The Neutron Meta-Particles and their Decay as Viewed in the Planck Vacuum Theory

The mean life of the free neutron is about fifteen minutes, after which it decays into a proton plus an electron and an electron-neutrino. According to the Planck vacuum (PV) theory, however, it is the neutron and “antineutron” metaparticles (MP)s that decay, in roughly fifteen minutes, into the stable electron and proton cores. The electron and proton core spins remain constant during the transformations—so there is no need for the neutrino spin correction during the decay process, bringing into question the validity of the neutrino itself. Calculations estimate the mean life (15.3 minutes) for the free neutron and “antineutron” MPs, and show that those MPs do not form a particle-antiparticle pair.


I. INTRODUCTION
T HIS paper derives the MP equations for the free neutron and "antineutron" MPs, and shows that the corresponding meta-state does not form a particle-antiparticle pair.
The theoretical foundation [1] [2] [3] of the PV theory rests upon the unification of the Einstein, Newton, and Coulomb superforces: where the ratio c 4 /G is the curvature superforce that appears in the Einstein field equations. G is Newton's gravitational constant, c is the speed of light, m * and r * are the Planck mass and length respectively [4, p.1234], and e * is the massless bare (or coupling) charge. The fine structure constant is given by the ratio α ≡ e 2 /e 2 * , where e is the observed electronic charge magnitude.
The two particle/PV coupling forces the electron core (−e * , m e ) and the proton core (e * , m p ) exert on the invisible PV state; along with their coupling constants  for the electron and proton cores, whereh is the reduced Planck constant. The Compton relation to the right of e 2 * /c comes from equating the Einstein and Coulomb superforces from (1). To reiterate, the equations in (2) represent the forces the free electron and proton cores exert on the invisible PV space, a continuum that is itself pervaded by a degenerate collection of Planck-particle cores (±e * , m * ) [5], leading to a bifurcated vacuum state with one positive branch (e * , m * ) and one negative branch (−e * , m * ). The positron and antiproton cores are (e * , m e ) and (−e * , m p ) respectively.
Section II starts with the 2x1 spinor equations derived from the covariant Dirac equation, and derives the superposition of the core and anticore equations that reflect the experimental fact that the core and anticore form a particle-antiparticle pair. Section III derives the equations for the neutron and "antineutron" MPs using the equations of Section II. Finally, Section IV calculates the mean life of the neutron and "antineutron" MPs.

II. DIRAC CORES
To start with, it is important to note that the Dirac equation is an equation of state, rather than an equation of motion. Consider the proton for example: where m p c 2 is the spin energy, e 2 * /c is the spin coefficient, and ω p = c/r p is the radian frequency associated with the spin energy. Furthermore, the following equations are equations of state in a 7-dimensional spacetime that consists of two separate 4-dimensional spacetimes [7].
The following four 2x1 spinor equations are derived by coupling the covariant Dirac equation [7] [8, p.90] to the PV state: (x 0 = ct and the sum is over j = 1, 2, 3) −i and which, from top to bottom, describe the electron, positron, proton, and antiproton cores respectively. The us and vs are the 2x1 spinor wavefunction solutions to the equations. Furthermore, equations (7)and (9) and (8)and(10) belong in the observed and unobserved 4-dimensional spacetimes respectively [7]. The gradient operator is used for convenience. Some feeling for the equations can be found in Appendix A.
The ratio e 2 * /c is the spin coefficient, where is the relativistic spin of the electron or proton cores. The Pauli spin vector is − → σ . The second expression is the scalar-product sum of − → S with the gradient operator ∂/∂x j ; that is, the PV gradient ∂/∂x j in the jth direction weighted by the relativistic spin in that direction. The spin coefficient can be positive or negative (see Appendix B).
Superposition [7], i.e. adding the separate components [e 2 * /c,u,v,m e ,m p ] from the electron and proton cores (7)-(10), leads to: for the electron-positron, and  (14) constitute the electron and proton annihilation equations in the PV theory-reflecting the experimental fact that the core and anticore form a particle-antiparticle pair.
A notation that is followed in all of the particle equations can be seen in equation (13): in the spin coefficient parenthesis, the first and second spins belong to the u and v respectively on the left of the comma in the gradient operator.
Essentially, it is the failure to generate the 2x1 null spinor solution 0 that leads to the decaying MPs in the following calculations.

III. META-PARTICLE EQUATIONS
In searching for an equation to model the free neutron state, it seems reasonable to use the superposition idea of Section II since the neutron decays essentially into an electron and a proton core. Thus the electron-proton superposition that defines the neutron MP in the PV theory is The corresponding superposition for the invisible "antineutron" MP state is The two simultaneous equations (15) and (16) represent the free neutron-"antineutron" meta-state.
The two terms on the right side of equations (15) and (16) cannot lead to a 2x1 null spinor because of the differing masses; so the neutron-"antineutron" MPs do not form a particle-antiparticle pair, and so they must decay.

IV. CONNECTIONS
The string of Compton relations in (5) shows that the electron and proton cores are very similar in nature-a fact that allows the neutron to be constructed from these cores. For example, from (5) the following relationships obtain: wherehω p = m p c 2 andhω e = m e c 2 . The parameter 1836 that connects the electron and proton cores in (17) has been around for a long time-it is usually thought of as the ratio of the proton mass to the electron mass. Equation (17) shows that that constant is much more than the simple mass ratio. In addition to (17) (8) and (10)and (7) respectively. From this 1836 constant, then, the PV theory concludes that 15.3 minutes is the mean life of the neutron and "antineutron" MPs.

APPENDIX A HARMONIC SOLUTION
Some feeling for the physics of equations (7)-(10) can be had from discarding their second coupling terms. For example, discarding the positron coupling term, the electron equation (7) leads to

APPENDIX B SPIN COEFFICIENT
The structure of the spin coefficient is given by