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## Dissenting view on quantum gravity

If our goal in physics is to produce a coherent mathematical model of nature then we should take a step back from the currently accepted theories and examine the phenomena of nature to be independent of these theories.  The great movements of the twentieth century were general relativity and quantum field theory.  General relativity describes gravity via a metric on a Lorentzian manifold.  The metric arises as a critical point of the Einstein-Hilbert action and relates matter to a stress-energy tensor.  Quantum field theory arises from an a numerically successful effort to understand subatomic physics.  These are theories that have a monumental amount of thought and effort behind them.

I have been engaged in attempting to employ parsimony as a guiding principle to a different sort of unity between gravity and quantum phenomena.  I have produced empirical evidence that the universe is a scaled 4-sphere.  With this new fact in hand, we can very simply explain quantization of energy directly while at the same time make a very small technical change to general relativity and gain conflictless unity of gravity and quantum phenomena.  We can identify possible physical universes with hypersurfaces of a 4-sphere and define the Einstein-Hilbert action over hypersurfaces.  This small change does not affect the empirical basis of general relativity because the Euler-Lagrange equations for the action is not different from the Einstein field equations but the possible metrics are all hypersurface induced metrics.  There is a fixed cosmological constant term that comes from the curvature of the ambient space, which is $h^2$ where $1/h$ is the radius of the universe which must be set with $h$ the Planck constant in order to ensure that spectrum of the Dirac operator is $\pm(2+k)h$ with $k=0,1,2,...$ with spacing consistent with energy quantization empirically observed.

We can formulate the Dirac equation for fermions naturally using classical spinor fields on $S^4(1/h) \times \mathbf{R}$ with a metric totally orthogonal in space and time components.  The latter because it is parsimonious to use absolute time which is sensible.  At the moment, our SI unit of second cannot be defined without assuming a universality of the behavior of cesium-133 atoms around the universe which is compact.  The situation here is much simpler than most of the theories of either general relativity or quantum field theory for curved spacetimes allows.  The important issue is not the level of generality and complexity but the match to observed nature.  The picture here contains a fundamental link between macroscopic and microscopic phenomena via setting the radius of the universe to $1/h$.

Of course there is a question about whether it is sensible to accept a higher macroscopic space dimension.  There is crystallographic evidence for four macroscopic space dimensions.  There is of course the question of the discrepancy between our apparent experience of three space dimensions but it is best to ask what ‘space dimensions’ will mean and what will the relation between space dimensions be to our actual experience.  One could easily understand ‘experienced space dimensions’ through the result of choosing a hypersurface of the 4-sphere as the physical universe.  Some thought will convince the reader that if the physical universe is determined by a gravitational field equation, then it will vary smoothly in a 4-sphere and if observers stay on the hypersurface then they might experience three space dimensions on the hypersurface differently from the ‘fourth space dimension’.

The picture presented above have some qualitiative implications.  Since quantization of energy is determined by the 4-sphere geometry, we are better off seeking a simplification of quantum field theory rather than trying to ‘quantize’ gravity.