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Quantum mechanics from general relativity: an approximation for a theory of inertia

series: Fundamental theories of physics, V. 18

This monograph is a sequel to my earlier work, General Relativity and Matter, which focused on the full set of implications of General Relativity as a fundamental theory of matter in all domains, from elementary particle physics to cosmology. It is shown there to exhibit an explicit unification of the gravitational and electromagnetic fields of force with the inertial manifestations of matter, expressing the latter explicitly in terms of a covariant field theory within the structure of this general theory. This monograph will focus, primarily, on the special relativistic limit of the part of this general field theory of matter that deals with inertia, in the domain where quantum mechanics has been evoked in contemporary physics as a fundamental explanation for the behavior of elementary matter.

In Chapter 2, after comparing the underlying concepts of the quantum and relativity theories, there will be a discussion of the critique of Einstein, Podolsky and Rosen, and Bohr's rejoinder.... Bell's inequalities will be discussed in the context of their use as an asymptotic limit of the nonlinear field theory of matter implied by general relativity.

In Chapters 3, 4, and 5, the logical and mathematical development of general relativity, as a theory of elementary matter, will be presented, including the new consequences as a result of incorporating the Mach principle. This leads to the new idea, expressed as the law of conservation of interaction (to replace the conservation of probability of the standard quantum view), and the derivation of the nonlinear inertial field equations will be demonstrated, whose linear limit is the formal structure of quantum mechanics, then to the full expression of the electromagnetic field equations that fully exploits the Mach principle in general relativity.

It will be seen in Chapter 6 how this theory of inertia leads to the formal expression of quantum mechanics, as a low energy approximation. In the context of this field theory of inertia, the Pauli exclusion principle will be derived from first principles, from the exact form of the nonlinear, spinor matter field equations. It will then be shown, as a linear approximation, how this exact result yields the description of the many-particle system that incorporates the rules of Fermi-Dirac statistics.

Next, in Chapter 7, the matter field equations will be applied to the problem of the bound electron-positron system. An exact bound state solution will be demonstrated for the nonlinear, coupled field equations that exhibits all of the physical features that are normally attributed to the 'annihilation' of the pair, though, here, without any actual annihilation of matter... It is shown in this monograph that the 'photon' concept may be abandoned, replacing it with matter fields alone...

In Chapter 8... The complete hydrogen spectrum will be derived from the matter field equations, including the Lamb splitting. The latter is associated in quantum electrodynamics with radiative shifts of the (otherwise) accidentally degenerate states of hydrogen [5]; in this theory the Lamb splitting occurs for an entirely different reason it is a consequence of a generalization of the electromagnetic interaction that appears in a natural way, that in turn lowers the symmetry of the ordinary Coulomb term in the Dirac Hamiltonian for hydrogen, causing thence a lifting of the accidental degeneracy in the states predicted by the Dirac theory of hydrogen.

The electron-proton scattering process will then be analyzed in the light of the generalization of the matter field equations, including the generalized form of the electromagnetic interaction...

The results of the analysis in this monograph indicate hints that the weak interaction and the strong interaction between elementary matter fields are indeed manifestations of a generalized electromagnetic interaction... The gravitational interaction is also automatically incorporated... It will also be demonstrated explicitly in this book that the 'quantization of electrical charge' may be derived...

In Chapter 9 of this monograph, there will be presented an outline of some results concerned with high energy, elementary particle physics...specific implications of the generalization of the electromagnetic interaction. (1) the structure of the neutron, (2) the problem of the different masses for the charged versus the neutral pions, (3) the problem of CP violation in the decay of the long- lived, neutral kaon, (4) the admissibility of time-reversal noninvariance in nuclear forces, viewed as a component of the generalized electromagnetic interaction and (5) the general prediction of massive mediating composite states in weak interactions that could be associated with the recently observed W+/- particle resulting from high energy p-p- interaction.

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