The neutrino theory of light is the proposal that the photon is a composite particle formed of a neutrino–antineutrino pair.
It is based on the idea that emission and absorption of a photon corresponds to the creation and annihilation of a particle–antiparticle pair.
The neutrino theory of light is not currently accepted as part of mainstream physics, as according to the Standard Model the photon is an elementary particle, a gauge boson.
He showed that the conditions imposed by Bose–Einstein commutation relations for the composite photon and the connection between its spin and polarization were incompatible.
Pryce also pointed out other possible problems, “In so far as the failure of the theory can be traced to any one cause it is fair to say that it lies in the fact that light waves are polarized transversely while neutrino ‘waves’ are polarized longitudinally,” and lack of rotational invariance.
[6] Starting in the 1960s, work on the neutrino theory of light resumed, and there continues to be some interest in recent years.
[16][17] The neutrino field satisfies the Dirac equation with the mass set to zero, The gamma matrices in the Weyl basis are: The matrix
Fermi and Yang[19] used a local interaction to bind a fermion–antiferminon pair in attempting to form a pion.
These polarization vectors satisfy the normalization relation, The Lorentz-invariant dot products of the internal four-momentum
Thus, the last two equations of (4) can be used to show that, Although the neutrino field violates parity and charge conjugation,[25]
Although many choices for gamma matrices can satisfy the Dirac equation, it is essential that one use the Weyl representation in order to get the correct photon polarization vectors and
[5] However, as Perkins[17] showed, this equation follows directly from summing over the polarization vectors, Eq.
Fermions are defined as the particles whose creation and annihilation operators adhere to the anticommutation relations while bosons are defined as the particles that adhere to the commutation relations The creation and annihilation operators of composite particles formed of fermion pairs adhere to the commutation relations of the form[21][22][23][24] with For Cooper electron pairs,[23] "a" and "c" represent different spin directions.
The size of the deviations from pure Bose behavior, depends on the degree of overlap of the fermion wave functions and the constraints of the Pauli exclusion principle.
[32] As Berezinski[6] noted, "The only actual difficulty is that the construction of a transverse four-vector is incompatible with the requirement of statistics."
A simple version of the proof is as follows: The expectation values of the commutation relations for composite right and left-handed photons are: where The deviation from Bose–Einstein statistics is caused by
Linear polarization photon operators are defined by A particularly interesting commutation relation is, which follows from (10) and (12).
Perkins[17][24] reasoned that the photon does not have to obey Bose–Einstein commutation relations, because the non-Bose terms are small and they may not cause any detectable effects.
Perkins[12] noted, "As presented in many quantum mechanics texts it may appear that Bose statistics follow from basic principles, but it is really from the classical canonical formalism.
This is not a reliable procedure as evidenced by the fact that it gives the completely wrong result for spin-1/2 particles."
Because of their underlying fermion structure, these integral spin particles are not fundamental bosons, but composite quasibosons.
There are some differences; bringing two of these composite particles close together will force their identical fermions to jump to excited states because of the Pauli exclusion principle."
Brzezinski in reaffirming Pryce's theorem argues that commutation relation (14) is necessary for the photon to be truly neutral.
However, Perkins[24] has shown that a neutral photon in the usual sense can be obtained without Bose–Einstein commutation relations.
The number operator for a composite photon is defined as Lipkin[21] suggested for a rough estimate to assume that
Perkins[12] showed that the effect of the composite photon's number operator acting on a state of
The main evidence indicating that photons are bosons comes from the Blackbody radiation experiments which are in agreement with Planck's distribution.
(16) and (17) are combined to give, The probability of finding the system with energy E is proportional to e−E/kT according to Boltzmann's distribution law.
For the conditions used in the blackbody radiation experiments of W. W. Coblentz,[34] Perkins estimates that 1 / Ω < 10−9, and the maximum deviation from Planck's law is less than one part in 10−8, which is too small to be detected.
With this scheme the pion and muon decay modes are: There is convincing evidence that neutrinos have mass.