Theoretical Research Programs:

Local Causality and Objective Reality:

Unlike our basic theories of space and time, quantum mechanics is not a locally causal theory. Moreover, it is widely believed that any hopes of restoring local causality within a realistic theory have been undermined by Bell’s theorem and its supporting experiments. In truth, however, a strictly local, deterministic, and realistic explanation of the correlations observed in the experiments exists. For example,  Dr. Christian has presented a local, deterministic, and realistic model within a Friedmann-Robertson-Walker spacetime with constant spatial curvature (S^3) exhibiting exact agreement with the probabilistic predictions of quantum theory without data rejection, superdeterminism, or backward causation. The key ingredient in this explanation is the topology of a quaternionic 3-sphere (S^3), which remains closed under multiplication, thus preserving the locality condition specified by Bell. It allows us to model the physical space as a quaternionic 3-sphere, and reveals that the illusion of quantum nonlocality stems from a twist in the Hopf fibration of the 3-sphere. Dr. Christian has elaborated on these features in several publications, with further theoretical and experimental work underway.

Local Origins of Quantum Correlations:

It is well known that quantum correlations are not only more disciplined (and thus stronger) compared to classical correlations, but they are more disciplined in a mathematically precise sense. This raises an important physical question: What is responsible for making quantum correlations more disciplined? It turns out that the observed discipline of quantum correlations can be explained by identifying the symmetries of our physical space with those of an octonionic 7-sphere. In fact, Dr. Christian has proved a general theorem showing that ALL quantum correlations can be understood as classical, local-realistic correlations among the set of points of an octonionic 7-sphere. Much of the research activity at the Centre is devoted to developing this result further.

Locally Causal Quantum Dynamics:

As noted above, quantum correlations are not only more disciplined than classical correlations, but are more disciplined in a mathematically very precise sense. This raises an important physical question: What is it that makes quantum correlations as disciplined as they are? A preliminary answer to this question has already been proposed by Dr. Christian in his pioneering book: Disproof of Bell’s Theorem, Illuminating the Illusion of Entanglement. He has shown that the remarkable disciple of quantum correlations stems from the fact that the tangent bundle of the octonionic  7-sphere happens to be trivial. One of our goals is to flesh out this answer in much more detail. In particular, we are investigating the time evolution of quantum correlations analogous to Schrödinger’s equation as Hamiltonian/Ricci flow within the topological setting of the octonionic 7-sphere, with the help of Ehrenfest equation and the already identified Born correspondence for this purpose. Moreover, in an appendix of a recent paper Dr. Christian has demonstrated that the Ehrenfest equation in quantum mechanics (which can be derived from Schrödinger’s equation) is nothing but an ensemble average of classical Hamiltonian equations of motion over a probability distribution of unknown (or hidden) variables:

Thus quantum dynamics is not some mysterious new non-classical dynamics but arises only if the hidden variables are not known precisely enough, similar to the unknown initial conditions in a coin toss experiment.

Geometry of the Quantum Vacuum:

Other research areas being pursued at the Centre concern investigating whether the quantum vacuum has a geometrical structure that can explain the observed masses of the elementary fermions, and whether torsion energy in elementary fermions can explain the cancellation of the enormous coulomb type energies at small scales. For the geometric structure of the vacuum, we have discovered that 7-spheres, as an initial layer, pack neatly in an E8 lattice with no spheres being loose. If one tries to pack 2-spheres in a 3D lattice, one finds that some of the spheres are loose. In fact, 7-spheres are the first higher dimensional spheres that pack with no loose spheres. We are also investigating how this can give the physical space unique spinorial properties that ties in with Dr. Christian’s work concerning parallelized 3- and 7-sphere topologies. For torsion energy, we have found that it can be negative, and if elementary fermions have such energy, it can be large enough as the missing negative mechanical energy to give us the masses of the elementary fermions we observe in Nature.

Passage of Time in Relativistic Physics

Contrary to our immediate sensation of past, present, and future as continually shifting non-relational modalities, time remains as tenseless and relational as space in all of the established theories of fundamental physics. Dr. Christian has developed an empirically adequate generalized theory of inertial structure in which proper time is causally compelled to be tensed within both spacetime and dynamics. This is accomplished by introducing the inverse of the Planck time at the conjunction of special relativity and Hamiltonian mechanics, which necessitates energies and momenta to be invariantly bounded from above, and lengths and durations similarly bounded from below, by their respective Planck scale values. The resulting theory abhors any form of preferred structure, and yet captures the transience of now along timelike worldlines by causally necessitating a genuinely becoming universe. This is quite unlike the scenario in Minkowski spacetime, which is prone to a block universe interpretation. The minute deviations from the special relativistic effects such as dispersion relations and Doppler shifts predicted by the generalized theory remain quadratically suppressed by the Planck energy, but they may nevertheless be testable in the near future, for example via observations of oscillating flavor ratios of ultra-high energy cosmic neutrinos, or of altering pulse rates of extreme energy binary pulsars.

Experimental Research Programs:

Macroscopic Signature of Spinorial Sign Changes:

In their landmark textbook on gravitation Misner, Thorne, and Wheeler have noted that there is something about the geometry of orientation that is not fully taken into account in the usual concept of orientation. They noted that rotations in space by 0, ±4π, ±8π, . . ., leave all objects in their standard orientation-entanglement relation with their surroundings, whereas rotations by ±2π, ±6π, ±10π, . . ., restore only their orientation but not their orientation-entanglement relation with their surroundings. They wondered whether there was a detectable difference in physics for the two inequivalent states of an object. Earlier Aharonov and Susskind had argued that there is a detectable difference for such states in quantum physics, but not classical physics, where both absolute and relative 2π rotations are undetectable. Dr. Christian has shown, however, that there is, in fact, a detectable difference between absolute and relative 2π rotations even in classical physics. In particular, he has derived the observability of spinorial sign changes under 2π rotations in terms of geodesic distances on the group manifolds SU(2) and SO(3). Moreover, he has proposed a macroscopic experiment which could infer the 4π periodicity in principle. The proposed experiment has the potential to transform our understanding of the relationship between classical and quantum physics of rotations by experimentally refuting Bell’s theorem.

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Numerical Computer Simulations:

Recently Dr. Christian’s analytical derivation of the EPR-Bohm correlation has been verified numerically in GAViewer (which is a computing implementation of Geometric Algebra) by our Programming Advisor Albert Jan Wonnink: cf. these simulations. Moreover, building on these original simulations by Albert Jan Wonnink, our Operating Director Fred Diether has built a numerical simulation that verifies Dr. Christian’s model more accurately. This simulation has been posted and discussed at his forum. The corresponding event-by-event simulations of Dr. Christian’s 3-sphere model can be found at his RPubs page (see, especially, this simulation).

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