### RESEARCH INTERESTS

Bryan's fields of study include the following:

The ideas go right to the heart of the interpretation of quantum mechanics: what is the meaning of the wave function? Does it describe (as Bohr, Heisenberg and Born suggest) a complete theory where the wave unction describes all we can know about the states of a system, such as a molecule, a pair of particles, rather than an ensemble of similarly prepared particles. The opposing side (Einstein, de Broglie and Schrodinger) suggested that Bohr’s notion of complementarity was wrong; that quantum mechanics was incomplete and a deeper, hidden variable theory underpins quantum mechanics. Indeed the notion of wave-particle duality is incorrect. Nature does not obey complementarity. .

The debate of the 1930’s was argued with gedanken experiments. The situation was murked by John von Neumannin 1936 who proved that no hidden variable theory can exist. This idea, influenced by Bohr, and the palatability of complementarity led to the repudiation of Einstein’s ideas. Bohr argued, with complementarity, that we can know position but not momentum, or we can know momentum but not position because the wave function describes one or the other. Einstein (EPR paradox) disagreed and proved that both position and momentum are simultaneously elements of physical reality, therefore quantum mechanics is incomplete. .

However, Einstein made the reasonable assumption that when two particles separate and each is beyond the range of the other's filtering device, (say a plane polarizer like sunglasses), then one filter cannot affect the other. This is called Einstein locality. .

Before going on, it should be pointed out that the idea of complementarity goes far beyond the philosophies of Plato: that the mind is not involved in measurement and what you see is what you get. These philosophies: epistemology (how we know) and ontology (what we can know) took a frantic turn based upon the acceptance of Bohr’s ideas. It is also curious that long before quantum theory, William Moore (philosopher and brother of the sculptor Henry Moore) articulated a philosophy that was popular when Bohr was a young man and contained the notions of “this or that” much like complementarity. Bohr found it easy to pull this philosophy into quantum theory. Wave function collapse and complementarity involve paradoxes and are inconsistent with experiment. .

It was not until John Bell wrote down his famous inequalities based upon the separability of particles (assuming Einstein locality) and the notion that quantum mechanics fails to satisfy the ideas so the notion of non-locality became entrenched. To be correct, Bell’s results have been used to rule out any hidden variable theory that obeys Einstein locality. But this conclusion is incorrect. .

In 2007 Bryan proved that Bell's spin assumption is the incorrect one, not the locality assumption. He found that by extending qm to allow for non-hermitian states, determinism and causality are restored to physics. .

He also found that indistinguishility, which only occurs at the microscopic level of particles, plays an important role in establishing physical reality. In fact physical reality is different between the microscopic and macroscopic because it is degenerate at the microscopic level. This degeneracy is the basic reason for the Heisenberg Uncertainty Relations. .

The experiments were performed in 1972 (Clauser), 1981 (Aspect), 1998 (Weils), 1997 and 2002?? (Gisin), all of which seem to show that quantum mechanics violates Bell’s inequalities. From these experiments new technologies are emerging: quantum computing; quantum cryptography and quantum teleportation. Any experiments and technologies that assume that an entangled state can exist to space like separations are not interpreted correctly. When entangled particles separate, they form biparticles, which obey Einstein locality. Without detail, the singlet state forms a resonance state, much like the spin magnetic monopole discussed about. When a singlet separates, it does so into one bi-particle. This product state contains scalar and second rank tensor contributions and these polarizations could be observed in coincidence experiments. .

Quantum mechanics cannot separate the Bell states like the non-hermitian states, and cannot be written as a product. It is, according to David Bohm, “an undivided whole”. Schrödinger in 1936 said entanglement was not “a” difference between quantum and classical mechanics but “the” difference. .

It is entanglement that causes all the fuss. Suppose that an entangled pair of, say photons, are produced and then separated as EPR described, then they are still an undivided whole even though separated by space-like distances. According to the Born concept of the wave function, when one of the pair is measured, its partner “instantaneously” collapses into the state that is complementary to the one being measured. This seems to confirm non-locality. Indeed Gisin has done experiments that show that the collapse happens 10,000,000 times faster than the speed of light! The way of reconciling this with Einstein’s relativity is to make arguments and conclude, as Clauser did, that quantum mechanics and relativity live in “peaceful coexistence”. Moreover, in a private conversation with Gisin, he stated that the notion of non-locality is beyond human understanding and we are in a new realm of physics for which no mechanism can be found to explain the results. .

With this background, Professor Sanctuary has shown:

In order to include coherent microstates into quantum mechanics, the hermiticity postulate must be changed to allow for non-hermitian state operators. This change completes quantum mechanics in the sense that EPR might have envisioned. Recall the famous statement by EPR: If, without in any way disturbing a system, we can predict with certainty (i.e. with probability equal to unity) the value of a physical quantity, then there exists an element of physical reality corresponding to this physical quality.

These notions are controversial but make convincing physical sense. In addition, the non-hermitain theory of single spins provides a way of understanding how the correlations are maintained between the two entangled yet separated particles. It also gives a mechanism for quantum teleportation which is almost prosaic.

- Statistical mechanics and kinetic theory
- Theory of NMR and NQR
- Structure of proteins from NMR
- Spin theory
- NMR of solids
- Quantum computing and teleportation
- Foundations of quantum theory

The ideas go right to the heart of the interpretation of quantum mechanics: what is the meaning of the wave function? Does it describe (as Bohr, Heisenberg and Born suggest) a complete theory where the wave unction describes all we can know about the states of a system, such as a molecule, a pair of particles, rather than an ensemble of similarly prepared particles. The opposing side (Einstein, de Broglie and Schrodinger) suggested that Bohr’s notion of complementarity was wrong; that quantum mechanics was incomplete and a deeper, hidden variable theory underpins quantum mechanics. Indeed the notion of wave-particle duality is incorrect. Nature does not obey complementarity. .

The debate of the 1930’s was argued with gedanken experiments. The situation was murked by John von Neumannin 1936 who proved that no hidden variable theory can exist. This idea, influenced by Bohr, and the palatability of complementarity led to the repudiation of Einstein’s ideas. Bohr argued, with complementarity, that we can know position but not momentum, or we can know momentum but not position because the wave function describes one or the other. Einstein (EPR paradox) disagreed and proved that both position and momentum are simultaneously elements of physical reality, therefore quantum mechanics is incomplete. .

However, Einstein made the reasonable assumption that when two particles separate and each is beyond the range of the other's filtering device, (say a plane polarizer like sunglasses), then one filter cannot affect the other. This is called Einstein locality. .

Before going on, it should be pointed out that the idea of complementarity goes far beyond the philosophies of Plato: that the mind is not involved in measurement and what you see is what you get. These philosophies: epistemology (how we know) and ontology (what we can know) took a frantic turn based upon the acceptance of Bohr’s ideas. It is also curious that long before quantum theory, William Moore (philosopher and brother of the sculptor Henry Moore) articulated a philosophy that was popular when Bohr was a young man and contained the notions of “this or that” much like complementarity. Bohr found it easy to pull this philosophy into quantum theory. Wave function collapse and complementarity involve paradoxes and are inconsistent with experiment. .

It was not until John Bell wrote down his famous inequalities based upon the separability of particles (assuming Einstein locality) and the notion that quantum mechanics fails to satisfy the ideas so the notion of non-locality became entrenched. To be correct, Bell’s results have been used to rule out any hidden variable theory that obeys Einstein locality. But this conclusion is incorrect. .

In 2007 Bryan proved that Bell's spin assumption is the incorrect one, not the locality assumption. He found that by extending qm to allow for non-hermitian states, determinism and causality are restored to physics. .

He also found that indistinguishility, which only occurs at the microscopic level of particles, plays an important role in establishing physical reality. In fact physical reality is different between the microscopic and macroscopic because it is degenerate at the microscopic level. This degeneracy is the basic reason for the Heisenberg Uncertainty Relations. .

The experiments were performed in 1972 (Clauser), 1981 (Aspect), 1998 (Weils), 1997 and 2002?? (Gisin), all of which seem to show that quantum mechanics violates Bell’s inequalities. From these experiments new technologies are emerging: quantum computing; quantum cryptography and quantum teleportation. Any experiments and technologies that assume that an entangled state can exist to space like separations are not interpreted correctly. When entangled particles separate, they form biparticles, which obey Einstein locality. Without detail, the singlet state forms a resonance state, much like the spin magnetic monopole discussed about. When a singlet separates, it does so into one bi-particle. This product state contains scalar and second rank tensor contributions and these polarizations could be observed in coincidence experiments. .

Quantum mechanics cannot separate the Bell states like the non-hermitian states, and cannot be written as a product. It is, according to David Bohm, “an undivided whole”. Schrödinger in 1936 said entanglement was not “a” difference between quantum and classical mechanics but “the” difference. .

It is entanglement that causes all the fuss. Suppose that an entangled pair of, say photons, are produced and then separated as EPR described, then they are still an undivided whole even though separated by space-like distances. According to the Born concept of the wave function, when one of the pair is measured, its partner “instantaneously” collapses into the state that is complementary to the one being measured. This seems to confirm non-locality. Indeed Gisin has done experiments that show that the collapse happens 10,000,000 times faster than the speed of light! The way of reconciling this with Einstein’s relativity is to make arguments and conclude, as Clauser did, that quantum mechanics and relativity live in “peaceful coexistence”. Moreover, in a private conversation with Gisin, he stated that the notion of non-locality is beyond human understanding and we are in a new realm of physics for which no mechanism can be found to explain the results. .

With this background, Professor Sanctuary has shown:

- Quantum correlations are a property of the system alone and have nothing to do with the way filters are set. The filters only select certain sub-ensembles of particles.
- The statistical interpretation of quantum mechanics assumes that every spin has a unique axis of quantization, and such spins have their own microstate (body fixed coordinate system).
- At this level, beyond the range of direct measurement, a single spin has two orthogonal axes of angular momentum and a quantum phase. The quantum phase orients atwo dimensional spin in three dimensional Cartesian space.

The view here is that the wave function describes a statistical ensemble of microstates prepared for measurement. This view follows the way experiments are performed: that a large number of events are collected and averaged. Many issues are resolved and new ideas emerge:

- Restores locality repudiates non-locality.
- Shows that a spin is a two dimensional system, not one dimensional.
- Introduces the concept of the biparticle (a separated formally entangled spin pair).
- Shows a spin has a superposed state of angular momentum formed from the two spin components.
- Resolves the double slit experiments.
- Shows that at the microstate level, the states are coherent and so the state operators are non-hermitian.
- Completes quantum mechanics so all attributes are simultaneously dispersion free.
- Shows that a microstate exists with the experimental proof being the violation of Bell’s Inequalities. These experiments distinguish the one and two dimensional spin. They do not distinguish locality from non-locality.
- Distinguishes microstates (that can only be indirectly measured) from macrostates (which are statistical ensembles of similarly prepared spins ready for direct measurement).
- Shows that hidden variable theories are unnecessary based on present experimental results.
- Supports the statistical interpretation of quantum mechanics.
- Resolves the detection loophole.
- Gives an explanation for why maximum violation of Bell’s Inequalities occurs when the three filter settings are 60 degrees apart.
- Gives an explanation for asymmetry in the EPR data (which cannot be explained by an isotropic singlet state).
- Shows that quantum channels do not exist and teleportation cannot happen in the usual way suggested, (that is non-locality or “EPR channels” are not responsible and do not exist).
- Introduces the concept of quantum phase, which orients a particle in its microstate.
- Introduces the concept of quantum correlations length, QCL, that is a measure of the degree of randomization that has occurred. A QCL of √3 is the longest for a spin ½ in its microstate; a QCL √2, corresponds to a phase randomized spin; and when it is unity, the QCL corresponds to the usual one dimensional spin encountered in experiments that prepare spins for direct measurement.
- Suggests that changing the description of a spin from 1D to 2D will have repercussions to the structure of nuclear matter.

In order to include coherent microstates into quantum mechanics, the hermiticity postulate must be changed to allow for non-hermitian state operators. This change completes quantum mechanics in the sense that EPR might have envisioned. Recall the famous statement by EPR: If, without in any way disturbing a system, we can predict with certainty (i.e. with probability equal to unity) the value of a physical quantity, then there exists an element of physical reality corresponding to this physical quality.

These notions are controversial but make convincing physical sense. In addition, the non-hermitain theory of single spins provides a way of understanding how the correlations are maintained between the two entangled yet separated particles. It also gives a mechanism for quantum teleportation which is almost prosaic.