The masses of the electron, the muon, and the tau are known with great precision, but in the Standard Model they are not explained: they are inserted as measured parameters. This work explores a different possibility. In the TS5D framework, what we observe as a particle in four dimensions may be the projection of a classical excitation living in a five-dimensional geometry. The fifth dimension, denoted e, is compact, like a circle, and is interpreted as an energy fibre. The key idea is that mass is not added directly to the particle. Instead, it emerges from the way an excitation is confined inside the hidden geometry. One may compare this to a musical instrument: a flute or a guitar string can only vibrate in certain ways because of its shape. Likewise, the geometry of the fifth dimension selects certain resonance modes. These resonances are seen by a 4D observer as masses. More precisely, the theory does not claim to predict absolute masses directly in MeV or kilograms. It first aims to explain mass ratios — for example, why the muon is about 207 times heavier than the electron, and why the tau is about 17 times heavier than the muon. The absolute scale must still be fixed by measurement. A central object in the model is the throat. This is the curved geometric structure formed when the effective size of the energy fibre changes with a logarithmic scale variable u. The throat acts like a waveguide: it restricts the possible hidden vibrations and selects transverse modes, meaning modes in directions that the 4D observer does not directly see. The proposed mechanism is therefore simple in spirit: the 5D geometry forms a throat; classical excitations occupy it; the throat selects allowed transverse modes; and the geometric energy of these modes appears in 4D as mass. The electron, muon, and tau would then correspond to three distinct modes of the same underlying geometric structure. This version deliberately avoids using quantum mechanics as a starting point. It uses classical geometry, classical fields, a Maxwell field, and a scalar condensate. Technical words such as “spinor,” “Dirac,” or “spectral index” are used as mathematical tools, not as assumptions of quantum theory. The result is not a complete derivation of the lepton masses. Some elements remain postulated or calibrated, especially the precise choice of the three occupied modes. The work should therefore be read as a conditional organization of mass ratios: if the geometric postulates of TS5D are accepted, then the lepton mass hierarchy can be related to a classical spectral problem on the throat. The program is also falsifiable. It gives two incompatible internal readings for the tau mass: 1776.934 MeV and 1776.968 MeV, separated by 34 keV. The Belle II experiment should eventually reach the precision needed to distinguish between them. Whatever the outcome, at least one branch of the model will be ruled out. This work therefore does not claim to have solved the mass problem completely. It proposes a precise route: to transform the question “why these masses?” into the geometric question “why these modes in this throat?”, with explicit assumptions, declared limits, and a quantified experimental test.
Noel COPINET (Thu,) studied this question.