### Author Topic: EM Drive Developments - related to space flight applications - Thread 3  (Read 1879250 times)

#### Rodal

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##### Re: EM Drive Developments - related to space flight applications - Thread 3
« Reply #1860 on: 06/16/2015 07:38 PM »
I have the following design equation for a box resonator.
L,M,N being the number of half wavelengths for the box dimensions d,b,a respectively.

Is there a similar equation for truncated cone shaped resonators?  I do not trust my ability to derive it.
Thanks.

Here is a closed-form solution for a cylindrical cavity:  https://en.wikipedia.org/wiki/Microwave_cavity#Cylindrical_cavity

You need a table of values for the zeros Xmn of Bessel Cylindrical function and the zeros X'mn of its derivative, here you have such a table, to 15 digits:

http://wwwal.kuicr.kyoto-u.ac.jp/www/accelerator/a4/besselroot.htmlx

You also have to separately calculate the cut-off frequency (https://en.wikipedia.org/?title=Cutoff_frequency#Waveguides) for different modes to verify that they are not cut-off, when using the closed-form solution and the table of values.

There is no closed-form solution for a truncated cone cavity.

There are exact solutions for the truncated cone, but you have to solve two separate eigenvalue problems, one eigenvalue problem in terms of Legendre Associated functions and another eigenvalue problem in terms of spherical Bessel functions.

Greg Egan shows an exact solution for modes that are constant in the azimuthal direction: TE0np and TM0np, here:  http://gregegan.customer.netspace.net.au/SCIENCE/Cavity/Cavity.html

TheTraveller has constructed an Excel spreadsheet solution based on Shawyer's ad-hoc approximation which approximates the truncated cone as large number of small cylindrical waveguides.  The problem is that he still uses equations that are based on a cylinder.  The electromagnetic field inside a cylinder has a longitudinal variation described by harmonic functions (sines and cosines, depending on the longitudinal mode number "p").  Instead,  the electromagnetic field inside a truncated cone varies according to spherical Bessel functions.

For an approximate solution you might as well use the cylindrical cavity exact solution:  https://en.wikipedia.org/wiki/Microwave_cavity#Cylindrical_cavity

and use the Mean of the Big and Small diameters as the diameter of the cylinder.
« Last Edit: 06/16/2015 08:29 PM by Rodal »

#### WarpTech

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##### Re: EM Drive Developments - related to space flight applications - Thread 3
« Reply #1861 on: 06/16/2015 07:41 PM »
If I understand correctly your intent to attribute cavity momentum to a field property, then the field will carry off equal and opposite momentum. So are you describing radiation reaction?

If you are, then because the system is closed, there is net zero momentum expressed externally.

You also need to account for forces that are 1000x greater than that expected of a photon rocket, and you seem intent on doing that using electromagnetism. Known physics says that this is impossible.

"Known" does not mean "understand", since I "know" that gravity can be mimicked by an EM effect, and this is not well understood by others. So this response does not surprise me.

In a Newtonian gravitational field, an object falls to lower its potential energy. It loses energy and gains mass in the process. It does not eject mass to conserve momentum;

E => E/sqrt(K)
m => m*K^3/2

In what I've proposed, the frustum "falls" forward to lower it's potential energy as it gains mass. The frustum is charged by a magnetron to raise it's potential energy and input more mass. It doesn't lose mass if it gains velocity.

The "New Physics" you want is right in front of you! I'm showing you how to mimic gravity using magnetic flux as a gauge-gravity potential. This is about as NEW as it gets! Gauge potentials are simply the potential for a phase shift. The phase shift caused by magnetic flux is indistinguishable from the phase shift caused by a gravitational field, acting on the identical wave function. Most people do not understand this clearly.
Todd

There is no problem in visualizing moving an object with an external electromagnetic field, external to the object.

But in the EM Drive the electromagnetic field is inside the cavity, instead of the cavity being inside an external electromagnetic field.

The example you give is of an object falling, with  a gravity field that is all around, external to the object as well.

In my model, the gravitational field external to the particle plays no role. Only the field that intersects the particle plays a role by attenuating the natural frequency of the harmonic oscillators. That is what is going on inside the frustum. IMO, it's the same thing.

Inside a proton, it's natural oscillations are attenuated more if it moves in one direction (increasing K) vs the other (decreasing K). Attenuation lowers its frequency and energy;

f => f/sqrt(K)
E => E/sqrt(K)

The Energy of its internal oscillation in a gravitational field is equivalent to it's Potential energy. As it falls, it's frequency is shifted lower due to the increasing phase shift, i.e. gravitational red-shift of matter waves.

I see no difference between this and how the EM Drive works. If there is nothing expelled, not even heat, then as the EM Drive falls forward it retains the added mass from the power source, which is converted into kinetic energy. The power source is losing mass of course in the process, unless it happens to be powered from solar panels.
Todd

#### Rodal

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##### Re: EM Drive Developments - related to space flight applications - Thread 3
« Reply #1862 on: 06/16/2015 07:44 PM »
In my model, the gravitational field external to the particle plays no role. Only the field that intersects the particle plays a role by attenuating the natural frequency of the harmonic oscillators. That is what is going on inside the frustum. IMO, it's the same thing.

Inside a proton, it's natural oscillations are attenuated more if it moves in one direction (increasing K) vs the other (decreasing K). Attenuation lowers its frequency and energy;

f => f/sqrt(K)
E => E/sqrt(K)

The Energy of its internal oscillation in a gravitational field is equivalent to it's Potential energy. As it falls, it's frequency is shifted lower due to the increasing phase shift, i.e. gravitational red-shift of matter waves.

I see no difference between this and how the EM Drive works. If there is nothing expelled, not even heat, then as the EM Drive falls forward it retains the added mass from the power source, which is converted into kinetic energy. The power source is losing mass of course in the process, unless it happens to be powered from solar panels.
Todd
The point was that in your example (and all known examples), you can accelerate the center of mass of an object using external fields (fields that are external to the object being moved).

There is no example in Physics that I know of, where one can accelerate the center of mass of an object by solely using an internal field, or an internal force.

For example, an astronaut cannot accelerate a spacecraft's center of mass by moving, inside the spacecraft, a magnet.

Can you provide an example where the center of mass of an object has been accelerated using a field or force internal to the object being accelerated?
« Last Edit: 06/16/2015 07:54 PM by Rodal »

#### deltaMass

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##### Re: EM Drive Developments - related to space flight applications - Thread 3
« Reply #1863 on: 06/16/2015 07:44 PM »
In a Newtonian gravitational field, an object falls to lower its potential energy. It loses energy and gains mass in the process. It does not eject mass to conserve momentum
Say what?? It gains mass?? And the complementary motion of the Earth towards it plays no role in CoM??? This is nonsense.

The Newtonian energetics (i.e. 1st order) dictates no such thing. Energy lost via potential energy decrease is exactly compensated by energy gained via kinetic energy increase.

What you are suggesting is
m g dh + dm c2 = 0
which ignores the kinetic energy term completely.
Here we take dh < 0 and dm >0.
Were that crazy equation true, then a 1000 ton mass elevated 100 Km in 1 gee would gain 10 mg.
I am forced to admit that this experiment would be very hard to do, so I can't rebut your theory on two fronts instead of just the one.

#### Cryogenic

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##### Re: EM Drive Developments - related to space flight applications - Thread 3
« Reply #1864 on: 06/16/2015 07:46 PM »
I didn't see this covered here yet, but I think this is worthy of front page news:

China’s Interstellar Probe May Be Propelled by Electric Thruster

Quote
According to the report, five deep space probes, propelled by electric thrusters, have explored the moon, asteroids and a comet. Japan-made "Hayabusa" was the first to bring samples from an asteroid back to earth, while US spacecraft "Dawn" was the first to probe on two asteroids in one mission

China aims to send craft to Mars in 200 days with electric thrusters
http://www.wantchinatimes.com/news-subclass-cnt.aspx?cid=1101&MainCatID=11&id=20150614000021

Quote
Experts believe that, given the significant weight reduction offered by electric propulsion, an array of 40 electric thrusters of 50 kilowatts would be able to send a 300-ton spacecraft to Mars in just 200 days.

Electric thruster propels China's interstellar ambitions
http://www.china.org.cn/china/2015-06/08/content_35768904.htm

Quote
China also plans to launch a hybrid propulsion communication satellite at the end of 2016. The electric propulsion system would be used in China's space station in the future, Wang says.

#### deltaMass

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##### Re: EM Drive Developments - related to space flight applications - Thread 3
« Reply #1865 on: 06/16/2015 07:48 PM »
This is wretchedly unscientific pseudo-journalism. The appellation "interstellar" is wholly inappropriate.

#### Rodal

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##### Re: EM Drive Developments - related to space flight applications - Thread 3
« Reply #1866 on: 06/16/2015 07:50 PM »
I didn't see this covered here yet, but I think this is worthy of front page news:

China’s Interstellar Probe May Be Propelled by Electric Thruster

Quote
According to the report, five deep space probes, propelled by electric thrusters, have explored the moon, asteroids and a comet. Japan-made "Hayabusa" was the first to bring samples from an asteroid back to earth, while US spacecraft "Dawn" was the first to probe on two asteroids in one mission

China aims to send craft to Mars in 200 days with electric thrusters
http://www.wantchinatimes.com/news-subclass-cnt.aspx?cid=1101&MainCatID=11&id=20150614000021

Quote
Experts believe that, given the significant weight reduction offered by electric propulsion, an array of 40 electric thrusters of 50 kilowatts would be able to send a 300-ton spacecraft to Mars in just 200 days.

Electric thruster propels China's interstellar ambitions
http://www.china.org.cn/china/2015-06/08/content_35768904.htm

Quote
China also plans to launch a hybrid propulsion communication satellite at the end of 2016. The electric propulsion system would be used in China's space station in the future, Wang says.

Electric thrusters have been used since at least the 1960's.  See ion thrusters, etc. (https://en.wikipedia.org/wiki/Ion_thruster )

This is what the article refers to, not the EM Drive.

The difference is that they work like any other conventional rocket, by expelling mass, while the EM Drive researchers claim that nothing is being expelled.
« Last Edit: 06/16/2015 08:39 PM by Rodal »

#### Notsosureofit

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##### Re: EM Drive Developments - related to space flight applications - Thread 3
« Reply #1867 on: 06/16/2015 08:06 PM »
FYI

http://www.nature.com/nphys/journal/vaop/ncurrent/full/nphys3366.html

"Here we consider low-energy quantum mechanics in the presence of gravitational time dilation and show that the latter leads to the decoherence of quantum superpositions. Time dilation induces a universal coupling between the internal degrees of freedom and the centre of mass of a composite particle. The resulting correlations lead to decoherence in the particle position, even without any external environment."
« Last Edit: 06/16/2015 08:08 PM by Notsosureofit »

#### Rodal

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##### Re: EM Drive Developments - related to space flight applications - Thread 3
« Reply #1868 on: 06/16/2015 08:13 PM »
FYI

http://www.nature.com/nphys/journal/vaop/ncurrent/full/nphys3366.html

"Here we consider low-energy quantum mechanics in the presence of gravitational time dilation and show that the latter leads to the decoherence of quantum superpositions. Time dilation induces a universal coupling between the internal degrees of freedom and the centre of mass of a composite particle. The resulting correlations lead to decoherence in the particle position, even without any external environment."

The main author, Igor, is a Postdoctoral Fellow at the Harvard-Smithsonian Center for Astrophysics at Harvard University in Cambridge Mass

I attach his (March 2015 update) article (with a huge number of co-authors) on Macroscopic Quantum Resonators

<<We have presented an updated version of the proposal for a medium-sized space mission, MAQRO, originally
proposed in 2010. This proposal was submitted in response to the ESA M4 call for a mission opportunity for a
medium-size space mission. The main scienti c objective of the mission is testing quantum theory using high-mass
matter-wave interferometry in combination with novel techniques from quantum optomechanics. The update includes
several signi cant changes with respect to the original proposal in order to address novel developments as well as critical
issues in the original mission proposal. In particular, we presented an update of the thermal shield design allowing
36
to perform high-mass matter-wave interference on a separate platform outside the spacecraft in order to ful l the
strict temperature and vacuum requirements of MAQRO. We introduced a novel type of matter-wave interferometer
adapted for a microgravity setting as well as novel schemes for loading test particles into the central optical trap to
meet the stringent requirements of MAQRO.
This novel approach promises to overcome principal limitations of ground-based experiments and to resolve technical
limitations of the earlier proposal by harnessing state-of-the-art space technology, well-established techniques
of matter-wave interferometry and recent developments in quantum optomechanics using optically trapped dielectric
particles. MAQRO will o er the unique opportunity to investigate a yet untested parameter regime allowing to probe
for a quantum-to-classical transition and for possible novel e ects at the interface between quantum and gravitational
physics. Moreover, the high sensitivity of the MAQRO instrument might even allow testing a speci c type of
low-energy dark-matter models[13, 14].
The present proposal highlights the rapid progress in recent years to achieve quantum control over macroscopic
optomechanical systems and to harness space as an intriguing new environment for tests on the foundations of physics.
MAQRO may prove a path nder for quantum technology in space, opening the door for a range of future applications
in high-sensitivity measurements using techniques from quantum optomechanics and matter-wave interferometry.>>

as well as his article on Universal decoherence

<<Phenomena inherent to quantum theory on curved space-time, such as Hawking radiation [1],
are typically assumed to be only relevant at extreme physical conditions: at high energies and
in strong gravitational elds. Here we consider low-energy quantum mechanics in the presence of
weak gravitational time dilation and show that the latter leads to universal decoherence of quantum
superpositions. Time dilation induces a universal coupling between internal degrees-of-freedom and
the centre-of-mass of a composite particle and we show that the resulting entanglement causes the
particle's position to decohere. We derive the decoherence timescale and show that the weak time
dilation on Earth is already sucient to decohere micro-scale objects. No coupling to an external
environment is necessary, thus even completely isolated composite systems will decohere on curved
space-time. In contrast to gravitational collapse models [2, 3], no modi cation of quantum theory
is assumed. General relativity therefore can account for the emergence of classicality and the e ect
can in principle be tested in future matter wave experiments with large molecules [4, 5] or with
trapped microspheres [>>

as well as his article on Optomechanical Quantum State Reconstruction
« Last Edit: 06/16/2015 08:27 PM by Rodal »

#### deltaMass

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##### Re: EM Drive Developments - related to space flight applications - Thread 3
« Reply #1869 on: 06/16/2015 08:47 PM »
Best place to station your quantum computer is in space, then, since it will decohere more slowly.

#### SeeShells

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##### Re: EM Drive Developments - related to space flight applications - Thread 3
« Reply #1870 on: 06/16/2015 08:52 PM »
I didn't see this covered here yet, but I think this is worthy of front page news:

China’s Interstellar Probe May Be Propelled by Electric Thruster

Quote
According to the report, five deep space probes, propelled by electric thrusters, have explored the moon, asteroids and a comet. Japan-made "Hayabusa" was the first to bring samples from an asteroid back to earth, while US spacecraft "Dawn" was the first to probe on two asteroids in one mission

China aims to send craft to Mars in 200 days with electric thrusters
http://www.wantchinatimes.com/news-subclass-cnt.aspx?cid=1101&MainCatID=11&id=20150614000021

Quote
Experts believe that, given the significant weight reduction offered by electric propulsion, an array of 40 electric thrusters of 50 kilowatts would be able to send a 300-ton spacecraft to Mars in just 200 days.

Electric thruster propels China's interstellar ambitions
http://www.china.org.cn/china/2015-06/08/content_35768904.htm

Quote
China also plans to launch a hybrid propulsion communication satellite at the end of 2016. The electric propulsion system would be used in China's space station in the future, Wang says.
China also plans to launch a hybrid propulsion communication satellite at the end of 2016. The electric propulsion system would be used in China's space station in the future, Wang says.

Electric propulsion systems are mainly of the ion thruster or Hall thruster types. They are essentially similar, using electricity to ionize the propellant, usually xenon, and accelerating the ions to produce thrust.

The biggest advantage of electric propulsion is that it uses a tenth of the amount of propellant required by traditional chemical propulsion systems. A typical 5-tonne chemical propulsion communication satellite contains three tonnes of fuel. With an electric propulsion system, it would only need 300 kg of propellant, Wang says.

#### SeeShells

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##### Re: EM Drive Developments - related to space flight applications - Thread 3
« Reply #1871 on: 06/16/2015 09:00 PM »
FYI

http://www.nature.com/nphys/journal/vaop/ncurrent/full/nphys3366.html

"Here we consider low-energy quantum mechanics in the presence of gravitational time dilation and show that the latter leads to the decoherence of quantum superpositions. Time dilation induces a universal coupling between the internal degrees of freedom and the centre of mass of a composite particle. The resulting correlations lead to decoherence in the particle position, even without any external environment."
Say's alot in the last paragraph, I agree.

"As a final remark, we note that the presented estimate
for the time-dilation-induced decoherence is likely to be
an underestimation of the actual effect. The internal
structure of the constituents is not taken into account
and additional mechanisms, such as nuclear processes,
may contribute to the decoherence effect. Additionally,
special relativistic time dilation and the decoherence during
the build-up of the superposition were neglected. We
therefore expect that the actual decoherence due to time
dilation is even stronger than predicted here."

#### Stormbringer

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##### Re: EM Drive Developments - related to space flight applications - Thread 3
« Reply #1872 on: 06/16/2015 09:06 PM »
http://phys.org/news/2015-06-theory-reality-nonlinear-optical-metamaterials.html

Synopsis: metamaterials with negative index of refraction created in testable quantities for the first time.

Question:  Jack Sarfati claims such materials would of necessity be interchangeable with negative mass/energy which can then be used in space drives related to the topic at hand. Does that article make his claim testable now?
When antigravity is outlawed only outlaws will have antigravity.

#### WarpTech

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##### Re: EM Drive Developments - related to space flight applications - Thread 3
« Reply #1873 on: 06/16/2015 10:35 PM »
In my model, the gravitational field external to the particle plays no role. Only the field that intersects the particle plays a role by attenuating the natural frequency of the harmonic oscillators. That is what is going on inside the frustum. IMO, it's the same thing.

Inside a proton, it's natural oscillations are attenuated more if it moves in one direction (increasing K) vs the other (decreasing K). Attenuation lowers its frequency and energy;

f => f/sqrt(K)
E => E/sqrt(K)

The Energy of its internal oscillation in a gravitational field is equivalent to it's Potential energy. As it falls, it's frequency is shifted lower due to the increasing phase shift, i.e. gravitational red-shift of matter waves.

I see no difference between this and how the EM Drive works. If there is nothing expelled, not even heat, then as the EM Drive falls forward it retains the added mass from the power source, which is converted into kinetic energy. The power source is losing mass of course in the process, unless it happens to be powered from solar panels.
Todd
The point was that in your example (and all known examples), you can accelerate the center of mass of an object using external fields (fields that are external to the object being moved).

There is no example in Physics that I know of, where one can accelerate the center of mass of an object by solely using an internal field, or an internal force.

For example, an astronaut cannot accelerate a spacecraft's center of mass by moving, inside the spacecraft, a magnet.

Can you provide an example where the center of mass of an object has been accelerated using a field or force internal to the object being accelerated?

Well, apparently I am arguing for something that I do not even believe is true, and I've mentioned it before. The magnetic gauge field "A" cannot be shielded by the conductors, it can even penetrate superconductors. (See Felsager, "Geometry, Particles and Fields") So it's not a closed system in this interpretation. It does not change anything regarding what I said however. There is still a gradient in magnetic flux, where it intersects the copper that induces a phase shift in the moving current densities, that mimics gravity.

My hypothesis follows below. Before anyone says "Gauge transformations have no effect on Maxwell's equations or the fields E and B", I will remind you that neither do gravitational fields. However, both influence the wave functions through a relative phase shift in the Action of the Lagrangian system.
Todd

How's that for new physics?

EDIT: The terms ∅1/r and ∅2/r2, are "Damping Factors", caused by attenuation of the waves. This is why they depend on frequency, phase and bandwidth of the coupling. I believe that a sub-atomic particle has a mass proportional to its resonant frequency and a size inversely proportional to its bandwidth. It is in this bandwidth that the interaction with gravity takes place, for each particle.
« Last Edit: 06/17/2015 01:44 AM by WarpTech »

#### WarpTech

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##### Re: EM Drive Developments - related to space flight applications - Thread 3
« Reply #1874 on: 06/16/2015 10:51 PM »
...
Were that crazy equation true, then a 1000 ton mass elevated 100 Km in 1 gee would gain 10 mg.
I am forced to admit that this experiment would be very hard to do, so I can't rebut your theory on two fronts instead of just the one.

You have it upside down and backwards. An object gains mass as it moves downward in a gravitational field. It loses mass as it moves upward.

m => m*K^3/2

K = 1/(1 - 2GM/rc^2)

As r increases, K decreases and so does m.

I wrote up my hypothesis in an earlier post.
Todd

#### deltaMass

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##### Re: EM Drive Developments - related to space flight applications - Thread 3
« Reply #1875 on: 06/16/2015 10:58 PM »
...
Were that crazy equation true, then a 1000 ton mass elevated 100 Km in 1 gee would gain 10 mg.
I am forced to admit that this experiment would be very hard to do, so I can't rebut your theory on two fronts instead of just the one.

You have it upside down and backwards. An object gains mass as it moves downward in a gravitational field. It loses mass as it moves upward.

m => m*K^3/2

K = 1/(1 - 2GM/rc^2)

As r increases, K decreases and so does m.

I wrote up my hypothesis in an earlier post.
Todd
Please re-read what I wrote. dh < 0 (falling) and dm > 0 (when lower).
The elevated mass, according to your crazy physics, should be smaller than what the mass was below.
But yes, I should have said that the elevated mass is lighter according to you. Slip o' the kbd.
« Last Edit: 06/16/2015 11:03 PM by deltaMass »

#### rfmwguy

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##### Re: EM Drive Developments - related to space flight applications - Thread 3
« Reply #1876 on: 06/16/2015 11:03 PM »
Quote from: rfmwguy

This has been my thought experiment...a point or points coupling to a natural entropic force. Surfing the wave so to speak or riding the wind. Sorry for the basic description...I cannot visualize particle or wave ejection/leakage thrusting forward nor thermal radiation of some sort. If emdrive works I'm convinced (without the math to prove it yet) that its being coupled to an elemental, natural force we have yet to measure directly. I'll leave it as an entropic force for the time being...the natural tendency for all energy and matter to disperse.

So how do you explain life? Self organizing, becoming more and more complex, Fibonacci patterned from micro to macro scale. Apparently it is defying this mighty force.

That's a good point, however all life is transitory; extremely short-lived on a cosmic scale. I have not come to grips with complexity versus time although my gut feel is the more complex the shorter lived a system is within an Entropic Force...if one exists.

Classic chemistry envokes thermodynamics of the system as the source of entropy...reaction, not a force. I'm veering into a controversial field, but am not entirely alone.

#### deltaMass

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##### Re: EM Drive Developments - related to space flight applications - Thread 3
« Reply #1877 on: 06/16/2015 11:05 PM »
http://phys.org/news/2015-06-theory-reality-nonlinear-optical-metamaterials.html

Synopsis: metamaterials with negative index of refraction created in testable quantities for the first time.

Question:  Jack Sarfati claims such materials would of necessity be interchangeable with negative mass/energy which can then be used in space drives related to the topic at hand. Does that article make his claim testable now?
Why don't you ask him and report back?

#### TheTraveller

##### Re: EM Drive Developments - related to space flight applications - Thread 3
« Reply #1878 on: 06/16/2015 11:07 PM »
You might want to bookmark this link: http://www.ustream.tv/channel/em-drive-experiment

This is my ustream video channel where I will try and broadcast a live 1st test of my humble DIYDrive experiment in July. I may upload some videos in the meantime as I get further into the build.

I have set chat up as well, but only plan to use it after a video upload or live event. I won't be routinely monitoring it. I'll hang here for most interactions.

For now, you can log on to ustream for free, preferably creating the same username as you have on NSF, so I will know who I'm chatting with.

If you share your dimensions,, flat or spherical end plates, Rf source (bandwidth if known) & excitation mode, I'll create a ss for your project.
"As for me, I am tormented with an everlasting itch for things remote. I love to sail forbidden seas.”
Herman Melville, Moby Dick

#### WarpTech

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##### Re: EM Drive Developments - related to space flight applications - Thread 3
« Reply #1879 on: 06/16/2015 11:13 PM »
...
As r increases, K decreases and so does m.

I wrote up my hypothesis in an earlier post.
Todd
Please re-read what I wrote. dh < 0 (falling) and dm > 0 (when lower).
The elevated mass, according to your crazy physics, should be smaller than what the mass was below.
But yes, I should have said that the elevated mass is lighter according to you. Slip o' the kbd.

You're equal to... I mean,

Δm = m0*(1/(1 - Rs/r2)^3/2 - 1/(1 - Rs/r1)^3/2)

if r2 > r1, the mass will be less. Rs = 2GM/c^2.
Todd

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