Synopsis

Quantum Gravity from Quantum Nonlinearity.

For many years Maxwell’s equations were mute testimony to the Lorentz coordinate transformations of special relativity, but the significance of this transformation was not fully understood until relativity itself had been discovered, The author of this book claims that an oversight has once again occurred in fundamental physics. A direct link between Quantum Mechanics and Gravity – perhaps the biggest scientific enigma of all time – has been overlooked.

In an entirely novel approach to Quantum-Gravity, this book suggests that Gravity is the manifestation of a very weak non-linearity in Quantum Mechanics; a non-linearity only apparent in the presence of large quantities of matter or very condensed wave functions. The reader will discover how this non-linearity is a natural consequence of a particular interpretation of the Quantum Equations.

This book however, does not share the same genre of totalising theories that emphatically and triumphantly declare a new dawn. Instead its thesis can only present itself as a fascinating hypothesis submitted for consideration. Should the theory presented here prove its mettle, then it would provide the key to opening up new vistas of theoretical and experimental research, thus helping to clear the conceptual log jam in which contemporary fundamental physics finds itself.

(48,000 words & 300 equations)

E-mail Tim Reeves mailto:tvreeves@yahoo.co.uk See also My Blog.

A limited number of free volumes are available to those who might wish to seriously review this book.

Mathematical Synopsis

1. Complex numbers are applied to the Diffusion Equation to derive the Schroedinger Equation.

2. The Central Limit Theorem (the foundation of diffusion), when reinterpreted in complex terms is the mathematical basis by which translational and rotational asymmetries in nature are obscured from view (Goodbye infinity).

3. Eigenstates emerge as the “Equilibrium States” of “Complex Diffusion”.

4. In order to arrive at the frame symmetries of Special Relativity the Schroedinger Equation is seen to be a derivative of an equation whose nonlinearity becomes increasingly marked at higher energies.

5. Quantum Wave fields, by virtue of varying wave numbers, are likely to have a differential in energy density. This differential, in turn, implies a differential in space contractions and time dilations, and hence a variation in the space-time metric. The weak nonlinearity behind the Schroedinger equation enables particles to get a purchase on this varying space-time metric thus giving rise to apparent Gravitational Forces.

6. All matter is surrounded by the exceedingly weak asymptotic tails of the wave functions of which it is composed. These wave functions form a very attenuated gas surrounding each and every concentration of material. If the hypothesised non-linearity of Quantum Mechanics is correct, then it is this Quantum Gas that is the cause of Gravity.

7. Some overlap with the solution domain of Einstein’s Equation is achieved: The Schwarzchild space-time and the 44 component of this equation (for static orthogonal isotropic space-times) are derived. In any case, however, it is noted that the form of the 44 component of Einstein's equation hints at a mathematical connection with gaseous diffusion.

8. The hot gaseous nature of gravitational fields suggests that for galactic distances there will be steeper than expected slopes in the space-time metric due to loss of heat from the field, thus giving rise to the apparent existence of Dark Matter. Also, for cosmic distances this loss of energy from the field will lead to depleted gravity in favour of energy lost to cosmic expansion and thereby to an apparent positive Cosmological Constant.

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