I understand that some here may not like this information but is it what it is.
The Traveller,
According to the two previous pages, it seems that:
1) you still base your understanding of the propellantless propulsion effect of the EmDrive in the same origin as Shawyer's, i.e. the existence of a force resulting from a non-zero sum of all radiation pressures upon materials within the cavity.
but:
2) you however now refute Shawyer's claim that the radiation pressure is greater at the big end, saying it would be the opposite: that the radiation pressures on side walls + small end combined are greater than the radiation pressure on the wide end, resulting in the EmDrive being pushed by this forward radiation pressure, small end leading. So no more invisible "thrust force" directed in the opposite, rear direction without matter ejected, that Shawyer yet introduced to try to mimic his system with classical Newtonian action-reaction.
You argue based on the momentum exchange with all walls and the photon incident angle varying across the tapered section.
Shawyer bases his "EmDrive theory" on Cullen's experiments and his 1952 paper, extrapolating measurement made with open cylindrical waveguides to tapered closed cavities, since he assumes that a closed tapered cavity is the same as a series of many shallow cylindrical open waveguides of decreasing diameter connected the one after the others (from the point of view of travelling waves, hence a pulsed operation).
Therefore Shawyer claims that the radiation pressure (and the group velocity) of microwaves is greater on the big end of the EmDrive than on the small end, which seems sound, but doing so he may neglect the wall component, which should add and sum up to zero (he claims this zero sum is indeed the case for a standing wave, but not for travelling waves).
Cullen showed (eq. 15 in his paper) that:
F = 2P/c ( λ / λg )
Since λ < λg (always) and the smaller the waveguide diameter, the longer the guide wavelength λg, it is easy to show that the force due to the radiation pressure of microwaves at the same input power acting on a plate in a wider waveguide is greater than the force acting on a plate in a narrow waveguide.
So do you now disagree with Cullen; or do you agree with him but saying instead that what is going on in open cylindrical waveguides cannot be extrapolated to closed tapered cavities?

The Traveller,
According to the two previous pages, it seems that:
1) you still base your understanding of the propellantless propulsion effect of the EmDrive in the same origin as Shawyer's, i.e. the existence of a force resulting from a non-zero sum of all radiation pressures upon materials within the cavity.
but:
2) you however now refute Shawyer's claim that the radiation pressure is greater at the big end, saying it would be the opposite: that the radiation pressures on side walls + small end combined are greater than the radiation pressure on the wide end, resulting in the EmDrive being pushed by this forward radiation pressure, small end leading. So no more invisible "thrust force" directed in the opposite, rear direction without matter ejected, that Shawyer yet introduced to try to mimic his system with classical Newtonian action-reaction.
You argue based on the momentum exchange with all walls and the photon incident angle varying across the tapered section.
Shawyer bases his "EmDrive theory" on Cullen's experiments and his 1952 paper, extrapolating measurement made with open cylindrical waveguides to tapered closed cavities, since he assumes that a closed tapered cavity is the same as a series of many shallow cylindrical open waveguides of decreasing diameter connected the one after the others (from the point of view of travelling waves, hence a pulsed operation).
Therefore Shawyer claims that the radiation pressure (and the group velocity) of microwaves is greater on the big end of the EmDrive than on the small end, which seems sound, but doing so he may neglect the wall component, which should add and sum up to zero (he claims this zero sum is indeed the case for a standing wave, but not for travelling waves).
Cullen showed (eq. 15 in his paper) that:
F = 2P/c ( λ / λg )
Since λ < λg (always) and the smaller the waveguide diameter, the longer the guide wavelength λg, it is easy to show that the force due to the radiation pressure of microwaves at the same input power acting on a plate in a wider waveguide is greater than the force acting on a plate in a narrow waveguide.
So do you now disagree with Cullen; or do you agree with him but saying instead that what is going on in open cylindrical waveguides cannot be extrapolated to closed tapered cavities?You should take the energy density per area into account. According to the work of Dr. Rodal we know that the field strength in the area of the smaller end plate is much larger than at the bigger plate. However, the total amount of incident power at the small end plate plus the equivalent vector component at conical sidewall should be the same per area unit squared, -F (small end plus sidewall vector component in this direction) +F (at the large plate), ...from a pure topological point of view.
https://forum.nasaspaceflight.com/index.php?action=dlattach;topic=37642.0;attach=1030954
However I think for traveling (reflected) waves there is a time related difference related to the reflection on both ends. I guess the reflection at the smaller side has a broad band characteristic compared to the big end. I.e. the wave is partly reflected before it reaches the small plate (partially earlier times). If the big end is flat there is also a phase dependent time dependent reflection involved. But for a proper curved big plate and a small end below cutoff the time difference of the reflected signal should be located at the small end. So maybe a time-delayed reflection of the incident wave at a undersized small end combined with a spherical big end plate leads to a nice net force because of the time delayed reflection at one end only?
Just a thought..
It is hard to think about such problems while the room temperature is still way over 30°C/86°F![]()
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You should take the energy density per area into account.
...
However I think for traveling (reflected) waves there is a time related difference related to the reflection on both ends.
...
So maybe a time-delayed reflection of the incident wave at a undersized small end combined with a spherical big end plate leads to a nice net force because of the time delayed reflection at one end only?
Just a thought..
It is hard to think about such problems while the room temperature is still way over 30°C/86°F![]()


So do you now disagree with Cullen; or do you agree with him but saying instead that what is going on in open cylindrical waveguides cannot be extrapolated to closed tapered cavities?
What I saying is you need to do a ray trace of the photon movement such that the superposition of their incident and reflected E fields, as they reflect off the walls and end plates, produces the E field lobes shown by various modeling software.
The electromagnetic force of each wall must be calculated according to Maxwell's equation, and the geometric vector calculations are all combined into zero.
You need to do one where reflected angle equals incident angle, basic optics.
Despite the path you drew being completely unphysical, if you do the momentum calculations correctly, accounting for the different angles at each reflection, and the fact that this would involve momentum transfer in a direction that is not perpendicular to the surface, you still will find no net force.
Your responsibility to provide these calculations though. You are the one claiming momentum can appear out of nowhere, you get to do the math behind your claim.
The shapes are due to the wave nature of photons and do not indicate a "typical path" the way you seem to be thinking. Go look up some diagrams of waves propagating in a waveguide to see some examples of how different lobes and photon travel path are. In a waveguide a frequency propagating at a steep angle with many bounces back and forth to move forward a little bit will appear to have lobes separated by large distances, since they correspond to one wavelength projected perpendicular to the direction of travel.
The electromagnetic force of each wall must be calculated according to Maxwell's equation, and the geometric vector calculations are all combined into zero.
This is perfectly true, but it only considers Maxwell and a steady-state situation. What about time dependance, delays, travelling waves associated to phenomena other than Maxwell as suggested by the posts of X_RaY and mwvp following ours?
Glad to see you understand why the guide wavelength increases and the group velocity decreases as the cavity diameter drops. At one time on this forum, that actuality would have brought howls of disbelief and denial.
Sure the angle of incidence equals the angle of emission. As the resultant radiation pressure from such side wall events is orthogonal to the side wall, the overall side wall radiation pressure is toward the small end.
You really sure the small end + side wall radiation pressure equals that on the big end?
Attached for your consideration.
Funny how the frustrum even looks like a rocket nozzle. Energy density decreases if work is done by the microwaves, accelerating the frustrum (forward), via Doppler-effect.
But you may say, the red-shift at the small-end is undone by the blue shift at the large-end? No, I think not!
............
Meberbs,
My dear soothsaying analyst,
Would you be so kind to put your comments into a mathematical form?
What might help to define is any invariance in the system such as volume, weight or charge.
The electromagnetic force of each wall must be calculated according to Maxwell's equation, and the geometric vector calculations are all combined into zero.
This is perfectly true, but it only considers Maxwell and a steady-state situation. What about time dependance, delays, travelling waves associated to phenomena other than Maxwell as suggested by the posts of X_RaY and mwvp following ours?
...
By the way mwvp, I always find your posts profoundly interesting (like notsosureofit's posts about dispersion). I don't get all your story about optomechanics, but as I have the feeling that there might be something down there, I regret that not many skilled people comment much on your ideas.
Funny how the frustrum even looks like a rocket nozzle. Energy density decreases if work is done by the microwaves, accelerating the frustrum (forward), via Doppler-effect.
But you may say, the red-shift at the small-end is undone by the blue shift at the large-end? No, I think not!
............
None of the arguments based on a direct transfer of momentum between photons (or EM waves) and the frustum are realistic...At the 1000 watts of a magnetron how much actual momentum potential do you believe that represents? No matter how you bounce the photons/waves around, invoking Doppler-effects and red/blues shifts, you cannot get more momentum potential than that initial 1000 watts of EM radiation.
There just isn’t any way that radiation or photon pressure can explain any useable anomalous force.... it just is not reasonable to believe the frustum—microwave relationship (based on bouncing photons) winds up a self contained perfect photon rocket. Let alone something better!
But you may say, the red-shift at the small-end is undone by the blue shift at the large-end? No, I think not!
A multi-mode cavity has more modes, density of states (in that foul tongue of QM which I abhor uttering) at the large end. More degrees of freedom. An increase in Entropy! Just like a heat engine.
None of the arguments based on a direct transfer of momentum between photons (or EM waves) and the frustum are realistic...At the 1000 watts of a magnetron how much actual momentum potential do you believe that represents? No matter how you bounce the photons/waves around, invoking Doppler-effects and red/blues shifts, you cannot get more momentum potential than that initial 1000 watts of EM radiation.
That's kind of fuzzy. Momentum depends on mass*velocity or field strength*wavelength. You're giving me an absolute rate of energy input, and leaving the mass issue out of the equation.
There just isn’t any way that radiation or photon pressure can explain any useable anomalous force.... it just is not reasonable to believe the frustum—microwave relationship (based on bouncing photons) winds up a self contained perfect photon rocket. Let alone something better!
It's very reasonable not to deduce the consequences of a dozen or so arcane and esoteric abstractions and principles. Alas, that I had the patience and eloquence.
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By the way mwvp, I always find your posts profoundly interesting (like notsosureofit's posts about dispersion). I don't get all your story about optomechanics, but as I have the feeling that there might be something down there, I regret that not many skilled people comment much on your ideas.
Thanks flux_capacitor. I grew weary of posting, wondering when something will come of this, some real news. Or an expert, waveguide microwave engineer would show up. I know there are other ways side-band heating/cooling, in Lorentz-invariant or Sagnac-like devices; molecular, chemical, laser, Peltier/electro-thermal, plasma, et. might be contrived.
It is rather frustrating to know, I'm practically certain, what's going on here. And nobody else seems to get it except, IMHO Traveller in some vague way. Others, maybe you and X-ray, with your sense of time-delay, understand that, in this Sagnac context, the speed of light is the speed of light and as you accelerate you shift freqquency, integrate the minute phase-shift with immense Q, exhaust low frequency as heat, and turn high frequency into frustrum momentum.
Here is the good news - we have a nozzle folks. It's called dispersion. It's highest on the phase-slope on the edge of the resonance curve. It in effect multiplies the beat frequency and momentum transfer.
See fig. 4 of "Measurement of Impulsive Thrust from a Closed Radio-Frequency Cavity in Vacuum", and on pg 3 reference to "phase angle quality factor".
Read what Bradshaw writes, pg 17 eq. 2.19: (group index = delta ln lambda / delta ln omega ) in
"Dispersion, controlled dispersion, and three applications" https://arxiv.org/abs/1005.5467
He describes the case where an interferometer has 100 x resolution with ng=100.
I read something very interesting in EW's latest paper @ http://arc.aiaa.org/doi/pdf/10.2514/1.B36120
pg. 3:
Quote
"The change in phase angle over frequency [dispersion!] was also calculated, and a new parameter dubbed the phase angle quality factor was developed to help quantify the characteristics of a given resonance condition. The phase angle quality factor was the change in phase angle over a given frequency range, and it was determined using the phase plot fromVNA and only considering the region of the steepest phase angle change centered on the resonance. Figure 4 depicts ...The bottom-left pane is the variation in phase angle for the system, and the bottom-right pane is the group delay.
The tuning study determined that, for this particular tapered test article, optimal thrust was present if the system had a quality factorat least several thousand and the maximum phase angle quality factor ["phase angle quality factor" - dispersion!] that could be achieved."
I've read there is a sort of privileged frame, and space, the vacuum itself is the road...
http://arxiv.org/pdf/0708.3519v4
Quote
"Consider that the vacuum medium is described by the vacuum states of
quantum fields and then its total momentum vanishes, it is reasonable for us to assume that
the vacuum medium as a whole is always resting with respect to all inertial observers. In
other words, the relative velocity between the vacuum medium and an arbitrary inertial
observer cannot be measured (i.e., it is an unobservable quantity), such that one can think it
always vanishes. On the other hand, consider that the velocity of light in vacuum is
invariant with respect to all inertial observers, and the eigenvalues of electron’s velocity
operator are equal to the velocity of light in vacuum, one can present the following
hypotheses: the velocity of light in vacuum ( 1 c = ) and the velocity of the vacuum medium
( ) are only two genuine velocities in our universe, they are invariant constants for all
inertial frames of reference; all other velocities are the apparent (or average) velocities of
massless fields moving in a zigzag manner. Such a zigzag motion, just as the
electromagnetic waves that are reflected back and forth by perfectly conducting walls as
they propagate along the length of a hollow waveguide, concerns two mutually orthogonal
0 u =
114D momentum components, i.e., a time-like 4D momentum (called the longitudinal
component) and a space-like 4D momentum (called the transverse component), respectively,
where the former corresponds to the usual 4D momentum of particles while the latter
contributes to the rest mass of particles."
According to: https://en.wikipedia.org/wiki/Dielectric_gas SF6 can get you 3 - 6 times 30kv/cm breakdown for air, and freon up to 17, pressurized.
Meberbs,
My dear soothsaying analyst,Please point to where I made any predictions of the future in this thread. Otherwise, please apologize for this insulting slander.Would you be so kind to put your comments into a mathematical form?
What might help to define is any invariance in the system such as volume, weight or charge.I have made specific mathematical statements many times. I have no idea what comments you are referring to here. If you think any statements I made were unclear due to some lack of statement of some assumption, please be specific as to what statements were unclear and what you don't understand about them.
But you may say, the red-shift at the small-end is undone by the blue shift at the large-end? No, I think not!
A multi-mode cavity has more modes, density of states (in that foul tongue of QM which I abhor uttering) at the large end. More degrees of freedom. An increase in Entropy! Just like a heat engine.The second statement literally does nothing to support your "No, I think not." It doesn't make the blue shift go away by some kind of magic. Entropy is not relevant to the discussion, since energy and momentum won't just appear out of nowhere just to make entropy increase. Nothing you are describing increases the density of states anyway.
What is frustrating is when people like you who apparently don't even know how to calculate momentum of an EM wave think they are somehow smarter than people who actually know what they are talking about. Try to recognize that maybe the reason that qualified people don't agree with you is because you are wrong.
