Quote from: Notsosureofit on 05/16/2015 02:12 PMQuote from: StrongGR on 05/16/2015 01:55 PMQuote from: Notsosureofit on 05/16/2015 01:39 PMQuote from: StrongGR on 05/16/2015 01:36 PMQuote from: Notsosureofit on 05/16/2015 01:23 PMQuote from: Rodal on 05/16/2015 04:06 AMQuote from: SeeShells on 05/16/2015 03:56 AMAnyone seen this little tidbit?http://phys.org/news/2015-05-newton-law-broken.htmlNon-equiibrium thermodynamicsI have to find my old copy of the book by S. R. De Groot, P. Mazur and other such books I have in boxesand see whether we can derive a force for the EM Drive based on Onsager's relations Still looking for my copy as well ! (old cavity work was on transport properties)The system in that paper is not isolated from the environment. For EM Drive this is not true. You have to cope with a closed system and to understand why third law appears to be violated, if the effect is confirmedYup !Do you remember if DeGroot mentioned photons ?That book is rather old. I just gave a cursory look and found nothing about photons. You should rather consider the case for electromagnetic radiation. What could make the thing resemble that of a non-isolated system is leakage of radiation out of the cavity. I have to guess that one has built it reducing such losses. The idea to look at gravitational effects, started by Minotti's paper, is because in this case there is not a boundary due to the cavity and system appears to be open (space-time is everywhere). So, the third law would be saved by the expulsion of gravitational momentum. The reason why people in the community of scientists did not consider the case is the smallness of the gravity with respect to all other effects and so, one should not expect it to account for such a measurement.As you can see from my crude dispersion argument, the g value (of the photons) is much larger than one might naively expect."In the accelerated frame of reference w/ the acceleration, g = (c^2/(2*L*f^2))*(c/(2*Pi))^2*X^2*((1/Rs^2)-(1/Rb^2)) [for this waveguide-like approximation]."I missed something. Did you write a paper about? Please, let me know as I have not followed this discussion from the start.

Quote from: StrongGR on 05/16/2015 01:55 PMQuote from: Notsosureofit on 05/16/2015 01:39 PMQuote from: StrongGR on 05/16/2015 01:36 PMQuote from: Notsosureofit on 05/16/2015 01:23 PMQuote from: Rodal on 05/16/2015 04:06 AMQuote from: SeeShells on 05/16/2015 03:56 AMAnyone seen this little tidbit?http://phys.org/news/2015-05-newton-law-broken.htmlNon-equiibrium thermodynamicsI have to find my old copy of the book by S. R. De Groot, P. Mazur and other such books I have in boxesand see whether we can derive a force for the EM Drive based on Onsager's relations Still looking for my copy as well ! (old cavity work was on transport properties)The system in that paper is not isolated from the environment. For EM Drive this is not true. You have to cope with a closed system and to understand why third law appears to be violated, if the effect is confirmedYup !Do you remember if DeGroot mentioned photons ?That book is rather old. I just gave a cursory look and found nothing about photons. You should rather consider the case for electromagnetic radiation. What could make the thing resemble that of a non-isolated system is leakage of radiation out of the cavity. I have to guess that one has built it reducing such losses. The idea to look at gravitational effects, started by Minotti's paper, is because in this case there is not a boundary due to the cavity and system appears to be open (space-time is everywhere). So, the third law would be saved by the expulsion of gravitational momentum. The reason why people in the community of scientists did not consider the case is the smallness of the gravity with respect to all other effects and so, one should not expect it to account for such a measurement.As you can see from my crude dispersion argument, the g value (of the photons) is much larger than one might naively expect."In the accelerated frame of reference w/ the acceleration, g = (c^2/(2*L*f^2))*(c/(2*Pi))^2*X^2*((1/Rs^2)-(1/Rb^2)) [for this waveguide-like approximation]."

Quote from: Notsosureofit on 05/16/2015 01:39 PMQuote from: StrongGR on 05/16/2015 01:36 PMQuote from: Notsosureofit on 05/16/2015 01:23 PMQuote from: Rodal on 05/16/2015 04:06 AMQuote from: SeeShells on 05/16/2015 03:56 AMAnyone seen this little tidbit?http://phys.org/news/2015-05-newton-law-broken.htmlNon-equiibrium thermodynamicsI have to find my old copy of the book by S. R. De Groot, P. Mazur and other such books I have in boxesand see whether we can derive a force for the EM Drive based on Onsager's relations Still looking for my copy as well ! (old cavity work was on transport properties)The system in that paper is not isolated from the environment. For EM Drive this is not true. You have to cope with a closed system and to understand why third law appears to be violated, if the effect is confirmedYup !Do you remember if DeGroot mentioned photons ?That book is rather old. I just gave a cursory look and found nothing about photons. You should rather consider the case for electromagnetic radiation. What could make the thing resemble that of a non-isolated system is leakage of radiation out of the cavity. I have to guess that one has built it reducing such losses. The idea to look at gravitational effects, started by Minotti's paper, is because in this case there is not a boundary due to the cavity and system appears to be open (space-time is everywhere). So, the third law would be saved by the expulsion of gravitational momentum. The reason why people in the community of scientists did not consider the case is the smallness of the gravity with respect to all other effects and so, one should not expect it to account for such a measurement.

Quote from: StrongGR on 05/16/2015 01:36 PMQuote from: Notsosureofit on 05/16/2015 01:23 PMQuote from: Rodal on 05/16/2015 04:06 AMQuote from: SeeShells on 05/16/2015 03:56 AMAnyone seen this little tidbit?http://phys.org/news/2015-05-newton-law-broken.htmlNon-equiibrium thermodynamicsI have to find my old copy of the book by S. R. De Groot, P. Mazur and other such books I have in boxesand see whether we can derive a force for the EM Drive based on Onsager's relations Still looking for my copy as well ! (old cavity work was on transport properties)The system in that paper is not isolated from the environment. For EM Drive this is not true. You have to cope with a closed system and to understand why third law appears to be violated, if the effect is confirmedYup !Do you remember if DeGroot mentioned photons ?

Quote from: Notsosureofit on 05/16/2015 01:23 PMQuote from: Rodal on 05/16/2015 04:06 AMQuote from: SeeShells on 05/16/2015 03:56 AMAnyone seen this little tidbit?http://phys.org/news/2015-05-newton-law-broken.htmlNon-equiibrium thermodynamicsI have to find my old copy of the book by S. R. De Groot, P. Mazur and other such books I have in boxesand see whether we can derive a force for the EM Drive based on Onsager's relations Still looking for my copy as well ! (old cavity work was on transport properties)The system in that paper is not isolated from the environment. For EM Drive this is not true. You have to cope with a closed system and to understand why third law appears to be violated, if the effect is confirmed

Quote from: Rodal on 05/16/2015 04:06 AMQuote from: SeeShells on 05/16/2015 03:56 AMAnyone seen this little tidbit?http://phys.org/news/2015-05-newton-law-broken.htmlNon-equiibrium thermodynamicsI have to find my old copy of the book by S. R. De Groot, P. Mazur and other such books I have in boxesand see whether we can derive a force for the EM Drive based on Onsager's relations Still looking for my copy as well ! (old cavity work was on transport properties)

Quote from: SeeShells on 05/16/2015 03:56 AMAnyone seen this little tidbit?http://phys.org/news/2015-05-newton-law-broken.htmlNon-equiibrium thermodynamicsI have to find my old copy of the book by S. R. De Groot, P. Mazur and other such books I have in boxesand see whether we can derive a force for the EM Drive based on Onsager's relations

Anyone seen this little tidbit?http://phys.org/news/2015-05-newton-law-broken.html

Quote from: SeeShells on 05/16/2015 02:53 PM...Gads I love the internet and wished it was there when I was going to school. I'm not ready to throw the slab of idea and thought meat into the shark pool yet but thanks for the links!!! Kudos!Not sure about that...wonder how much individual thought process, creativity and imagination is overwhelmed by the huge amount of information available from the Internet nowadays. Many scientists think that it may have the opposite effect on individual intelligence and thought process as the mind needs as much or more exercise (to produce connections of neurons, etc.) as human muscles. With so many "answers" freely available at a click of one's fingers, there is much less exercise of one's brain Hopefully not a future of people thinking that Physics and Engineering is just a question of getting answers from a huge Internet cookbook of recipes and from black-box computer software instead of using mathematics and experiments to find out how Nature operates...

...Gads I love the internet and wished it was there when I was going to school. I'm not ready to throw the slab of idea and thought meat into the shark pool yet but thanks for the links!!! Kudos!

Quote from: StrongGR on 05/16/2015 04:12 PMQuote from: Notsosureofit on 05/16/2015 02:12 PMQuote from: StrongGR on 05/16/2015 01:55 PMQuote from: Notsosureofit on 05/16/2015 01:39 PMQuote from: StrongGR on 05/16/2015 01:36 PMQuote from: Notsosureofit on 05/16/2015 01:23 PMQuote from: Rodal on 05/16/2015 04:06 AMQuote from: SeeShells on 05/16/2015 03:56 AMAnyone seen this little tidbit?http://phys.org/news/2015-05-newton-law-broken.htmlNon-equiibrium thermodynamicsI have to find my old copy of the book by S. R. De Groot, P. Mazur and other such books I have in boxesand see whether we can derive a force for the EM Drive based on Onsager's relations Still looking for my copy as well ! (old cavity work was on transport properties)The system in that paper is not isolated from the environment. For EM Drive this is not true. You have to cope with a closed system and to understand why third law appears to be violated, if the effect is confirmedYup !Do you remember if DeGroot mentioned photons ?That book is rather old. I just gave a cursory look and found nothing about photons. You should rather consider the case for electromagnetic radiation. What could make the thing resemble that of a non-isolated system is leakage of radiation out of the cavity. I have to guess that one has built it reducing such losses. The idea to look at gravitational effects, started by Minotti's paper, is because in this case there is not a boundary due to the cavity and system appears to be open (space-time is everywhere). So, the third law would be saved by the expulsion of gravitational momentum. The reason why people in the community of scientists did not consider the case is the smallness of the gravity with respect to all other effects and so, one should not expect it to account for such a measurement.As you can see from my crude dispersion argument, the g value (of the photons) is much larger than one might naively expect."In the accelerated frame of reference w/ the acceleration, g = (c^2/(2*L*f^2))*(c/(2*Pi))^2*X^2*((1/Rs^2)-(1/Rb^2)) [for this waveguide-like approximation]."I missed something. Did you write a paper about? Please, let me know as I have not followed this discussion from the start.FYICleanup and detypo of the take on applying the Equivalence Principle.The proposition that dispersion caused by an accelerating frame of reference implied an accelerating frame of reference caused by a dispersive cavity resonator. (to 1st order using massless, perfectly conducting cavity)Starting with the expressions for the frequency of an RF cavity:f = (c/(2*Pi))*((X/R)^2+((p*Pi)/L)^2)^.5For TM modes, X = X[sub m,n] = the n-th zero of the m-th Bessel function.[1,1]=3.83, [0,1]=2.40, [0,2]=5.52 [1,2]=7.02, [2,1]=5.14, [2,2]=8.42, [1,3]=10.17, etc.and for TE modes, X = X'[subm,n] = the n-th zero of the derivative of the m-th Bessel function.[0,1]=3.83, [1,1]=1.84, [2,1]=3.05, [0,2]=7.02, [1,2]=5.33, [1,3]=8.54, [0,3]=10.17, [2,2]=6.71, etc.Rotate the dispersion relation of the cavity into doppler frame to get the Doppler shifts, that is to say, look at the dispersion curve intersections of constant wave number instead of constant frequency.df = (1/(2*f))*(c/(2*Pi))^2*X^2*((1/Rs^2)-(1/Rb^2))and from there the expression for the acceleration g from:g = (c^2/L)*(df/f) such that:g = (c^2/(2*L*f^2))*(c/(2*Pi))^2*X^2*((1/Rs^2)-(1/Rb^2))Using the "weight" of the photon in the accelerated frame from:"W" = (h*f/c^2)*g => "W" = T = (h/L)*dfgives thrust per photon:T = (h/(2*L*f))*(c/(2*pi))^2*X^2*((1/Rs^2)-(1/Rb^2))If the number of photons is (P/hf)*(Q/2*pi*f) then:NT = P*Q*(1/(4*pi*L*f^3))*(c/(2*pi))^2*X^2*((1/Rs^2)-(1/Rb^2))This does fit (as far as I've gotten) the concept of a self-accelerating Dirac wavepacket (which does conserve momentum).---------------------------------------------------------------------------------------------------------------------------Yes the search function is terribledf is delta f not the differential, Q is the effective Q due to phase shift etc.

Quote from: Notsosureofit on 05/16/2015 04:19 PMQuote from: StrongGR on 05/16/2015 04:12 PMQuote from: Notsosureofit on 05/16/2015 02:12 PMQuote from: StrongGR on 05/16/2015 01:55 PMQuote from: Notsosureofit on 05/16/2015 01:39 PMQuote from: StrongGR on 05/16/2015 01:36 PMQuote from: Notsosureofit on 05/16/2015 01:23 PMQuote from: Rodal on 05/16/2015 04:06 AMQuote from: SeeShells on 05/16/2015 03:56 AMAnyone seen this little tidbit?http://phys.org/news/2015-05-newton-law-broken.htmlNon-equiibrium thermodynamicsI have to find my old copy of the book by S. R. De Groot, P. Mazur and other such books I have in boxesand see whether we can derive a force for the EM Drive based on Onsager's relations Still looking for my copy as well ! (old cavity work was on transport properties)The system in that paper is not isolated from the environment. For EM Drive this is not true. You have to cope with a closed system and to understand why third law appears to be violated, if the effect is confirmedYup !Do you remember if DeGroot mentioned photons ?That book is rather old. I just gave a cursory look and found nothing about photons. You should rather consider the case for electromagnetic radiation. What could make the thing resemble that of a non-isolated system is leakage of radiation out of the cavity. I have to guess that one has built it reducing such losses. The idea to look at gravitational effects, started by Minotti's paper, is because in this case there is not a boundary due to the cavity and system appears to be open (space-time is everywhere). So, the third law would be saved by the expulsion of gravitational momentum. The reason why people in the community of scientists did not consider the case is the smallness of the gravity with respect to all other effects and so, one should not expect it to account for such a measurement.As you can see from my crude dispersion argument, the g value (of the photons) is much larger than one might naively expect."In the accelerated frame of reference w/ the acceleration, g = (c^2/(2*L*f^2))*(c/(2*Pi))^2*X^2*((1/Rs^2)-(1/Rb^2)) [for this waveguide-like approximation]."I missed something. Did you write a paper about? Please, let me know as I have not followed this discussion from the start.FYICleanup and detypo of the take on applying the Equivalence Principle.The proposition that dispersion caused by an accelerating frame of reference implied an accelerating frame of reference caused by a dispersive cavity resonator. (to 1st order using massless, perfectly conducting cavity)Starting with the expressions for the frequency of an RF cavity:f = (c/(2*Pi))*((X/R)^2+((p*Pi)/L)^2)^.5For TM modes, X = X[sub m,n] = the n-th zero of the m-th Bessel function.[1,1]=3.83, [0,1]=2.40, [0,2]=5.52 [1,2]=7.02, [2,1]=5.14, [2,2]=8.42, [1,3]=10.17, etc.and for TE modes, X = X'[subm,n] = the n-th zero of the derivative of the m-th Bessel function.[0,1]=3.83, [1,1]=1.84, [2,1]=3.05, [0,2]=7.02, [1,2]=5.33, [1,3]=8.54, [0,3]=10.17, [2,2]=6.71, etc.Rotate the dispersion relation of the cavity into doppler frame to get the Doppler shifts, that is to say, look at the dispersion curve intersections of constant wave number instead of constant frequency.df = (1/(2*f))*(c/(2*Pi))^2*X^2*((1/Rs^2)-(1/Rb^2))and from there the expression for the acceleration g from:g = (c^2/L)*(df/f) such that:g = (c^2/(2*L*f^2))*(c/(2*Pi))^2*X^2*((1/Rs^2)-(1/Rb^2))Using the "weight" of the photon in the accelerated frame from:"W" = (h*f/c^2)*g => "W" = T = (h/L)*dfgives thrust per photon:T = (h/(2*L*f))*(c/(2*pi))^2*X^2*((1/Rs^2)-(1/Rb^2))If the number of photons is (P/hf)*(Q/2*pi*f) then:NT = P*Q*(1/(4*pi*L*f^3))*(c/(2*pi))^2*X^2*((1/Rs^2)-(1/Rb^2))This does fit (as far as I've gotten) the concept of a self-accelerating Dirac wavepacket (which does conserve momentum).---------------------------------------------------------------------------------------------------------------------------Yes the search function is terribledf is delta f not the differential, Q is the effective Q due to phase shift etc.I have put your text in a LaTeX format and enclose it here. But the question is: Where does your acceleration come from?

Quote from: StrongGR on 05/16/2015 04:45 PMQuote from: Notsosureofit on 05/16/2015 04:19 PMQuote from: StrongGR on 05/16/2015 04:12 PMQuote from: Notsosureofit on 05/16/2015 02:12 PMQuote from: StrongGR on 05/16/2015 01:55 PMQuote from: Notsosureofit on 05/16/2015 01:39 PMQuote from: StrongGR on 05/16/2015 01:36 PMQuote from: Notsosureofit on 05/16/2015 01:23 PMQuote from: Rodal on 05/16/2015 04:06 AMQuote from: SeeShells on 05/16/2015 03:56 AMAnyone seen this little tidbit?http://phys.org/news/2015-05-newton-law-broken.htmlNon-equiibrium thermodynamicsI have to find my old copy of the book by S. R. De Groot, P. Mazur and other such books I have in boxesand see whether we can derive a force for the EM Drive based on Onsager's relations Still looking for my copy as well ! (old cavity work was on transport properties)The system in that paper is not isolated from the environment. For EM Drive this is not true. You have to cope with a closed system and to understand why third law appears to be violated, if the effect is confirmedYup !Do you remember if DeGroot mentioned photons ?That book is rather old. I just gave a cursory look and found nothing about photons. You should rather consider the case for electromagnetic radiation. What could make the thing resemble that of a non-isolated system is leakage of radiation out of the cavity. I have to guess that one has built it reducing such losses. The idea to look at gravitational effects, started by Minotti's paper, is because in this case there is not a boundary due to the cavity and system appears to be open (space-time is everywhere). So, the third law would be saved by the expulsion of gravitational momentum. The reason why people in the community of scientists did not consider the case is the smallness of the gravity with respect to all other effects and so, one should not expect it to account for such a measurement.As you can see from my crude dispersion argument, the g value (of the photons) is much larger than one might naively expect."In the accelerated frame of reference w/ the acceleration, g = (c^2/(2*L*f^2))*(c/(2*Pi))^2*X^2*((1/Rs^2)-(1/Rb^2)) [for this waveguide-like approximation]."I missed something. Did you write a paper about? Please, let me know as I have not followed this discussion from the start.FYICleanup and detypo of the take on applying the Equivalence Principle.The proposition that dispersion caused by an accelerating frame of reference implied an accelerating frame of reference caused by a dispersive cavity resonator. (to 1st order using massless, perfectly conducting cavity)Starting with the expressions for the frequency of an RF cavity:f = (c/(2*Pi))*((X/R)^2+((p*Pi)/L)^2)^.5For TM modes, X = X[sub m,n] = the n-th zero of the m-th Bessel function.[1,1]=3.83, [0,1]=2.40, [0,2]=5.52 [1,2]=7.02, [2,1]=5.14, [2,2]=8.42, [1,3]=10.17, etc.and for TE modes, X = X'[subm,n] = the n-th zero of the derivative of the m-th Bessel function.[0,1]=3.83, [1,1]=1.84, [2,1]=3.05, [0,2]=7.02, [1,2]=5.33, [1,3]=8.54, [0,3]=10.17, [2,2]=6.71, etc.Rotate the dispersion relation of the cavity into doppler frame to get the Doppler shifts, that is to say, look at the dispersion curve intersections of constant wave number instead of constant frequency.df = (1/(2*f))*(c/(2*Pi))^2*X^2*((1/Rs^2)-(1/Rb^2))and from there the expression for the acceleration g from:g = (c^2/L)*(df/f) such that:g = (c^2/(2*L*f^2))*(c/(2*Pi))^2*X^2*((1/Rs^2)-(1/Rb^2))Using the "weight" of the photon in the accelerated frame from:"W" = (h*f/c^2)*g => "W" = T = (h/L)*dfgives thrust per photon:T = (h/(2*L*f))*(c/(2*pi))^2*X^2*((1/Rs^2)-(1/Rb^2))If the number of photons is (P/hf)*(Q/2*pi*f) then:NT = P*Q*(1/(4*pi*L*f^3))*(c/(2*pi))^2*X^2*((1/Rs^2)-(1/Rb^2))This does fit (as far as I've gotten) the concept of a self-accelerating Dirac wavepacket (which does conserve momentum).---------------------------------------------------------------------------------------------------------------------------Yes the search function is terribledf is delta f not the differential, Q is the effective Q due to phase shift etc.I have put your text in a LaTeX format and enclose it here. But the question is: Where does your acceleration come from?The accelerated frame or reference in which the asymmetry of the cavity is balanced out. That is as though the cavity was cylindrical in this case. Notice you would probably need the coordinate changes to do this as a proper derivation. As we said, that might have to constitute a (mathematical) proof.

Yes the search function is terribledf is delta f not the differential, Q is the effective Q due to phase shift etc.

Quote from: StrongGR on 05/16/2015 04:45 PMYes the search function is terribledf is delta f not the differential, Q is the effective Q due to phase shift etc.I have put your text in a LaTeX format and enclose it here. But the question is: Where does your acceleration come from?

...I have put your text in a LaTeX format and enclose it here. But the question is: Where does your acceleration come from?

Thank you ! I'll look up LaTex (new to me) How does one edit the pdf ? ( df should be delta f, for example)Its the (taking the extremes of the) equivalent wavelength change along the cavity axis of the resonant frequency in the rest frame. It should really be the result of an integral over that length to get a more general case ( included dielectrics for example )

Quote from: StrongGR on 05/16/2015 04:45 PM...I have put your text in a LaTeX format and enclose it here. But the question is: Where does your acceleration come from?Watch out for errors on the transcription to LaTeX pdf.For example, first equation (1) reads 2c/Pi instead of c/(2*Pi)http://forum.nasaspaceflight.com/index.php?action=dlattach;topic=36313.0;attach=830511

Today i did the first test with the Emdrive (microwave oven magnetron and cooper frustum) The setup (magnetron and frusum) was suspended in a pendulum. I applied power for 40 Seconds with no visible thrust. Tomorrow will will try again with the magnetron on the small side. You have any suggestion for what should be the distance from the small side?After this i will adjust the power to the filament of magnetron and the frequency.To fine adjust the frequency i thought i can put 2 coils over the magnetron magnets to modify the magnetic field.My website;http://www.masinaelectrica.com/emdrive-independent-test/

Quote from: Rodal on 05/16/2015 05:20 PMQuote from: StrongGR on 05/16/2015 04:45 PM...I have put your text in a LaTeX format and enclose it here. But the question is: Where does your acceleration come from?Watch out for errors on the transcription to LaTeX pdf.For example, first equation (1) reads 2c/Pi instead of c/(2*Pi)http://forum.nasaspaceflight.com/index.php?action=dlattach;topic=36313.0;attach=830511Fixed. Thanks.

Quote from: StrongGR on 05/16/2015 05:24 PMQuote from: Rodal on 05/16/2015 05:20 PMQuote from: StrongGR on 05/16/2015 04:45 PM...I have put your text in a LaTeX format and enclose it here. But the question is: Where does your acceleration come from?Watch out for errors on the transcription to LaTeX pdf.For example, first equation (1) reads 2c/Pi instead of c/(2*Pi)http://forum.nasaspaceflight.com/index.php?action=dlattach;topic=36313.0;attach=830511Fixed. Thanks.It would be helpful to mark revision number both inside the file and in the title. Maybe with a date inside.

4) Also this link may be helpful, giving a table of the Xmn and X'mn to 15 digits accuracyhttp://wwwal.kuicr.kyoto-u.ac.jp/www/accelerator/a4/besselroot.htmlx

Quote from: deuteragenie on 05/16/2015 08:01 PMQuote from: Rodal on 05/16/2015 05:20 PM4) Also this link may be helpful, giving a table of the Xmn and X'mn to 15 digits accuracyhttp://wwwal.kuicr.kyoto-u.ac.jp/www/accelerator/a4/besselroot.htmlxTry: Wolfram alpha Thanks. That link ( https://www.wolframalpha.com/input/?i=besseljzero[1%2C1 ) only gives X_{mn} which are only useful for TM modesIs there a way that Wolfram Alpha can give X'_{mn} which are needed for TE modes ?

Quote from: Rodal on 05/16/2015 05:20 PM4) Also this link may be helpful, giving a table of the Xmn and X'mn to 15 digits accuracyhttp://wwwal.kuicr.kyoto-u.ac.jp/www/accelerator/a4/besselroot.htmlxTry: Wolfram alpha

Quote from: Rodal on 05/16/2015 08:22 PMQuote from: deuteragenie on 05/16/2015 08:01 PMQuote from: Rodal on 05/16/2015 05:20 PM4) Also this link may be helpful, giving a table of the Xmn and X'mn to 15 digits accuracyhttp://wwwal.kuicr.kyoto-u.ac.jp/www/accelerator/a4/besselroot.htmlxTry: Wolfram alpha Thanks. That link ( https://www.wolframalpha.com/input/?i=besseljzero[1%2C1 ) only gives X_{mn} which are only useful for TM modesIs there a way that Wolfram Alpha can give X'_{mn} which are needed for TE modes ?I don't think so. But I believe you have Mathemagica:http://www.me.rochester.edu/courses/ME201/webexamp/derbesszer.pdf - see ln67

I am back with an updated draft after some terrible news around about NASA dismissing these researches. They should not as, otherwise, it could happen as with Galilei having his detractors even not trying to look in the telescope, just dismissing on faith.I have analysed the case of the frustum and the results appear to be striking. One must admit that geometry comes to rescue not just general relativity. For this particular geometry the cavity can be made susceptible to gravitational effects if your choice of the two radii of the cavity is smart enough. This is something to be confirmed yet, just my theoretical result, but shocking anyway.As usual, any comment is very welcome.http://forum.nasaspaceflight.com/index.php?action=dlattach;topic=36313.0;attach=830137

These equations appear rather interesting as, by a proper choice of parameters, one can make a gravitational effect more or less relevant in the physics of the problem. It is the case to say that geometry comes to rescue.

Quote from: StrongGR on 05/16/2015 04:45 PMQuote from: Notsosureofit on 05/16/2015 04:19 PM...FYICleanup and detypo of the take on applying the Equivalence Principle.The proposition that dispersion caused by an accelerating frame of reference implied an accelerating frame of reference caused by a dispersive cavity resonator. (to 1st order using massless, perfectly conducting cavity)Starting with the expressions for the frequency of an RF cavity:f = (c/(2*Pi))*((X/R)^2+((p*Pi)/L)^2)^.5....Rotate the dispersion relation of the cavity into doppler frame to get the Doppler shifts, that is to say, look at the dispersion curve intersections of constant wave number instead of constant frequency.df = (1/(2*f))*(c/(2*Pi))^2*X^2*((1/Rs^2)-(1/Rb^2))......It comes from "work" done by the waves on the copper, i.e. EM induction, which slows down the wave and steals it's momentum. It mimics gravity in this regard, because photons lose energy going "up".I'm still working on a slightly different version of this. My time has been severely limited this past week however.Todd D.

Quote from: Notsosureofit on 05/16/2015 04:19 PM...FYICleanup and detypo of the take on applying the Equivalence Principle.The proposition that dispersion caused by an accelerating frame of reference implied an accelerating frame of reference caused by a dispersive cavity resonator. (to 1st order using massless, perfectly conducting cavity)Starting with the expressions for the frequency of an RF cavity:f = (c/(2*Pi))*((X/R)^2+((p*Pi)/L)^2)^.5....Rotate the dispersion relation of the cavity into doppler frame to get the Doppler shifts, that is to say, look at the dispersion curve intersections of constant wave number instead of constant frequency.df = (1/(2*f))*(c/(2*Pi))^2*X^2*((1/Rs^2)-(1/Rb^2))......

...FYICleanup and detypo of the take on applying the Equivalence Principle.The proposition that dispersion caused by an accelerating frame of reference implied an accelerating frame of reference caused by a dispersive cavity resonator. (to 1st order using massless, perfectly conducting cavity)Starting with the expressions for the frequency of an RF cavity:f = (c/(2*Pi))*((X/R)^2+((p*Pi)/L)^2)^.5....Rotate the dispersion relation of the cavity into doppler frame to get the Doppler shifts, that is to say, look at the dispersion curve intersections of constant wave number instead of constant frequency.df = (1/(2*f))*(c/(2*Pi))^2*X^2*((1/Rs^2)-(1/Rb^2))...