Some fresh air in propellantless ideas that may (or may not) be related to the EmDrive (explained in the following post next after this one).
American physicist Jack Sarfatti (
Wikipedia) has a
new hypothesis for low-power warp drive.
• Basic summary:
https://www.academia.edu/38649950/Low_Power_Warp_Drive_for_Dummies• Long essay:
https://www.academia.edu/6582748/Sarfatti_Stargate_March282014• Presentation slides:
https://www.academia.edu/17018485/Metric_Engineering_the_Fabric_of_Space-Time_Dark_Energy_Propellantless_Warp_Drive_and_WormholeLet's sum up his ideas with simpler words, translated from his messages on Jim Woodward's email list and his other stuff gathered online (papers and videos).
In the Einstein field equations, Einstein's constant:
χ = (8π G)/c⁴is a coupling constant that tells how the RHS mass-energy stress density tensor Tμν couples with the LHS gravitational field Gμν. Its value represents the strength of such coupling. Therefore, the coupling is usually very low, due to the fourth power of the speed of light in the denominator, a very large number making the constant very small. One can say that "spacetime is darned stiff".
Sarfatti proposes a new way to soften the natural stiffness of spacetime with a small amount of EM energy density, enabling large spacetime distortions locally, i.e. a low-power warp drive. This is new as a warp drive would usually need (Alcubierre metric) a gigantic amount of "exotic material" of negative energy: about a Jupiter-equivalent mass.
The thing is, Sarfatti considers the speed of light in the coupling constant to not be the constant
c as in the vacuum, but the speed of light in the medium. He proposes the idea (testable and popper-falsifiable) that some special material (possibly high Tc superconducting metamaterial) with very high electric permittivity Ɛ and magnetic permeability μ would give a very large refractive index n (as n² = Ɛ×μ) which would make the speed of light very low inside the medium, writing the coupling constant:
χ = (8π G n⁴)/c⁴in the particular case of a local scalar field not uniform in time and space at different parts of such solid metamaterial (spatially inhomogenous & time-dependent anisotropic matter).
Please note at this stage that this proposal has nothing to do with other fringe ideas involving "slow light" i.e. variation of the group velocity in some optical materials or metamaterials.
Also, do not throw the baby out with the bath water yet, regarding past unhappy marriages of Maxwell with Einstein. It is true that electromagnetic susceptibilities cannot usually describe a physical response of matter, subjected to electric and magnetic fields, satisfying
general covariance (which is a basic principle of relativity). Indeed, such material reacts to these fields in a non-inertial frame of reference (i.e. accelerating)
differently than in an inertial frame. Consequently, those electromagnetic susceptibilities seem to not be adapted to GR, even in the case of a linear response.
But, and this seems to be new, contrary to other past models, Sarfatti does not use EM susceptibilities in the standard way, i.e. as in linear response theory. He uses tetrad transformations and generalizes the 3D permittivity and permeability space tensors to 4D spacetime, whose inner product is a
zero rank tensor invariant. Therefore, his equations are:
- consistent with Newtonian limit
- obey special relativity locally
- obey the general covariance of general relativity & background independence
Warning: "Local invariance" of the speed of light must not be confused with the "global spatial homogeneity" of the speed of light in a chunk of material. A "scalar invariant" is a scalar quantity that is invariant under a specified class of coordinate transformations, which is achieved, by definition, with a tensor of rank 0, with respect to the specified class of transformations.
So Sarfatti's conjecture has nothing to do with changes in the value of a constant like
c within a particular coordinate system, that might result from the presence of an optical medium, or from any other physical influence such as a gravitational field.
Einstein's relativity principle only requires that the
laws of physics be invariant under inertial frame transformations; it doesn't require that a law of physics make precisely the same
predictions for the results of direct measurements of a given quantity at every
point in space – which is how Carl H. Brans defined a "locally measured invariant". That's the reason why it's important to distinguish carefully between "constancy" and "invariance" in such context.
Hence, for a fixed gravitational field, when EM susceptibilities tend to infinite (i.e. in real-world when the value of Ɛ×μ becomes very large) then the mandatory EM energy becomes ridiculously low.
Explained in a more compact way:
for Gμν = cst, if Ɛμ → ∞ then Tμν → 0
It is worth noting that Tμν here is not the mass-energy of the whole spaceship. It is the stress-energy density of the EM pump field ("fuel" of the warp drive) permeating the thickness of the fuselage - not the ship as a whole. Consider it as the electric field between the plates of a special capacitor with a metamaterial between the plates, or the magnetic field inside a solenoid wound with such special metamaterial in the core.
Russian physicist Alexander Balakin has published a paper 12 years ago where, while not considering Sarfatti's more recent idea of G(permittivity tensor × permeability tensor)² for the matter-geometry coupling, uses mandatory tensors and tetrad transformations:
• Balakin, A. B. (September 2007). "Extended Einstein-Maxwell model".
Gravitation and Cosmology.
13(51): 163–177.
arXiv:0710.0606.
Finally, a possible recent candidate material to test Sarfatti's conjecture has been discovered by Korean researchers:
• Chang, T. et al. (30 August 2016).
"Broadband giant-refractive-index material based on mesoscopic space-filling curves".
Nature Communications.
7: 12661. doi:10.1038/ncomms12661.