Existing mathematics suffices to describe a photon decay process analogous to the statistical decay of radio isotopes. A zero force concept is used. In the quantized Maxwell equations for wave propagation, the conjugate variables p (momentum) and lambda (wavelength) do not commute, nor do energy and wavetime commute. Time reversal theorems are inapplicable to the photon. Decay takes place throughout the path of the photon, hence between its emission in a distant galaxy and its observation on earth.

Exponential decay in nature is accurately described by a first order time derivative operator d/dt. The decay constant introduced is 1/h , which causes diffusion throughout the life of the photon. This appears in the expanded form of the wave equation (see below) as a first order term mathematically equivalent in form to a diffusion.

Differences exist between any wave and the preceding and following waves. This time ordered process is equivalent to an increase of entropy due to the dissipation of energy into time through the 'fuzziness' or uncertainty of the action quantum. Cumulative loss is proportional to the distance travelled. The energy of the wave diffuses into the time domain of the action, and momentum into the distance domain. The complex-dimensioned momentum and energy dissolve into the simpler forms of distance and time. The result is equivalent to an ordinary dissipation, such as in water waves.

Planck's action quantum h and the speed of light c appear in proportional relations between the complex-dimensioned variables of energy and momentum, and the one-dimensional variables wavelength, wavenumber, wavetime, and frequency. With the speed of light, and the phase and spin, these completely describe the interstellar photon at all times. The resulting equation (below) describes an exponential decay which closely resembles the Hubble red shift, and is proportional to the distance travelled. The observed redshift amounts to a photon halftime of some 6.5 billion years.

This process is applied only to the Hubble red shift, and is not an explanation for relative Doppler shifts observed in galactic rotation, or in the velocity shifts of nearby stellar proper motions, for which photon decay is very small. In the great distance limit, it is difficult to distinguish between Doppler shift due to relative motion in radial distance, and photon decay. Radial motion is limited to well under the speed of light because of energy losses. In a flat infinite universe radial velocity would be both positive and negative, but at very great distances both positive and negative Doppler shift would be exceeded by photon decay. Estimators of distance, such as parallax and Cepheid variables, are thus of paramount importance in determining actual distances in order to separate photon decay and Doppler-velocity shift. Parallax instruments at an outer planet would be useful.

This diffusion is the second appearance of diffusion in the general electromagnetic wave, for it is well known that the propagation of a step wavefront into the electromagnetic medium is a diffusion at the speed of light; and that permittivity is exactly analogous to the diffusivity in a thermodynamic or other statistical diffusion.

At the very least, this theory offers an explanation for the Hubble Red Shift which is simple and empirically reasonable. In the tradition of preferring the simplest explanation (Occams razor), the existing mathematical procedures in physics permit a natural photon decay theory, to be preferred until better measures of stellar distances allow adequate discrimination between photon decay and other theories of the Hubble Red Shift (such as a Doppler effect, proportional to receding velocity corresponding to an observed Spectral Red Shift of 75 (km/sec)/Mpc).

Planck's quantum action h can be replaced, if preferred, by p.lambda (momentum.wavelength)