I did not say anything about any mechanism in nature. This is just a mathematical manipulation of the numeric values. If you have the absolute masses m1, m2 an

I did not say anything about any mechanism in nature. This is just a mathematical manipulation of the numeric values. If you have the absolute masses m1, m2 and m3, you can store instead of those 3 numbers other 3 numbers, m1, m2/m1 and m3/m1. This stores the same information, because whenever you need e.g. m3, you can recover it by multiplying m3/m1 with m1. You can do the same thing with one hundred absolute masses, replacing them with a single absolute mass together with 99 dimensionless mass ratios. As I have already said, sometimes there are good reasons to do so, e.g. in particle/nuclear/atomic physics you can increase the accuracy of computations if only a single absolute mass is used, the mass of the electron, for which there are accurate measurement methods, while all the other masses are replaced with dimensionless ratios between the corresponding absolute masses and the mass of the electron, because such mass ratios can be measured accurately based on the movements in combined electric and magnetic fields. This includes the standard model, where the absolute mass of the electron is necessarily one of the parameters of the model, but all the other masses can be replaced with dimensionless mass ratios, e.g. the mass ratios between the muon mass and the electron mass or between the tauon mass and the electron mass. Similarly, any parameter used to characterize the strength of the electromagnetic interaction is not dimensionless (in any system of units where the elementary charge is one of the base units, and such systems are better than the alternatives), and one such parameter must be included in the standard model. The parameters that characterize the weak interaction are also not dimensionless, but they can be converted to dimensionless parameters in a similar way with the masses, by using ratios (vs. the electromagnetic interaction) that are incorporated in the mixing angles parameters. The end result is that the standard model is expressed using a large number of dimensionless parameters together with only a few parameters that have dimensions, because this representation is more convenient. Nevertheless, there are alternative representations where most parameters have dimensions, by rewriting the model equations in different forms, so there is nothing essential about having dimensions or not.