Covariant Compactification: progress towards a TOE(F) – Part 4
This is the fourth instalment of a series of videos explaining the theory I’ve been building up over 20 years.
This one builds up, in stages, the following picture. The geometric quantities described in the previous parts can locally be decomposed into Fourier modes. A unitary gauge potential modulates these modes. The resulting waveforms can be ascribed an instantaneous four-wavenumber. Over a given region of spacetime, they can be ascribed an energy-momentum. This is not a local quantity, but a quantity associated with the whole of that region of spacetime – however large it is.
A wave packet composed of such waveforms obeys an uncertainty relation, of the same form as the Heisenberg uncertainty principles, relating its spread in spacetime to its spread in energy-momentum.
As the modulation of the waveform – a local change in its phase – is determined by the gauge potential and not by the field strength of the potential, the waveform experiences the Aharonov-Bohm effect.
Thus we start to see two phenomena emerging from a purely geometric theory which are usually viewed as quantum effects. (This analysis will be developed further in the final part of this video series.)
This is not achieved with any radically new physics. Most of the analysis video is already established physics. In particular, most of it is taken from a combination of signal processing theory and The Classical Theory of Fields by Landau and Lifshitz. (With the results of experiments into Aharonov-Bohm type effects and the theory and observation of gravitational waves giving further clues.)
What is entirely new, to the best of my knowledge, is the conceptual structure within which this analysis is applied. The analysis in Landau and Lifshitz is taken as showing the similarities between classical field theory and quantum theory. The underlying thesis of this video, by contrast, is that these similarities occur because quantum physics arises from the dynamics of geometric field configurations.
Some other useful links relating to this video:-
“Widths and uncertainties” – MIT OpenCourseWare on properties of wavepackets in Fourier analysis
Aharonov-Bohm effect for gravity: