ProfessorB.Sc. (University of British Columbia, 1967)
Ph.D. (University of British Columbia, 1971)
Postdoctoral Fellow (U. of Leiden, Holland, 1972-74)
Web Page: http://sanctuary-group.mcgill.ca/
Text eBook: Physical Chemistry by Laidler, Meiser and Sanctuary Publish 2011.
Introductory chemistry for high school
General chemistry for AP programs and college
Introductory physics, non-calculus for high school
General physics, calculus for AP programs and college
Organic chemistry at the college level
All the above have hundreds of interactions, between 6 to 8 hours of short voice comments to help explain the material, and each comprise between 100 and 200 hours of individual student study.
See my personal web page for movies of spin and a description of my interests into physical chemistry and my blog on the foundation of quantum mechanics which also includes entries about physical chemistry:
Web Page: Sanctuary Group
Blog: Foundations of Quantum Mechanics and Physical Chemistry
Multimedia: Science tutorials
Foundations of quantum mechanics and physical chemistry.
Quantum mechanics, likely one of the greatest achievements of modern physics, has been plagued by errors since its inception. These errors have to do primarily with the interpretation of quantum mechanics and not with its successful application to many practical problems. However the interpretation of quantum mechanics is important for two main reasons: first a theory without interpretation is only logic, or mathematics. All physical theories must be interpreted. Second, incorrect interpretations lead to incorrect conclusions and paradoxes. There are no paradoxes in science, only wrong interpretations. The major errors in modern physics are the conclusion that it is impossible to describe all attributes of a system simultaneously, and that non-locality is a property of nature. Non-locality means that over space like separations, two systems beyond the range of interaction between them have a “connectivity” due to “quantum channels” that acts instantaneously. This is incorrect as well as be irrational.
So entrenched is non-locality in physics that journals, like Physical Review Letters will reject any paper without external peer review that questions the veracity of non-locality.
The other major error is the current view, or lack of, for a simple spin ½. What do a pair of spins look like when paired due to the Pauli principle? Movies give a visualization on my group page.
We have found that nature obeys Einstein Locality. We also have discovered that the intrinsic spin of ½ is really a two dimension system, not a one dimensional point particle.
First, let us state that Einstein, Podolsky and Rosen where right in 1935 when they assumed locality and showed that position and momentum, two non-commuting operators, are simultaneously elements of physical reality. Usually, because of violation of Bell's Inequalities, and Bell's Theorem, people believe that the locality assumption is incorrect and so repudiate EPR. However Bell made an error in his spin assumption, not the locality assumption.
The major errors in interpreting quantum mechanics:
1935: Bohr, in replying to EPR, gives a rambling and virtually incomprehensible account of complementarity. This states that quantum mechanics is the most fundamental theory and, since it cannot describe position and momentum simultaneously, then, in contrast to EPR, Bohr concludes that not all observables are simultaneously elements of physical reality. He was never clear on this concept. For example in 1962, someone came to his office and described his interpretation of complementarity to Bohr in the hope to test his ideas, to which Bohr responded “You still have it wrong.” but did not say how (see Max Jammer's book, The Philosophical Foundations of Quantum Mechanics, 1973). Bohr was wrong but still today, people believe in complementarity and the wave particle duality.
1935 to present: Greek philosophers did not know about quantum mechanics. They agreed with Einstein that for a system, all it attributes are simultaneously elements of physical reality. Two areas of philosophy are relevant to quantum theory: epistemology (how we can know) and ontology (what we can know). Because of the notion of complementarity, philosophers have been trying to reconcile how nature can describe one thing and not the other, and vice versa. They have also been trying to reconcile non-locality. Since EPR are correct on both counts, the last 60 years of philosophical efforts in these areas are now moot.
About this time, Born suggested that the wave function describes all we can know about a single system, say a particle. This is incorrect. The wave function describes a statistical ensemble of similarly prepared states.
Another idea that evolved in the epistemological debate, wave function collapse, is completely incorrect. It states that a wave function describes a particle and since the wave function can exist over a large region, then so does the particle. When we measure the particle, the wave function collapses into the state that happens to describe the pure state of the particle with a probability obtained from quantum mechanics. These notions are incorrect. First a particle is a well defined system that is localized in one place. At any instant of time, all its elements of reality exist simultaneously. If you believe in the tracks in a bubble chamber come from single particles, or in the ability to assemble nano-particles into nano-structures, then it should be clear a particle is not delocalized over all space. Consider the famous Schrödinger's Cat paradox which Schrödinger introduced to show the absurdity of superposition at the macroscopic level. At the microscopic level, the superposition is an expression of our ignorance. We do not know what state a system is in, so we assume it is in all of them with some probability distribution.
1936: John von Neumann incorrectly proved their can be no dispersion free states. If he had been correct it would mean there could be no deeper theories (like hidden variables) underpinning quantum mechanics. That is Einstein's assertion in the EPR paper, that quantum mechanics is incomplete, could not be correct. Von Neumann, brilliant mathematician and father of the modern computer, was well respected. His influence was so great that people believed his proof. Forty years later John Bell pointed out that von Neumann's proof was mathematically correct but he made an incorrect assumption: that expectation values of observables are linea—is incorrect.
1964: In 1964 he derived his famous inequalities. The math is so straightforward that no errors are likely ever to be found, although people still try. Bell's error, ironically, was also in his assumptions, just like he found for von Neumann's work. Bell made more assumptions than Einstein Locality, which he considered vital. The second is a spin has two values, +1/2 or -1/2 (to make it simpler, lets just say ±1. I have found that a spin has a 2D structure and this leads to a new spin angular momentum that cannot be predicted from qm. It is a result of the indistinguishability of a spins two axes of quantization. The new resonance or exchange spin is hermitian but has a magnitude with is √2 larger than the usual spin ½ from quantum mechanics. This extra correlation is the sole cause of the violation of Bell's Inequalities. Therefore locality is restored to quantum mechanics.
The erroneous conclusion that nature is non-local has spawned some careful experiments in order to show quantum mechanics violate Bell's Inequalities. There is nothing wrong with these experiments except that they are incorrectly interpreted as proving non-locality. Furthermore, no-one can has explained how non-locality works in EPR experiments (usually called “quantum weirdness”). The error here is not in the experiments but in the assumption that violation of Bell's Inequalities means nature is non-local. When people start to use the words: weird, spook, magic and trickery to describe physical processes, then you get the idea that some things do not add up.
1993: Teleportation. Sorry Sci-Fiction buffs, it cannot happen. It is believed that “quantum channels” exist over long distances, like Gisin's 10 km experiments. They cannot and quantum channels do not exist beyond a few picometers.
1936 to present: entanglement. Schrödinger introduced the notion of entanglement in 1936. It is generally believed that entanglement is responsible for non-locality—wrong. There is no doubt that many quantum states are entangled, but this entanglement cannot exist after particles have separated and are beyond the range of each other's interactions. In fact when an entangled pair of spins separate, only a biparticle state remains. A biparticle state obeys Einstein locality and is a well defined mathematical system. It is composed, however, of non-hermitian coherent microstate operators.
In my research, I have shown that a spin exists in a microstate that is beyond the range of direct measurement. It is manifest as a resonance state of four hermitian spins, each of which is dispersion free but have the same eigenvalues and eigenvectors that differ only by a sign. In other words, these for an isolated particle with spin, these four degenerate orientations cannot be distinguished. Quantum theory cannot resolve this degeneracy in physical reality, which directly leads to the Heisenberg Uncertainty Relations.
In experiments that directly measure, the system must first be prepared for measurement. To measure particles with spin, it is usual to use a magnetic field (but watch out for the Lorentz force if you want to use electrons). Photons can be prepared by passing beams through devices like quarter wave plates. These disrupt the spins so that two of its three axes are randomized and leads to the usual view of a spin being in a state of either +1/2 or -1/2 and consistent with being a point particle. In contrast, EPR experiments, using coincidence counting techniques, do not directly measure a spin, but a pair of spins. Therefore these experiments can be sensitive to the spin's microstate and it is found to have two orthogonal axes of spin quantization. One end is +1/2 and the other is -1/2, or vice versa. In addition to being a two dimensional quantity, a spin also has a quantum phase. This orients the two dimensional spin in three dimensional real space. The quantum phase is also needed to produce the √2 . The quantum phase is defined by the spin commutation relations:
A surprising point about this approach is that the quantum phase leads to the state of a single spin being non-hermitian. Even so, due to indistinguishabiltiy, the states formed are always hermitian, Non-hermitian states have non-orthogonal eigenstates, and so a single particle with spin can interfere with itself.
Since a single electron can interfere with itself it resolves the double slit experiment when single electrons, fired one at a time, build up an interference pattern. It also resolves the detection loophole in EPR experiments.
Another observation is that there are four degenerate √2 in the body fixed frame of a single spin. These produce a resonance situation between these four dispersion free states producing a state of zero net angular momentum. Could this be the elusive magnetic monopole?
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 is 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 a one dimensional point particle.
- Discovers a new spin angular momentum of magnitude √2 larger than the usual spin. This cannot be predicted from quantum mechanics. It requires extending quantum theory to include non-hermitian spin states.
- Introduces the concept of the biparticle (a separated formally entangled spin pair); entanglement cannot persist after entangled particles separate.
- Shows a spin has a superposed state of zero angular momentum—that is it is a resonance state that has the properties expected for a magnetic monopole.
- 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.
- The violation of Bell's Inequalities is due to the √2 spin, not non-locality. These experiments distinguish the one and two dimensional spin. Violation of Bell's Inequalities do not distinguish local from non-local events.
- 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. (of 45 degrees in the CHSH form)
- Gives an explanation for asymmetry in the EPR data (which cannot be explained if it is assumed that isotropic singlet state exists after the two spins separate.)
- Shows that quantum channels do not exist and teleportation cannot happen in the usual way suggested; non-locality and “EPR channels” are not responsible. EPR or quantum channels do not exist over large distances.
- 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.”
CHEM-203 Survey of Physical Chemistry
CHEM-233 Topics in Physical Chemistry