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#540 by StrongGR on 12 Sep, 2016 14:34
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Playing devil's advocate, the point of a locally varying constant in Brans-Dicke theory reminds me of a skeptical discussion I followed some time ago on another forum about Brans' view in 1962 (and what is understood nowadays from his view) stating that gravitational potential energy-momentum is not locally defined in Einstein's GR, because the Einstein stress-energy pseudotensor is not a covariant quantity, hence that no meaningful covariant values can be assigned locally to this quantity. That would be the main issue for the local aspects of Brans-Dicke theory related to the EmDrive.
But trying to avoid comparing apples and oranges leads to how φ is defined respectively in the Brans-Dicke theory, and Einstein's general theory of relativity. In The Meaning of Relativity, discussing 1916 GR, Einstein was talking specifically about gtt/2 as the GR version of the Newtonian potential φ. But Brans-Dicke φ is an invariant scalar field, unlike gtt(x), and not Einstein's own original φ as per his earliest attempts at a relativistic theory of gravity. Can you clarify this point?
The scalar field in the Brans-Dicke theory is a genuine relativistic scalar field while the component of the metric gtt reduces to Newton potential (let me call it V rather than φ to avoid confusion) in the limit of weak fields. The Newton potential enters into the metric tensor (the way geometry is changed) while the scalar field of the Brans-Dicke theory just decides what value should take locally the Newton constant.
About the stress-energy tensor, you are right. There is no generally accepted definition for it in general relativity. But I am working with weak fields and there is no problem whatsoever in this case. Also, I am using a covariant form of stress-energy tensor as was originally formulated by Landau and Lifshitz and generally accepted in the scientific community. -
#541 by Rodal on 12 Sep, 2016 15:24
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Playing devil's advocate, the point of a locally varying constant in Brans-Dicke theory reminds me of a skeptical discussion I followed some time ago on another forum about Brans' view in 1962 (and what is understood nowadays from his view) stating that gravitational potential energy-momentum is not locally defined in Einstein's GR, because the Einstein stress-energy pseudotensor is not a covariant quantity, hence that no meaningful covariant values can be assigned locally to this quantity. That would be the main issue for the local aspects of Brans-Dicke theory related to the EmDrive.
But trying to avoid comparing apples and oranges leads to how φ is defined respectively in the Brans-Dicke theory, and Einstein's general theory of relativity. In The Meaning of Relativity, discussing 1916 GR, Einstein was talking specifically about gtt/2 as the GR version of the Newtonian potential φ. But Brans-Dicke φ is an invariant scalar field, unlike gtt(x), and not Einstein's own original φ as per his earliest attempts at a relativistic theory of gravity. Can you clarify this point?
The scalar field in the Brans-Dicke theory is a genuine relativistic scalar field while the component of the metric gtt reduces to Newton potential (let me call it V rather than φ to avoid confusion) in the limit of weak fields. The Newton potential enters into the metric tensor (the way geometry is changed) while the scalar field of the Brans-Dicke theory just decides what value should take locally the Newton constant.
About the stress-energy tensor, you are right. There is no generally accepted definition for it in general relativity. But I am working with weak fields and there is no problem whatsoever in this case. Also, I am using a covariant form of stress-energy tensor as was originally formulated by Landau and Lifshitz and generally accepted in the scientific community.
Dr. Frasca, any comments on latest upper limit experimental observations of the change of G with time and space, would be appreciated
Reference:
page 110 (for change with time) of Wheeler's book:
http://bit.ly/2cR6KAv
Gravitation and Inertia
By Ciufolini and Wheeler
Princeton University Press
ISBN-10: 0691033234
ISBN-13: 978-0691033235
Also page 111 change in G with space.
It has been 20+ years since this book was published. So comments are appreciated.
Also
Glab≈G∞[1-U/(ω+2)] Eq. 3.2.25
where
Glab = value of G measured in the lab using nearby masses
G∞= G far from the gravity generating body
Wheeler also writes that Brans Dicke ω >~620 from light deflection measurements, Radar time delay experiments and especially the Lunar Laser Ranging analysis.
Comments on the constraint on the minimum value for Brans Dicke ω >~620 and its ramifications for the EM Drive calculations, are also appreciated.
Thanks
Attachment: a chart from Chen (2015) showing larger minimum values for Brans Dicke ω
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#542 by tchernik on 12 Sep, 2016 16:03
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Just to say I'm fascinated by the latest exchanges of Dr. Frasca and other knowledgeable posters. Seems like this could be a strong candidate to explain both the thrust and the puzzling optical effects reported by Star Drive... and it could offer proof of an alternative to Einstein's GR.
Exciting developments. -
#543 by StrongGR on 12 Sep, 2016 16:44
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Dr. Frasca, any comments on latest upper limit experimental observations of the change of G with time and space, would be appreciated
Reference:
page 110 (for change with time) of Wheeler's book:
http://bit.ly/2cR6KAv
Gravitation and Inertia
By Ciufolini and Wheeler
Princeton University Press
ISBN-10: 0691033234
ISBN-13: 978-0691033235
Also page 111 change in G with space.
It has been 20+ years since this book was published. What is the latest data regarding upper limit observations for changes in G in time and in space?
Also
Glab≈G∞[1-U/(ω+2)] Eq. 3.2.25
where
Glab = value of G measured in the lab using nearby masses
G∞= G far from the gravity generating body
Wheeler also writes that Brans Dicke ω >~620 from light deflection measurements, Radar time delay experiments and especially the Lunar Laser Ranging analysis.
Comments on Brans Dicke ω >~620 and its ramifications for the EM Drive calculations, are also appreciated.
Thanks
These are really interesting questions. The frustum with a localized energy density is a rather lucky situation. Due to the fact that the energy density arises from an e.m. field, the omega constant is not relevant at all for the discussion. People generally takes it to be very large to get agreement with general relativity but I would like to emphasize that the discussion of how one recovers general relativity from Brans-Dicke theory has gone an extended discussion in these later years. This limit is not so easy to understand and, in some cases, it is not just to take omega becoming larger. This is especially true for Brans-Dicke-Maxwell theory.
What I get is a consistency equation that is independent from omega (this is easy to check just by inspection) and, just locally, yields as a solution a coupling constant different inside with respect to outside where standard Newton constant is indeed recovered.
As soon as I will get some time, I will put done some mathematical worksheet to get numerical values for the gravitational constant inside the frustum. Of course, I should invent values to put in as we are all expecting December... -
#544 by TheTraveller on 12 Sep, 2016 16:47
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The thrust is generated because of the asymmetrically offset alteration of the gravitational constant in relation to the cavity's center of mass? Hence, the greater the offset achieved (TE212 vs TE013 for instance), the greater the thrust measured (assuming the same Q value)?
Q varies with the mode. TE212 with or without a dielectric has a lower Q than TE013. -
#545 by Rodal on 12 Sep, 2016 16:54
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...What I get is a consistency equation that is independent from omega (this is easy to check just by inspection) and, just locally, yields as a solution a coupling constant different inside with respect to outside where standard Newton constant is indeed recovered...
Yes, this local independence from Brans-Dicke ω inside the truncated cone cavity appears to be a new, unfamiliar result. Certainly different from the discussion in Wheeler's book:
Glab≈G∞[1-U/(ω+2)] Eq. 3.2.25
which has a clear inverse dependence on Brans-Dicke ω, requires small value of Brans-Dicke ω for a significant change in (1-Glab/G∞) and where for ω->∞ we clearly recover 1-Glab/G∞=0 -
#546 by StrongGR on 12 Sep, 2016 17:04
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...What I get is a consistency equation that is independent from omega (this is easy to check just by inspection) and, just locally, yields as a solution a coupling constant different inside with respect to outside where standard Newton constant is indeed recovered...
Yes, this local independence from Brans-Dicke ω inside the truncated cone cavity appears to be a new, unfamiliar result. Certainly different from the discussion in Wheeler's book:
Glab≈G∞[1-U/(ω+2)] Eq. 3.2.25
which has a clear inverse dependence on Brans-Dicke ω, and where for ω->∞ we clearly recover Glab=G∞
There is a technical explanation for this: The stress-energy tensor of the e.m. field is traceless. -
#547 by Rodal on 12 Sep, 2016 17:10
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And the reason why this would not have been measured before is because the forces involved in asymmetric electromagnetically resonant cavities are too small (microNewtons) and nobody had attempted to measure them before?...What I get is a consistency equation that is independent from omega (this is easy to check just by inspection) and, just locally, yields as a solution a coupling constant different inside with respect to outside where standard Newton constant is indeed recovered...
Yes, this local independence from Brans-Dicke ω inside the truncated cone cavity appears to be a new, unfamiliar result. Certainly different from the discussion in Wheeler's book:
Glab≈G∞[1-U/(ω+2)] Eq. 3.2.25
which has a clear inverse dependence on Brans-Dicke ω, and where for ω->∞ we clearly recover Glab=G∞
There is a technical explanation for this: The stress-energy tensor of the e.m. field is traceless.
I wonder whether there are any Cosmological events that have functioned as an equivalent of an asymmetric electromagnetically resonant cavity to verify whether there is indeed a resulting self-acceleration... -
#548 by Bob012345 on 12 Sep, 2016 18:06
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...What I get is a consistency equation that is independent from omega (this is easy to check just by inspection) and, just locally, yields as a solution a coupling constant different inside with respect to outside where standard Newton constant is indeed recovered...
Yes, this local independence from Brans-Dicke ω inside the truncated cone cavity appears to be a new, unfamiliar result. Certainly different from the discussion in Wheeler's book:
Glab≈G∞[1-U/(ω+2)] Eq. 3.2.25
which has a clear inverse dependence on Brans-Dicke ω, and where for ω->∞ we clearly recover Glab=G∞
There is a technical explanation for this: The stress-energy tensor of the e.m. field is traceless.
Can you offer practical methods to greatly increase the thrust or is all the Brans-Dicke discussion just academic? -
#549 by StrongGR on 12 Sep, 2016 19:40
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And the reason why this would not have been measured before is because the forces involved in asymmetric electromagnetically resonant cavities are too small (microNewtons) and nobody had attempted to measure them before?
I wonder whether there are any Cosmological events that have functioned as an equivalent of an asymmetric electromagnetically resonant cavity to verify whether there is indeed a resulting self-acceleration...
Because nobody studied large concentrations of e.m.field energy in a small volume and nobody thought to put it on a pendulum. Please, note that the solution outside the cavity is the Newton constant. This is smoothly joined with the inside solution. On a large (cosmological) scale, Brans-Dicke model coincides with general relativity provided at least omega is large enough (indeed, for Brans-Dicke-Maxwell model things are not that simple).
Of course, this is not self-accelerating. It accelerates at expenses of gravity. -
#550 by StrongGR on 12 Sep, 2016 19:43
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Can you offer practical methods to greatly increase the thrust or is all the Brans-Dicke discussion just academic?
Yes, of course. This was already done in the previous part of the paper where the dependences on the radii of the cavity, its angular opening and other parameters as well were all clearly stated. -
#551 by tchernik on 12 Sep, 2016 19:56
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Of course, this is not self-accelerating. It accelerates at expenses of gravity.
Excuse my meddling, but what do you mean by this? in this theory, does the Emdrive act as a "gravity dampener" and only works in a significant gravity field (e.g. around Earth)? or does it create a gravity-like effect and then it 'falls' on it? -
#552 by StrongGR on 12 Sep, 2016 20:09
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Of course, this is not self-accelerating. It accelerates at expenses of gravity.
Excuse my meddling, but what do you mean by this? in this theory, does the Emdrive act as a "gravity dampener" and only works in a significant gravity field (e.g. around Earth)? or does it create a gravity-like effect and then it 'falls' on it?
This is an interesting question. The answer relies on the simple fact that, while e.m. fields are shielded by the cavity and so, no net momentum can be observed, gravitational disturbances can escape the cavity providing the needed reaction. -
#553 by Rodal on 12 Sep, 2016 21:59
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And the reason why this would not have been measured before is because the forces involved in asymmetric electromagnetically resonant cavities are too small (microNewtons) and nobody had attempted to measure them before?
I wonder whether there are any Cosmological events that have functioned as an equivalent of an asymmetric electromagnetically resonant cavity to verify whether there is indeed a resulting self-acceleration...
Because nobody studied large concentrations of e.m.field energy in a small volume and nobody thought to put it on a pendulum. Please, note that the solution outside the cavity is the Newton constant. This is smoothly joined with the inside solution. On a large (cosmological) scale, Brans-Dicke model coincides with general relativity provided at least omega is large enough (indeed, for Brans-Dicke-Maxwell model things are not that simple).
Of course, this is not self-accelerating. It accelerates at expenses of gravity.
Consider the case of an astrophysical maser: a naturally occurring source of stimulated emission, in the microwave portion of the electromagnetic spectrum. A naturally occurring analog of the man-made man-invented MASER. (*)
However, naturally occurring masers lack the resonant cavity engineered for terrestrial laboratory MASERs.
Now think of the Brans Dicke solution you obtained for the asymmetric resonant cavity, where it experiences an acceleration as a result of gravity in this Brans Dicke model. Can you think of a naturally occurring cosmological events that can function as an equivalent of the asymmetric electromagnetically resonant cavity ?
Of course it is hopeless to find a naturally occurring event that has a copper asymmetric cavity. A copper asymmetric cavity is clearly a man-made object. But just like astrophysical masers are naturally occurring analogs of man-made Masers, that lack the resonant cavity of man-made Masers, it would be interesting if there would be a naturally occurring analog of your solution as well.
Why would it be interesting? because beyond being interesting for its own scientific sake, it would be interesting because:
A) it may explain some naturally occurring cosmological phenomena hereto unexplained to this date (there are many unexplained cosmological phenomena of course
)
B) it may further and more strongly validate your solution, which would be interesting, given the controversial nature of EM Drive experiments up to now.
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(*) Before their discovery in 1965, many scientists thought that molecules could not exist in space. The emission was at first attributed to an unknown form of interstellar matter named by UC Berkeley astronomers as Mysterium see: http://bit.ly/2cSmIWL, but the emission was soon identified by Harvard and MIT astronomers as line emission from OH molecules in compact sources within molecular clouds. 
Later, H2O emission in 1969, CH3OH emission in 1970 and SiO emission in 1974 were discovered, all coming from within molecular clouds. These were termed "masers", as from their narrow line-widths and high effective temperatures it became clear that these sources were amplifying microwave radiation.
Even later, naturally occurring Masers were discovered around highly evolved Late-type stars . Naturally occurring Masers were also discovered in external galaxies in 1973, and in the Solar System in comet halos.
Another unexpected discovery was made in 1982 with the discovery of emission from an extra-galactic source with an unrivalled luminosity about 106 times larger than any previous source. This was termed a megamaser because of its great luminosity; many more megamasers have since been discovered.
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#554 by demofsky on 13 Sep, 2016 01:34
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.....As soon as I will get some time, I will put done some mathematical worksheet to get numerical values for the gravitational constant inside the frustum. Of course, I should invent values to put in as we are all expecting December...
I have to say that it would be very interesting to see calculations based on this approach to compare with known results from some of the builders here as well as published results. For instance, if they are close then we may have a guide as to how many artifacts a particular apparatus is introducing.
And can I say that this forum really amazes me at times!! The dialog today between Dr. Frasca, Dr. Rodal and others has been pure pleasure!! -
#555 by birchoff on 13 Sep, 2016 02:18
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Marco, I have three questions:
1/ Can you explain in layman terms how his your Brans-Dicke theory different from Minotti's who also explains the anomalous thrust of asymmetric EM resonators?
2/ Does your development of the Brans-Dicke theory predict if a powerful and efficient (superconducting or not) asymmetric RF resonant cavity, or array of cavities, can achieve enough thrust to lift a body within Earth gravitational field (aka lift engine) or does the predicted thrust/weight ratio is always tiny, containing the space flight applications to deep space probes only?
3/ EmDrive apart, if the effect can scale up at the square of the energy density of the EM field and hence can truly alter some physical constants, do you think a huge amount of concentrated energy could warp spacetime enough so it could locally go beyond neutrons' critical density threshold and create a mini black hole?
1) Differently form Minotti's approach, Brans-Dicke theory (it is not mine) is a model accepted by the community since '60s. It has been a workhorse to unveil possible deviations from general relativity. It introduces a set of constants, the most important is omega, that provide an understanding about how Einstein's equations could change. For these reasons, it has been and is today an accepted theory by all the scientific community. What it is seen is that the agreement between Einstein's theory and Brans-Dicke theory is perfect provided the omega parameter is taken large enough. So, this for the cosmological and planetary scales. But, inside a resonant cavity, with a large e.m. field, things could be quite different as I show. Particularly, Newton constant could become quite large due the square of the energy density of the e.m. field inside. This kind of physical setup has not been analyzed before for Brans-Dicke theory and the results appear to be absolutely striking.
2) Now, one has formulas to project an optimized cavity to take thrust to its maximum from a physical standpoint. For a superconducting cavity what really matters is the Q factor and this largely increases thrust. This is all due to Einstein's theory of general relativity with the proper correction arising from Brans-Dicke model (just a change in the Newton constant). This change should be computed in the design phase.
3) No, I fear this is impossible.
What role if any does the dielectric play in the solution you have proposed? -
#556 by dustinthewind on 13 Sep, 2016 03:40
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Of course, this is not self-accelerating. It accelerates at expenses of gravity.
Excuse my meddling, but what do you mean by this? in this theory, does the Emdrive act as a "gravity dampener" and only works in a significant gravity field (e.g. around Earth)? or does it create a gravity-like effect and then it 'falls' on it?
This is an interesting question. The answer relies on the simple fact that, while e.m. fields are shielded by the cavity and so, no net momentum can be observed, gravitational disturbances can escape the cavity providing the needed reaction.
Would it be possible that what is happening in the cavity is the index of free space may be being modified (by the idea you mentioned), changing the mass of light. As the light gains mass/slows in time, there is a back reaction on the dielectric of free space pushing the free space back, and as the light strikes the front of the cavity, the light provides more impulse than it did at the back of the cavity. Energy is then lost from the light to the vacuum.
This polarizeable vacuum possibly being some mix of matter/anti-matter. The anti-matter being negative mass but runs backwards in time (Similar to Richard Feynman's proposal Wiki Link) so appears to be positive mass but reverse in charge. This anti-matter having the effect of modifying time (This may be my own modification of the idea so far as I am aware) when it is polarized in the presence of normal matter leading to the effects of Lorentz contraction for fast moving objects or large gravitational bodies. Gravity being some gradient in the passage of time or possibly the vacuum being accelerated because of the gradient in time?
The idea coming from papers concerning light being measured to have more momentum inside water, having a higher index of refraction, and them having measured a back reaction of the light when entering the water. Is it possible with the vacuum too?
Or is this not really connected to what your talking about?
The Woodward effect is also mentioned in the wiki link at the bottom.
Closed timelike curves?
http://www.lightandmatter.com/html_books/genrel/ch07/ch07.html#Section7.3 -
#557 by StrongGR on 13 Sep, 2016 06:38
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Consider the case of an astrophysical maser: a naturally occurring source of stimulated emission, in the microwave portion of the electromagnetic spectrum. A naturally occurring analog of the man-made man-invented MASER. (*)
However, naturally occurring masers lack the resonant cavity engineered for terrestrial laboratory MASERs.
Now think of the Brans Dicke solution you obtained for the asymmetric resonant cavity, where it experiences an acceleration as a result of gravity in this Brans Dicke model. Can you think of a naturally occurring cosmological events that can function as an equivalent of the asymmetric electromagnetically resonant cavity ?
Of course it is hopeless to find a naturally occurring event that has a copper asymmetric cavity. A copper asymmetric cavity is clearly a man-made object. But just like astrophysical masers are naturally occurring analogs of man-made Masers, that lack the resonant cavity of man-made Masers, it would be interesting if there would be a naturally occurring analog of your solution as well.
Why would it be interesting? because beyond being interesting for its own scientific sake, it would be interesting because:
A) it may explain some naturally occurring cosmological phenomena hereto unexplained to this date (there are many unexplained cosmological phenomena of course )
B) it may further and more strongly validate your solution, which would be interesting, given the controversial nature of EM Drive experiments up to now.
----------------------
(*) Before their discovery in 1965, many scientists thought that molecules could not exist in space. The emission was at first attributed to an unknown form of interstellar matter named by UC Berkeley astronomers as Mysterium see: http://bit.ly/2cSmIWL, but the emission was soon identified by Harvard and MIT astronomers as line emission from OH molecules in compact sources within molecular clouds.
Later, H2O emission in 1969, CH3OH emission in 1970 and SiO emission in 1974 were discovered, all coming from within molecular clouds. These were termed "masers", as from their narrow line-widths and high effective temperatures it became clear that these sources were amplifying microwave radiation.
Even later, naturally occurring Masers were discovered around highly evolved Late-type stars . Naturally occurring Masers were also discovered in external galaxies in 1973, and in the Solar System in comet halos.
Another unexpected discovery was made in 1982 with the discovery of emission from an extra-galactic source with an unrivalled luminosity about 106 times larger than any previous source. This was termed a megamaser because of its great luminosity; many more megamasers have since been discovered.
Dr. Rodal, I am not an expert in cosmology unfortunately. People were going on looking for substantial differences between Brans-Dicke and Eisntein theories but, so far, it was only possible to fix a higher limit on omega. On a scale for a cosmological maser, I would expect no significant difference between these two models. But things could be interesting if the intensity of the emitted e.m. radiation by the cosmological maser is large enough to get a backreaction on gravity. This, in turn, could modify the value of the coupling constant making possible to observe some deviations, even if really small. This effect is similar to that of the resonant cavity. Otherwise, we can safely neglect any correction due to the scalar field and take it a constant. The game changer for the resonant cavity is just the energy density of the e.m. field in a small volume.
Let me emphasize, once again, that if this effect should be confirmed in the resonant cavity, consequences for our understanding of gravity would be overwhelming. -
#558 by tleach on 13 Sep, 2016 06:38
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Q varies with the mode. TE212 with or without a dielectric has a lower Q than TE013.
I wasn't asking about the dielectric and I specifically stated that Q should be constant for the purposes of my inquiry.
Intuitively, just by looking at monomorphic's resonant cavity renderings, it appears to me as though a TE013 mode results in a high EM field density locus that is further from the center of mass of the frustum than it is in the case of a TE012 mode.
What I'm asking is, with Q being equal (the Q factor, as defined as 2π times the ratio of the stored energy to the energy dissipated per oscillation cycle (is that the definition we settled on? I can't remember...), could be maintained, independent of the mode, by controlling the amount of energy dissipated per cycle), would TE013 yield a higher thrust than TE012? If so, why? Is it due to the larger asymmetry observed in TE013? -
#559 by StrongGR on 13 Sep, 2016 06:40
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What role if any does the dielectric play in the solution you have proposed?
A dielectric can increase thrust.
)