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#1940 by WarpTech on 19 Jan, 2017 16:21
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It makes no difference if the speed of light is constant.
Thanks. I agree. However, look at my highlighted statement above. The definition is NOT optional when dealing with an EM field, stress-energy tensor. In that problem, to get mass one must divide by c2. So regardless of which way you choose, you still end up with G/c4. The choice is, do we pull that 1/c2 into Einstein's constant, or leave it outside as a multipler to Einstein's constant. Either way, if c is now a variable, it must be included. So I don't see this as a physical choice, just a mental one.
If the speed of light is variable with time, what you state is only true if you insist that that the EM field, stress-energy tensor is identical to its form for the case of c constant with time.
Again, this depends on the physical definition of the stress-energy tensor for the case of c variable with time, and this can only be decided by cosmological measurements, and not by insistence that the stress-energy tensor has to have a particular physical meaning for the case of c variable with time. It is agreed that no physical stress-energy tensor exists for the gravitational field, so one cannot decide this based on dimensional arguments without cosmological measurements. And, if the speed of light is constant with time, (as Einstein thought), all this discussion will turn out to be moot.
Unless there is physical evidence to the contrary, your choice for Einstein's constant can be defended on dimensional grounds and physical intuition.
It appears from this discussion, that when Jean-Pierre Petit states that the cosmological evidence supports his choice for Einstein's constant, Petit is making a particular choice for time-dependence of the stress-energy tensor that has to be closely examined, as to formal validity and consistency, for the case of variable speed of light.
In the end, this discussion boils down to the validity of the definition of the stress-energy tensor chosen by Petit for the case of variable speed of light.
Flux-capacitor any comments on the time dependence of the stress-energy tensor chosen by Petit for the case of variable speed of light ?
I have not read Petit's articles to be able to support why Petit choses this particular form of time dependence of the stress-energy tensor
I agree there is no stress-energy tensor for the gravitational field. My model does not require one, since gravity is emergent from the standard model of Q.E.D. That is why I'm talking about the stress-energy tensor of the EM field, not the gravitational field. Where;
G00 = 8pi*G/c4*.5*(ε0E2 + B2/μ0)
The leading "constant" is not a choice.
Also, when I am speaking of a VSL, I am referring to the "coordinate speed of light" in the frame of a distant observer. Not the locally constant speed of light, which is a "definition" per NIST. In the frame of a distant observer, the FRW metric (for k = 0) has the same refractive index dependence as the PV Model metric, for the null line element.
0 = (c*dt)2 - (a(t))2*[(dr)2 + r2(dΩ)2]
0 = (c*dt)2/K - K*[(dr)2 + r2(dΩ)2]
dr/dt => c/a(t) = c/K(t) in the PV Model
So in this sense, both are referring to the coordinate speed of light being a variable. Evidence for this, in the PV Model is the same as the evidence for GR. In a Schwarzschild metric, the coordinate speed of light is variable, as evidenced by the advanced perihelion of Mercury, light bending past a star, gravitational time dilation (Pound & Rebka) and gravitational length contraction (GPS). These are all evidence, IMO.
Edit: Also, I prefer Penrose's model, because in the early universe space was at a minimum density. Therefore, per the PV Model, K << 1 and c/K >> c. As matter condensed, K increased to the present value. So in that sense, c/K was faster in the past. However, in the case of the Big Bang model, the early universe started from a singularity, (K -> inf), and was then hot and dense. IF I assume that the laws of physics were the same then as they are now, then at that time c/K << c, the OPPOSITE prediction. Then c/K would be increasing as the universe expands, not reducing. Hence, I have never been a big proponent of the BB model.
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#1941 by Rodal on 19 Jan, 2017 16:36
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That equation can only be shown to hold if the speed of light is constant (which I admit has been a good model so far to model our universe, and was the model chosen by Einstein).
I agree there is no stress-energy tensor for the gravitational field. My model does not require one, since gravity is emergent from the standard model of Q.E.D. That is why I'm talking about the stress-energy tensor of the EM field, not the gravitational field. Where;
G00 = 8pi*G/c4*.5*(ε0E2 + B2/μ0)
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that equation
G00 = 8pi*G/c4*.5*(ε0E2 + B2/μ0)
cannot be shown to hold a-priori for what Petit is discussing, a variable speed of light theory modeling the history of the cosmos since the Big Bang. That equation cannot be proven a-priori to have held during cosmological periods of time since the Big Bang, or to extrapolate it that it will hold true over cosmological times into the future which is what Petit is discussing. That can only be supported by cosmological measurements and not a priori.
-------------Quotegravity is emergent from the standard model of Q.E.D.
that is so far, a hypothesis. It may be true or not. It remains to be proven based on cosmological measurements. -
#1942 by WarpTech on 19 Jan, 2017 17:04
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That equation can only be shown to hold if the speed of light is constant (which I admit has been a good model so far to model our universe, and was the model chosen by Einstein).
I agree there is no stress-energy tensor for the gravitational field. My model does not require one, since gravity is emergent from the standard model of Q.E.D. That is why I'm talking about the stress-energy tensor of the EM field, not the gravitational field. Where;
G00 = 8pi*G/c4*.5*(ε0E2 + B2/μ0)
...
that equation
G00 = 8pi*G/c4*.5*(ε0E2 + B2/μ0)
cannot be shown to hold a-priori for what Petit is discussing, a variable speed of light theory modeling the history of the cosmos since the Big Bang. That equation cannot be proven a-priori to have held during cosmological periods of time since the Big Bang, or to extrapolate it that it will hold true over cosmological times into the future which is what Petit is discussing. That can only be supported by cosmological measurements and not a priori.
-------------Quotegravity is emergent from the standard model of Q.E.D.
that is so far, a hypothesis. It may be true or not. It remains to be proven based on cosmological measurements.
Well, I would say there is no evidence what so ever that G00 above has changed or will change. The COBE data, WMAP data, or the predicted finale' of the Universe when all the black holes have evaporated and the only thing left is an EM field of photons. Nothing we have seen or what is predicted for the future, IMO would seem to imply this equation will fail. The only reason to question it is the hypothesis that there was a "big bang" that started from a singularity. There is no direct evidence for this, just unverified hypotheses and interpretations.
In regards to my hypothesis. I start with the assumption that gravity is a loss of power caused by damping. From this I can predict gravitational time dilation and length contraction, and all the other tests of GR that have been confirmed by experiment. I'd say it is a well tested hypothesis! It is tested and supported by the same evidence that supports the hypothesis that space-time is a curved manifold. There is no test yet that can distinguish between them, but my model is compatible with the SM of physics, where GR is not.
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#1943 by Rodal on 19 Jan, 2017 17:30
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That equation can only be shown to hold if the speed of light is constant (which I admit has been a good model so far to model our universe, and was the model chosen by Einstein).
I agree there is no stress-energy tensor for the gravitational field. My model does not require one, since gravity is emergent from the standard model of Q.E.D. That is why I'm talking about the stress-energy tensor of the EM field, not the gravitational field. Where;
G00 = 8pi*G/c4*.5*(ε0E2 + B2/μ0)
...
that equation
G00 = 8pi*G/c4*.5*(ε0E2 + B2/μ0)
cannot be shown to hold a-priori for what Petit is discussing, a variable speed of light theory modeling the history of the cosmos since the Big Bang. That equation cannot be proven a-priori to have held during cosmological periods of time since the Big Bang, or to extrapolate it that it will hold true over cosmological times into the future which is what Petit is discussing. That can only be supported by cosmological measurements and not a priori.
-------------Quotegravity is emergent from the standard model of Q.E.D.
that is so far, a hypothesis. It may be true or not. It remains to be proven based on cosmological measurements.
Well, I would say there is no evidence what so ever that G00 above has changed or will change. The COBE data, WMAP data, or the predicted finale' of the Universe when all the black holes have evaporated and the only thing left is an EM field of photons. Nothing we have seen or what is predicted for the future, IMO would seem to imply this equation will fail. The only reason to question it is the hypothesis that there was a "big bang" that started from a singularity. There is no direct evidence for this, just unverified hypotheses and interpretations.
In regards to my hypothesis. I start with the assumption that gravity is a loss of power caused by damping. From this I can predict gravitational time dilation and length contraction, and all the other tests of GR that have been confirmed by experiment. I'd say it is a well tested hypothesis! It is tested and supported by the same evidence that supports the hypothesis that space-time is a curved manifold. There is no test yet that can distinguish between them, but my model is compatible with the SM of physics, where GR is not.
Here is discussion of change in Maxwell's equations:
In the latest versions of string theory, physical particles and fields are confined to the neighborhoods of D–branes and their propagation may be affected by recoil of the branes caused by that propagation [https://arxiv.org/abs/gr-qc/9909085 ]. This leads to modifications of the Maxwell equations, which predict dispersive light propagation and thus violation of the Strong Equivalence Principle at some level (not expected to occur for the very mundane conditions of the EM Drive experiment).FYI:
https://academic.oup.com/mnras/article/465/3/3261/2454764/Eotvos-experiments-with-supermassive-black-holes
"Abstract
By examining the locations of central black holes in two elliptical galaxies, M32 and M87, we derive constraints on the violation of the strong equivalence principle for purely gravitational objects, i.e. black holes, of less than about two-thirds, ηN < 0.68 from the gravitational interaction of M87 with its neighbours in the Virgo cluster. Although M32 appears to be a good candidate for this technique, the high concentration of stars near its centre substantially weakens the constraints. On the other hand, if a central black hole is found in NGC 205 or one of the other satellite ellipticals of M31, substantially better constraints could be obtained. In all cases, the constraints could improve dramatically with better astrometry." -
#1944 by WarpTech on 19 Jan, 2017 17:57
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By the way, in the above equation you have no indices for E and B. E and B are vectors, which therefore have indices (as the tensor G00 has indices). I presume this was because of the informality involved in this conversation in a forum thread, which I fully understand since I get what you are driving at, but I wanted to note that this did not escape me, in case somebody else notes it too and feels forced to correct it.
I agree there is no stress-energy tensor for the gravitational field. My model does not require one, since gravity is emergent from the standard model of Q.E.D. That is why I'm talking about the stress-energy tensor of the EM field, not the gravitational field. Where;
G00 = 8pi*G/c4*.5*(ε0E2 + B2/μ0)
...
Also, in this discussion sometimes the covariant indices for G and T have been used (in the posts and in the references) and sometimes the contravariant indices for G and T are used, while in the Wikipedia discussion sometimes the mixed indices are used (appropriately, when dealing with the Trace of the tensor). This did not escape me either . Same comment as above.
There are no indices on the 00 component. It's just energy density. E2 and B2 are the square magnitudes of the vectors, they are not themselves vectors and have no indices.
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#1945 by Rodal on 19 Jan, 2017 18:09
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Understood and no problem with that notation in our informal exchange in this thread. I was just making the point that I would formally write these quantities as the dot products of the vectors...
By the way, in the above equation you have no indices for E and B. E and B are vectors, which therefore have indices (as the tensor G00 has indices). I presume this was because of the informality involved in this conversation in a forum thread, which I fully understand since I get what you are driving at, but I wanted to note that this did not escape me, in case somebody else notes it too and feels forced to correct it.
I agree there is no stress-energy tensor for the gravitational field. My model does not require one, since gravity is emergent from the standard model of Q.E.D. That is why I'm talking about the stress-energy tensor of the EM field, not the gravitational field. Where;
G00 = 8pi*G/c4*.5*(ε0E2 + B2/μ0)
...
Also, in this discussion sometimes the covariant indices for G and T have been used (in the posts and in the references) and sometimes the contravariant indices for G and T are used, while in the Wikipedia discussion sometimes the mixed indices are used (appropriately, when dealing with the Trace of the tensor). This did not escape me either . Same comment as above.
There are no indices on the 00 component. It's just energy density. E2 and B2 are the square magnitudes of the vectors, they are not themselves vectors and have no indices.
E2 = E·E
using indices with summation convention: E2 = E·E = EiEi
for example, in (cylindrical coordinates)
=(Er2+Eθ2+Ez2)((Sin(ωt))2
or in (spherical coordinates)
=(Eθ2+Eφ2+Er2)((Sin(ωt))2
(where I separate the harmonic variation in time in case of a harmonic variation)
ditto for B2
B2 = B·B
Just making the point for the general audience of what the quantities mean, and in case somebody complains about the notation. Just the fact that Wikipedia shows E2, that does not mean that is the best notation. I think that E·E with bolded quantities showing the dot product of the vectors is better, or showing the summation convention with indices EiEi is more clear.
I think that E2 is less clear than EiEi , and it does not save any space. But i have no problem with it.
More importantly I disagree with Wikipedia showing the contravariant component of T in that equation, and the covariant component of σ.
That (contravariant components for T and covariant components for σ) does not make sense. Wikipedia needs editing for consistency of components in tensor expressions.
Also the scalar E·E should be associated with the mixed component of T or with a Kronecker delta, or Wikipedia should show a unit contravariant tensor associated with that diagonal entry when relating to the contravariant component of T.
It does not make sense to have a matrix for a contravariant T, where some entries are shown as scalar, others are vector components, and yet others are covariant tensor components !. The person that posted that in Wikipedia did not bother to edit it for consistency so that all matrix components would finally be expressed as contravariant tensor components for consistency.
There are similar issues with tensor components in the discussion of Einstein's constant (sometimes shown with covariant G and T and sometimes with contravariant G and T and sometimes mixed G and T).
If Wikipedia is serious about tensor components they should deal with them more carefully, otherwise why bother to even show contravariant components in some equations? They could show only covariant components and say that they are only dealing with flat space.
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#1946 by qraal on 19 Jan, 2017 19:45
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The article is in preprint form here:
https://arxiv.org/abs/1604.04183Thought this might be interesting
http://physicsworld.com/cws/article/news/2017/jan/18/dark-energy-emerges-when-energy-conservation-is-violated -
#1947 by rfmwguy on 19 Jan, 2017 21:24
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Finally got around to making that quick slideshow on testing this past spring and summer:
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#1948 by Monomorphic on 19 Jan, 2017 23:05
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Integer dimensions for a ~2.449Ghz TE013 flat-end frustum:
Big_Diameter = 30cm
Height = 24cm
Small_Diameter = 18cm
A ~2cm diameter loop antenna of wire radius ~0.03cm, mounted axially ~1cm away from either end-plate, should excite TE013 at ~50ohm impedance. Max E-field ~40 kV/m with ~2.5W RF input.
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#1949 by rfmwguy on 19 Jan, 2017 23:35
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Integer dimensions for a ~2.449 TE013 flat-end frustum:
I like this model. 40kV/M @ 2.75W is awesome. Any idea on H or B?
Big_Diameter = 30cm
Height = 24cm
Small_Diameter = 18cm
A ~2cm diameter loop antenna of wire radius ~0.03cm, mounted axially ~1cm away from either end-plate, should excite TE013 at ~50ohm impedance. Max E-field ~40 kV/m with ~2.5W RF input. -
#1950 by Monomorphic on 19 Jan, 2017 23:47
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I like this model. 40kV/M @ 2.75W is awesome. Any idea on H or B?
Looks like ~135A/m.
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#1951 by WarpTech on 19 Jan, 2017 23:47
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Integer dimensions for a ~2.449Ghz TE013 flat-end frustum:
Big_Diameter = 30cm
Height = 24cm
Small_Diameter = 18cm
A ~2cm diameter loop antenna of wire radius ~0.03cm, mounted axially ~1cm away from either end-plate, should excite TE013 at ~50ohm impedance. Max E-field ~40 kV/m with ~2.5W RF input.
What's the Q, 2,100,000? -
#1952 by rfmwguy on 19 Jan, 2017 23:55
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We're talking serious power densities with minimal input...I like this model. 40kV/M @ 2.75W is awesome. Any idea on H or B?
Looks like ~135A/m. -
#1953 by sanman on 20 Jan, 2017 01:16
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http://www.nature.com/nature/journal/v541/n7637/full/nature21024.html
Editor's summary in العربية
An essential technique in the field of quantum optics is the production of squeezed light, which has fluctuations below the vacuum limit, at least, in either the amplitude or phase of the light field. Fluctuations in one of these variables can be reduced at the expense of the other, conforming to Heisenberg's uncertainty limit. Such squeezed states of light are of considerable importance in quantum information systems and precision metrology, including gravitational-wave detectors. In this paper, Leitenstorfer and colleagues open up an exciting direction in this area by generating squeezed light in transient mid-infrared light fields and detecting quantum fluctuations directly in the time domain with few-femtosecond laser pulses. They succeed in observing squeezed and increased quantum fluctuations in adjacent time regions. In contrast to existing quantum detection techniques, the quantum properties can be characterized without the need to amplify or change them.
So squeezed light can have a smaller wavelength relative to its energy? Or conversely, a greater amount of energy relative to its wavelength?
What if squeezed light were put into EMdrive frustrum cavity instead of regular microwaves?
Would it result in any change in performance?
Think of the Heisenberg uncertainty relationships.
Δx*Δp > h/2
ΔE*Δt > h/2
The RHS is constant. Squeezed light is contracting one variable at the expense of expanding the other. So dx gets smaller, dp gets larger, means the wavelength is squeezed. Note, this is the effect of a gravitational field in the PV Model.
Δx/√K * Δp√K > h/2
ΔE/√K * Δt√K > h/2
as K increases, the wavelength and period get squeezed.
I was just wondering - if Squeezed Light can be possible, can Stretched Light also be possible? Or is that what they call Amplitude Squeezed Light?
Regardless of how it's accomplished, we can all see what the converse situation would look like - a lower signal-to-noise ratio that raises the background noise. Shall we call it excitation of the Vacuum Fluctuations?
Consider that if those background fluctuations are what you're trying to push off of, then your Action-Reaction could benefit from a more vigorously fluctuating (hotter?) Vacuum.
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#1954 by WarpTech on 20 Jan, 2017 05:43
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Think of the Heisenberg uncertainty relationships.
Δx*Δp > h/2
ΔE*Δt > h/2
The RHS is constant. Squeezed light is contracting one variable at the expense of expanding the other. So dx gets smaller, dp gets larger, means the wavelength is squeezed. Note, this is the effect of a gravitational field in the PV Model.
Δx/√K * Δp√K > h/2
ΔE/√K * Δt√K > h/2
as K increases, the wavelength and period get squeezed.
I was just wondering - if Squeezed Light can be possible, can Stretched Light also be possible? Or is that what they call Amplitude Squeezed Light?
Regardless of how it's accomplished, we can all see what the converse situation would look like - a lower signal-to-noise ratio that raises the background noise. Shall we call it excitation of the Vacuum Fluctuations?
Consider that if those background fluctuations are what you're trying to push off of, then your Action-Reaction could benefit from a more vigorously fluctuating (hotter?) Vacuum.
In my model, that would be "warp drive", or K < 1, c/K > c.
I look at it this way. The QED Zero Point Field, (ZPF) is the lowest allowed energy state for an oscillator in a potential. So the oscillators that make up matter (atoms) do not naturally drop below this minimum energy state. The atoms are driven by the ZPF of the vacuum to be in equilibrium with it. The presence and interaction with external matter causes damping, or a loss of power from the oscillator-vacuum system. The particle falls, looking for equilibrium in an asymmetrical environment. In other words, the symmetry is broken. Gravity has a symmetry, just as other forces in the SM have a symmetry. They exist only when the symmetry is broken. -
#1955 by Peter Lauwer on 20 Jan, 2017 11:12
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Integer dimensions for a ~2.449Ghz TE013 flat-end frustum:
Big_Diameter = 30cm
Height = 24cm
Small_Diameter = 18cm
A ~2cm diameter loop antenna of wire radius ~0.03cm, mounted axially ~1cm away from either end-plate, should excite TE013 at ~50ohm impedance. Max E-field ~40 kV/m with ~2.5W RF input.
Looks good. So, a 0.6 mm wire diameter. It would be nice, though, if a little thicker wire (say 1 mm) can be used. How will affect that the parameters? -
#1956 by TheTraveller on 20 Jan, 2017 11:33
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Finally got around to making that quick slideshow on testing this past spring and summer:
Dave,
So why not remove the oil bath damper, swap the stiff wire for fishing line, remove the rotation restraints and get your thruster to do 90 deg or greater rev in both directions? Should be a simple change. Will totally destroy the deniers claims.
Yes? -
#1957 by TheTraveller on 20 Jan, 2017 11:52
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Integer dimensions for a ~2.449Ghz TE013 flat-end frustum:
Big_Diameter = 30cm
Height = 24cm
Small_Diameter = 18cm
A ~2cm diameter loop antenna of wire radius ~0.03cm, mounted axially ~1cm away from either end-plate, should excite TE013 at ~50ohm impedance. Max E-field ~40 kV/m with ~2.5W RF input.
To all those that believe the SPR resonance calculations solution is BS, I present the attached.
Resonance: SPR 2.465GHz vs FEKO 2.449Ghz. Suggest the antenna modified the FEKO solution by 15.6MHz or 0.6%.
Sorry but SPR solution rules. But hey cut metal as per FEKO and ensure the Rf amp has the bandwidth to track the real resonance.
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#1958 by rfmwguy on 20 Jan, 2017 12:16
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It was enough to prove to me deflection forces were there at a much faster rise time than a thermal signature could induce, especially with a thick copper endplate. It was time for someone with infinitely more resources than I have to continue development and ultimately launch this bird into space. No matter what fundraisers I would have began, it would still have been just my humble effort... skeptics would remain regardless. I believe DIYers first responsibility is to observe it for themselves only, then align with a group or entity that has a similar vision...ad astra.Finally got around to making that quick slideshow on testing this past spring and summer:
Dave,
So why not remove the oil bath damper, swap the stiff wire for fishing line, remove the rotation restraints and get your thruster to do 90 deg or greater rev in both directions? Should be a simple change. Will totally destroy the deniers claims.
Yes? -
#1959 by Peter Lauwer on 20 Jan, 2017 12:19
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Finally got around to making that quick slideshow on testing this past spring and summer:
Dave,
So why not remove the oil bath damper, swap the stiff wire for fishing line, remove the rotation restraints and get your thruster to do 90 deg or greater rev in both directions? Should be a simple change. Will totally destroy the deniers claims.
Yes?
Come on... you can't make a serious measurement device with fishing line.
