By science we mean the representatives of the ket |nñ, called states, subject to the constraint that all states are electrically neutral.
n = 1, |nñ = 2(4). There are two independent partitions in this subspace, called our world:
(1) gives the formal structures for classical particle theories of Newton; and (2) for classical wave theories of Einstein and Dirac [
The structures (1) and (2) have a common origin, the ket |1ñ, hence one can construct a unified theory of these theories, called Invariant Operator Theory [
We define the dimensionality of a state as a number equal to the algebraic sum of the primitive elements of a partition. This quantity is equal to eight for the Newton, Einstein, and Dirac theories. Because of wave-particle duality it must also apply to particulate states of the hydrogen atom, and must apply generally―this is dimensionality theorem. In this section we construct micro-physical states subject to the additional constraint imposed by the dimensionality theorem.
n = 1/2, 1, 2, 3, …, ¥ in this subspace called the Fermion world.
n = 1/2 gives the Dirac solution with the partition.
where 2 =
But this solution is inconsistent with the dimensionality theorem, and must be replaced by
the second entry of
The neutron is known to reside in the atomic nucleus. Until our work not much was known about the electron neutrino, but now the mystery surrounding this particle has disappeared [
The Fermion world consists of three subworlds, namely, the nucleus, lepton, and antilepton subworlds. The nucleus corresponding to n = 1/2 is called alpha particle.
n = 1 in this subspace called the boson world. The associated partitions are
Partition (5) must be rejected because it is not independent of the classical partition (1). Thus, (6) gives the formal structure of the bosom state of rest.
The representation of (6) is a union of a spin zero particle, a spin zero antiparticle, a spin one particle, and a spin one antiparticle, corresponding to the photon, graviton, a vetor boson, and an antivector boson respectively. (6) then gives the unification of the fundamental interactions, with the vector boson a strongly or weakly interacting nuclear particle (strongly interacting if neutrons are involved, and weakly interacting if neutrinos are involved) [
The boson particle represented by (6) is electrically neutral. To ensure that the boson world and antiworld are electrically neutral nature provides muon and muon-neutrinos, and their antiparticles.
A survey of the literature of particle physics shows that Abdus Salam, Steven Weinberg, and Sheldon Glashow obtained a representation (electro-weak theory) consisting of five particles, namely, photon, three vector bosons, and Higgs boson. This was a laudable effort but the theory violates the cardinal constraints of electrical neutrality and dimensionality.
The final subspace S’ which is independent of the foregoing subspaces is defined by n = 1, |1ñ = 2(4), and the partition,
Partition (7) gives the formal structure of a manifestly interacting world (chaotic world)―a world appropriate for astrophysics. The world is chaotic because it is impossible to construct 4 × 4 matrices from juxtaposition of a 2 × 2 and 6 × 6 matrices.
There are two representations which ensure electrical neutrality of the states. The first consists of a neutron or antineutron interacting with a charged vector boson and its antiparticle; and the second is interaction of a neutron or antineutron with a neutral vector boson and its antiparticle. In a low energy scenario, the neutron is replaced by a neutrino and the vector boson by a meson. The interaction involving neutrons and charged vector bosons is called normal star (or star), while the interaction involving neutrons and neutral vector bosons are called neutron star. These interactions, called strong nuclear interactions, occur in stars via a process called fusion, the telltale sign being light and particles from luminous stars like our sun [