Minimum accelerations from quantised inertia
M. E. McCulloch
Abstract and summary · read the original at the source
In one page
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.
Why it matters hereChapter 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.
What it claims
01Quantised 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
Published and peer-reviewed02Because 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
Published and peer-reviewed03Read 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
Published and peer-reviewed04Applied 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
Published and peer-reviewed05The 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
Designed, not yet built06McCulloch 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
What to watch
Read it · abstract
Abstract
It has recently been observed that there are no disc galaxies with masses less than 10⁹ M⊙ and this cutoff has not been explained. It is shown here that this minimum mass can be predicted using a model that assumes that 1) inertia is due to Unruh radiation, and 2) this radiation is subject to a Hubble-scale Casimir effect. The model predicts that as the acceleration of an object decreases, its inertial mass eventually decreases even faster stabilising the acceleration at a minimum value, which is close to the observed cosmic acceleration. When applied to rotating disc galaxies the same model predicts that they have a minimum rotational acceleration, i.e.: a minimum apparent mass of 1.1 × 10⁹ M⊙, close to the observed minimum mass. The Hubble mass can also be predicted. It is suggested that assumption 1 above could be tested using a cyclotron to accelerate particles until the Unruh radiation they see is short enough to be supplemented by manmade radiation. The increase in inertia may be detectable.
The way in
https://doi.org/10.1209/0295-5075/90/29001LICENCE. Published as EPL (Europhysics Letters) 90, 29001 (2010). Checked directly rather than taken from an aggregator label: Unpaywall and OpenAlex both return oa_status bronze with a null licence for this DOI, and the author manuscript on arXiv, 1004.3303v1 of 19 April 2010, is filed under the arXiv non-exclusive distribution licence version 1.0, which grants arXiv distribution rights and no re-use. No Creative Commons statement appears in the manuscript text or on the arXiv abstract page, checked on 2026-09-08. So this sheet carries the summary, the claims and the author’s own abstract, and sends the reader to the full text at the source. TEXT. The claims below are read from the complete arXiv manuscript, whose section, equation and figure numbering the locators use; the abstract reproduced here is the published one. McCulloch wrote from Marine Science and Engineering at the University of Plymouth and the School of Physics at the University of Exeter. The companion sheets in this library are the same model applied to Martin Tajmar’s cryogenic rotating rings at /library/stm-5f5929fc9c and to the emdrive at /library/stm-830d5d4620.
How to cite it
M. E. McCulloch (2010) Minimum accelerations from quantised inertia. doi:10.1209/0295-5075/90/29001
Where it sits in the curriculum
Inertia and gravity from the vacuumInertial mass reduction and transmedium craftThe unified picture