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#2840 by mwvp on 14 Feb, 2016 00:33
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...In this paper, in 2014, the author notes
Quotethat the Yang-Mills equations describe the behavior of dark energy equation of state with a given type under certain restrictions imposed by the gauge symmetry.
Uhm, I don't suppose there's any such thing as "Yang-Mills Theory for Big Dummies", is there?..
Although (as noted in my post above) I don't follow why he only considered the time derivative of the Poynting vector field (the second term in the equation below) in his force consideration and did not consider the stress tensor (the first term in the equation below)
You seem very fond of the stress tensor. Isn't that based on the Poynting vector? If I want to calculate the radiation pressure in an ideal cavity resonator with static energy, isn't the Poynting vector enough? -
#2841 by Rodal on 14 Feb, 2016 01:01
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No, they are completely different quantities. Although in free space, the pressure from a plane electromagnetic wave (which is itself an idealization) hitting normal to a surface can be obtained from the average Poynting vector,..
Although (as noted in my post above) I don't follow why he only considered the time derivative of the Poynting vector field (the second term in the equation below) in his force consideration and did not consider the stress tensor (the first term in the equation below)
You seem very fond of the stress tensor. Isn't that based on the Poynting vector? If I want to calculate the radiation pressure in an ideal cavity resonator with static energy, isn't the Poynting vector enough?
in a cavity one cannot use that idealized approximation because in a cavity instead one has oblique incidence of polarized waves that are not plane electromagnetic waves in free space, instead one has TE transverse electric modes and TM transverse magnetic mode shapes.
The stress tensor is a second order tensor representing force per unit area, the components normal to the surface of the unit cube represent pressure (or tension) and the off-diagonal matrix components represent surface shears on the unit cube.
The Poynting vector is of course a vector representing the rate of energy transfer per unit area.
Both of them belong in the momentum conservation equation.
where (*):
f = force per unit volume
σ = stress tensor
where ⊗ is the dyadic product (http://web.stanford.edu/class/me331b/documents/VectorBasisIndependent.pdf)
∇ = divergence
S = Poynting vector
where x is the vector cross product
Notice that the cross product is different than the dyadic product and that one cannot calculate the stress tensor based on the Poynting vector. To calculate the stress tensor one must have full knowledge of three vector components of the E field and all three components of the H vector field, so one must have full knowledge of all 6 components of the electromagnetic vector field of E and H.
Asking somebody why they forgot to include the stress in an equation does not mean special fondness for stresses
, it just means that you cannot solve the equations of equilibrium entirely in terms of energy. Conservation of momentum demands that both (divergence of) stress and (rate of change of) Poynting vector be taken into account, otherwise one is going to calculate an incorrect imbalance force that is completely fictitious.
_____________
(*) To calculate the force one must integrate these equations over the volume and use the divergence theorem.
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#2842 by Rodal on 14 Feb, 2016 02:20
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Unfortunately, the answer is no. Even more, there is controversy about the Wikipedia article on Yang Mills and simplified explanations of Yang Mills....In this paper, in 2014, the author notes
Quotethat the Yang-Mills equations describe the behavior of dark energy equation of state with a given type under certain restrictions imposed by the gauge symmetry.
Uhm, I don't suppose there's any such thing as "Yang-Mills Theory for Big Dummies", is there?
...
The reason is that there is not one theory of Yang-Mill, but there are several possible such theories . They differ upon the gauge group under consideration. Yang-Mills theories are an example of gauge theory, but not all gauge theories are Yang-Mills theories.
One can quantize Yang Mills theories and obtain specific quantum field theories. Quantum chromodynamics is a (quantized) Yang-Mills theory with coupling to certain fermions. -
#2843 by mwvp on 14 Feb, 2016 02:28
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...in a cavity one cannot use that idealized approximation because in a cavity instead one has oblique incidence of polarized waves that are not plane electromagnetic waves in free space.
The stress tensor is a second order tensor representing force per unit area, the components normal to the surface of the unit cube represent pressure (or tension) and the off-diagonal matrix components represent surface shears on the unit cube.
The Poynting vector is of course a vector representing the rate of energy transfer per unit area.
Both of them belong in the momentum conservation equation.
...
Asking somebody why they forgot to include the stress in an equation does not mean special fondness for stresses , it just means that you cannot solve the equations of equilibrium entirely in terms of energy. Conservation of momentum demands that both (divergence of) stress and (rate of change of) Poynting vector be taken into account, otherwise one is going to calculate an incorrect imbalance force that is completely fictitious.
Ok. Thanks a lot for the excellent definitions and amplification (again). After staring at them, and the Maxwell Stress Tensor Wikipedia page for the last half hour, I think I get it this time. It helps that I've been writing Matlab code and working with matrices this week. When you posted it a month ago, I thought it was some sort of relativistic formulation of electromagnetism and math foreign to my humble background. No excuses for my not bothering to check the units (force/area vs power/area), apologies.
Anyways, for our context, a microwave cavity sans electrostatic and magneto-static fields, I would expect the Poynting term to be significantly larger than the stress tensor contribution. Think so?
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#2844 by Rodal on 14 Feb, 2016 02:47
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For a resonant cavity with standing waves,averaged over a complete cycle each of the terms (taking the net resultant for the stress term) in the conservation of momentum equation are zero.
...in a cavity one cannot use that idealized approximation because in a cavity instead one has oblique incidence of polarized waves that are not plane electromagnetic waves in free space.
The stress tensor is a second order tensor representing force per unit area, the components normal to the surface of the unit cube represent pressure (or tension) and the off-diagonal matrix components represent surface shears on the unit cube.
The Poynting vector is of course a vector representing the rate of energy transfer per unit area.
Both of them belong in the momentum conservation equation.
...
Asking somebody why they forgot to include the stress in an equation does not mean special fondness for stresses , it just means that you cannot solve the equations of equilibrium entirely in terms of energy. Conservation of momentum demands that both (divergence of) stress and (rate of change of) Poynting vector be taken into account, otherwise one is going to calculate an incorrect imbalance force that is completely fictitious.
Anyways, for our context, a microwave cavity sans electrostatic and magneto-static fields, I would expect the Poynting term to be significantly larger than the stress tensor contribution. Think so?
For a transient problem in a cavity, there is no exact solution. Using Mathematica to post-process the results of Meep's trasient solution run by aero for a few cases, I did not find what you say to be the case.
What I found was that the Poynting vector field averaged over a cycle was increasing with time exponentially, therefore its time rate of change was also increasing exponentially and the stress terms were also increasing exponentially, and they were of commensurate magnitude.
Why would you expect the time rate of change term to be much larger than the divergence of the stress term?
If that would be the case, one would have a momentum imbalance under Maxwell's equations, but we know that Shawyer and Yang are wrong in thinking so (neglecting heat transfer) , considering the resonant cavity as a closed system, the net force must be zero and therefore for non-zero rate of change of the Poynting vector, the divergence of the stress term must be of equal magnitude so that they both add up to zero net force:
That's why Alexander Trunev invokes General Relativity and Yang Mills field in order to justify the EM Drive as an open system so that the force is non-zero. In essence Trunev, Minotti and White all invoke the Quantum Vacuum and General Relativity to justify the non-zero net force. They all agree that under Maxwell's equations the EM Drive would experience no anomalous force/power exceeding the one for a photon rocket. -
#2845 by ThinkerX on 14 Feb, 2016 03:07
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Quote
That's why Alexander Trunev invokes General Relativity and Yang Mills field in order to justify the EM Drive as an open system so that the force is non-zero. In essence Trunev, Minotti and White all invoke the Quantum Vacuum and General Relativity to justify the non-zero net force. They all agree that under Maxwell's equations the EM Drive would experience no anomalous force/power exceeding the one for a photon rocket.
Keeping in mind this is preliminary, and we have an uncertain translation of Trunev's paper...
Are Minotti's and Trunev's theories compatible? The 'thicker skin' test for Minotti's theory has been brought up now and again. (Something our DIY crowd should look into.) Would this test also be a way of investigating Trunev's theory?
Also, are the theories of Minotti and Trunev compatible with the 'bigger is better' frustum concept?
Is the 'Not-so-sure-of-it' theory compatible with those of Minotti and Trunev?
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#2846 by Rodal on 14 Feb, 2016 03:25
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I think that Trunev does not go into enough detail to be able to answer what is the effect of the copper wall thickness in his formulation.QuoteThat's why Alexander Trunev invokes General Relativity and Yang Mills field in order to justify the EM Drive as an open system so that the force is non-zero. In essence Trunev, Minotti and White all invoke the Quantum Vacuum and General Relativity to justify the non-zero net force. They all agree that under Maxwell's equations the EM Drive would experience no anomalous force/power exceeding the one for a photon rocket.
Keeping in mind this is preliminary, and we have an uncertain translation of Trunev's paper...
Are Minotti's and Trunev's theories compatible? The 'thicker skin' test for Minotti's theory has been brought up now and again. (Something our DIY crowd should look into.) Would this test also be a way of investigating Trunev's theory?
Also, are the theories of Minotti and Trunev compatible with the 'bigger is better' frustum concept?
Is the 'Not-so-sure-of-it' theory compatible with those of Minotti and Trunev?
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#2847 by Rodal on 14 Feb, 2016 03:34
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Trunov actually states that the Yang Mills field is very dependent on the position of the excitation source: at the small end (A), at the big end(B) or on the side surface (C) (and he shows the differences in his fig 6)Doc or others, cannot determine for sure, but these look like a large diameter, centered signal injection for this model. Am I correct? Cannot read the Russian paper or keys.
Regarding the position of the excitation, I don't see an answer to your question. He quotes the NASA Brady et.al.,
Brady D.A., White H.G., March P., Lawrence J.T., Davies F.J. Anomalous Thrust production from an RF Test Device Measured on Low-Thrust Torsion Pendulum, AIAA 2014-4029.
stating that according to the Brady report the anomalous force depends on the position of the antenna exciting the microwave resonance in the cavity, but he does not seem to discuss this issue any further than that.
Regarding the magnetron, he does make the point, early on in the paper that he does not make the assumption assumed by Greg Egan for example, of standing waves in the cavity. He does not even assume that the electric field E varies like a single sine in time and the magnetic field B like a single cosine in time (his equation number 4), but instead he points out that he uses his full equation number 2.
According to the figures below, the largest magnitude is achieved with the excitation source on the side surface conical walls of the frustum (C). The lowest magnitude is with the excitation source at the small end (A).
Back in August 2015 I used Mathematica to post-process the results from Meep run by aero for the excitation sources at the big end and at the small end of the frustum for NSF 1701 of rfmwguy and for a Yang-Shell model, and I recommended to position the excitation source at the big end and avoid placing it at the small end, which is consistent with Trunov's results (I used a different reason to recommend the placement at the big end: I used the distribution of the stress tensor for my recommendation). I did not analyze having the excitation source on the wall.
Trunov contrasts this with the Maxwell electromagnetic fields which he says are not that dependent on the position of the excitation source. -
#2848 by mwvp on 14 Feb, 2016 05:41
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Anyways, for our context, a microwave cavity sans electrostatic and magneto-static fields, I would expect the Poynting term to be significantly larger than the stress tensor contribution. Think so?
For a resonant cavity with standing waves,averaged over a complete cycle each of the terms (taking the net resultant for the stress term) in the conservation of momentum equation are zero.
For a transient problem in a cavity, there is no exact solution. Using Mathematica to post-process the results of Meep's trasient solution run by aero for a few cases, I did not find what you say to be the case.
What I found was that the Poynting vector field averaged over a cycle was increasing with time exponentially, therefore its time rate of change was also increasing exponentially and the stress terms were also increasing exponentially, and they were of commensurate magnitude.
Why would you expect the time rate of change term to be much larger than the divergence of the stress term?
Off the cuff, because the time rate of change is large, relative to the values of the E and B fields, and the energy stored. A few dozen volts, a few amps, in a (vacuum/air) medium of E 0 and Mu 0, even amplified by the cavity Q 3 orders of magnitude I doubted would much compare to the radiation pressure calculated from the Poynting vector, dS/dt, that allows a kilowatt to propagate or a megawatt to reverberate in the cavity at those volt and amp levels. Just because the time rate of change/frequency is so high relative to field divergence.
And I should have explicitly stated I had in mind the radiation pressure in a steady-state cavity, not an anomalous thrust or anisotropic momentum context.
I haven't seen the Maxwell stress divergence term used in an RF context often, in many texts and lectures, but the Poynting vector's role in radiation pressure always is. Except in the context of electrorheologic fluids and electroactive polymers I've read about Maxwell stress, but that's a quite different thing.
I'll write some more code this week and find out, be more rigorous, and stop blurting out vague notions. -
#2849 by StrongGR on 14 Feb, 2016 10:15
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Unfortunately, the answer is no. Even more, there is controversy about the Wikipedia article on Yang Mills and simplified explanations of Yang Mills....In this paper, in 2014, the author notes
Quotethat the Yang-Mills equations describe the behavior of dark energy equation of state with a given type under certain restrictions imposed by the gauge symmetry.
Uhm, I don't suppose there's any such thing as "Yang-Mills Theory for Big Dummies", is there?
...
The reason is that there is not one theory of Yang-Mill, but there are several possible such theories . They differ upon the gauge group under consideration. Yang-Mills theories are an example of gauge theory, but not all gauge theories are Yang-Mills theories.
One can quantize Yang Mills theories and obtain specific quantum field theories. Quantum chromodynamics is a (quantized) Yang-Mills theory with coupling to certain fermions.
Yang-Mills theory are completely out of place here. Yang-Mills theories tend to form a mass gap at low energies making them short ranged. Indeed, they work for strong interactions and electroweak interactions. They arise with a gauge group that can be commutative or not. In the former case one recovers an electromagnetic-like theory without self-interaction. You have no more the problem of the mass gap but it is a kind of well-known long-ranged theory.
Finally, gravitational waves are transverse waves not longitudinal. -
#2850 by QuantumG on 14 Feb, 2016 10:27
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Thomas A. Garrity has a nice book on guage theory for mathematicians and another book on grad level math for those who missed it. They're both fun reads.
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#2851 by cee on 14 Feb, 2016 14:50
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Good news, Dr. Trunev responded to an email regarding the availability of an English translation of his papers and kindly responded.QuoteThat's why Alexander Trunev invokes General Relativity and Yang Mills field in order to justify the EM Drive as an open system so that the force is non-zero. In essence Trunev, Minotti and White all invoke the Quantum Vacuum and General Relativity to justify the non-zero net force. They all agree that under Maxwell's equations the EM Drive would experience no anomalous force/power exceeding the one for a photon rocket.
Keeping in mind this is preliminary, and we have an uncertain translation of Trunev's paper...
Are Minotti's and Trunev's theories compatible? The 'thicker skin' test for Minotti's theory has been brought up now and again. (Something our DIY crowd should look into.) Would this test also be a way of investigating Trunev's theory?
Also, are the theories of Minotti and Trunev compatible with the 'bigger is better' frustum concept?
Is the 'Not-so-sure-of-it' theory compatible with those of Minotti and Trunev?
"thank you for your interest in my article GENERAL RELATIVITY AND THEORY OF ELECTROMAGNETIC DRIVE published on http://ej.kubagro.ru/2015/10/pdf/61.pdf. I recommend also to read the second article on this subject THEORY OF ELECTROMAGNETIC DRIVE WITH ELEMENTARY PARTICLES CURRENT AND VACUUM POLARIZATION on http://ej.kubagro.ru/2016/01/pdf/80.pdf
I will prepare an English translation of these two articles and publish in the next issue of the magazine in the form of an article with the addition of new results."
Thank you,
Alexander Trunev
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#2852 by glennfish on 14 Feb, 2016 15:07
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Good news, Dr. Trunev responded to an email regarding the availability of an English translation of his papers and kindly responded.QuoteThat's why Alexander Trunev invokes General Relativity and Yang Mills field in order to justify the EM Drive as an open system so that the force is non-zero. In essence Trunev, Minotti and White all invoke the Quantum Vacuum and General Relativity to justify the non-zero net force. They all agree that under Maxwell's equations the EM Drive would experience no anomalous force/power exceeding the one for a photon rocket.
Keeping in mind this is preliminary, and we have an uncertain translation of Trunev's paper...
Are Minotti's and Trunev's theories compatible? The 'thicker skin' test for Minotti's theory has been brought up now and again. (Something our DIY crowd should look into.) Would this test also be a way of investigating Trunev's theory?
Also, are the theories of Minotti and Trunev compatible with the 'bigger is better' frustum concept?
Is the 'Not-so-sure-of-it' theory compatible with those of Minotti and Trunev?
"thank you for your interest in my article GENERAL RELATIVITY AND THEORY OF ELECTROMAGNETIC DRIVE published on http://ej.kubagro.ru/2015/10/pdf/61.pdf. I recommend also to read the second article on this subject THEORY OF ELECTROMAGNETIC DRIVE WITH ELEMENTARY PARTICLES CURRENT AND VACUUM POLARIZATION on http://ej.kubagro.ru/2016/01/pdf/80.pdf
I will prepare an English translation of these two articles and publish in the next issue of the magazine in the form of an article with the addition of new results."
Thank you,
Alexander Trunev
That's going to make TT smile a bit.
" It is found that the pulse modulation greatly improves the efficiency of conversion of electromagnetic energy into thrust. " -
#2853 by Rodal on 14 Feb, 2016 15:31
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Unfortunately, the answer is no. Even more, there is controversy about the Wikipedia article on Yang Mills and simplified explanations of Yang Mills....In this paper, in 2014, the author notes
Quotethat the Yang-Mills equations describe the behavior of dark energy equation of state with a given type under certain restrictions imposed by the gauge symmetry.
Uhm, I don't suppose there's any such thing as "Yang-Mills Theory for Big Dummies", is there?
...
The reason is that there is not one theory of Yang-Mill, but there are several possible such theories . They differ upon the gauge group under consideration. Yang-Mills theories are an example of gauge theory, but not all gauge theories are Yang-Mills theories.
One can quantize Yang Mills theories and obtain specific quantum field theories. Quantum chromodynamics is a (quantized) Yang-Mills theory with coupling to certain fermions.
Yang-Mills theory are completely out of place here. Yang-Mills theories tend to form a mass gap at low energies making them short ranged. Indeed, they work for strong interactions and electroweak interactions. They arise with a gauge group that can be commutative or not. In the former case one recovers an electromagnetic-like theory without self-interaction. You have no more the problem of the mass gap but it is a kind of well-known long-ranged theory.
Finally, gravitational waves are transverse waves not longitudinal.
Thank you. Without any objection to the above statements, trying to understand (*) what Trunov may specifically have had in mind when using Yang Mills theory, the following may be of interest :Quote from: TrunovIt is known that Yang-Mills theory is the basic model for quantum chromodynamics, and Einstein's theory is the basic model for a quantum theory of gravity [7-8]. In this and in the other case there is a problem of quantization due to the nonlinearity of the models [45]. The above theory allows us to combine the Yang-Mills theory and Einstein's theory in solving the problem of quantization. This kind of association may be based on the metric (17) with the field equations of mixed type and the equation of state, permitting and singular solutions of the type of geon, and solutions of the type (32). This approach allows capturing the diversity of matter, which produces nature.
In other words, it appears that what he has in mind is combining the Yang-Mills theory and Einstein's theory in solving the problem of unification, in his previous papers on this subject.
Regarding gravitational waves, trying to understand what Trunov has in mind (*), as an example he mentions his formulation permits solutions of the geon type:
(a geon is an electromagnetic-gravitational wave which is held together in a confined region by the gravitational attraction of its own field energy. They were first investigated theoretically in 1955 by J. A. Wheeler, who coined the term as a contraction of "gravitational electromagnetic entity"QuoteAssociated with an electromagnetic disturbance is a mass, the gravitational attraction of which under appropriate circumstances is capable of holding the disturbance together for a time long in comparison with the characteristic periods of the system. Such gravitational-electromagnetic entities, or "geons"; are analyzed via classical relativity theory...Conclusions: the geon completes the scheme of classical physics; one's interest in following geons into quantum domain will depend upon one's view of the relation between very small geons and elementary particles.
)
Geons
John Archibald Wheeler
Phys. Rev. 97, 511 – Published 15 January 1955
http://journals.aps.org/pr/abstract/10.1103/PhysRev.97.511
Are geons a viable entity?
Stability of gravitational and electromagnetic geons
G P Perry and F I Cooperstock
Classical and Quantum Gravity, Volume 16, Number 6
http://arxiv.org/pdf/gr-qc/9810045
____________________________________
(*) There are several things I don't follow in his paper, starting with why he only considers the time rate of change of the Poynting vector as giving a force and does not consider the divergence of stress term in the momentum conservation equation -
#2854 by glennfish on 14 Feb, 2016 16:05
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#2855 by Rodal on 14 Feb, 2016 16:56
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Thank you for taking the initiative to privately contact Dr. Trunev. Much appreciated !
Good news, Dr. Trunev responded to an email regarding the availability of an English translation of his papers and kindly responded.QuoteThat's why Alexander Trunev invokes General Relativity and Yang Mills field in order to justify the EM Drive as an open system so that the force is non-zero. In essence Trunev, Minotti and White all invoke the Quantum Vacuum and General Relativity to justify the non-zero net force. They all agree that under Maxwell's equations the EM Drive would experience no anomalous force/power exceeding the one for a photon rocket.
Keeping in mind this is preliminary, and we have an uncertain translation of Trunev's paper...
Are Minotti's and Trunev's theories compatible? The 'thicker skin' test for Minotti's theory has been brought up now and again. (Something our DIY crowd should look into.) Would this test also be a way of investigating Trunev's theory?
Also, are the theories of Minotti and Trunev compatible with the 'bigger is better' frustum concept?
Is the 'Not-so-sure-of-it' theory compatible with those of Minotti and Trunev?
"thank you for your interest in my article GENERAL RELATIVITY AND THEORY OF ELECTROMAGNETIC DRIVE published on http://ej.kubagro.ru/2015/10/pdf/61.pdf. I recommend also to read the second article on this subject THEORY OF ELECTROMAGNETIC DRIVE WITH ELEMENTARY PARTICLES CURRENT AND VACUUM POLARIZATION on http://ej.kubagro.ru/2016/01/pdf/80.pdf
I will prepare an English translation of these two articles and publish in the next issue of the magazine in the form of an article with the addition of new results."
Thank you,
Alexander Trunev
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#2856 by Rodal on 14 Feb, 2016 17:41
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Hot from the Reddit online library.
The paper's contribution is that it allows evanescent wave solutions to occur inside the EM Drive cavity, apparently even under Shawyer's prescription forbidding small end diameters smaller than the one for cutoff of a cylindrical waveguide of the same diameter.
http://arxiv.org/pdf/1509.02603v1.pdf
However, assuming that such evanescent waves inside the EM Drive would indeed be possible, the Lorentz force that the author addresses cannot by itself result in self-acceleration of the EM Drive:
1) One cannot move a spacecraft's center of mass by banging on the wall of the spacecraft, moving the furniture to one corner or emitting waves inside one end of the spacecraft. One must actually eject mass or energy out of the spacecraft to move the center of mass.
2) The author's Lorentz force equation is written for a particle of electric charge q. Even if there would be such particles with charge q inside the EM Drive cavity (which the author never justifies), if they are inside, and they are not emitted outside the cavity, this cannot result in moving the spacecraft center of mass. For his Lorentz force equation to allow self-acceleration, there would need to be an outside field interaction, a field that would penetrate the copper walls of the EM Drive. What field would that be? The author does not begin to address this problem.
Hence, unless mass or energy is emitted out of the EM Drive or somehow it couples with an external field (in which case it would become an open system), internal evanescent waves would not allow self-acceleration of the EM Drive, and such solution (although interesting for other applications) does not seem to advance the state of discourse on the EM Drive conundrum. -
#2857 by rfmwguy on 14 Feb, 2016 17:44
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Paper read a couple of times. My take is yang-mills perhaps allows an opening IF macroscopic scaling is possible. His suggestion for more experimental evidence helps the cause. Best paper I've read on possible explanation, certainly worthwhile for institutional investigation. Geons, huh? Interesting find, doc. Now, if your institutional thread gets read by the right people...you might have helped get this thing moving in the right direction.
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#2858 by ThinkerX on 14 Feb, 2016 20:22
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Point of clarification:
Yang-Mills theory. Is Yang the same Yang behind the Chinese EM Drive experiments?
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#2859 by QuantumG on 14 Feb, 2016 20:26
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Point of clarification:
Yang-Mills theory. Is Yang the same Yang behind the Chinese EM Drive experiments?
No. https://en.wikipedia.org/wiki/Chen-Ning_Yang
, it just means that you cannot solve the equations of equilibrium entirely in terms of energy. Conservation of momentum demands that both (divergence of) stress and (rate of change of) Poynting vector be taken into account, otherwise one is going to calculate an incorrect imbalance force that is completely fictitious.