Dear Nathalie Olivi-Tran

The link doesn't show the article but I found it on your personal website (http://tran.nathalie.free.fr/masspart2n.pdf).

It is really interesting - and your other "hobby papers" too! (I am e.g. impressed by "A possible explanation of the nature of dark matter by Newtonian mechanics"). However, it will take some time to read/understand it all because I am not a phenomenological physicist. Nevertheless, your concepts are quite similar to what I normally use.

With kind regards, Sydney

Dear Nathalie Olivi-Tran

You use the idea that spacetime (not space itself?) “is composed of small hypercubes of 1 Planck length”, etc.

However there is the problem of the gap of about 1020 between the Planck length and the minimal length scale (the observed minimal length of electromagnetic waves). In between there are no observable electromagnetic waves and no observable particles (because of the principle of asymptotic freedom).

If I want to express the mass of a particle in amounts of energy I can use E = mc2. In other words, if I want to transform mass into free energy (quanta) I have to perform the operation c2 to every stored quantum within the boundary of the mass. But what is represented by the operation c2?

If I concentrate quanta in a point of space I am changing the local properties (in relation to the average properties around). From the geometrical point of view – we are talking about “real space theory” – I am transferring topological deformation to this point in space. But a topological deformation that doesn’t violate the general properties of space itself results in an increase of surface area.

Now what have I done? I have concentrated an amount of quanta to a small volume in space – resulting in a local increase of surface area – and at the same time I have decreased the average amount of surface area of the volume around the point of concentration because of the transfer of quanta to the center of the volume.

Now it is clear that I have to add surface area (c2) to every stored quantum within the boundary of the mass that will be transformed to a free quantum again because the speed of light is the universal velocity of the quantum. In other words the energy of the mass of a particle is always related to an integer power of 2.

Therefore, the statement in the title of your paper that “The masses of the first family of fermions and of the Higgs boson are equal to integer powers of 2” is 100% correct.

With kind regards, Sydney