....FYI: Marco's 1st draft paper went out on an email today from Paul M. and was distributed to about 35 individuals, including myself to my surprise. A swath of replies went back and forth, including a copy and paste of one of our posts here, between Dr. Rodal and myself. The comments were not constructive, as both Jack S. and Eric D. discarded the notion of gravity in the frustum, because GR would require overcoming the G/c^4 factor. What these Dr's are missing is that we are not effecting the full spectrum from long wavelength RF to high energy quarks with what is happening in the frustum. It is only mimicking what gravity does in a very narrow bandwidth of the EM spectrum. The factor G/c^4 is only applicable for gravity that affects the FULL bandwidth of all energy and particles. G/c^4 comes from the integral over all modes in the field. We are not affecting all modes, just a few in a relatively low energy regime.That's IMO of course.Todd

this is a reference to NASA's experiments with an interferometer, where the laser beam goes through small portholes on a pillbox shaped cylindrical EM Drive cavity. It is my understanding that NASA has not measured any thrust forces from this experiment involving a pillbox shaped EM Drive cavity.NASA expected no significant thrust either, because the pillbox-shaped cavity is entirely symmetric in the longitudinal direction (parallel to the laser beam) and because the cavity did not contain any polymer dielectric insert in the experiments (as so far performed).

I would like to remember that White is not using exotic matter at all. Rather, he is working with strong RF fields to try to develop a warp bubble. This was stated here even if implicitly. Finally, an EmDrive device has been properly described here. Using strong external fields to modify locally a space-time has been described here.If this will be confirmed in the next few months, it will represent a major breakthrough in experimental general relativity since Eddington confirmed the bending of light near the sun. Applications would follow if this idea will appear scalable but it will be a shocking result anyway. We look forward to hear from White very soon.Marco Frasca (2005). Strong coupling expansion for general relativity Int.J.Mod.Phys.D15:1373-1386,2006 arXiv: hep-th/0508246v3

What if the photon rocket utilized the same construction with a cavity that would make the light move slower? http://news.harvard.edu/gazette/1999/02.18/light.htmlAs it is possible to slow the light, then the lower its speed the bigger its thrust.That's one thing. The other is that the thrust is multiplied by the number of bounccs.That applies to MW waves in the resonating cavity. Hence - the bigger the number of bounces, the bigger the thrust.You can actually amplify the photon rocket thrust as well.

...In my opinion the engine resembles a very stiff speaker calculated for resonance frequency of 2,45MHz. The stiffer the material the better it resonates in this frequency. It's not only the Q that matters. That may be the reason the Cannae engine has lower efficiency - it is made of thinner metal that is less stiff....Quote from: Rodal on 05/08/2015 01:40 PMThe problem is that I can hear music from an open speaker (a "waveguide") but I cannot hear anything out of a speaker that is a closed cavity, such that all internal surfaces are perfectly reflective (the closed cavity of the EM Drive).And if you open the big base of the EM Drive cavity, so that it becomes a speaker, then it is a very inefficient photon rocket, and therefore the claims of Shawyer don't make sense because they are thousands of time greater thrust per input power than a photon rocket All right. Than maybe the magnetic field of the microwaves resonating inside the cavity "pushes" against the magnetic field of Earth. Anyway, the reversed parabolic (speaker-like) shape may send more waves to the wide end.Whatever the reason it moves, all I am saying is that it has to be tested. Not only for different Q, but also different shapes, different MW injection positions and different stiffness of the 'emiting' structure.

The problem is that I can hear music from an open speaker (a "waveguide") but I cannot hear anything out of a speaker that is a closed cavity, such that all internal surfaces are perfectly reflective (the closed cavity of the EM Drive).And if you open the big base of the EM Drive cavity, so that it becomes a speaker, then it is a very inefficient photon rocket, and therefore the claims of Shawyer don't make sense because they are thousands of time greater thrust per input power than a photon rocket

Quote from: WarpTech on 05/08/2015 04:21 PM....FYI: Marco's 1st draft paper went out on an email today from Paul M. and was distributed to about 35 individuals, including myself to my surprise. A swath of replies went back and forth, including a copy and paste of one of our posts here, between Dr. Rodal and myself. The comments were not constructive, as both Jack S. and Eric D. discarded the notion of gravity in the frustum, because GR would require overcoming the G/c^4 factor. What these Dr's are missing is that we are not effecting the full spectrum from long wavelength RF to high energy quarks with what is happening in the frustum. It is only mimicking what gravity does in a very narrow bandwidth of the EM spectrum. The factor G/c^4 is only applicable for gravity that affects the FULL bandwidth of all energy and particles. G/c^4 comes from the integral over all modes in the field. We are not affecting all modes, just a few in a relatively low energy regime.That's IMO of course.ToddI don't know who Jack S. and Eric D. are. If the letter is in reference to forum posts, I'm glad I had posted this some time ago:http://forum.nasaspaceflight.com/index.php?topic=36313.msg1371241#msg1371241Quote from: Rodal this is a reference to NASA's experiments with an interferometer, where the laser beam goes through small portholes on a pillbox shaped cylindrical EM Drive cavity. It is my understanding that NASA has not measured any thrust forces from this experiment involving a pillbox shaped EM Drive cavity.NASA expected no significant thrust either, because the pillbox-shaped cavity is entirely symmetric in the longitudinal direction (parallel to the laser beam) and because the cavity did not contain any polymer dielectric insert in the experiments (as so far performed).So if Jack S. and Eric D. (whoever they are) are discussing "the notion of gravity in the frustum" I already pointed out that the Interferometer tests were not conducted with a frustum but instead with a pillbox shaped cylindrical geometry. As to the size of the spacetime distortion everybody is in agreement that one expects it to be extremely small. That's the relevance of Marco Frasca's papers: and why Frasca's papers are so interesting, regarding the appropriate coupling.QUESTION: In any case what are these people (Jack S. and Eric D. ) so excited about that they are writing about it? What's the harm with Dr. White trying to find out?As Frasca wrote in his webpage:QuoteI would like to remember that White is not using exotic matter at all. Rather, he is working with strong RF fields to try to develop a warp bubble. This was stated here even if implicitly. Finally, an EmDrive device has been properly described here. Using strong external fields to modify locally a space-time has been described here.If this will be confirmed in the next few months, it will represent a major breakthrough in experimental general relativity since Eddington confirmed the bending of light near the sun. Applications would follow if this idea will appear scalable but it will be a shocking result anyway. We look forward to hear from White very soon.Marco Frasca (2005). Strong coupling expansion for general relativity Int.J.Mod.Phys.D15:1373-1386,2006 arXiv: hep-th/0508246v3

Quote from: Rodal on 05/08/2015 01:40 PM....And if you open the big base of the EM Drive cavity, so that it becomes a speaker, then it is a very inefficient photon rocket, and therefore the claims of Shawyer don't make sense because they are thousands of time greater thrust per input power than a photon rocket I need to study @notsosureofit's GR calculation, but I think the point that is being missed here is, the resonant cavity acts as an EM Momentum amplifier. The Q factor comes in not "Just" as the number of photons stored, but also; In GR as in PV, as the energy density inside the cavity increases, the wave velocity decreases. As velocity decreases, momentum increases. That "effective mass" of the photons in the cavity kicks in stronger.p ~ E/v and in the cavity v << cThis makes it a not-so "inefficient" photon rocket!In the EM Drive design I proposed, we want the Q in the resonant cavity to be very high, but we do not want a high Q in the frustum. We want the backward-moving waves to expand, and the reflected waves moving forward to be attenuated. So we want a low Q, high attenuation in the frustum.Todd

....And if you open the big base of the EM Drive cavity, so that it becomes a speaker, then it is a very inefficient photon rocket, and therefore the claims of Shawyer don't make sense because they are thousands of time greater thrust per input power than a photon rocket

Quote from: WarpTech on 05/08/2015 02:16 PMQuote from: Rodal on 05/08/2015 01:40 PM....And if you open the big base of the EM Drive cavity, so that it becomes a speaker, then it is a very inefficient photon rocket, and therefore the claims of Shawyer don't make sense because they are thousands of time greater thrust per input power than a photon rocket I need to study @notsosureofit's GR calculation, but I think the point that is being missed here is, the resonant cavity acts as an EM Momentum amplifier. The Q factor comes in not "Just" as the number of photons stored, but also; In GR as in PV, as the energy density inside the cavity increases, the wave velocity decreases. As velocity decreases, momentum increases. That "effective mass" of the photons in the cavity kicks in stronger.p ~ E/v and in the cavity v << cThis makes it a not-so "inefficient" photon rocket!What if the photon rocket utilized the same construction with a cavity that would make the light move slower? http://news.harvard.edu/gazette/1999/02.18/light.htmlAs it is possible to slow the light, then the lower its speed the bigger its thrust.That's one thing. The other is that the thrust is multiplied by the number of bounccs.That applies to MW waves in the resonating cavity. Hence - the bigger the number of bounces, the bigger the thrust.You can actually amplify the photon rocket thrust as well.See here:Source: Wiki, http://upload.wikimedia.org/wikipedia/commons/8/8e/Photon-Thrust-Amplification.jpg

Quote from: Rodal on 05/08/2015 01:40 PM....And if you open the big base of the EM Drive cavity, so that it becomes a speaker, then it is a very inefficient photon rocket, and therefore the claims of Shawyer don't make sense because they are thousands of time greater thrust per input power than a photon rocket I need to study @notsosureofit's GR calculation, but I think the point that is being missed here is, the resonant cavity acts as an EM Momentum amplifier. The Q factor comes in not "Just" as the number of photons stored, but also; In GR as in PV, as the energy density inside the cavity increases, the wave velocity decreases. As velocity decreases, momentum increases. That "effective mass" of the photons in the cavity kicks in stronger.p ~ E/v and in the cavity v << cThis makes it a not-so "inefficient" photon rocket!

Bend this light path with optical fiber and you receive a powerful thruster.Like this:A very simple idea... nobody ever checked it yet, I suppose. I think this setup may be worth checking. Please consider the fact that it is not c in the nominator, but the actual speed of light in the optical fiber. The slower the speed of the light in this apparatus, the greater the thrust!The EmDrive works based on similar principle.

Quote from: Rodal on 05/08/2015 01:53 PMQuote from: Notsosureofit on 05/08/2015 01:45 PM....You are too fast for my old fingers...Ultimately, what needs to be shown here is that the "covariant force vector equal to zero" on a photon in the accelerated frame is the same vector in the cavity rest frame (ie. can be transformed to) such that the force on a photon in the rest frame is a result of the (velocity) dispersion due to the shape of the cavity boundary conditions. That transformation would show that the effect is to be expected under General Relativity.The Q only enters in the case of a gravitational interaction through its role in calculating the number of photons (Total mass/energy) in the cavity. If it was a Newtonian momentum interaction only the Power enters. (I get zero when I try Newtonian for the reasons you have mentioned)Note: I should probably use "Classical" instead of "Newtonian" but I think you would get the idea that we are looking at the 4-volume as an invariant rather than an integration over the surface of the boundary conditions of classical momentum exchange. That can apply as the summation of the (false gravitational?, ie. frame-dependent) forces on the individual photons to give the resultant force on the cavity.I very much appreciate the explanation, unfortunately, I may not be able to understand this until I see the explicit mathematical formula for the 4-volume invariant, particularly the derivation of that invariant Unfortunately, I cannot do it intuitively as you can.That would, of course, constitute a proof.

Quote from: Notsosureofit on 05/08/2015 01:45 PM....You are too fast for my old fingers...Ultimately, what needs to be shown here is that the "covariant force vector equal to zero" on a photon in the accelerated frame is the same vector in the cavity rest frame (ie. can be transformed to) such that the force on a photon in the rest frame is a result of the (velocity) dispersion due to the shape of the cavity boundary conditions. That transformation would show that the effect is to be expected under General Relativity.The Q only enters in the case of a gravitational interaction through its role in calculating the number of photons (Total mass/energy) in the cavity. If it was a Newtonian momentum interaction only the Power enters. (I get zero when I try Newtonian for the reasons you have mentioned)Note: I should probably use "Classical" instead of "Newtonian" but I think you would get the idea that we are looking at the 4-volume as an invariant rather than an integration over the surface of the boundary conditions of classical momentum exchange. That can apply as the summation of the (false gravitational?, ie. frame-dependent) forces on the individual photons to give the resultant force on the cavity.I very much appreciate the explanation, unfortunately, I may not be able to understand this until I see the explicit mathematical formula for the 4-volume invariant, particularly the derivation of that invariant Unfortunately, I cannot do it intuitively as you can.

....You are too fast for my old fingers...Ultimately, what needs to be shown here is that the "covariant force vector equal to zero" on a photon in the accelerated frame is the same vector in the cavity rest frame (ie. can be transformed to) such that the force on a photon in the rest frame is a result of the (velocity) dispersion due to the shape of the cavity boundary conditions. That transformation would show that the effect is to be expected under General Relativity.The Q only enters in the case of a gravitational interaction through its role in calculating the number of photons (Total mass/energy) in the cavity. If it was a Newtonian momentum interaction only the Power enters. (I get zero when I try Newtonian for the reasons you have mentioned)Note: I should probably use "Classical" instead of "Newtonian" but I think you would get the idea that we are looking at the 4-volume as an invariant rather than an integration over the surface of the boundary conditions of classical momentum exchange. That can apply as the summation of the (false gravitational?, ie. frame-dependent) forces on the individual photons to give the resultant force on the cavity.

Quote from: WarpTech on 05/08/2015 02:16 PMQuote from: Rodal on 05/08/2015 01:40 PM....And if you open the big base of the EM Drive cavity, so that it becomes a speaker, then it is a very inefficient photon rocket, and therefore the claims of Shawyer don't make sense because they are thousands of time greater thrust per input power than a photon rocket I need to study @notsosureofit's GR calculation, but I think the point that is being missed here is, the resonant cavity acts as an EM Momentum amplifier. The Q factor comes in not "Just" as the number of photons stored, but also; In GR as in PV, as the energy density inside the cavity increases, the wave velocity decreases. As velocity decreases, momentum increases. That "effective mass" of the photons in the cavity kicks in stronger.p ~ E/v and in the cavity v << cThis makes it a not-so "inefficient" photon rocket!In the EM Drive design I proposed, we want the Q in the resonant cavity to be very high, but we do not want a high Q in the frustum. We want the backward-moving waves to expand, and the reflected waves moving forward to be attenuated. So we want a low Q, high attenuation in the frustum.ToddSorry if this was already stated but, what is quantitatively the energy density inside the cavity (with a given Q of say, 10000) ? And how much quantitatively the wave velocity would decrease due to this energy density ? According to strict and uncontroversial interpretation of GR ?

Quote from: TheTraveller on 05/07/2015 08:46 PMQuote from: Rodal on 05/07/2015 07:59 PMQuote from: TheTraveller on 05/07/2015 07:54 PM....Did you or anyone else ever write an excel spreadsheet to calc Shawyers Design Factor? If so pls link it or if not please consider doing it as your skills there are much better than mine.Yes I have calculated it, but it is a Mathematica program, not an Excel spreadsheet. I posted (earlier in the thread) comparisons of the measurements vs. predictions using Shawyer's and McCulloch's formulas.You may want to PM @aero to ask whether he did it with Excel (if my memory is correct @aero also calculated Shawyer's Design Factor, as I recall having exchanges in this forum with him).And of course, when running your program, you will first check your results vs. Shawyer's published Design Factor results, etc., to make sure that your program is correct.Mathematica looks interesting but maybe later as I suspect there would be a learning curve.Is this still your Design Factor equation?Thanks for your assistance. Most appreciated.I recognize that equation is my Mathematica-writing, but I need a link to the message where I posted it, in order to remember the context. Too long ago

Quote from: Rodal on 05/07/2015 07:59 PMQuote from: TheTraveller on 05/07/2015 07:54 PM....Did you or anyone else ever write an excel spreadsheet to calc Shawyers Design Factor? If so pls link it or if not please consider doing it as your skills there are much better than mine.Yes I have calculated it, but it is a Mathematica program, not an Excel spreadsheet. I posted (earlier in the thread) comparisons of the measurements vs. predictions using Shawyer's and McCulloch's formulas.You may want to PM @aero to ask whether he did it with Excel (if my memory is correct @aero also calculated Shawyer's Design Factor, as I recall having exchanges in this forum with him).And of course, when running your program, you will first check your results vs. Shawyer's published Design Factor results, etc., to make sure that your program is correct.Mathematica looks interesting but maybe later as I suspect there would be a learning curve.Is this still your Design Factor equation?Thanks for your assistance. Most appreciated.

Quote from: TheTraveller on 05/07/2015 07:54 PM....Did you or anyone else ever write an excel spreadsheet to calc Shawyers Design Factor? If so pls link it or if not please consider doing it as your skills there are much better than mine.Yes I have calculated it, but it is a Mathematica program, not an Excel spreadsheet. I posted (earlier in the thread) comparisons of the measurements vs. predictions using Shawyer's and McCulloch's formulas.You may want to PM @aero to ask whether he did it with Excel (if my memory is correct @aero also calculated Shawyer's Design Factor, as I recall having exchanges in this forum with him).And of course, when running your program, you will first check your results vs. Shawyer's published Design Factor results, etc., to make sure that your program is correct.

....Did you or anyone else ever write an excel spreadsheet to calc Shawyers Design Factor? If so pls link it or if not please consider doing it as your skills there are much better than mine.

I did, but the Excel file is not suitable for distribution, having all of my work scattered throughout a 500 line file with little or no embedded explanations. That is, it's un-usable even for me, without considerable time discovering what I intended to do. For example, here is my design factor, Df, equations. I think the variables are: Lo - lengthLg1-diameterLg2-diameterDf = 0.844 Df=S_o*Lo((1/Lg1) - (1/lg2)) where S_o = (1-(Lo^2/(Lg1*Lg2)))^-1 Combining Df = Lo*( 1 - (Lo^2/(Lg1*Lg2)))^-1 *((1/Lg1)-(1/Lg2))

Edit: I used to have Penrose, Roger (1965). "A remarkable property of plane waves in general relativity". Rev. Mod. Phys. 37: 215–220. Bibcode:1965RvMP...37..215P. doi:10.1103/RevModPhys.37.215around here somewhere, I'll look.

And regarding Shawyer's design factor, I did program Dr. Rodel's equation and did match his numbers but it was some time ago and is now lost in the fog of the past.

Quote from: Notsosureofit on 05/08/2015 06:28 PMEdit: I used to have Penrose, Roger (1965). "A remarkable property of plane waves in general relativity". Rev. Mod. Phys. 37: 215–220. Bibcode:1965RvMP...37..215P. doi:10.1103/RevModPhys.37.215around here somewhere, I'll look.Amazing ! Found it after all these years. I have to re-read and re-understand it of course, but check Fig. 1. "The sandwich wave" where you have a section of curved space-time sandwiched between flat. That alone is closer to this situation than anything I've seen so far.The previous article, Rosen, Joe. "Embedding of Various Relativistic Riemannian Spaces in Pseudo-Euclidean Spaces" contains tables of transforms. That could prove invaluable !

Consider the following EM Drive design:1st component: A symmetrical resonator cavity that is optimized to store energy at high Q, and plays no role in thrust. Here, we want to store the lowest order mode that the waveguide can sustain because it has the slowest wave velocity inside the waveguide. By targeting the slowest wave velocity, we are maximizing the amount of stored electromagnetic momentum for a given amount electromagnetic energy.p = E/v, where v << c inside the waveguide.E = P*t, energy is power in x time (assuming a lossless cavity)2nd component: We need a frustum that matches the diameter of the resonant chamber "at the small end" and slowly expands to a TBD length and diameter. As the waveguide expands, the wavelength will be increasing proportional to the increasing wave velocity. We want it to expand to near it's free space value....

Its great to see continuing discussions on this emdrive forum. There are Theorists and there are Observers. I tend to fall into the latter category and appreciate all those willing to build their own test articles, sharing plans & results. Onwards and upwards...

Quote from: WarpTech on 05/08/2015 05:51 AMConsider the following EM Drive design:1st component: A symmetrical resonator cavity that is optimized to store energy at high Q, and plays no role in thrust. Here, we want to store the lowest order mode that the waveguide can sustain because it has the slowest wave velocity inside the waveguide. By targeting the slowest wave velocity, we are maximizing the amount of stored electromagnetic momentum for a given amount electromagnetic energy.p = E/v, where v << c inside the waveguide.E = P*t, energy is power in x time (assuming a lossless cavity)2nd component: We need a frustum that matches the diameter of the resonant chamber "at the small end" and slowly expands to a TBD length and diameter. As the waveguide expands, the wavelength will be increasing proportional to the increasing wave velocity. We want it to expand to near it's free space value....Is this design analogous to the "Modified Aluminum Cavity for TE011 Mode Resonance" previously presented by Paul March? Note, there appears to be two chambers separated by a 1/16" plate (aluminum?). As an avid follower of this thread I have not noticed any comments about this dual chamber design. However, I could be misinterpreting the attached image. This has been a truly fascinating discussion which has never ceased capturing my attention. I feel fortunate to passively witness. Thank you all, especially the replicators. -Matthew Trimble

Quote from: WarpTech on 05/08/2015 05:51 AMConsider the following EM Drive design:1st component: A symmetrical resonator cavity that is optimized to store energy at high Q, and plays no role in thrust. Here, we want to store the lowest order mode that the waveguide can sustain because it has the slowest wave velocity inside the waveguide. By targeting the slowest wave velocity, we are maximizing the amount of stored electromagnetic momentum for a given amount electromagnetic energy.p = E/v, where v << c inside the waveguide.E = P*t, energy is power in x time (assuming a lossless cavity)2nd component: We need a frustum that matches the diameter of the resonant chamber "at the small end" and slowly expands to a TBD length and diameter. As the waveguide expands, the wavelength will be increasing proportional to the increasing wave velocity. We want it to expand to near it's free space value....Is this design analogous to the "Modified Aluminum Cavity for TE011 Mode Resonance" previously presented by Paul March? Note, there appears to be two chambers separated by a 1/16" aluminum plate. As an avid follower of this thread I have not noticed any comments about this dual chamber design. However, I could be misinterpreting the attached image. This has been a truly fascinating discussion which has never ceased capturing my attention. I feel fortunate to passively witness. Thank you all, especially the replicators. -Matthew Trimble

QuoteBend this light path with optical fiber and you receive a powerful thruster.Like this:A very simple idea... nobody ever checked it yet, I suppose. I think this setup may be worth checking. Please consider the fact that it is not c in the nominator, but the actual speed of light in the optical fiber. The slower the speed of the light in this apparatus, the greater the thrust!The EmDrive works based on similar principle.I'm sorry but to "bend" the light 180° around like that is equivalent in terms of momentum exchange to just bouncing it : in your above drawing the fibre bundle would receive 2F to the right from this momentum exchange. The total force on an isolated rigid craft would still be 0, as in the first drawing.