Table of Contents

Introduction

The Hubble Red Shift has been recorded often in spectrographic data. Photon Decay theory is based on the idea that water waves have been the model for thought about waves for millennia, an instinct for billions of years. Entropy [NB: increase of 'chaos', or loss of 'structure'] drives the diffusion of photon momentum and energy into their conjugate dimensions of wavelength and wavetime throughout the path of the photon -- typically during billions of light-years.

The decay of waves of all kinds is well known in mathematics, engineering and physics. Waves are used to describe water, sound, and electric field propagation (such as light and other electro-magnetic or photoelectric waves). Water and sound waves are already described with decay constants, and it is simple to apply a decay process to electric field radiation, such as photon propagation. The figure shows a decay process with a very short time scale and high damping coefficient, so the wave amplitude reduces appreciably after only a few waves. [NB: and also the wave-frequency nu decreases appreciably ('red shift') as a measure of energy loss, re Planck's quantum energy equation E = h. nu ] :

Photons appear to decay the same way, only it requires billions of years (about 6.5 x 10^9 years) for a photon to decay to half its energy
[NB: which by Planck's relation means: half frequency, thus redshift] .

Photons have about the same fundamental quality as do the elements and isotopes, including radioactive isotopes. It is thus reasonable to expect that in photons, too, do decay by entropic processes, and that a good fit should be possible with existing mathematics. In the case of radioactivity the decay is by a random process which is inherently statistical in nature. But the photon decay is somewhat different, as it is progresses smoothly, and undulates both above and below zero: the envelope of the photon decay is equivalent to the radioactivity amplitude.

The conventional argument against photon decay is that the sky brightness is wrong if the decay rate is set to be equivalent to the redshift. A modern explanation of photon decay is timely. In fact, conventional arguments contradict each other, since some argue that the sky should be brighter if redshift is caused by photon decay, while others argue it should be darker.

An isotropic, emitted electric field wave is already a diffusion equation. The permittivity of the vacuum is equivalent to the diffusivity which is found in statistical diffusion of heat and chemical processes. The main idea is that within the wave itself, energy and momentum of wave action diffuse into the abundant conjugate dimensions of time and distance, from which they are entropically forbidden to return.
[ N.B: In other words, along their long galactic travel photons lose energy to their environment, which is the intergalactic medium they travel in - 'warming' it up as they go (explaining the cosmic background radiation 'CBR' - yielding a temperature of about 3 degrees Kelvin). ]

The stress-energy tensor of Pauli and others evolves into a stress-action tensor which is faintly introduced here. The stress-action tensor is a field, greatly elongated into a path. I have taken the liberty of extending the idea to a stress-action tensor field path integral, placing the stress-energy tensor into a Gaussian framework in which c=1. The integral is composed of a gravitational term, an electrodynamic term, and a statistical term based on the entropy-driven diffusion of the more complex exterior conjugates of momentum and energy into the dimensions of distance and time which are interior conjugates under the action.

The rate of the diffusion of the energy into its conjugate time and of the momentum into its conjugate distance in the free-ranging photon is the same as the velocity of light, but it takes place in a path between these states which is many orders of magnitude smaller than the ordinary diffusion of electric field modulation in space. More properly, this is a change of dimension, or, in mathematics, a domain change. This diffusion takes place only during the brief wavetime and short wavelength (10^-14 second and 10^-9 meter for light) of the typical photon, and second, it takes place only through the very narrow uncertainty region in which momentum is not distinct from distance and energy is not distinct from time (10^-34 Kilogram*meter/second and 10^-34 Joule second). That is why the net rates of diffusion of momentum into wavelength, and energy into time, are so slow. The rate of diffusion is shorter for short, high energy waves such as X-rays because the intensity of this photon's energy in the energy domain is much greater. Conversely, for long waves, the lower energy transfers less energy through the diffusion path between these state domains.

It is important, by the way, to know the difference between a wave and a spectrum, particularly in the sense of the Fourier and Green's function integrals. Fourier transformations are not actually adequate for photons because they decay while the Fourier integral ranges from minus infinity to plus infinity; for photons the Green's function is more appropriate because it ranges from zero the origin where the photon is emitted, to infinity. In the long run photon decay - as an increase of entropy - precludes time reversal.

One familiar implication is that distance and time are primitives of the action. Another is that a linear correlation between Hubble Red Shift and distance remains. Relative velocities within distant objects (groups of stars, galaxies, etc.) can be correctly interpreted as Doppler velocity shifts, but absolute distance and velocity measurements can not even in principle be both obtained without measurement of by some other means. Usually, this is EITHER spectrographic measure which gives an estimate which is ambiguously either velocity or decay; or parallax and the Cepheid variable star period-luminosity extrapolation which provide estimates of distance. Photon decay theory permits somewhat less information but it is of a more reliable quality.

A galactic object such as the Hickson Compact Group is a good example which has both internal relative velocities, some motion is probable toward or away from the Earth, and is some distance away. That is, it displays both absolute Doppler Shift and Red Shift (which cannot be distinguished unless an independent estimate exists for its distance or group velocity) and relative Doppler shift within the group. It is believed to be gravitationally cohesive, and all its components are relatively near each other, so the velocities of each component can be estimated in comparison with the velocity of the group; but red shift resulting from the actual distance of the group (photon decay) cannot be completely separated - even in principle - from red shift caused by the velocity of the whole group, without an independent distance ans speed estimate.

It might be possible to assign a number which is the product of the distance times velocity to distant objects; that will certainly have something to do with the red shift no matter what causes the red shift.

Doppler Shift is only useful for localized, relative velocities of objects within a group, such as :