Newton's first law, the inertial one, says that the default acceleration is zero, so, in a vacuum, objects move happily along at constant velocity until something external pushes on them.

MiHsC or quantised inertia (see the references below) predicts something slightly (usually undetectably) different: that the default acceleration is non-zero and equal to 2c^2/Theta where c is the speed of light and Theta is the Hubble scale, so 2c^2/Theta = 6.9*10^-10 m/s^2. This is tiny, but is equal to the recently-observed cosmic acceleration that some have attributed to 'dark energy', and model by grotesquely adding a cosmological constant term to Einstein's field equation. I'll try and explain here how MiHsC predicts the observed cosmic acceleration using just its two assumptions, which are:

1) Inertia is caused by Unruh radiation (a kind of wave) and..

2) ..these waves must fit exactly into the Hubble scale (like a Hubble-scale Casimir effect or cosmic seiche).

The thing about Unruh waves is that as an object's acceleration decreases the Unruh waves it sees get longer. With a boundary this becomes significant. If you make small waves in a bath with, say, an electric toothbrush, then most of the little waves will propagate, but if you make large waves with a paddle, then you'll have to get the wavelength exactly right or the waves won't fit. The point is that for longer wavelengths, a smaller proportion of the waves are allowed because of the boundary condition: this resonant behaviour is called a seiche in oceanography and happens a lot with waves in lakes and harbours. This implies straight away that Newton's first law (default acceleration = 0) won't quite work in MiHsC, because if the acceleration is zero, or close enough to zero, the Unruh waves are as large or larger than the observable universe, ie: unobservable, and as Mach said: if it can never be observed, forget it! (to paraphrase).

In MiHsC, the same process as in the bath works with objects moving into deep space. As they move away from other gravitating matter their acceleration drops. Therefore, the Unruh waves they see lengthen, and a greater proportion are disallowed, so that the inertia of the object eventually decreases very fast, making it easier to accelerate even with a distant gravitating mass, and this stabilises the acceleration at a minimum of 2c^2/Theta. Happily, this is the acceleration that has been seen in the deep cosmos. It has been attributed to the vague concept of dark energy, and modelled by adding the cosmological constant term (an adjustable parameter) to Einstein's field equations, but MiHsC predicts it far more easily, and without any adjustable parameters.

References:

McCulloch, M.E, 2010. Minimum accelerations from quantised inertia.

*EPL*, 90, 29001. http://arxiv.org/abs/1004.3303
McCulloch, M.E., 2007. The Pioneer anomaly as modified inertia.

*MNRAS*, 376, 338. http://arxiv.org/abs/astro-ph/0612599
## 2 comments:

Hi Mike,

I really like where you are going with the MiHsC idea. I have a technical background but only enough to vaguely appreciate the details. I'm reading through most of your papers and looking at counter arguments. Before I saw this blog entry I had already decided that there was a good chance that MiHsC might explain the cosmic acceleration "problem". I have also considered the possibility that MiHsC might play a roll in cosmic inflation which (to my understanding) is still just hand waving. I have no basis for this speculation but if matter condenses out but is still in a small 4space then its inertia should be very small allow the matter to move outward at a very high rate (dragging 4space with it) until inertia kicked in and slowed things down.

Does this make any sense?

Tom Krehbiel

Hi Tom. You are indeed right that MiHsC predicts something like inflation. When the cosmos was young and small MiHsC predicts a much smaller inertial mass and a much larger minimum acceleration (assuming a constant speed of light..).

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