device that works far far less efficiently than a simple photon rocket and is entirely useless!!!!!"? Or maybe, "Hey, this would work but you need gigawatts of power!!!! Maybe that's the academic world but somehow, I doubt that. So, what do you think they are really trying to say with these papers?
Can you realistically imagine proposing gigawatt levels of power in meter sized coils carrying 100 amps of current? Wouldn't they just melt?
I have no idea why they haven't calculated the power requirements, especially since there is an easy way to do so since the energy flux is equal to c times the momentum flux. Them not calculating it in no way changes the fact that this is a ton of power, and yes it probably would melt something if you tried to build such a device.
It does not matter why they aren't discussing the power numbers, because the power numbers are what they are. Do you have anything to add that is actually based on math or physics?
I emailed one of the authors, professor Yahalom, about the power levels for that 2.74N force and I'll let you know if he answers.
Had a neat idea connected with studying EMdrive. I'm thinking that dark matter might just be the center of mass of counterpropagating photons happening on a massive scale.
I rebuilt the torsional pendulum support in preparation for the new 30W amplifier and electronics. The structure is now entirely 3"x3"x1/8" aluminum square tube and 1/4" stainless steel bolts. It is also 10 inches shorter. With the center of gravity lower, and the more robust materials, it is the most stable it has ever been by far. The dampening paddle was also improved.
All electronics and batteries will be mounted on the left side of the pendulum center, the same side the frustum is mounted. I will get started on that tomorrow.
I rebuilt the torsional pendulum support in preparation for the new 30W amplifier and electronics. The structure is now entirely 3"x3"x1/8" aluminum square tube and 1/4" stainless steel bolts. It is also 10 inches shorter. With the center of gravity lower, and the more robust materials, it is the most stable it has ever been by far. The dampening paddle was also improved.
All electronics and batteries will be mounted on the left side of the pendulum center, the same side the frustum is mounted. I will get started on that tomorrow. 
Thank you. Looks like a solid build. However, There is a potential problem. The frustum is likely grounded to the beam from those two bolts. If so, an extra DC return path is potentially introduced (through the beam) which may introduce Lorentz force if the DC in this extra return path interacts with stray or Earth magnetic field. Better not to have it.
I rebuilt the torsional pendulum support in preparation for the new 30W amplifier and electronics. The structure is now entirely 3"x3"x1/8" aluminum square tube and 1/4" stainless steel bolts. It is also 10 inches shorter. With the center of gravity lower, and the more robust materials, it is the most stable it has ever been by far. The dampening paddle was also improved.
All electronics and batteries will be mounted on the left side of the pendulum center, the same side the frustum is mounted. I will get started on that tomorrow. 
Thank you. Looks like a solid build. However, There is a potential problem. The frustum is likely grounded to the beam from those two bolts. If so, an extra DC return path is potentially introduced (through the beam) which may introduce Lorentz force if the DC in this extra return path interacts with stray or Earth magnetic field. Better not to have it.
Should not all power to the frustum in Monomorphic's design be in ghz, rather than DC? He is not mounting a magnetron on the frustum. So all DC power currents should be between the battery(s), signal generator and maybe amp, but from there microwave frequency by coax to the antenna, inside the frustum. Even induced currents in the frustum walls would be mirroring the AC profile of the resonanting microwaves. Wouldn't that even make any current flow between the frustum and any ground, again an AC mirror of the resonating microwaves?
But I may just be naive about it all, as I have always been more interested in, on and over the edge theory, rather than the nuts and bolts of RF.
I rebuilt the torsional pendulum support in preparation for the new 30W amplifier and electronics. The structure is now entirely 3"x3"x1/8" aluminum square tube and 1/4" stainless steel bolts. It is also 10 inches shorter. With the center of gravity lower, and the more robust materials, it is the most stable it has ever been by far. The dampening paddle was also improved.
All electronics and batteries will be mounted on the left side of the pendulum center, the same side the frustum is mounted. I will get started on that tomorrow. 
Thank you. Looks like a solid build. However, There is a potential problem. The frustum is likely grounded to the beam from those two bolts. If so, an extra DC return path is potentially introduced (through the beam) which may introduce Lorentz force if the DC in this extra return path interacts with stray or Earth magnetic field. Better not to have it.
Should not all power to the frustum in Monomorphic's design be in ghz, rather than DC? He is not mounting a magnetron on the frustum. So all DC power currents should be between the battery(s), signal generator and maybe amp, but from there microwave frequency by coax to the antenna, inside the frustum. Even induced currents in the frustum walls would be mirroring the AC profile of the resonanting microwaves. Wouldn't that even make any current flow between the frustum and any ground, again an AC mirror of the resonating microwaves?
But I may just be naive about it all, as I have always been more interested in, on and over the edge theory, rather than the nuts and bolts of RF.
You have DC supply to the signal generator and the Amp. The DC needs to go back to the battery after it leaves the amp. Of cause there is the negative lead for DC to return. But if Amp is grounded to the beam, and if battery is grounded to the beam too, there is another path for DC to return. If the frustum is grounded too, there is the third path for DC to return. NASA's 2014 experiment had this problem. Better not to allow those extra return paths to exist. Even if the battery is not ground, if the signal generator is grounded, AMP negative lead->RF cable shield->frustum->beam->signal generator grounding->battery is still a likely return path. Many people do not pay attention to this problem, including experienced electrical engineers. I am aware of it only because I make DIY tube amplifiers and I was stung once by ground loops picking up noise.
I rebuilt the torsional pendulum support in preparation for the new 30W amplifier and electronics. The structure is now entirely 3"x3"x1/8" aluminum square tube and 1/4" stainless steel bolts. It is also 10 inches shorter. With the center of gravity lower, and the more robust materials, it is the most stable it has ever been by far. The dampening paddle was also improved.
All electronics and batteries will be mounted on the left side of the pendulum center, the same side the frustum is mounted. I will get started on that tomorrow. 
Good job Monomorphic. I am sure a lot of people can't wait to see the results of your new build. There is always excitement when you post new progress. It is great that you are sharing the details of your work with the community.
I rebuilt the torsional pendulum support in preparation for the new 30W amplifier and electronics. The structure is now entirely 3"x3"x1/8" aluminum square tube and 1/4" stainless steel bolts. It is also 10 inches shorter. With the center of gravity lower, and the more robust materials, it is the most stable it has ever been by far. The dampening paddle was also improved.
All electronics and batteries will be mounted on the left side of the pendulum center, the same side the frustum is mounted. I will get started on that tomorrow. 
Fine!
Let's see the results with good-quality spherical ends. I think the inertial-gravitational phenomenon were optical (due to radiation rays), if real, and the Q could have been little biased, you remember, but let's see...
I rebuilt the torsional pendulum support in preparation for the new 30W amplifier and electronics. The structure is now entirely 3"x3"x1/8" aluminum square tube and 1/4" stainless steel bolts. It is also 10 inches shorter. With the center of gravity lower, and the more robust materials, it is the most stable it has ever been by far. The dampening paddle was also improved.
All electronics and batteries will be mounted on the left side of the pendulum center, the same side the frustum is mounted. I will get started on that tomorrow. 
Fantastic Jamie - Outstanding Build!!!
One question - and I may have missed this in speed reading the last month or so of threads, if I did my apologies - are you planning on opening the thruster up and inspecting the copper coating between power levels as you go through your test program. I am hoping your approach for coating the inside of the printed frustum is successful but if it does have problems it will be useful to know the power level where said problems appeared.
Good Luck with your tests !!! Can't wait to see the results.
graybeardsyseng
Herman
I rebuilt the torsional pendulum support in preparation for the new 30W amplifier and electronics. The structure is now entirely 3"x3"x1/8" aluminum square tube and 1/4" stainless steel bolts. It is also 10 inches shorter. With the center of gravity lower, and the more robust materials, it is the most stable it has ever been by far. The dampening paddle was also improved.
All electronics and batteries will be mounted on the left side of the pendulum center, the same side the frustum is mounted. I will get started on that tomorrow. 
Thank you. Looks like a solid build. However, There is a potential problem. The frustum is likely grounded to the beam from those two bolts. If so, an extra DC return path is potentially introduced (through the beam) which may introduce Lorentz force if the DC in this extra return path interacts with stray or Earth magnetic field. Better not to have it.
Should not all power to the frustum in Monomorphic's design be in ghz, rather than DC? He is not mounting a magnetron on the frustum. So all DC power currents should be between the battery(s), signal generator and maybe amp, but from there microwave frequency by coax to the antenna, inside the frustum. Even induced currents in the frustum walls would be mirroring the AC profile of the resonanting microwaves. Wouldn't that even make any current flow between the frustum and any ground, again an AC mirror of the resonating microwaves?
But I may just be naive about it all, as I have always been more interested in, on and over the edge theory, rather than the nuts and bolts of RF.
You have DC supply to the signal generator and the Amp. The DC needs to go back to the battery after it leaves the amp. Of cause there is the negative lead for DC to return. But if Amp is grounded to the beam, and if battery is grounded to the beam too, there is another path for DC to return. If the frustum is grounded too, there is the third path for DC to return. NASA's 2014 experiment had this problem. Better not to allow those extra return paths to exist. Even if the battery is not ground, if the signal generator is grounded, AMP negative lead->RF cable shield->frustum->beam->signal generator grounding->battery is still a likely return path. Many people do not pay attention to this problem, including experienced electrical engineers. I am aware of it only because I make DIY tube amplifiers and I was stung once by ground loops picking up noise.
Ground loops are often very challenging to find and eliminate. I fight noise and hum in audio and rf systems all the time. Here are a few links with some data which has been helpful to me -
http://web.mit.edu/jhawk/tmp/p/EST016_Ground_Loops_handout.pdfhttp://arrakis-systems.com/pdfs/installgroundloops.pdfsome of my favorites
http://kc.flexradio.com/knowledgebasearticle50426.aspxhttps://hackaday.com/2017/03/09/wtf-are-ground-loops/http://www.epanorama.net/documents/groundloop/BTW - LED lights are frequently a BAD source of electrical noise. . . not a specific ground loop problem but often impress noise that is hard to eliminate or which will camouflage other noise sources. I love LED lights but in some situations I have to retrograde to old fashioned (but quiet) inky (incandescent) light sources.
graybeardsyseng
The frustum is likely grounded to the beam from those two bolts. If so, an extra DC return path is potentially introduced (through the beam) which may introduce Lorentz force if the DC in this extra return path interacts with stray or Earth magnetic field. Better not to have it.
That is a very easy fix. Simple to use non-conductive bolts or to remove the tiny portion of the copper foil that is touching the current brass bolts.
One question - and I may have missed this in speed reading the last month or so of threads, if I did my apologies - are you planning on opening the thruster up and inspecting the copper coating between power levels as you go through your test program. I am hoping your approach for coating the inside of the printed frustum is successful but if it does have problems it will be useful to know the power level where said problems appeared.
I will definitely open up the cavity for inspections. That is a pretty simple task since the end-plates are bolted on, not soldered. In fact, I did open up the flat end-plate frustum recently and noticed some strange markings on the large end-plate copper. First thought was arcing, but I have so far only put 5W into that cavity. Second thought is a splatter of some liquid chemical that etched the pattern. I'm not sure how to tell the difference.
I rebuilt the torsional pendulum support in preparation for the new 30W amplifier and electronics. The structure is now entirely 3"x3"x1/8" aluminum square tube and 1/4" stainless steel bolts. It is also 10 inches shorter. With the center of gravity lower, and the more robust materials, it is the most stable it has ever been by far. The dampening paddle was also improved.
All electronics and batteries will be mounted on the left side of the pendulum center, the same side the frustum is mounted. I will get started on that tomorrow. 
Thank you. Looks like a solid build. However, There is a potential problem. The frustum is likely grounded to the beam from those two bolts. If so, an extra DC return path is potentially introduced (through the beam) which may introduce Lorentz force if the DC in this extra return path interacts with stray or Earth magnetic field. Better not to have it.
Should not all power to the frustum in Monomorphic's design be in ghz, rather than DC? He is not mounting a magnetron on the frustum. So all DC power currents should be between the battery(s), signal generator and maybe amp, but from there microwave frequency by coax to the antenna, inside the frustum. Even induced currents in the frustum walls would be mirroring the AC profile of the resonanting microwaves. Wouldn't that even make any current flow between the frustum and any ground, again an AC mirror of the resonating microwaves?
But I may just be naive about it all, as I have always been more interested in, on and over the edge theory, rather than the nuts and bolts of RF.
You have DC supply to the signal generator and the Amp. The DC needs to go back to the battery after it leaves the amp. Of cause there is the negative lead for DC to return. But if Amp is grounded to the beam, and if battery is grounded to the beam too, there is another path for DC to return. If the frustum is grounded too, there is the third path for DC to return. NASA's 2014 experiment had this problem. Better not to allow those extra return paths to exist. Even if the battery is not ground, if the signal generator is grounded, AMP negative lead->RF cable shield->frustum->beam->signal generator grounding->battery is still a likely return path. Many people do not pay attention to this problem, including experienced electrical engineers. I am aware of it only because I make DIY tube amplifiers and I was stung once by ground loops picking up noise.
I was only questioning what kind of ground loop might exist between the frustum and ground. The comment I was responding to suggested problems with a DC ground loop and it seemed(s) to me that any grounded current from the frustum in Monomorphic's build would be an AC current. Am I wrong in assuming that even though that might result in some noise, it would not creat the same issues that a DC current ground might.
In any case, once again Monomorphic has already addressed a fix.
There is another random thought that since we (meaning those actually doing the work) haven't yet confirmed thrust in a reproducible and controlled build, there is no way to know whether grounding the frustum might be necessary to achieve thrust. No matter what the mechanism of thrust turns out to be.
If it is easy to isolate the frustum from ground in Monomorphic's build, maybe it would be best to run the tests first with a ground and then without.
Am I wrong in assuming that an AC current to ground would not create the same issue that a DC ground current would?
I have to ask a question here since I have been locked out.
With reference to the Newton's cradle, if I have a five ball Newton's cradle and I lift two balls and then let them go, what will happen when the two balls collide with the three remaining balls?
I have to ask a question here since I have been locked out.
With reference to the Newton's cradle, if I have a five ball Newton's cradle and I lift two balls and then let them go, what will happen when the two balls collide with the three remaining balls?
If the balls are two on a side, it will go three-two-three-two until it stops and the energy is converted to heat and other losses. If the balls are on each end, they will each bounce while the three stand still until the energy is lost.
I never stated it was a violation. But if you read all their works you will see that the momentum of the field matches the momentum gained by the object under the Lorentz force, I.e. the forces are large and there is no mechanism which necessarily reduces the action of the force to the low level of the photon rocket.
Actually, I saw no calculation of the energy required, so this statement is baseless.
So, the assumption it can be no better than a photon rocket may be challenged as the fields are not simple plane waves.
No, the energy/momentum relation is general, not strictly for plain waves. In addition to being something directly in electrodynamics, energy/momentum relations for massless particles are enforced by special relativity as well.
But the issue really isn't their model of momentum conservation but their model of Lorentz force generation. They might be right about that and wrong about how the momentum is conserved.
...
p.s. One of the authors, Yahalom, is affiliated with the Isaac Newton Institute at Cambridge so he might be considered somewhat of an expert on the Third Law and momentum conservation
Do you like countering your own points?
I believe they indirectly argue the field momentum is much larger than a photon rocket equivalent
I do not see them claiming this.
In the paper they calculate the force as around 2 Newtons, not 2 micro Newtons which isn't consistent with being supported by the field momentum at the energy levels they give which are implied by the currents they use. That implies they believe the fields can carry that large amount of momentum away. Perhaps a better argument would be to just claim that if Newton's Third Law is violated, the net force by definition is an external force and thus they don't need to discuss momentum conservation at all. 
Yes, I did seem to counter my own point but I'm not trying to win an argument or debate but just to discuss this interesting topic. 
I worked all this out for myself using MathCAD about 20 years ago. Based on this sheet, they are only considering the current in the pair of wires "I1I2". What is not shown is the voltage, capacitance, charge and electric field at the ends of those wires when the current goes to zero. The force due to charges and electric fields will oppose the force due to currents and magnetic fields. When both are included, the 2N of force is suddenly < 2uN and we are back to the thrust of a photon rocket. If the system is large, it could oscillate back and force at a relatively low frequency with much greater force, but the CM will not move except for the asymmetry in the EM radiation, (aka photon rocket).
I don't know your setup and your assumptions for that calculation but if you are trying to say anytime you switch it off it exactly must cancel out the well known Lorentz force, and under any conceivable configuration of times and currents and geometries, I'm very dubious and would have to see the details. I'm not saying your calculation didn't do that but were you specifically messing with conditions to make the events in each wire spacelike wrt each other?
Specifically, the Third Law can break down in specific circumstances precisely because the speed of light is finite and events can have a spacelike separation even while they are being independently controlled faster than light can mediate between the interaction between them. Pulses can be independently designed and arranged that compliment the net forces and counter unwanted forces. For example, the field from pulse in one wire might cause a force in a distant wire in such a way that there is no ability for a counter force to even exist on the first wire. That spacelike separation and control could include unwanted electrical effects through proper design. Though technically challenging, that breaks the symmetry and opens up new possibilities.
A couple more points. The wires here are loops so they have no ends. If you are saying switching on and off counters the Lorentz force, I believe the switching times can be engineered much smaller than the steady pulse times where the Lorentz force acts to mitigate those forces while preserving the criteria suggested above.
I have my own configuration in mind which I would like to simulate with a 3D dynamic simulator that has the full Maxwell equations. It should be able to handle picosecond resolution in a volume of a few cubic cm. Do you have any thoughts about that? Thanks.
I have to ask a question here since I have been locked out.
With reference to the Newton's cradle, if I have a five ball Newton's cradle and I lift two balls and then let them go, what will happen when the two balls collide with the three remaining balls?
If the balls are two on a side, it will go three-two-three-two until it stops and the energy is converted to heat and other losses. If the balls are on each end, they will each bounce while the three stand still until the energy is lost.
Exactly, two balls must come out. If one ball comes out at twice the velocity then we conserve momentum but not kinetic energy.
So next question: Is conservation of energy the stronger law or does nature treat momentum and energy as the same?