Historical research guide · 0715 · 2015
Testing quantised inertia on the emdrive
M. E. McCulloch
In one minute
Mike McCulloch, of Plymouth University’s school of marine science and engineering, has spent years on one idea: that inertia — a body’s resistance to being pushed — is the vacuum’s reply to acceleration, carried by Unruh radiation, the faint glow an accelerating body sees. In his model, quantised inertia, only those Unruh wavelengths that fit inside the horizon around the body are allowed, so inertia thins out when acceleration is very small. Here he turns the same rule on a laboratory object: the tapered microwave cavity called the emdrive, which several groups had reported drifting towards its narrow end. Photons bouncing inside such a cavity accelerate so violently that the Unruh waves they see are the size of the cavity itself, so the cavity walls do the selecting. More waves fit at the wide end, the photons carry more inertial mass there, and conserving momentum pushes the cavity the other way. The formula has no adjustable parameters, and it names its own test: shorten the cavity and the thrust should reverse.
Connection
Chapter 8 asks how a craft moves without throwing anything overboard, and this is the cleanest published attempt to derive such a force from first principles rather than fit it — a formula with no free parameters, applied to eight documented cavities. It reaches back into chapter 3, because the mechanism is the vacuum setting inertia, and forward into chapter 1, because the reading it needs is the one the field has not yet taken. The NASA Eagleworks measurement McCulloch tests against is on this site at /library/stm-a46c32725a, and Martin Tajmar’s SpaceDrive rebuild at TU Dresden, at /library/stm-0d21110734, is the high-accuracy follow-up: sweeping four resonances on a balance that resolves below a nanonewton, that group found every reading inside a noise level of 10 to 30 nN and set a bound at or below the classical light-pressure value of 3.3 nN per watt. That bound is now the level any future emdrive measurement has to clear, and McCulloch’s reversal prediction is the specific experiment that would speak to his model either way.
From the source
In quantised inertia, the inertial mass of a body comes from the Unruh radiation it sees when it accelerates, and that radiation is subject to a Casimir-like selection: only wavelengths that fit exactly into twice the Hubble distance are allowed, so a greater share is disallowed at small accelerations and inertial mass falls away in a new way.Section 1, Eq. 1
Inside a tapered microwave cavity the photons bounce so fast that their acceleration makes the Unruh waves about the size of the cavity, so the cavity walls replace the Hubble horizon as the selector. More waves fit at the wide end, the photons carry more inertial mass there, and conserving momentum requires a force on the cavity towards its narrow end for photons travelling in either direction.Section 2, Eqs. 3 to 6; Section 4, the intuitive account with Fig. 1
Approximating the resonance of the Unruh waves in three dimensions rather than only across the axis gives a thrust equal to six times the power times the quality factor times the axial length, divided by the speed of light, multiplied by the difference of the reciprocals of the axial length plus four times each end width. The model has no adjustable parameters.Section 2, Eqs. 8 to 14; Section 3, closing sentence
Against the eight fully documented cavities — two from Shawyer, the Cannae drive, four from the NASA team including the vacuum run, and the Tajmar and Fiedler vacuum test — the model predicts 3.8, 149, 7.3, 0.23, 0.57, 0.11, 0.64 and 0.02 millinewtons where the reported thrusts were 16, 80 to 214, 9, 0.091, 0.05, 0.055, 0.03 and 0.02 to 0.11 millinewtons: the right order of magnitude in every case, with two cases out by more than a factor of ten.Section 3, Table 1
The model names a definite test: making the axial length equal to the diameter of the small end should reverse the sign of the thrust, because the Unruh waves then fit better at the narrow end than at the wide one. It also predicts the force rises with input power and with the cavity quality factor, and that a dielectric, by lowering the speed of light inside, should enhance it.Section 4, final two paragraphs; Section 5
McCulloch states the two assumptions his account rests on and marks them as the ones to argue with: that the microwave photons carry a finite inertial mass, and that the speed of light is changing inside the cavity — which is exactly why he asks for a controlled laboratory test rather than a further astrophysical fit.Section 4, third paragraph; Section 1, on the ambiguity of astrophysical tests
The way in
https://doi.org/10.1209/0295-5075/111/60005How to cite it
M. E. McCulloch (2015) Testing quantised inertia on the emdrive doi:10.1209/0295-5075/111/60005