Can the mass of a proton be measured through algebra? I found a paper called the Absolute Relativity Theory and I thought it was intriguing. (Link: https://arxiv.org/pdf/0908.2562v1.pdf)
The authors claim they can measure the mass of the proton / neutron and electron using only algebra.
They also claim they can predict the existence of particles not yet found, and also give their characteristics.
Does anyone know if this idea that mass can be calculated algebraically is present in other theories ?
Is this theory widespread within the mathematical (or physical) community ?
 A: I admittedly didn't read the category theory-based sections carefully (mostly because I don't know nearly enough category theory to actually judge their results fairly), but the end results are what you're asking about anyway, so let's talk about those (i.e. section III).
Unfortunately, all of the author's calculations are too far off from the actual values of things for the theory to hold any water. The calculated age of the universe (18.18 Gyr, given without uncertainty) is significantly different from the measured age ($13.799\pm.021$ Gyr). Since this age is also used in the calculation of $G$, those results are also thrown into question. The authors explain this away as bias based on faulty assumptions about constancy of constants, but they cannot do the same for later calculations.
The authors report a .0007% discrepancy between the calculated mass of the proton and its measured counterpart, or a relative error of $7\times 10^{-5}$. The mass of the proton has been measured to a precision of $2\times 10^{-8}$, so they are reporting a discrepancy that is one thousand times larger than experimental error. They report no biases here, claiming that the closeness to the experimental result proves their theory correct. Instead of confirming their theory, this unforgivably large discrepancy damns it.
Similarly, the calculated masses of the muon and tau lepton (which they call the "electron $\mu$" and "electron $\tau$") are also at odds with experimental results. The authors obtain a value of $105.9$ MeV/c^2 for the muon mass, whereas the actual measured muon mass is $105.6583745\pm.0000024$ MeV/c^2. The discrepancy here is on the order of $3\times 10^{-3}$, which is, one hundred thousand times larger than the experimental uncertainty of $2\times 10^{-8}$, an even worse discrepancy than before. 
The tau lepton mass is calculated by the authors to be $1.82146$ GeV/c^2, whereas the measured value is $1.77682\pm .00016$ GeV/c^2. Relative error on the calculated value is $2.5\times 10^{-2}$, and the relative uncertainty on the measured value is $9\times 10^{-5}$. Once again, the discrepancy between theory and experiment is hundreds of times larger than the uncertainty in experiment.
My verdict? This theory does not predict anywhere near the correct values for the physical constants, even when the authors said it did. Therefore, it cannot be an accurate description of reality.
