I usually avoid discussing things like the invisible interiors of black holes, since any predictions are not directly testable, but there is one component of black holes that has been solidly observed and is unexplained: relativistic jets, and these past few days I've realised that, as well as a minimum, MiHsC predicts a maximum acceleration that might get rid of black hole singularities in a way that could be tested by predicting these jets.

I've already shown that MiHsC predicts a minimum acceleration for nature similar to the size of the observed cosmic acceleration (McCulloch, 2010). To recap: MiHsC assumes that inertial mass is caused by Unruh radiation (a radiation seen by objects that accelerate) and that only Unruh waves that fit exactly into the Hubble scale are allowed (since partial waves would reveal what lies behind the horizon: a logical impossibility). The wavelength (L) of the Unruh radiation seen increases as an object's acceleration reduces, and is given by L = 8c^2/a, where a is the acceleration. At tiny accelerations the Unruh wavelengths stretch so that a greater proportion of the waves do not fit within the cosmos (width of cosmos W = 2.6x10^26 metres wide), and at an acceleration of a = 8c^2/W ~ 7x10^-10 m/s^2 no Unruh waves can fit at all. The point is that before an object moving out into deep space manages to achieve this tiny acceleration the MiHsCian collapse of its inertial mass boosts its acceleration. The result is that its acceleration (relative to other matter) can never drop below 7x10^-10 m/s^2. This explains the recently-observed cosmic acceleration.

The Hubble scale is one horizon beyond which we cannot see, another obvious one is the tiny Planck scale (1.6x10^-35 m), so it makes sense to say that Unruh waves shorter than the Planck scale cannot exist (again using Mach's philosophy that only things that can be seen in principle can exist) and so it should be impossible in MiHsC for accelerations to be so large that the Unruh waves are shorter than the Planck scale (lp). Since the Unruh wavelength = 8c^2/a > lp this means that a < 8c^2/lp so a < 4.5x10^52 m/s^2.

The great Sakharov (1966) predicted a similar maximal acceleration, also using Unruh radiation, but without connecting it to inertial mass. Also Caianiello (1984) predicted a similar size of maximum acceleration in a very different way: starting from the uncertainty principle. This maximum may be testable on Earth: Papini (1995) have suggested that light resonating in cavities might be used to generate accelerations this large and that type-I superconductors could experience accelerations as large as this already.

Now back to the black holes. Non-rotating
black holes have the problem that general relativity embarrassingly predicts that they have infinite-density
singularities at their centres. MiHsC changes this dramatically because it suggests that at soon as the acceleration reaches the maximum near the centre the inertial mass will collapse. I can't picture what such a collapse would do yet, but it is interesting because the physics will somehow have to adjust to keep the acceleration below the maximum (smoothing the singularity) and the energy released could power the unexplained relativistic jets.

**References**

Caianiello, E.R., 1984. Lett. Nuovo Cimento, 370.

McCulloch, M.E., 2010. Minimum accelerations from quantised inertia. EPL, 90, 29001. arXiv

Papini G., A. Feoli, G. Scarpetta, 1995. Phys. Lett. A., 50.

Sakharov, A.D., 1966. JETP Lett., 3, 288.

## No comments:

Post a Comment