Photon Decay

ABSTRACT

This article reinterprets the Hubble constant, H, as a linear photon decay constant, rather than a Doppler shift, giving a photon life 1/H = 1.4 x 1010 years. If instead, we assume photons decay exponentially like other particles, then taking the half-life of a photon as P = ln(2)/H, there is no need to introduce the notion of a Big Bang into the history of the universe, and this presents a simple soluton to Olbers' Paradox. However the Olbers universal microwave backround radiation peaking at M (109 Hertz) might be assumed to be decayed α Lyman radiation from very distant stars, at frequency L equivalent to its 122 nm wavelength, radiated P.log2(L/M) ago. Thus this suggests that while there are no observable evidence of the traditional Big Bang in this interpreation of the red-shift, there is evidence of a different sort of big bang from the microwave background: namely a peak in the number of observable stars in the universe: 166 Billion years ago.

ASSUMPTIONS (approximations, from Wikipedia)

 c velocity of light 3.0 x 10 8 metres/sec H Hubble constant 2.3 x 10 -18 Hertz (70 Km/s/Mpc, 1 Mpc=3.1 × 1022 metres) P inverse Hubble constant 3.0 x 10 17 secs (ln(2)/H = 9.7 x 109 years) L α Lyman radiation frequency 2.5 x 1016 Hertz (122 nm) M peak microwave background frequency 1.6 x 1011 Hertz (160.2 GHz)

OCCAM'S RAZOR

Occam's Razor may be interpreted as saying:
assume a function of a dependent variable is constant unless proved otherwise;
if otherwise (otherwise 1): assume the function is linear unless proved otherwise;
if otherwise at this point (otherwise 2), oops: Occam's razor gives little guidance. The function is curved. The function may arbitrarily be assumed at this point to be any curved form one considers appropriate: maybe quadratic or hyperbolic or Lorentzian or exponential, or whatever.

The simple linear assumption that the Hubble constant can be applied to all distant objects implies that objects at a distance of c/H light-seconds will be travelling at the speed of light. This has led to the suggestion that there was a Big Bang 1/H seconds ago.

Subtle modifications of this conclusion have been made, allowing for relativity and the delay in arrival of the photons, but the arguements still depend on the "otherwise 1", the simple linear theory. The arguements about the acceleration of the expansion of the universe appear to be about the "otherwise 2" in Occam's Razor: how to introduce curvature. Curvature can instead be introduced by reinterpreting the observed red-shift a different way.

EXPONENTIAL DECAY

If the observed red-shift of distant galaxies is interpreted not as a Doppler Shift, but as a decay of the photon's energy and frequency, one arrives at an equivalent interpretation of the simple linear Hubble theory. The decay in photon's energy over time is linear in this simple theory, so that after 1/H seconds: the photons have zero energy. This seems rather abrupt and non-physical. I think this is an 'otherwise 2' case.

My suggestion here is to introduce curvature by taking the analogy from studies of other particles with limited lifetimes, where their decay has been found to correspond well with an exponential function of time. We might simplistically take the half-life of a photon to be ln(2)/H = P seconds. This explains Olbers' paradox: why most of the sky is black. Photons from stars in the black regions have decayed in frequency to be outside our visible spectrum.

Current models of fundamental particles do not easily accommodate the concept of photons decaying. But then they also do not predict the values of many of the fundamental physical dimensionless constants, so these models are in need of some modification.

MICROWAVE BACKGROUND

Olbers' Paradox is wrong of course. There is a uniformly bright sky, but not in the visible spectrum. The brightness peaks in the microwave region of the spectrum: around 160 GHz. If we assume this is red-shifted α Lyman radiation from very distant stars, then this suggests that while there is no evidence of the traditional Big Bang in the decaying photon theory, at an epoch P.log2(L/M) secs ago, there was a peak in the number of observable stars in the universe:

P.log2(L/M)
= P.log2(1.4 x 105)
= 17.1 P = 5.1 x 1018 secs = 166 Billion years ago.
Alternatively, maybe it is from an even more red shifted real Big Bang, from the collision of two half-universe sized black holes. If during the infinite life of the universe: black holes inexorably accrete other black holes, eventually there will be only two, and then this collision has to happen.

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written 4 December 2015