Historical research guide · 0695 · 2010
Minimum accelerations from quantised inertia
M. E. McCulloch
In one minute
Mike McCulloch, at the University of Plymouth, builds inertia out of the vacuum and then reads a number off the sky. His model, quantised inertia, rests on two assumptions: an accelerating object sees Unruh radiation, a warm bath the vacuum shows only to things that accelerate, and that bath is cut off at the far end by the size of the observable universe — a Casimir effect on a Hubble scale, with the longest waves simply not fitting. Slow the object down and more of those waves are excluded, so its inertial mass falls, and falls faster than the acceleration does. The consequence is that acceleration cannot go to zero. There is a floor, and McCulloch computes it: close to the cosmic acceleration usually attributed to dark energy. Applied to spinning disc galaxies the same floor sets a minimum apparent mass of about 1.1 billion suns, which is where astronomers find the observed cutoff. He then proposes a laboratory test with a particle accelerator.
Connection
Chapter 3 is the claim that inertia is not a built-in property of matter but the vacuum’s reaction to acceleration; this paper is that claim doing arithmetic, taking one assumption about the zero-point field and returning a galaxy mass to two significant figures and a cosmic acceleration for free. Chapter 8 gets the part that matters for hardware — if inertia is set by the vacuum then it is in principle adjustable, and McCulloch names the machine that would show it. Chapter 13 gets the join: the same model that fixes a galaxy’s rotation also produces the acceleration attributed to dark energy, which is the site’s thesis that these are one subject. Read it beside the Tajmar-ring application at /library/stm-5f5929fc9c.
From the source
Quantised inertia rests on two assumptions: that an object’s inertial mass is a drag from the Unruh radiation it sees when it accelerates, and that this radiation is subject to a Hubble-scale Casimir effect, so only wavelengths that fit exactly into twice the Hubble diameter are allowed. Longer Unruh waves are progressively disallowed as acceleration falls, which reduces inertia gradually rather than abruptly.Abstract; Introduction, the paragraph introducing MiHsC, and Eq. 1
Because inertial mass falls faster than acceleration does at very low accelerations, the model predicts a floor: even where the gravitational mass nearby is zero, an object must still accelerate, at two times the speed of light squared divided by the Hubble diameter. That value is close to the observed cosmic acceleration attributed to dark energy.Sec. 2, Method and Results, Eqs. 4 and 5
Read as an unexplained dark mass inside a radius of 500 parsecs, the same floor gives 2.3 times ten to the thirty-ninth kilograms, or 1.1 billion solar masses — which matches the observed cutoff below which no rotationally supported disc galaxies are found, reported by McGaugh and colleagues in 2009.Sec. 2, Eqs. 6 and 7
Applied instead to the whole observable universe, the model gives an apparent mass of about two times ten to the fifty-third kilograms, close to the mass the observable universe must have to be flat, so quantised inertia offers a candidate explanation of the flatness problem as well.Sec. 3, Discussion, Eqs. 8 and 9
The first assumption can be tested directly, and McCulloch specifies the experiment: accelerate a particle around a one-kilometre accelerator ring at nine-tenths of the speed of light, giving an acceleration of 7.3 times ten to the thirteenth metres per second squared and an Unruh wavelength of 9.7 kilometres — short enough to be supplemented with man-made radio waves, applied at 22 kilometres in the laboratory frame to allow for the particle’s motion. If inertia really comes from Unruh radiation, the particle’s inertial mass rises and its trajectory shows it.Sec. 4, A suggested practical test, Eq. 10
McCulloch lists the model’s own unfinished business: there is no proven reason why bound and unbound trajectories should behave differently, it is not established how Unruh waves that long interact with matter or with the Hubble scale, and it is unclear why the very large accelerations inside stars and inside atoms need not be counted.Sec. 3, Discussion, final paragraph, items 1 to 4
The way in
https://doi.org/10.1209/0295-5075/90/29001How to cite it
M. E. McCulloch (2010) Minimum accelerations from quantised inertia doi:10.1209/0295-5075/90/29001