The solution that I have in mind is very simple: the idea is that there is no strong force per se — spacetime is globally hyperbolic with physical universe modeled as a hypersurface of a 4-sphere whose radius depends on Planck’s constant and is fixed.  Matter arises as the second fundamental form of the embedding into the 4-sphere — this can explain both the energy-momentum tensor of Einstein’s gravity as well as Dirac’s matter for particles that are eigenspinors of the hypersurface Dirac operator which picks up a second fundamental form.  Now the idea is that quarks are not really particles but principal curvatures of nuclear particles.  This type of model would have confinement automatically and would explain the triplet of quarks associated with most of the nuclear particles.

My solution to confinement is that quarks are not particles at all but principal curvatures of an embedding of the physical universe M into a scaled 4-sphere S4(1/h) where nuclear particles have three principal curvatures. In this solution, you can’t see quarks in isolation but you could smash particles and find traces of the dissolving geometric structure.


I don’t think Tesla knew the ‘mind of God’ laws of nature although he was clearly a brilliant inventor and understood electromagnetism as a genius electical engineer. I think the fundamental problem IN physics today is that the sophistication of approaches to a unification of gravity and quantum mechanics is based on some very bad foundations of cosmology not to mention a cut-throat medieval institution of kings, kingdoms, ego. It’s suicidal for young people to go into areas where innovative and revolutionary thinking is necessary because you’ll be ostracized by the ‘cool kids’ doing the hypersophisticated baroque mathematical physics say string theory and to a lesser extent loop quantum gravity. I think the key step beyond what Gerhardt has done is to get a sharper sense of marrying Einstein’s matter and Dirac’s matter in static globally hyperbolic spacetime with hypersurface of S4 as space, a clear clean and beautiful geometrical merge as a shiny new physics that starts getting rid of the obscurantism. Boy, string theory, what an enormously massive overambitious project that sucks young talented theorists like a vacuum leading them like lemmings into a career in a monastary without any possibility of producing experimental results.

For globally hyperbolic models with compact slices quantization of gravity and unified gravity, Yang-Mills, and Higgs is a solved problem with mass gap:
Gerhardt-Unified1 and Gerhardt-Unified2.  So the real issue is whether we can make sense of whether our actual universe can be described by the S4 picture of hypersurfaces of a 4-sphere and more importantly whether the quantization phenomena in our universe is ultimately due to this geometry (which is what I believe) and whether there is a more concrete and simpler set of concepts that can describe laws of nature that begins with a concrete realization of unified physics and so on.

Since 2008 I have been advocating in various forms that our actual universe is not flat and infinite but in fact a globally hyperbolic space with compact time slices that are hypersurfaces in a scaled 4-sphere.  Intuition suggests that there should be a positive mass gap in such a case as is observed empirically.  It is thus nice that Claus Gerhardt in Gerhardt-Unified2 has provided a unified theory of gravity and quantum Yang-Mills using canonical quantization and formalized a positive mass gap in an analysis unified with gravity.  On one hand, this is not the Millenium Prize problem which is to show that there is a mass gap in the flat infinite Minkowski space where lack of compactness may hurt the prospects.  On the other hand, I am completely convinced that Jorma Jormakka’s construction of classical Yang-Mills fields with energies arbitrarily close to zero is right (and the more sophisticated solutions of Dynin and Farinella are wrong without knowing this with authority just because complications produce difficult to verify steps and it is much easier for me to understand why a quantization of the classical solutions with arbitrarily small energies would also lead to the same for the quantized versions in Jormakka’s solution).  My picture of the universe can be seen also as a variation of the brane-worlds picture of Randall-Sundram type with bulk being S^4(1/h) which resolves the hierarchy problem although the issue of large extra dimensions does not have empirical evidence.  On the other hand quasicrystals have 4D crystal symmetries which seem odd without a fourth space dimension.

The actual universe has a mass gap and therefore the actual universe is more likely to be a globally hyperbolic Lorentzian manifold.  Going back to my original observation, a uniform thermal background is much easier to understand in a closed universe rather than in an expanding universe — I don’t believe that there is any expansion of the universe and the redshift itself is direct evidence of the wrong non-spherical geometry being employed in cosmology.  In such a geometry cosmic background radiation could easily be an infinite time equilibrium.

The cosmic background radiation of 2.7 K is said to be something complicated. I think there are two issues: (a) the redshift is due to getting the spherical bulk geometry of the universe wrong and is just a geometric artifact, so there is no expansion, and (b) the 2.7 K is quite natural to be considered an infinite time thermal equilibrium. I don’t believe for a second that there was even an ‘early universe’. I believe we live in a static eternal universe or something slightly different–a universe that is always a hypersurface of a fixed four-sphere. In fact the gravitational equations can be thought of as the Ricci curvature of the hypersurface and stress energy tensor can be thought of as the second fundamental form of its embedding. You solve the hierarchy problem same as Randall-Sundrum. You solve the mass gap problem by work of Gerhardt who shows that for globally hyperbolic spacetime with compact slice there is always a mass gap. You get your rigorous quantum field theory from algebraic qft which is rigorous for this type of space. You don’t need a complicated string theory. You don’t need dark energy or dark matter. You have a physics that makes sense.


The root of all true culture is the longing of man to be reborn as a genius and a saint, said Nietzsche
I now understand the motivation to provoke with words of comically extreme hatred — for which I feel so bad now because it’s not behaviour that I wanted to have and is most unsaintly and evil.  I had in mind some bizarre evocation of genius and saint.
Anyway, I hope you will recover and forgive and move on.  My maternal uncle is dying and I am being forced to deal with the specter of death myself.  My sister committed suicide recently.  This all gives me the wrongness of my ideas.  It is my goal to seek genius and saintliness within myself.  That’s something that cannot be done by simple binary concoctions and drama.  I realize this now because I am silly.  I hope you will forgive me.

Physicists had followed the following historical broad trajectory regarding quantum field theory on curved spacetime according to Wald-QFT-curved:

The main initial development of the theory occurred in the late 1960’s driven primarily by the desire to analyze the phenomenon of particle creation occurring in the very early universe.  By 1969, one can find the theory formulated in recognizably modern form and applied to cosmology in the paper of Parker.  In the early 1970’s the theory was applied to the study of particle creation near rotating and charged black holes, where the discovery of classical “superradiant scattering” (analogous to stimulated emission) strongly suggested that spontaneous particle creation should occur.  This line of research culminated in the analysis by Hawking of particle creation resulting from gravitational collapse of body to form a black hole.  It was thereby discovered that black holes radiate as perfect black bodies at temperature T=k/2\pi where k is the surface gravity of the black hole.  This result solidified an undoubtedly deep connection between the laws of black hole physics and the laws of thermodynamics, the ramifications of which continue to be pondered today.

As a direct consequence of Hawking’s remarkable discovery, there occurred in mid-to-late 1970’s a rapid and extensive development of quantum fields in curved spacetime and its applications to a variety of phenomena.  A good summary of this body of work can be found in Birrell and Davies.  Further important applications to cosmology were made in the early 1980’s as the methods and results of quantum field theory in curved spacetime were used to calculate the perturbations generated by quantum field flctuations during inflation.  Many of these lines of investigation begun in late 1970’s and 1980’s continue to be pursued today.

Although it would be more difficult to point to major historic landmarks, during the past twenty years the theoretical framework of quantum field theory on curved spacetime had undergone significant development, mainly through the incorporation of key aspects of the algebraic approach to quantum field theory.  As a result the theory of a linear quantum field propagating in a globally hyperbolic spacetime can be formulated in an entirely mathematically rigorous manner insofar as the definition of the fundamental field observables is concerned.

Against this backdrop the question of interest to me is whether if we consider a fixed curved spacetime that is different from Minkowski space, which I believe should be M \sub S^4\times\mathbf{R} whether the mathematically rigorous quantum field theory for this globally hyperbolic model could simplify quantum field theory itself.  My instincts are to suggest that quantum phenomena generally are due to this sort of model of the actual universe and that the mass gap conjecture for Minkowski space should have a negative solution (by Jormakka’s approach say) and we have a mass gap in the actual universe because we live in a compact curved universe where quantum field theory is an overcomplex model and mass gap and other problems are resolved by compactness.  This intuition would provide us with simple resolutions of many problems such a thermal equilibrium of cosmic background radiation.





So this is based on conjecture that will require a generation of work to clear up.  The most successful scientific theory is Standard Model quantum field theory and then there is general relativity.  The problem I think is the more successful standard model.  The issue is that physicists learn quantum mechanics on flat space first and then they build up to quantum field theory.  The success of quantum field theory is for small scale events.  There is a quantum field theory for curved spacetime.  The problem I think is that underlying this building up of the standard model are computations on flat Minkowski space which are generalized to curves spacetimes Rindler/de Sitter/more general globally hyperbolic, and so on.  But I believe that the quantization phenomena themselves are fundamentally due to spacetime being a globally hyperbolic spacetime with structure S^4\times\mathbf{R} or perhaps more generally to a compact hypersurface with a time dimension.  Thus a lot of the complication in physics might be due to refining intuition on solving problems on flat Minkowski spacetime and then generalizing.  For example of what simplifies in the situation I describe, the Laplace spectrum of a compact M is discrete so there is a discrete spectrum and a basis of eigenfunctions so the plane wave solutions that are the basic elements of quantum mechanics don’t show up here.

Look, this is a really serious problem in physics.  The Standard Model is not mathematically rigorous which is the reason why the mass gap problem is one of the open Clay problems.  In fact there won’t be any justified mass gap in a flat Minkowski space because our universe is simply not non-compact.  In fact, there is no expansion of the universe and the empirical ‘evidence’ of flat curvature is simply nonsense, as are hypothetical objects such as dark matter and dark energy.  There is something wrong with thousands of talented physicists trying to justify things on a flat Minkowski space with obscene effort when the correct theory is on a closed universe probably just a sphere.

One can approach this issue more rigorously by algebraic quantum field theory on a manifold Haag-Kastler, Dimock, etc. and then make sense of a Standard Model on a closed globally hyperbolic spacetime (space-compact) and then try to make sense of things.  Or one could notice that for any hypersurface of a 4-sphere of fixed radius, one obtains a space version of Einstein’s equations, one should be able to produce a Yang-Mills theory and a quantum field theory without mathematical problems whose local behaviour should be the same as the established Standard Model because we are dealing with small scale phenomena and we could expect QFT as a linearization of the right theory.  String theory goes further into speculation land as Lee Smolin and Peter Woit and others complain.  The right direction might be toward trying to see which compact geometry matches what the current observations are and clean up quantum theory to focus on simpler geometries where renormalization may not be as bad as flat space and of course a no-Big Bang theory has no singularities.  That’s the problem I think with physics right now.  I think quantization of gravity is probably not the right problem and that quantum field theory is an overcomplicated description of nature that is simpler in actuality having to do with compact geometry of space.