Stability of Photons

                                                                                                                                                                 

Light Photons

While a non-zero photon mass has been under theoretical and experimental study for years, the possible implication of a finite life time of a photon remains a point to discuss. The tight experimental upper bound of the photon mass restricts the kinematically allowed final states of photon decay to the lightest neutrinos or particles beyond standard model if this channel is the concern of experimental studies.

A non-zero photon mass is often dismissed on theoretical grounds as insertion of mass term into QED calculations breaks gauge invariance and might therefore disturbs renormalizability. i.e. consistency of the theory at quantum level.

The question of a photon mass in QED is then purely experimental as there is no dispute over a small mass assigned to the photon (m>0) [This would take Electroweak gauge group SU(2)_LX U(1)_γ   ---- the hypercharge U(1)_γ,  that can be used for calculations. ] The resulting mass for the hypercharge gauge boson eventually generates again a massive photon.

Particles beyond the standard model could not only increase the rate of γ -->  v₁ v₂ , but also serve as final states  themselves, as some extensions to the standard model feature additional massless states, for example, sterile neutrinos, hidden photons, Goldstone bosons and axions. These weakly sub- eV particles are less constrained than neutrinos and photon decay could be the indirect or direct effect of these states. Although, mainly of academic interest we mention that a massive photon provides the possibility of faster-than-light particles- and a decaying photon always predicts them.

The question of photon decay is therefore relevant even if the lightest neutrinos have an inaccessible heavy final state.

                                           (Ref. Julian Heeck, How stable is the photon? Phy. Rev. Letters,2013)

The Octaves of Light

                                                                      The light beam

                                                                    Stream of light

The topmost note, for example (0.0, violet)
has a frequency (F) of 7.8e14 cycles per second, or Hertz,
and a duration (D) which is the reciprocal of that frequency (1/F)
or 1.3e-15 seconds per cycle.

(Scientific notation compresses 780,000,000,000,000 to 7.8 * 10^14, and then further to 7.8e14, where 'e' stands for 'exponent'. And 1.3 * 10^-15 is thus 0.000,000,000,000,001,3 . These two numbers multiplied together equal one, aka 1.0e0.)

Light at this frequency has a wavelength (L) of 3.8e-7 meters
but sound at the same frequency, traveling 850,000 times slower
would have a wavelength 850,000 times shorter (about 20 octaves)
which wavelength we'll call 'S': 4.5e-13 meters.
Since light of this wavelength would be considered gamma radiation,
we might call the equivalent sound 'acoustic gamma'.

(The speed of sound in air depends on the temperature: to get the mnemonically-handy ratio of 850,000, we have to specify air at body temperature, 98.6°F or 37°C.)

First octave:

0.0   F=7.8e14Hz   L=3.8e-7m   I=380bytes   S=4.5e 13m   D=1.3e 15seconds

3.8e-7 meters (L) is 380 nanometers (nm) or 3800 Angstroms. An Angstrom is the distance spanned by a small atom, so the wavelength of violet light is comparable to a row of 3800 atoms. A stretch of DNA 380 nanometers long would be able to encode 380 amino acids. If we ever decide to use DNA for data storage ('I' for information) we could fit 380 bytes into the same stretch. This is the approximate length of the Lord's Prayer in its more-or-less original Greek.

4.5e-14 meters (S) is 45 femtometers, where ten protons or neutrons span one femtometer, so the wavelength of sound at the frequency of violet light, in air at 37°C, is as wide as 450 neutrons. This is much bigger than the largest atomic nucleus, but much smaller than the smallest atom. ('Strings' are believed to be so much smaller than neutrons that this same distance could hold 5e22 strings.)

For Example:

D: age of humans with fire

95.4   F=1.5e-14Hz   L=2.0e22m   S=2.4e16m   D=2.1e06years

95.5   F=1.4e-14Hz   L=2.2e22m   S=2.5e16m   D=2.3e06years

L: Sun to Andromeda galaxy

95.6   F=1.3e-14Hz   L=2.3e22m   S=2.7e16m   D=2.4e06years

95.7   F=1.2e-14Hz   L=2.5e22m   S=2.9e16m   D=2.6e06years

95.8   F=1.1e-14Hz   L=2.6e22m   S=3.1e16m   D=2.8e06years

95.9   F=1.1e-14Hz   L=2.8e22m   S=3.4e16m   D=3.0e06years

S: Sun to Alpha Centauri

96.3   F=8.0e-15Hz   L=3.7e22m   S=4.4e16m   D=4.0e06years

96.4   F=7.5e-15Hz   L=4.0e22m   S=4.7e16m   D=4.2e06years

S: Sun to Saturn

81.5   F=2.3e-10Hz   L=1.3e18m   S=1.6e12m   D=1.4e02years

81.6   F=2.1e-10Hz   L=1.4e18m   S=1.7e12m   D=1.5e02years

D: oldest tortoise

81.7   F=2.0e-10Hz   L=1.5e18m   S=1.8e12m   D=1.6e02years

F: Neptune's year

81.8   F=1.9e-10Hz   L=1.6e18m   S=1.9e12m   D=1.7e02years

81.9   F=1.7e-10Hz   L=1.7e18m   S=2.0e12m   D=1.8e02years

82   F=1.6e-10Hz   L=1.9e18m   S=2.2e12m   D=2.0e02years

82.1   F=1.5e-10Hz   L=2.0e18m   S=2.4e12m   D=2.1e02years

82.2   F=1.4e-10Hz   L=2.1e18m   S=2.5e12m   D=2.3e02years

F: Pluto's year

82.3   F=1.3e-10Hz   L=2.3e18m   S=2.7e12m   D=2.4e02years

82.4   F=1.2e-10Hz   L=2.5e18m   S=2.9e12m   D=2.6e02years

82.5   F=1.1e-10Hz   L=2.6e18m   S=3.1e12m   D=2.8e02years

82.6   F=1.1e-10Hz   L=2.8e18m   S=3.3e12m   D=3.0e02years

82.7   F=9.9e-11Hz   L=3.0e18m   S=3.6e12m   D=3.2e02years

82.8   F=9.3e-11Hz   L=3.2e18m   S=3.8e12m   D=3.4e02years

82.9   F=8.7e-11Hz   L=3.5e18m   S=4.1e12m   D=3.7e02years

83   F=8.1e-11Hz   L=3.7e18m   S=4.4e12m   D=3.9e02years

L: Sun to Pleiades

83.1   F=7.5e-11Hz   L=4.0e18m   S=4.7e12m   D=4.2e02years

D: age of science

83.2   F=7.0e-11Hz   L=4.3e18m   S=5.0e12m   D=4.5e02years

D: age of Reformation

83.3   F=6.6e-11Hz   L=4.6e18m   S=5.4e12m   D=4.8e02years

SI: all human thoughts, ever

81.1   F=3.0e-10Hz   L=1.0e18m   S=1.2e12m   D=1.1e02years

81.2   F=2.8e-10Hz   L=1.1e18m   S=1.3e12m   D=1.1e02years

F: human generation

79.1   F=1.2e-09Hz   L=2.5e17m   S=2.9e11m   D=2.6e01years

S: Sun to Earth

78.3   F=2.1e-09Hz   L=1.4e17m   S=1.7e11m   D=1.5e01years

78.4   F=2.0e-09Hz   L=1.5e17m   S=1.8e11m   D=1.6e01years

78.5   F=1.8e-09Hz   L=1.6e17m   S=1.9e11m   D=1.7e01years

F: transits of Venus

77.5   F=3.7e-09Hz   L=8.2e16m   S=9.7e10m   D=8.7e00years

77.6   F=3.4e-09Hz   L=8.8e16m   S=1.0e11m   D=9.3e00years

L: Sun to Alpha Centauri

76.6   F=6.8e-09Hz   L=4.4e16m   S=5.2e10m   D=4.6e00years

F: ave. asteroid's year

76.7   F=6.4e-09Hz   L=4.7e16m   S=5.6e10m   D=5.0e00years

76.8   F=5.9e-09Hz   L=5.1e16m   S=6.0e10m   D=5.3e00years

76.9   F=5.5e-09Hz   L=5.4e16m   S=6.4e10m   D=5.7e00years

F: human cell culture 2x

65.6   F=1.4e-05Hz   L=2.1e13m   S=2.5e07m   D=2.0e01hours

65.7   F=1.3e-05Hz   L=2.3e13m   S=2.7e07m   D=2.1e01hours

65.8   F=1.2e-05Hz   L=2.5e13m   S=2.9e07m   D=2.3e01hours

65.9   F=1.1e-05Hz   L=2.6e13m   S=3.1e07m   D=1.0e00days

                                                                                        (ref. Jorn Barger, March 2005)