Dear all
solving the gravitational wave propagation integral(and thus the Einstein field equations in weak field limit because the integral is then an equivalent formulation of them) in the weak field limit and in the case of a cylindrically symmetric hollow resonator with an oscillating internal energy density I have found out that even in the original
einstein theory (without hoyle-narlikar modifications) there is a difference in the radiated gravitational field between the two + and - z directions if in addition to the 00-component of the energy-momentum tensor (mass energy density) and the 0a / a0 energy current density terms there are non-zero stress components in radial or axial direction.
For what follows I described the cavity in local cylindrical coordinates with it's symmetry axis
aligned along the z axis. I modelled the cavity using mass density distributions of lorentzian shape which allows for an analytic solution of the integral in a constant retardation phase approximation. This also allows to derive an analytic expression for the 0z component of T from the 00 component via the continuity equation. After solving the integral for the h field I determined the scalarat two different locations "above" and "below" the resonator. I assumed a length for the resonator of 1 m and a diameter of 20 cm. The thickness of the walls is determined by the coefficients of the lorentzian shape functions more less to be of the order of mm to cm. ...
Thank you so much for your contribution !
Much appreciated
QUESTIONS:
1) Your calculation is for a constant cross-section cylindrical cavity (please correct me if I am wrong) without an unsymmetrically placed dielectric insert. What do you expect to find for a tapered cavity as proposed by Shawyer?
2) Does your calculation show greater amplitude differences between the wave fields above and below the resonator for thicker thickness of the metal used in the cavity ? (as predicted for example by Minotti in his gravito-magnetic formulation)
3) My understanding is that the amplitude difference between the wave fields above and below the resonator gives a net force/PowerInput that is several orders of magnitude smaller not only than the force/PowerInput claimed by EM Drive experimenters (not just smaller than Shawyer/Yang, and smaller than NASA), but actually significantly smaller than the force/PowerInput of a perfectly collimated photon rocket. Is my understanding correct?
(The problem is that G/c4 has such a small magnitude)
...
Thank you.
1: Yes, the curves of the h scalar shown above are the ones that are generated by a constant cross-section cylinder.
I chose this geometry first, because in contrast to the tapered geometry, the propagation integral has an analytic solution.
Regarding this question I would actually like to ask a question to someone who knows a lot about electromagnetic field induced maxwell stresses in the walls of a resonating cavity.
In my calculations I mathematically introduced an axial stress component which of course does not restrict it's origin to be electromagnetic in nature. The stress could have any origin. But could it be that physically the cavity field modes of a cylindrical cavity never generate axial stress components, so that this is the reason why such an effect can only occur in other geometries? For an amplitude difference to show up I found out that either axial or radial stresses or a superposition of them is needed. If the Tphiphi component was the only non-zero component, the calculations showed a zero amplitude difference independent of the stress amplitude.
Specifically has anyone investigated the axial stresses in constant cross-section vs. tapered cavities induced by the physically existing electromagnetic field modes?
Could it be that there are only non-zero axial components in the tapered geometry?
2: I haven't investigated this, but I will. It is not difficult to change the code in this respect.
"...but actually significantly smaller than the force/PowerInput of a perfectly collimated photon rocket. "
3: Before giving an answer to this I have to calculate the total momentum flux density from the field equations. I will try to do this soon.


For builders, attached is a quote I received for <100 Angstrom (0.01 micrometer) planing and polishing. Not cheap, but this is one of the few companies that can do this. I settled for 0.5 micron polishing and 2-3 micrometers flatness. This is significantly better than what I used before and will see if it has any impact on my tests.
For builders, attached is a quote I received for <100 Angstrom (0.01 micrometer) planing and polishing. Not cheap, but this is one of the few companies that can do this. I settled for 0.5 micron polishing and 2-3 micrometers flatness. This is significantly better than what I used before and will see if it has any impact on my tests.
Does anyone have an opinion which inject method I should use before I run the sweep?
Is Shawyer injecting RF into both of these coax or is one for spectrum analysis?
For builders, attached is a quote I received for <100 Angstrom (0.01 micrometer) planing and polishing. Not cheap, but this is one of the few companies that can do this. I settled for 0.5 micron polishing and 2-3 micrometers flatness. This is significantly better than what I used before and will see if it has any impact on my tests.
Dave, for what it's worth for the DIY community, angstrom level polishing of soft metals can be done with...
India Ink. India Ink is basically a suspension of Buckminsterfullerenes (buckyballs) in water.
For builders, attached is a quote I received for <100 Angstrom (0.01 micrometer) planing and polishing. Not cheap, but this is one of the few companies that can do this. I settled for 0.5 micron polishing and 2-3 micrometers flatness. This is significantly better than what I used before and will see if it has any impact on my tests.Are you planning to electroplate the internals with 99% silver that alone could provide a 18% increase in Q?
Shell
For builders, attached is a quote I received for <100 Angstrom (0.01 micrometer) planing and polishing. Not cheap, but this is one of the few companies that can do this. I settled for 0.5 micron polishing and 2-3 micrometers flatness. This is significantly better than what I used before and will see if it has any impact on my tests.
Dave, for what it's worth for the DIY community, angstrom level polishing of soft metals can be done with...
India Ink. India Ink is basically a suspension of Buckminsterfullerenes (buckyballs) in water.Thank you! Did not know this...very nice

http://arxiv.org/pdf/physics/9811001.pdf
I wish my math wasn't so rusty, just good enough to let me see how evanescent actions could come into effect and maybe amplify this effect. Help this old gal here, am I seeing this wrong?
Shell
[...] a full relativistic study of the streamlines followed by the electron probability density show clearly that no superluminal velocities are present. The same result is true for photons, as we will discuss elsewhere.
...
Shell,
I would like to draw your attention to the following paper by Doran et al. "SPACETIME ALGEBRA AND ELECTRON PHYSICS" (2005):
http://arxiv.org/pdf/quant-ph/0509178.pdf
...
This is the whole lab, in my opinion, there is no other room.
Behind the entrance door is the short anteroom or loading bay.
...
Shell,
I would like to draw your attention to the following paper by Doran et al. "SPACETIME ALGEBRA AND ELECTRON PHYSICS" (2005):
http://arxiv.org/pdf/quant-ph/0509178.pdf
...Talking about awesome, this paper "SPACETIME ALGEBRA AND ELECTRON PHYSICS" from the Cavendish Laboratory at Cambridge University is truly awesome !
Thank you so much !
This is the whole lab, in my opinion, there is no other room.
Behind the entrance door is the short anteroom or loading bay.
I watched again just to take my time and I see at least 5 drives spread out in the lab from small to quite large, from conical to rectangular frustums. It looks like he has been busy.
Shell
http://arxiv.org/pdf/physics/9811001.pdf
I wish my math wasn't so rusty, just good enough to let me see how evanescent actions could come into effect and maybe amplify this effect. Help this old gal here, am I seeing this wrong?
Shell
(Long time lurker here -- since thread #2.)
Shell,
I would like to draw your attention to the following paper by Doran et al. "SPACETIME ALGEBRA AND ELECTRON PHYSICS" (2005):
http://arxiv.org/pdf/quant-ph/0509178.pdf
As the authors point out, superluminal group-velocity is perhaps just an artifact of our current mathematical framework. By switching to a different framework, called geometric algebra, they show (p.54) that:Quote[...] a full relativistic study of the streamlines followed by the electron probability density show clearly that no superluminal velocities are present. The same result is true for photons, as we will discuss elsewhere.
I have come to know about this new algebra through my work in signal processing. Specifically, the introduction of a two-dimensional generalization of Gabor's analytic signal from his famous 1946 paper was only possible once Michael Felsberg switched to this mathematical framework during his PhD studies.
For those interested, his PhD thesis can be found here:
http://www.informatik.uni-kiel.de/inf/Sommer/doc/Dissertationen/Michael_Felsberg/diss.pdf
Why am I bringing this up? Because I believe that this algebra, developed in the 19th century, can sometimes provide more insight into the geometric elegance of our universe. It has also been shown that variants of geometric algebra are isomorphic to both the complex numbers set and to quaternions. Thus, one can simply write Maxwell's equations as ∂F=J, where F=E+jcB is the electromagnetic field multivector, and J is the electric current density. Then, the equation simply tells us that the gradient of the field F is proportional to the electromagnetic sources J.
For a geometric algebra primer for electrical engineers, please see Chappel et al. "Geometric Algebra for Electrical and Electronic Engineers" (2014). Section VII also discusses special relativity. The paper is available (open access) here:
http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=6876131
One final remark: I love this forum, you guys are awesome!
This is the whole lab, in my opinion, there is no other room.
Behind the entrance door is the short anteroom or loading bay.
I watched again just to take my time and I see at least 5 drives spread out in the lab from small to quite large, from conical to rectangular frustums. It looks like he has been busy.
ShellThe more I look at this, with only Mr. Shawyer standing around, all alone, those old familiar EM Drives he wrote about in older reports, none of them shown working, moving only by a push of his hands, the famous rotational Demonstrator shown on a video (instead of shown in the BBC video going around and around), ...
the more like this looks like the "EM Drive Museum"
reminding me of a time, not long ago, when anything seemed possible, when people dared to dream big and take risks...
...
Thank you.
1: Yes, the curves of the h scalar shown above are the ones that are generated by a constant cross-section cylinder.
I chose this geometry first, because in contrast to the tapered geometry, the propagation integral has an analytic solution.
Regarding this question I would actually like to ask a question to someone who knows a lot about electromagnetic field induced maxwell stresses in the walls of a resonating cavity.
In my calculations I mathematically introduced an axial stress component which of course does not restrict it's origin to be electromagnetic in nature. The stress could have any origin. But could it be that physically the cavity field modes of a cylindrical cavity never generate axial stress components, so that this is the reason why such an effect can only occur in other geometries? For an amplitude difference to show up I found out that either axial or radial stresses or a superposition of them is needed. If the Tphiphi component was the only non-zero component, the calculations showed a zero amplitude difference independent of the stress amplitude.
Specifically has anyone investigated the axial stresses in constant cross-section vs. tapered cavities induced by the physically existing electromagnetic field modes?
Could it be that there are only non-zero axial components in the tapered geometry?
2: I haven't investigated this, but I will. It is not difficult to change the code in this respect.
"...but actually significantly smaller than the force/PowerInput of a perfectly collimated photon rocket. "
3: Before giving an answer to this I have to calculate the total momentum flux density from the field equations. I will try to do this soon.On a DIY subject, did you consider going ahead with the manufacture of a self-made 2-chamber Klystron (several tens of kW ?) using a 3 D printer to make the buncher and catcher chambers ?
Are you , or were you able to get a suitable Helmholtz coil for the external E-beam confining axial magnetic field ?
Any updates appreciated. Sounded promising. Thanks
...
I had the idea to build it in my local fablab but because I am doing this in my free time beside ph d work due to lack of time and money I stopped sometime in the planning phase.
I still would like to do this because I would really like to see a 10+ kW Klystron with feedback loop in action in any of the frustrums build by the people here.
Actually recently, being curious and willing to work full time on the microwave resonator concept, I sent an application to SPR Ltd. (Shawyers company) because this would be the only way to have enough time to pursue all projects.
I sent my formal and complete application to
SPR Ltd.
Unit 40.
Broadmarsh Centre
Havant
Hampshire
PO9 1HS
United Kingdom
they wrote upon it: Return to sender (me), adress unknown, no such number no such zone.
Does SPR exist after all? If they do, can't they show the decency to send a one sentence mail that they are not in need of scientists and engineers?
A lot of questions.