Author Topic: EM Drive Developments Thread 1  (Read 797497 times)

Offline Rodal

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Re: EM Drive Developments
« Reply #760 on: 09/18/2014 10:20 PM »
Rodal could you tell us in a few words if Schwinger's explanation of the Casimir effect as originating from charge effects (more like van der Waals ...) discards the ZPE/vacuum turmoil playing any (direct) role in Casimir forces ?

<<The Casimir effect is often invoked as decisive evidence that the zero-point energies of quantum fields are ‘‘real.’’ On the contrary, Casimir effects can be formulated and Casimir forces can be computed without reference to zero-point energies. They are relativistic, quantum forces between charges and currents. The Casimir force (per unit area) between parallel plates vanishes as , the fine structure constant, goes to zero>> (  http://cua.mit.edu/8.422/Reading%20Material/Jaffe2005_Casimir.pdf  )

Just my understanding [*] (readers should do their own research and arrive at their own conclusions):

Yes in the restricted sense of rejecting a number of ideas like:

A) "negative energy" produced by the Casimir force,

B) "negative mass" produced by the Casimir force, and any number of "strange" ideas of people that see the Casimir force as something to enable stabilizing wormholes, faster than light travel with Alcubierre drives, etc.

C) Schwinger disagreed with a claim (by Scharnhorst and Barton) that light speeds greater than the speed of light in vacuum are possible in a parallel plate capacitor (the original Casimir effect geometry) .

On the other hand Schwinger saw the vacuum as being full of virtual particle pairs, and responsible for the Lamb shift. Also towards the end of his life he had some unusual ideas about cold fusion (http://www.lenr-canr.org/acrobat/SchwingerJcoldfusiona.pdf)

*** Schwinger was not the only one really bothered by "negative energy" and "negative mass" arising from Casimir's effect, also great physicists as Pauli, Feynman and DeWitt were just as bothered and said at different points in time that there was something wrong with Casimir's explanation, but Schwinger was the one that finally explained it, using Quantum Mechanics calculations, as being due to a retarded van der Waal force ****

_____________
[*] The debate is not closed.  For example Schwinger makes an adiabatic approximation assumption.

how the "vacuum wavelength exclusion" effect serving the Casimir way of explaining the experimental results predicts correct magnitude for flat plates ...?




A lucky intuition by Casimir.  In Casimir's own words "I went my own clumsy way"  His assumption works fine for plates, not for other geometries.  Failed in his attempt to predict the fine structure constant  (which is buried in Schwinger's explanation but practically disappears for flat plates) as due to the quantum vacuum.  This to me is critical: we know now that the fine structure constant, α, is a fundamental physical constant, namely the coupling constant characterizing the strength of the electromagnetic interaction between elementary charged particles.  It seems to me that those who use Casimir's explanation for the Casimir force not only fail at predicting the correct sign of the Casimir force for different geometries (which is bad enough) but also are lead to the idea that the fine structure constant can be predicted from the quantum vacuum, something that has been shown to be wrong.



BTW if you feel pedagogically inclined and know the answer : from QFT, are the wave propagation speeds c for all the fields, including those that have massive associated particles ?

I would have to think about that...
« Last Edit: 09/19/2014 01:05 PM by Rodal »

Offline Rodal

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Re: EM Drive Developments
« Reply #761 on: 09/18/2014 11:03 PM »
It is also interesting that in quantum electrodynamics (the theory used by Schwinger to calculate Casimir's effect), the fine structure constant α is the coupling constant determining the strength of the interaction between electrons and photons [*]. The theory does not predict its value. It must be determined experimentally. It is one of ~ 20 empirical parameters in the Standard Model of particle physics, whose value is not determined within the Standard Model.

______________
[*] Yes, in a powered microwave resonator we have photons and we also have electrons (as part of the atoms on the walls of the resonator).


Offline Rodal

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Re: EM Drive Developments
« Reply #762 on: 09/18/2014 11:21 PM »
It is interesting how Schwinger's paper about cold fusion (http://www.lenr-canr.org/acrobat/SchwingerJcoldfusiona.pdf)  begins (he could have been talking about EM drives):


<<A totally unexpected phenomenon has been discovered in a certain field of science. It could have significant implications for the future of mankind, .... The overwhelming reaction of the experts in the field is rejection, based on the absence of other effects that are considered to be necessary companions of this new phenomenon. To quote one expert: “We know a lot about what happens. . . . We no longer have the latitude to say ‘Well, some strange event occurred and generated those things.’” Nevertheless, this new possibility seems to have enough validity that one skeptic said: “It’s hard to believe it. But there seems to be something to this.” And he went on to say: “It should not be necessary, however, to understand the mechanism before embracing the concept. If a proven track record can be established . . . you have to believe it.”>>

Offline aero

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Re: EM Drive Developments
« Reply #763 on: 09/18/2014 11:56 PM »
Quote
[*] Yes, in a powered microwave resonator we have photons and we also have electrons (as part of the atoms on the walls of the resonator).

We have a lot of other stuff there too. Remember the experiments were in atmosphere. I won't guess as to how much the air in the cavity ionized or if such could have simulated the second metallic plate or to what effect.

Point is, the internals of the cavity and interactions are more complex than have been analyzed to date. Known physics may apply, I'm pretty sure, but we really don't know enough to claim correct application of applicable all known physics. Disregarding any unknown physics, but I'm willing to try to avoid unknown physics for now.
« Last Edit: 09/19/2014 01:35 AM by aero »
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Offline Rodal

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Re: EM Drive Developments
« Reply #764 on: 09/19/2014 02:05 AM »
Quote
[*] Yes, in a powered microwave resonator we have photons and we also have electrons (as part of the atoms on the walls of the resonator).

We have a lot of other stuff there too. Remember the experiments were in atmosphere. I won't guess as to how much the air in the cavity ionized or if such could have simulated the second metallic plate or to what effect.

Point is, the internals of the cavity and interactions are more complex than have been analyzed to date. Known physics may apply, I'm pretty sure, but we really don't know enough to claim correct application of applicable all known physics. Disregarding any unknown physics, but I'm willing to try to avoid unknown physics for now.

@aero

If the internals of the EM drive cavities matter, including internal cavity ionization, does it follow that if they were to repeat the tests in a vacuum chamber, your concerns still would apply, because you wouldn't know whether the cavity internals were properly evacuated?  (i.e. do we know whether the EM drive cavity is hermetically sealed or whether the cavity is very leaky?)
« Last Edit: 09/19/2014 02:10 AM by Rodal »

Offline aero

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Re: EM Drive Developments
« Reply #765 on: 09/19/2014 02:48 AM »
I got the impression that it leaked like a sieve, but don't know of any proof except for the absence of any information regarding air tight sealing. I do know this, quoting from Dr. White, et. al. report:

Quote
The thrust performance of this next generation tapered test article has been analytically determined to be in the 0.1 newton per kilowatt regime. Vacuum compatible RF amplifiers with power ranges of up to 125 watts will allow testing at vacuum conditions which was not possible using our current RF amplifiers due to the presence of electrolytic capacitors. The tapered thruster has a mechanical design such that it will be able to hold  pressure at 14.7 pounds per square inch (psi) inside of the thruster body while the thruster is tested at vacuum to  preclude glow discharge within the thruster body while it is being operated at high power.

That implies to me that the device we're discussing operated at atmospheric pressure. I've heard no mention of any different fill gas, so I assume air.

Edit: Actually, on Figure 22 is says, "In 750mm air" - Also, Figure 26 shows the dielectric they plan for their next generation RF thruster. It looks to me like it fills the cavity completely. I can't guess how much room there will be for air. Not much?
« Last Edit: 09/19/2014 05:40 AM by aero »
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Offline Rodal

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Re: EM Drive Developments
« Reply #766 on: 09/19/2014 12:09 PM »
Figure 26 shows the dielectric they plan for their next generation RF thruster. It looks to me like it fills the cavity completely. I can't guess how much room there will be for air. Not much?

1) The dielectric resonators must have been responsible for the NASA-measured thrust forces, for both the Cannae and the Frustum devices, as when they removed the dielectric resonators from either of them, they could not measure any thrust. 

2) The calculated Electric Field in the dielectric resonators is much, much stronger than in the rest of the cavity.

3) The volumes of the dielectric resonators are significantly smaller than the total inner volumes of the cavities.  One can assess the dielectric resonators relative size and location from Fig. 14, p.10, as the dielectric resonator appears red (in the Electric Field calculation display) surrounded by a narrow amount of yellow and a lot of blue.   Fig. 14 shows the PTFE (Teflon) dielectric resonator for the Cannae device.  It appears to have a cylindrical shape (small diameter/length ratio).  Fig. 26, p.21 showing the "Next Generation RF [Frustum] Thruster" shows an annular-shaped (a disc with an inner hole) dielectric resonator.  Yes, the annular-shaped dielectric resonator takes a significant amount of the area at the small diameter end of the Frustum, but it takes a rather insignificant amount of the total volume inside the cavity.

4) Notice the very un-symmetric location of the dielectric resonators.  For both the Cannae and the Frustum devices, the dielectric resonators are located towards one end of the device.  The direction of measured thrust is the same as the relative location of the dielectric resonator.  Defining "left" and "right" in fixed-in-space extrinsic coordinates: with the dielectric resonator located towards the right of the device's center of mass, thrust occurred towards the right.  When the device was turned around by 180 degrees such that the dielectric resonator was located towards the left of the center of mass, thrust occurred towards the left.

5) The picture of the Frustum seems to show a diameter ratio ( (large diameter)/(small diameter) ) = 1.71 instead of the guesstimated ratio ( (large diameter)/(small diameter) ) = 9.9"/6.6" = 1.50 based on the photograph and the cross-section of the Faztek beam.  Also the picture seems to show a  ( (large diameter)/(length) ) = 1.20 instead of the guesstimated ratio ( (large diameter)/(length) ) = 9.9"/9.0" = 1.10, and ( (length)/( small diameter) ) = 1.43 instead of the guesstimated ratio ( (length)/( small diameter) ) =  9.0"/6.6" = 1.36.  Therefore the ratios I guesstimate from this picture, divided by your guesstimated ratios are:  1.14, 1.09 and 1.05 respectively.  The differences are relatively small, the maximum difference being for the diameter ratio (14% difference between our estimates) and the smallest difference being for the estimation of the  ( (length)/( small diameter) ) ratio (5% difference between our estimates).  In any case, please double-check these dimensional ratios and let us know what you think.

______________________________________

Images from "Anomalous Thrust Production from an RF Test Device Measured on a Low-Thrust Torsion Pendulum" by David A. Brady*, Harold G. White†, Paul March‡, James T. Lawrence§, and Frank J. Davies**, July 28-30, 2014, Cleveland, OH, AIAA 2014-4029, Propulsion and Energy Forum, 50th AIAA/ASME/SAE/ASEE Joint Propulsion Conference

the article notes: "This material is declared a work of the U.S. Government and is not subject to copyright protection in the United States." (Also see: http://en.wikipedia.org/wiki/Copyright_status_of_work_by_the_U.S._government) as posted in http://www.libertariannews.org/wp-content/uploads/2014/07/AnomalousThrustProductionFromanRFTestDevice-BradyEtAl.pdf
« Last Edit: 09/19/2014 03:42 PM by Rodal »

Offline JohnFornaro

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Re: EM Drive Developments
« Reply #767 on: 09/19/2014 12:34 PM »
Just a reminder that "analytical determination" is not the  equal of "experimental determination".

Solo dicendo.
Sometimes I just flat out don't get it.

Offline Rodal

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Re: EM Drive Developments
« Reply #768 on: 09/19/2014 12:44 PM »
Just a reminder that "analytical determination" is not the  equal of "experimental determination".

Solo dicendo.
I think that John is referring to the fact that the specific force of the Frustum was experimentally determined by NASA to be:

SPECIFIC FORCE=  0.003 N/kW to 0.0054 N/kW

So, an analytically determination that the future Frustum will have

SPECIFIC FORCE=0.1 N/kW

is an extrapolation by NASA that the future Frustum will have a specific force 19 to 33 times greater than the one experimentally measured.  I imagine that John is "solo dicendo" that it is unknown whether NASA's order of magnitude extrapolation will be realized in practice.

Solo riportati
« Last Edit: 09/19/2014 01:39 PM by Rodal »

Offline frobnicat

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Re: EM Drive Developments
« Reply #769 on: 09/19/2014 02:00 PM »
More theoretical musing (at the risk of forking the discussion even more) :
In classical analytical understanding of systems, one can in principle always relate a macroscopic system wide effect to known microscopic elementary interactions in a given fundamental theory. While this is not always evident to show how a surprising/unforeseen macroscopic effect effectively derives from well known elementary theories (example superconductivity), it is always the case that the system's behaviours won't break the fundamental laws of its parts, in particular the conservation laws. Superconductivity kind of breaks the Ohm law (in the sense that a 0 resistance is both surprising from order/entropy arguments and technically problematic if deriving I=U/R) but Ohm law is an emergent effect for large systems, not a fundamental elementary theory. A macroscopic effect emergent on some particular geometry or bulk arrangement of parts can "break" some previously established emergent "law" but this is not the same as needing a different fundamental elementary theory of parts.

The "space drives" effects are measured at macroscopic scale and seems to require very specific arrangements of parts (geometry of atoms, parameters of RF photons...) otherwise it would probably have been observed numerous times in the past on macroscopic precision devices (accelerometers...). This is not shocking, superconductivity were never met before we gathered specific conditions (and even more very specific for hight temp. superconductivity)

The results indicate either a net deviation from energy-momentum conservation, or a need for exotic physics to explain how "net momentum from power" is observed locally but conserved globally (at Universe scale) without pushing on expelled known radiations (with at most 1/c thrust/power efficiency). Question is : how can this be addressed from an elementary point of view ? For the system to experience unheard of net momentum effects, then the parts would have to experience unheard of net momentum effects : the possibility of this new macroscopic effect implies the existence of new effect(s) at a microscopic scale (as contrary to Ohm law, momentum exchanges laws are elementary). This can't be just a matter of geometry, this should be understood at the level of particles -> and it should have empirically testable consequences on microscopic systems and elementary interactions. The number of degrees of freedom and conditions you can put a single particle (or a few atoms) are much less than for macroscopic shapes. If the thruster as a whole puts some of its parts at specific conditions, those can't be extreme conditions, space curvature, E/M field ... can't exceed what is routinely investigated in the lab (and in my microwave oven).

In such specific but presumably quite not exceptional microscopic conditions there should be an effect that is not part of contemporary admitted frameworks. But (but but) there seems to be no need for such : classical momentum exchanges between known particles(corresponding fields) at microscopic/instant places of the relativistic background of standard model (Feynman diagrams vertices if you like) seem to explain perfectly all precision measurements involving microscopic systems devoid of emergent phenomenons (because to small). How comes ? Would the microscopic counterparts of space drives effects be too small in magnitude to be distinguishable from SM's quantitative predictions ? Not sure I could do some meaningful order of magnitude comparison here but I find hard to believe. Experiments with ultracold atoms in RF/laser cavities comes to mind here, with tremendous energy levels/frequencies precisions... all in agreement with SM.
« Last Edit: 09/19/2014 02:07 PM by frobnicat »

Offline Rodal

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Re: EM Drive Developments
« Reply #770 on: 09/19/2014 02:26 PM »
More theoretical musing ...
@frobnicat

Please take a look at my post above (with the images).  Do you have any comment on the known fact that NASA could not measure any thrust when they removed the small size (relative to the cavity) dielectric resonators?  They only measured thrust when the dielectric resonators were inside the EM drives.  Also, the measured thrusts forces pointed to the same direction (with respect to the center of mass) as the off-center positioning of the dielectric resonators.  Also, the (COMSOL finite element) calculations of the Electric Field showed the Electric Field to be orders of magnitude larger in the dielectric resonators than elsewhere in the EM drives.  Evidently the thrust measurements are foremost related to the dielectric resonators.
« Last Edit: 09/19/2014 02:31 PM by Rodal »

Offline Rodal

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Re: EM Drive Developments
« Reply #771 on: 09/19/2014 02:36 PM »
.. If the thruster as a whole puts some of its parts at specific conditions, those can't be extreme conditions, space curvature, E/M field ... can't exceed what is routinely investigated in the lab (and in my microwave oven)...
Yes, but, we do not have in our homes, our microwave oven positioned on an inverted torsional pendulum (known to exhibit parasitic modes of motion due to coupling of swinging with torsional motion) where we attempt to measure  microNewton torsional forces.  And we don't have a magnetic damper attempting to overdamp the motion of the inverted pendulum to attempt to eliminate parasitic modes of motion.
« Last Edit: 09/19/2014 03:51 PM by Rodal »

Offline frobnicat

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Re: EM Drive Developments
« Reply #772 on: 09/19/2014 03:47 PM »
.. If the thruster as a whole puts some of its parts at specific conditions, those can't be extreme conditions, space curvature, E/M field ... can't exceed what is routinely investigated in the lab (and in my microwave oven)...
Yes, but, we do not have at our homes, our microwave oven positioned on an inverted torsional pendulum (known to exhibit parasitic modes of motion due to coupling of swinging with torsional motion) where we attempt to measure  microNewton torsional forces.  And we don't have a magnetic damper attempting to overdamp the motion of the inverted pendulum to attempt to eliminate parasitic modes of motion.
Obviously but what I meant (I hope that was clear) is that the local (atom scale) conditions are mundane, from the point of view of an atom. And there is not that many much local configurations possible to consider in the vicinity of an atom, various superpositions of various freq EM radiations, gravity, gradients of those, what else ? And atoms, or small bunch of atoms, have been played around for quite some long in precision measurements devices to further the understanding and quantitative verification/use of microscopic fundamental frameworks. It should be possible to derive likely prediction of quantitative correction microscopic effects from the macroscopic empirical claim... don't know the relative magnitude though.

for your previous remark, if we are looking for classical explanations to the results, the dielectric part seems to play an important role. It could be because of the strong EM gradients there, non linearities maybe, maybe harmonics made there, maybe heat effects, maybe ionization, maybe different coupling with the generator (feedback of power to the generator). I can't propose any specific mechanism beyond what seems to have been addressed already. And even if the effect (as claimed) is bogus it's likely to be impossible to (classically) explain the results without a very close inspection of the experiment by third parties with fresh stance, a lot of time and instrumentation. Hope your attempts to model the mechanical aspects of the pendulum can further out the subject but I fear this won't settle much.

Clearly the presence of very strong magnets and induced currents in the damping system is not desirable. Wouldn't it be possible to devise a system of much much lower stiffness, with a natural swinging torsional motion period not shorter but longer than the experimental pulses (more than a minute), with no damping at all during the power on testing phases ?
I mean, an almost freely rotating thin strip torsion pendulum, slowly put into place (at the middle of fixed moving range), put to rest with active electrostatic control, and then off the control, check 0 speed for a little while, ok everything is stable, at equilibrium, and then measure rate of change of speed when powering on the device. Put all the device, with battery and RF generator (20W for a few minutes shouldn't weigh more than a few pounds) inside a good shielding conducting box inside a thick polystyrene box (or inside a dewar) to prevent any heat/EM exchange with exterior. And I would be happy with that setup even if not in a vacuum chamber but just an hermetic chamber, and very much more convinced if effects still hold.
( add maybe an active heat venting system, active only between power on sessions, so thermally isolated system wont melt in the long run )

« Last Edit: 09/19/2014 04:16 PM by frobnicat »

Offline Rodal

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Re: EM Drive Developments
« Reply #773 on: 09/19/2014 03:56 PM »

Clearly the presence of very strong magnets and induced currents in the damping system is not desirable. Wouldn't it be possible to devise a system of much much lower stiffness, with a natural swinging motion period not shorter but longer than the experimental pulses (more than a minute), with no damping at all during the power on testing phases ?

Yes, of course, for example the hanging pendulum that has been used to get gravity (inverse square law) measurements, Casimir force measurements and many other types of sensitive measurements by the Physics community.   In a hanging pendulum gravity works as a stabilizing force, returning the mass to the center of swinging motion, so NO swinging stiffness is needed for the hanging pendulum.  That's how the pendulum of a Coo Coo clock works.  Gravity in an inverted pendulum works as a de-stabilizing force, making the mass go off-center. So an inverted pendulum needs swinging stiffness to keep the mass in the center.   Inverted pendulums need the magnetic dampening force to attempt to eliminate parasitic modes. 

 I imagine that NASA's Dr. White would reply that those hanging pendulums do not fit inside his small vacuum chamber, but I would answer that the reported NASA tests were not conducted in a vacuum anyway.

As I discussed in earlier posts, of the three places that NASA has proposed for further tests (JPL, Glenn and John Hopkins) I would be most interested in John Hopkins testing because it is reported to have a Cavendish type, hanging pendulum instead of the inverted pendulums that the NASA reports are considered at JPL and Glenn.  Also  as I discussed in earlier posts, Prof. Martinez-Sanchez at MIT has inverted pendulum thrust measurement devices at MIT that he designed to have the thruster horizontal at all times, to eliminate coupling of swinging modes with torsional modes.
« Last Edit: 09/19/2014 04:14 PM by Rodal »

Offline JohnFornaro

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Re: EM Drive Developments
« Reply #774 on: 09/19/2014 04:16 PM »
I imagine that John is "solo dicendo" that it is unknown whether NASA's order of magnitude extrapolation will be realized in practice.

Gazakly, might I abuse my own language.

Ohm law is an emergent effect for large systems, not a fundamental elementary theory.

I did not know that.  I thought it was not just a good idea, but that it was the law.

Quote
The "space drives" effects are measured at macroscopic scale and seems to require very specific arrangements of parts...

Which is why free dissemination of the geometry of the experimental apparatus is so crucial to the discussion at hand.

Quote
For the system to experience unheard of net momentum effects, then the parts would have to experience unheard of net momentum effects : the possibility of this new macroscopic effect implies the existence of new effect(s) at a microscopic scale ... This can't be just a matter of geometry, this should be understood at the level of particles ...

And I would add that theory must drive the design of the geometry.  Our alchemical ancestors, to bluntly summarize, played with pentagrams and other geometry, and used that mistakenly thought to be theoretical background to design and execute their experiments.  It turns out that one can change lead to gold, but only by using incredible amounts of energy as guided by theory.  The geometry of that transformative mechanism has nothing whatsoever to do with the ancestral primitive geometry.

Evidently the thrust measurements are foremost related to the dielectric resonators.

I cannot answer the question, but I remind all that this data is not yet in the public realm.
« Last Edit: 09/19/2014 05:43 PM by JohnFornaro »
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Offline JohnFornaro

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Re: EM Drive Developments
« Reply #775 on: 09/19/2014 04:29 PM »
Solo riportati

Solo riporto?  Don't know the idiomatic phrase.
Sometimes I just flat out don't get it.

Offline Rodal

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Re: EM Drive Developments
« Reply #776 on: 09/19/2014 04:45 PM »
Solo riportati

Solo riporto?  Don't know the idiomatic phrase.
I stand corrected, kemosabe

Solo riporto :)
« Last Edit: 09/19/2014 04:52 PM by Rodal »

Offline aero

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Re: EM Drive Developments
« Reply #777 on: 09/19/2014 04:58 PM »
Here is a paper written to describe the Casimir energy between a metallic plate and a dielectric plate within a cavity. The configuration is somewhat similar to the Tapered Cavity tested at EagleWorks.

http://math.scichina.com:8081/sciAe/EN/abstract/abstract377962.shtml#

I wonder if someone can help interpret this paper. To me, it does not seem consistent with what has been published elsewhere, in particular I see an unfamiliar term

Quote
where -pi/(24a^2) is the Casimir force between two ideal conducting plates separated by a.

But also this paper is developed in a reference system where c=1, h-bar=1. That is a common system but how does one convert the results into standard units of measure.

I forgot, if I ever knew how.
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Online RonM

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Re: EM Drive Developments
« Reply #778 on: 09/19/2014 05:06 PM »
Here is a paper written to describe the Casimir energy between a metallic plate and a dielectric plate within a cavity. The configuration is somewhat similar to the Tapered Cavity tested at EagleWorks.

http://math.scichina.com:8081/sciAe/EN/abstract/abstract377962.shtml#

I wonder if someone can help interpret this paper. To me, it does not seem consistent with what has been published elsewhere, in particular I see an unfamiliar term

Quote
where -pi/(24a^2) is the Casimir force between two ideal conducting plates separated by a.

But also this paper is developed in a reference system where c=1, h-bar=1. That is a common system but how does one convert the results into standard units of measure.

I forgot, if I ever knew how.

http://en.wikipedia.org/wiki/Speed_of_light

http://en.wikipedia.org/wiki/Planck_constant

Offline aero

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Re: EM Drive Developments
« Reply #779 on: 09/19/2014 06:46 PM »
Here is a paper written to describe the Casimir energy between a metallic plate and a dielectric plate within a cavity. The configuration is somewhat similar to the Tapered Cavity tested at EagleWorks.

http://math.scichina.com:8081/sciAe/EN/abstract/abstract377962.shtml#

I wonder if someone can help interpret this paper. To me, it does not seem consistent with what has been published elsewhere, in particular I see an unfamiliar term

Quote
where -pi/(24a^2) is the Casimir force between two ideal conducting plates separated by a.

But also this paper is developed in a reference system where c=1, h-bar=1. That is a common system but how does one convert the results into standard units of measure.

I forgot, if I ever knew how.

http://en.wikipedia.org/wiki/Speed_of_light

http://en.wikipedia.org/wiki/Planck_constant

Well yes I know that, but the author uses "1" in the equations derivation for each of these terms so where do I substitute the real values back into the end result to get real measurable values? Am I forced to carefully follow the derivation through to the end then know where the c's and h-bars go? (numerator, denominator, power, etc.)

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