Historical research guide · 0670 · 2011
The Tajmar effect from quantised inertia
M. E. McCulloch
In one minute
Mike McCulloch, at the University of Plymouth, takes one of the most awkward laboratory results in the field and predicts it from a single assumption. Martin Tajmar’s group in Austria found that a ring of niobium, aluminium or stainless steel, cooled to five kelvin and spun up, appears to drag laser gyroscopes that never touch it — by about three parts in a hundred million of the ring’s own acceleration, and by roughly half that when the ring turns the other way. McCulloch applies quantised inertia, his model in which an object’s inertial mass comes from Unruh radiation raised by its acceleration relative to all other matter, with the longest of those waves cut off by the size of the observable universe: a Casimir effect on a Hubble scale. Cooling the apparatus strips away the local accelerations, the gyroscope’s inertia dips slightly, and the spinning ring restores it — so to conserve momentum the gyroscope must move with the ring. The predicted ratios match the measured ones, including the difference between the two spin directions.
Connection
Chapter 3 is the claim that inertia is not a given property of matter but the vacuum’s reaction to acceleration; this paper is that idea used as a working instrument, taking a cold-laboratory measurement and returning a number to two significant figures. Chapter 11 is where rotating superconductors and cryogenic rings are the hardware, and quantised inertia offers a route to the same signals that does not depend on the superconducting transition. The Tajmar-group measurements themselves are on this site at /library/stm-1cb16dd1bc and /library/stm-21102decd7.
From the source
Tajmar’s group reports that rings of niobium, aluminium, stainless steel and other materials, cooled to five kelvin and spun, produce an acceleration in nearby accelerometers and laser gyroscopes that are not in frictional contact with them, in the same direction as the ring, of about 3 plus or minus 1.2 times ten to the minus eight of the ring’s acceleration for clockwise rotations and about half that for anticlockwise ones — a signal resembling Lense-Thirring frame dragging but twenty orders of magnitude larger, and carrying a parity violation frame dragging does not have.Introduction, first paragraph, citing Tajmar et al. 2007, 2008 and 2009 (references 1 to 3)
Quantised inertia, also written as modified inertia due to a Hubble-scale Casimir effect, holds that inertial mass is caused by Unruh radiation appearing when a body accelerates relative to all other matter, and that this radiation is subject to a Casimir effect on the scale of the cosmos in which the longer Unruh waves are increasingly disallowed: the inertial mass equals the gravitational mass multiplied by one minus beta times pi squared times the speed of light squared, divided by the acceleration times the Hubble diameter, with beta of 0.2 and a Hubble diameter of 2.7 times ten to the twenty-six metres. The same expression had already been applied to the Pioneer deceleration and to the Earth-flyby velocity jumps.Introduction, Equation 1 and Equation 2, citing McCulloch 2007 and 2008 (references 5 and 8)
The mechanism proposed for the cold ring is a change in the gyroscope’s inertia: cooling removes the accelerations of nearby vibrating atoms, leaving the gyroscope sensitive to its much smaller acceleration relative to the fixed stars — 0.0371 metres per second squared at the latitude of Seibersdorf, the Coriolis term plus the Earth’s orbital term — so its Unruh waves lengthen, more of them are cut off, and it loses roughly two parts in a hundred million of its mass. When the ring accelerates at 2.5 metres per second squared the gyroscope suddenly sees a far larger acceleration, its Unruh waves shorten, fewer are disallowed, and its inertial mass rises again; conserving momentum with respect to the ring then requires the heavier gyroscope to move with the ring.Method and Results, Equations 3 to 10; Discussion, first paragraph
The model predicts an acceleration ratio of 1.78 plus or minus 0.16 times ten to the minus eight before the gyroscope’s own rotation is taken into account, and once the gyroscope spins with the ring at one third of the Earth’s rotation rate the prediction splits by direction: 2.67 plus or minus 0.24 times ten to the minus eight for clockwise rotation against the observed 3 plus or minus 1.2, and 1.34 plus or minus 0.12 times ten to the minus eight for anticlockwise against the observed value of about 1.5 plus or minus 1.2. The parity violation is therefore a secondary consequence of the gyroscope changing its own acceleration relative to the fixed stars.Method and Results, Equations 11 and 12 and the closing paragraph; Conclusions
The named test that would separate this model from the alternatives is hemispheric: repeated in the southern hemisphere the gyroscope should still follow the ring’s direction of rotation, but the larger signal should appear for anticlockwise ring rotations rather than clockwise ones. McCulloch states that this corrects his own earlier prediction of an exact mirror-image result, which he attributes to using the wrong reference frame.Discussion, final paragraph; Conclusions, third paragraph
The second named test uses the existing apparatus: reducing the mass of the ring by a factor of ten thousand should leave the gyroscope-to-ring ratio unchanged at the lower gyroscope 0.0553 metres away while making the gyroscope at 0.2283 metres read about 13.6 percent lower, turning the predicted decay with vertical distance into something measurable. The author adds that the modified inertia would not show up in a torsion-balance equivalence-principle test, because two balls rigidly joined on a cross bar share the same acceleration relative to the distant masses and so have their inertial masses modified equally.Discussion, second and third paragraphs; Conclusions, final paragraph
The way in
https://arxiv.org/abs/1106.3266How to cite it
M. E. McCulloch (2011) The Tajmar effect from quantised inertia doi:10.1209/0295-5075/95/39002