The Dark Matter Mass Spectrum
We start with the mass spectrum for subatomic nuclei. This mass spectrum just needs to be rescaled to give us the primary mass spectrum for the dark matter. Discrete Scale Relativity proposes that these mass spectra are exactly self-similar with the nuclear masses scaled up by a factor of 1.70 x 10^56.
To convert this mass distribution for subatomic nuclei into the mass distribution of stellar scale dark matter objects, 1 Atomic Mass Unit (A) = 0.145 solar mass. For example, the highest peak (proton analogue) on the left hand side of the proposed dark matter graph would have a mass of 0.145 solar mass and the peak just to the right (He nucleus analogue) would have a mass of (4)(0.145) = 0.58 solar mass, and so on.
The full range of dark matter masses is 8 x 10^–5 solar mass to about 35 solar mass.
There is a very large and very narrow secondary peak at 8 x 10^–5 solar mass which corresponds to the electron. It is virtually a delta function (all the same mass). These objects are Kerr-Newman singularities with no event horizon and only a very thin envelope (radius 4 x 10^–17 cm) of almost infinitesimally small and light subquantum scale particles surrounding them. Thus they are nearly naked singularities. They are roughly as abundant as the proton and He nucleus analogues combined, but their masses are nearly 2,000 times smaller, and so their contribution to the total dark matter mass is secondary.
The dominant contributions to the dark matter mass are made by the proton and He nucleus analogues, which are Kerr-Newman black holes and are every bit as “primordial” and fundamental as protons and alpha particles. The MACHOs discovered by microlensing observations are primarily members of this subclass. Proton analogues outnumber He nucleus analogues by roughly 90% by numbers, assuming one has a truly representative sample.
Then, as in the atomic scale case, there is a long tail of more massive but much less abundant Kerr-Newman ultracompacts. The massive black holes discovered by LIGO are members of this subclass.
We can also note that the mass distribution of stars is roughly the same as the mass distribution of the dark matter objects in the 0.145 solar to 35 solar mass range. The reason is fairly obvious to those who understand Discrete Scale Relativity. Hint: Do atoms and atomic nuclei have roughly the same mass spectra?
Do I expect academic physicists to summarily dismiss all of the above as pure nonsense? Most definitely! However that may change, albeit very slowly, if Discrete Scale Relativity’s predictions for the dark matter continue to gather observational support.