Talk slidesManuscriptsAcknowledgements
This page presents an approach to unification with a simple basis but intriguing implications. The model is based on featureless strands (or featureless extended entities) and equates events with crossing changes. Surprisingly, this mapping allows to deduce the principles of thermodynamics, Einstein's field equations, the Schrödinger equation, and the Dirac equation. As a further surprise, the model yields the Lagrangians of quantum electrodynamics, of the weak and of the strong interaction. The model does not yield any further interaction, gauge group or symmetry group.
The strand model also seems to satisfy all the requirements for a unified description. In particular, the strand model is based on Planck units, does not use points and continuity as fundamental concepts, and does not assume that sets exist at Planck scales. The model has no free parameters, seems to be unique and works in three spatial dimensions. However, dimensionality is not a parameter, but a result of the model.
Even more astonishingly, the strand model (draadmodel, modèle à fils, Fadenmodell, modello a fili) allows to calculate particle masses, particle mixings and coupling strengths, including their dependence on energy. The strand model also fulfils a famous wish: it fits on a T-shirt.
Comments are possible on the research discussion page.
Some predictions of the model (with their timing), made before conclusive experiments at the LHC, on neutrinos, on electric dipole moments, about QCD, and in astrophysics:
Talk slides:
Slides of a talk summarizing the manuscripts 1, 2, 3, including the experimental predictions of the model. In addition, the first seven slides present the foundations of the model. They form a summary of a future manuscript 0 on the topic.
Talk B. Deducing general relativity from extended entities (C. Schiller, August 2008)
Slides of a talk on the way to deduce the structure of the vacuum, special relativity, general relativity and cosmology from extended entities. Einstein's field equations and black hole entropy are derived. The slides summarize manuscript 2.
Slides of a talk on manuscript 3. It includes, as additional result, the way to model quantum entanglement of photons and matter particles as strand entanglement. Among others, methods to calculate masses of charged elementary fermions are presented.
Manuscripts:
Classical electrodynamics - including Coulomb's law, interference, relativistic invariance and the full Maxwell's equations - is deduced from a simple model based on featureless extended entities. Quantum effects are described as results of the extension of the fundamental entities. The model describes the photon, including its spin and its quantum behaviour. The model also works in curved space-time; it reproduces the known results for high curvature, such as black-hole radiation and the Fulling-Davies-Unruh effect. Maximum values for electric and magnetic fields in nature are predicted, and the power limit for light and energy sources is confirmed. A new type of underlying symmetry is predicted.
Einstein's field equations are deduced from a model of space-time based on featureless extended entities. Curvature is built from defects in space-time. In addition, extended entities yield a model for matter, for horizons and for the graviton, including its spin value. The model reproduces all known quantum-gravity effects, all black-hole properties - including a logarithmic correction to the black-hole entropy and a clarification of the Barbero-Immirzi parameter - and holography. The model predicts a minimum length, a maximum curvature, the absence of singularities, the generalized uncertainty principle, and the absence of effects of doubly special relativity.
The extended-entity model also yields a new approach to cosmology, predicts the existence of a cosmic horizon, and proposes an alternative to inflation and modified Newtonian dynamics. The predicted values of the present particle density and of the present cosmological constant agree with experiments. The cosmological constant is predicted to decrease with time. The model provides a natural explanation of dark energy. The acceleration value at which rotation curves in galaxies deviate from the inverse-square law is predicted to vary with distance. A minimum momentum, a minimum force, a minimum electric and magnetic field and a minimum power are predicted to exist in nature. The fluctuations of the cosmic background radiation are expected to be scale-invariant.
It is argued that Schrödinger's and Dirac's equations can be deduced from a topological model of matter and photons based on featureless extended entities. The wave function, spin and quantum phase have intuitive descriptions. The probabilities appearing in quantum measurements are compatible with the Kochen-Specker theorem and do not rely on non-contextual hidden variables. The model reproduces Heisenberg's indeterminacy relations and the Hilbert space structure, provides a topological explanation for entanglement, provides general models for matter, antimatter, and real and virtual particles, and explains electric charge quantization and minimal coupling. The Weinberg-Witten theorem is satisfied. The model provides a basis for stochastic quantization, for the entwined-paths model, and for Zitterbewegung. At high energies, the model predicts the lack of higher dimensions, a minimum intrinsic electric dipole moment, the absence of divergences, and maximal values for electric and magnetic fields. The fine-structure constant, including its energy dependence, is calculable; first crudely calculated bounds contain the experimental value.
Acknowledgements:
I thank HA, FS, FB, JS, LF, WS, SP, CL, RH, LK and SG for the interesting discussions we had.
The unification project is independent of the sponsors of the textbook and is not funded or supported by any of them. Sponsors for the unification project are of course welcome.