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Werner Hofer
University of Liverpool, UK

Elements of a Physics for the 21st Century

Given the experimental precision in condensed matter physics — positions are measured with errors of less than 0.1pm, energies with about 0.1meV, and temperature levels are below 20mK — it can be inferred that standard quantum mechanics, with its inherent uncertainties, is a model at the end of its natural lifetime. In this talk I want to explore the elements of a future physical framework beyond this model. It is quite clear that extended electrons, which lend themselves to a spacetime description of wave properties, will be key to such a framework. After all, even Einstein considered the question, what electrons actually are, as the main question in all physical theory. The important elements here are the density of electron charge, and the density of electron spin [1,2]. The first has been used for close to fifty years in condensed matter theory [3], the second only becomes accessible on the basis of geometric algebra, because it requires a general description of a vector algebra in Euclidean space of arbitrary dimensions.

Interactions with external fields occur to first instance via these spin densities, since they alter the energy balance within the electron and thus lead to changes in the dynamics. Wavefunctions, in this picture, are secondary quantities, and composed of suitable combinations of mass densities and spin densities [2]. The framework is consistent with classical mechanics, as shown in a local version of the Ehrenfest theorem, and also consistent with standard quantum mechanics, as these wavefunctions obey the Schrodinger equation.

Photons, another element, are easily incorporated into this framework; they are formally similar to the spin density component of electrons, albeit with a different velocity. These photons, in Aspect-type experiments, violate the Bell inequalities in the same way as in the experiments, even though they are strictly local and independent entities [4].

Finally, I shall report on some work in progress extending the framework into the nuclear regime. It is shown that the fine structure constant αf can be interpreted as a distance or energy scale connecting the atomic to the nuclear regime. The interpretation is based on scattering experiments on neutrons by Littauer et al [5] and the neutron radius found in these experiments. Another element of the framework is then potentially a high-density phase of electrons if they are part of an atomic nucleus. How a model of atomic nuclei, similar to atomic models in density functional theory [3], could be constructed on the basis of these findings will be briefly discussed.

[1] WA Hofer, Heisenberg, uncertainty, and the scanning tunnelling microscope, Frontiers of Physics 7, 218 (2012)
[2] WA Hofer, Unconventional Approach to Orbital-Free Density Functional Theory Derived from a Model of Extended Electrons, Foundations of Physics 41, 754 (2011)
[3] P Hohenberg and W Kohn, Inhomogeneous Electron Gas, Physical Review 136, B864 (1964)
[4] WA Hofer, Solving the Einstein-Podolsky-Rosen puzzle: The origin of nonlocality in Aspect type experiments, Frontiers of Physics 7, 504 (2012)
[5] RM Littauer, HF Schopper, RR Wilson, Structure of the Proton and Neutron, Physical Review Letters 7, 144 (1961)

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