@JackSarfatti superconducting metamaterial
@JackSarfatti I envisioned such a material for low power warp drive in my 11-1-11 @DARPA @NASA Orlando talk @100YSS
The importance of gyroscopes for the construction of real LIFs[i]
“Local inertial frames have a fundamental role in Einstein geometrodynamics. The spatial axes of a local inertial frame along the world line of a freely falling observer are mathematically defined using Fermi-Walker transport (eq. 3.4.25); that is, along … her geodesic they are defined using parallel transport. These axes are physically realized with gyroscopes. … The most advanced gyroscopes … measure the very tiny effect due to the gravimagnetic field of the Earth: the ‘dragging of inertial frames,’ that is, the precession of the gyroscopes by the Earth’s angular momentum, which in orbit, is of the order of a few tens of milliarcseconds/year. There are two main types of gyroscopes … mechanical and optical. The optical gyroscopes … are usually built with optical fibers or with ring lasers.” (6.12)
Fermi-Walker Transport, De Sitter (Geodetic)&Lense-Thirring Effects
For weak gravity fields in the first Einstein 20^{th} Century correction to Newton’s 17^{th} century gravity theory: S^{a} is a spacelike 4-vector outside its local light cone that describes the spin of the test gyroscope about its rotation axis. The test gyroscope travels along a timelike worldline x^{a} (s) with tangent vector u^{a}. S^{a}u_{a} = 0 and the equation for Fermi-Walker transport is
S^{a}_{;}_{b}u^{b} = u^{a} (a^{b}S_{b}) = u^{a}(u^{b}_{;}_{g}u^{g}S_{b}) (3.4.25)
Where a semi-colon “;” always stands for the covariant partial derivative with respect to the Levi-Civita connection that describes fictitious forces on the test gyroscope that are, in reality, real forces on the detector measuring the motion of the gyro. Repeated upper and lower indices are summed through 0,1,2,3. The local observable objectively real proper acceleration first-rank tensor directly measured by accelerometers clamped to the center of mass of the test gyro is
a^{b} = u^{b}_{;}_{g}u^{g}
If the arbitrary timelike world line of the center of mass of the test gyro (remember LIFs have three of them forming a spacelike triad base frame) is a geodesic, then, by definition, the proper acceleration tensor a^{b} = 0. Therefore,
S^{a}_{;}_{b}u^{b} = 0
This is the equation for Fermi-Walker transport.
“A mechanical gyroscope is … made of a wheel-like rotor, torque-free to a substantial level, whose spin determines the axis of a local, nonrotating frame. Due to very tiny general relativistic effects … that is, the ‘dragging of inertial frames’ and the geodetic precession, this spin direction may differ from a direction fixed in ‘inertial space’ that may be defined by a telescope always pointing toward the same distant galaxy assumed to be fixed with respect to some asymptotic quasi-inertial frame (see 4.8).”
Inertial Navigation From ICBMs to Starships
“Mechanical gyroscopes are based on the principle of conservation of angular momentum of an isolated system … with no external forces and torques. … the spinning rotor maintains its direction fixed in ‘space’ (apart from dragging effects as Earth rotates but, however, a vector with general orientation, fixed with respect to the laboratory walls, describes a circle on the celestial sphere in 24 hours, a spinning rotor … describes a circle with respect to the laboratory walls in 24 hours … In a moving laboratory, using three ‘inertial sensors’, that is, three gyroscopes to determine three fixed directions (apart from relativistic effects…) plus three accelerometers to measure linear accelerations and a clock (and possibly three gravity gradiometers to correct for torques due to gravity gradients, one can determine the position of the moving laboratory with respect to its initial position. This can be done by a simple integration of the accelerations measured by the three accelerometers along the three fixed directions determined by the gyroscopes [held by gimbals]. Position can thus be determined solely by measurements internal to the [starship] laboratory … a priori independently of external information is called ‘inertial navigation’ … an onboard computer integrates the accelerations … one is able to find velocity, attitude, and position of the object.”
The word “acceleration” here means off-geodesic proper tensor acceleration not the old Newtonian kinematic acceleration measured by Doppler radar in Einstein’s somewhat misleading popular “happiest thought quote” I discussed earlier whose Siren’s song that has shipwrecked many a wannabe physicist-philosopher Flying Dutchman searching for Ithaca. However, for a starship in free float on a timelike geodesic we can dispense with the gyroscopes to preserve “direction.” “Instead one may use gradiometers …”
“The needs of air navigation have generated a powerful drive for a compact, light weight gyroscopic compass of high accuracy … Today, optical gyros have displaced the mechanical gyro … A wave-guide is bent into a circle. A beam splitter takes light from a laser and sends it round the circle in two opposite directions. Where the beams reunite, interference between them gives rise to wave crests and troughs. If the wave-guide sits on a turning platform, the wave crests reveal the rotation of the platform or the airplane that carries it.
While mechanical gyroscopes are based on the principle of conservation of angular momentum, optical gyroscopes (really optical rotation sensors) are essentially based on the principle of the constancy of the speed of light c in every inertial frame. Therefore, in a rotating circuit and relative to the {LNIF} observers moving with it, the round trip travel time of light depends on the sense of propagation of light with respect to the circuit angular velocity relative to a local inertial frame.” [LIF]
From the general connection of continuous Lie groups[ii] of symmetries of closed dynamical systems to conserved local currents and global “charges” that form the group’s non-commuting Lie algebra[iii], we conclude that the operation of the gyroscope corresponds to the three rotational symmetries of Einstein’s 1905 special relativity’s Poincare group. Therefore, the Sagnac effect[iv] basis of the optical gyros correspond to the three Lorentz boosts of that same Poincare group that formally express the constancy of the speed of light in inertial frames. Newton’s action-reaction third law comes from the three space translation symmetry’s conservation of linear momentum and the conservation of energy comes from the time translation symmetry – if these symmetries are not broken. Does the accelerometer’s operation depend on the Rindler boosts of constant proper accelerating hyperbolic world lines of test particles? These are outside of the Poincare group requiring Roger Penrose’s twistor conformal group.[v] The Poincare group is a subgroup of the conformal group that also includes dilations.
1) John Cramer describes Woodward’s core thesis. “Let’s consider the problem of reactionless propulsion first. Woodward extended the work of Sciama in investigating the origins of inertia in the framework of general relativity by consideration of time-dependent effects that occur when energy is in flow while an object is being accelerated. The result is surprising. It predicts large time-dependent variations in inertia, the tendency of matter to resist acceleration.” This is the local tensor proper acceleration of the rest-massive test particle pushed off a timelike geodesic of the local curvature tensor field caused by real not fictitious forces. The fictitious forces appear to act on the test particle, but in reality they don’t. They describe real forces on the measuring device observing the test particle. The Levi-Civita connection in the mathematics of general relativity describes the real forces on the observing measuring apparatus not the test object being measured. “The inertial transient effects predicted by the Sciama-Woodward calculations are unusual … in that they have G in the denominator, and dividing by a small number produces a large result.” John Cramer definitely thinks that James Woodward’s inertial transient data is real “convincing evidence,” although it’s only “tens of micronewton level thrusts delivered to a precision torsion balance.” It’s important to understand that “thrusts” are not weightless warp drives free of time dilation relative to the clock-synchronized external observer left behind. Supposing best-case scenario, that Woodward’s effect is real and can be scaled up by many powers of ten. It’s still no good to get to the stars because of time dilation and the blueshifts of stuff in the way of the front of the starship. It would be good for airplanes and spacecraft on near solar system missions – if it really worked.
Jack Sarfatti "Recently (Anderson 1995; Bonnor 1996) there has been a revival of interest in the question as to whether the cosmological expansion also proceeds at smaller scales. There is a tendency to reject such an extrapolation by confusing it with the intrinsically unobservable
”expansion” (let us refer to this as ”pseudo-expansion”) described above.
By contrast, the metric of Friedman–Robertson–Walker (FRW) in general relativity is intrinsically dynamic with the increase (decrease) of proper distances correlated with red–shift (blue–shift). It does so on any scale provided the light travel time is much longer than the wave period. Thus, the cosmological metric alone does not dictate a scale for expansion and in principle, it could be present at the smallest practical scale as real – as opposed to pseudo–expansion, and observable in principle.
However, it is reasonable to pose the question as to whether there is a cut–off at which systems below this scale do not partake of the expansion. It would appear that one would be hard put to justify a particular scale for the onset of expansion. Thus, in this debate, we are in agreement with Anderson (1995) that it is most reasonable to assume that the expansion does indeed proceed at all scales. However, there is a certain ironical quality attached to the debate in the sense that even if the expansion does actually occur at all scales, we will show that the effects of the cosmological expansion on smaller spatial and temporal scales would be undetectable in general in the foreseeable future and hence one could just as comfortably hold the view that the expansion occurs strictly on the cosmological scale."
It's not clear yet if this is fatal for Jim's theory. It may not be if Jim is simply invoking an advanced Wheeler-Feynman radiative reaction effect. In spin 1 electromagnetism the Mach effect back from the future ~ "jerk" d^3x(test particle)/dt^3, however Jim claims that for spin 2 gravity this same retro-causal effect ~ d^2x(test particle)/dt^2
Electromagnetic radiative reaction is dual to local zero point vacuum energy, i.e. random ZPF virtual photons responsible for spontaneous emission. Therefore, MET if it worked would be a ZERO POINT spin 2 graviton reaction-less engine analogous to the random spin 1 virtual photons in Wheeler-Feynman-Hoyle-Narlikar theory are a past effect whose future cause are the photon absorbers with our future event horizon as the final absorber of last resort. Jim's device uses spin 2 virtual gravitons not spin 1 virtual photons, but the idea is the same.
That is, if I understand his claim correctly Jim claims a modified off-geodesic Newton 2nd law of motion
F = (D/ds)[(Mach Cosmology Effect)P]
D/ds is the covariant derivative with respect to proper time of the test particle
F is the non-gravity 4-force on the test particle
P is the 4-momentum of the test particle
D/ds = d/ds + Inertial pseudo forces including Newton's gravity "force without force" (Levi Civita terms).
The future horizon, if it's a total absorber, gives
(Mach Cosmology Effect) ~ 1 on the average.
OK Jim's idea of the MET thruster is very simple if you accept the above
If there is a dynamic Machian oscillation then even when F = 0 and even in a local inertial frame where the pseudo forces vanish by the Einstein equivalence principle
0 = Pd(Mach Coefficient)/ds + (Mach Coefficient)dP/ds
However, the fly in Jim's ointment is
"we will show that the effects of the cosmological expansion on smaller spatial and temporal scales would be undetectable in general in the foreseeable future and hence one could just as comfortably hold the view that the expansion occurs strictly on the cosmological scale"
On Jun 26, 2013, at 10:30 PM, JACK SARFATTI <instbio@gmail.com> wrote:
This paper is essential for Jim's MET
the issue is how large scale cosmic structure influences the small-scale of Jim's machine
On Jun 26, 2013, at 9:45 PM, David Mathes wrote:
29. arXiv:astro-ph/9803097 [pdf, ps, other]
The influence of the cosmological expansion on local systems
F. I. Cooperstock, V. Faraoni, D. N. Vollick (University of Victoria)
Comments: To appear in the Astrophysical Journal, Latex
Journal-ref: Astrophys.J. 503 (1998) 61
Subjects: Astrophysics (astro-ph); General Relativity and Quantum Cosmology (gr-qc)