Adopted momentum model for an ideal massless particle

Adopt as a separate model premise for ideal massless particles, independent of Adopted massive-particle momentum, observer measurement and isolated-collision conservation whose formula $P=mU$ uses $m>0$ and does not define a massless case:

(i) The object. An ideal massless particle of the model is described by a nonzero future null vector $P\in V$ (Timelike, null, spacelike and causal vectors of a Lorentz vector space, Time orientation, future and past timelike/null/causal vectors, and the closed cones) whose SI unit is kilogram metre per second (SI units and coordinate conventions of the special-relativity framework). Such a $P$ is not of the form $mU$ for any $m>0$ and any future timelike $U$ with $\eta (U,U)=-c^2$: a positive multiple of a timelike vector is timelike, and the zero vector is neither timelike, null nor spacelike, so the massive expression $mU$ with this normalized $U$ degenerates to $0$ at $m=0$ and does not describe a nonzero null momentum. The particle therefore has no four-velocity, no proper-time parametrisation and no rest frame. Its scale is fixed by a measured energy in an observer's frame.

(ii) Observer identification. Relative to a future unit observer $n$, the model identifies the measured energy and spatial momentum of the particle with the quantities $E_n(P)=-c\eta (P,n)$ and $q_n(P)=h(P)$ of Observer energy, spatial momentum, invariant mass, rest energy and kinetic energy of a four-momentum. Necessarily $E_n(P)=c\mathrm{\mid }{q}_n(P)\mathrm{\mid }>0$, by Positivity, mass shell and kinetic energy of the observer quantities of a four-momentum,(a)(i), and no rest mass, rest energy or kinetic energy is assigned to the particle — the definition of $T_n$ requires a rest-mass parameter $m$ and no such parameter is introduced here. This clause is a formulation convention identifying mathematical quantities with the quantities the model calls measured; it is not a measurement report and no experiment is claimed.

(iii) No identification with light or quantum objects. The ideal massless particle is not identified here with light, with a classical wave or with any quantum object: no frequency, wavelength, quantisation, polarisation or Planck constant enters this premise, and the identification of light with massless particles requires the wave model and its own postulates on a separate page.

(iv) No process. This premise asserts no interaction of massless particles and no decay or production process; such processes require a stipulated dynamics. Empirical support for the assumption is a nonlogical relation of the framework, not a proof, and the idealisations inherited from the flat spacetime model and the ideal-point description travel to every consumer of this premise.