Quantum Mechanics And The Collective Unconscious

Chapter One: The Quantum Story

Historical Introduction

Loosely, classical pysics can be said to have begun at the time of Copernicus (1473 - 1543), whose work was followed up by Galileo (1564 - 1642), Kepler (1571 - 1630) and eventually Isaac Newton (1642 - 1727). And we give the name Newtonian physics to the over-arching structure of the laws of mechanics he created. Descartes (1596 - 1650) may be said to have been the leading figure in the development of a philosophical structure to underpin the developing deterministic universal theory on which Newton set the coping stone.

Of course it didn't end with Newton: James Clerk Maxwell (1831 - 1879), perhaps the most luminous of Newton's successors, produced a matching set of theories dealing with electromagnetism and optics, showing that light, magnetism and electricity travel as waves, at the speed of light, apparently overturning Newton's belief that light was corpuscular in nature.

By the late 19th century, many leading scientists regarded study of the physical universe as a done deal, with a few blank spaces remaining to be filled in by further detailed research. But the wave/particle dissonance remained essentially unexplained, and in time would undermine the Newtonian and Maxwellian certainties.

Here in order of their birth dates are the key scientists who progressed the destruction of the classical model of the universe.

Max Planck, 1858 - 1947, established in 1900 that energy could be emitted only in quanta, and this is taken to be the foundation stone of quantum mechanics.

Philipp Lenard, 1862 - 1947, studied cathode rays and photoelectric effects, showing at the end of the 19th century that their behaviour was not consistent with classical electromagnetic wave theory.

In order to explain Lenard's results, Albert Einstein, 1879 - 1955, published a paper establishing the quantum basis of the photoelectric effect in 1905, known as the 'light-quantum hypothesis'; in the same year he also published his special theory of relativity.

Neils Bohr, 1885 - 1962, described the structure of the atom, with electrons emitting photons (quanta) as they move from one energy level (orbit) to another, mostly in the early 1920s.

Erwin Schrodinger, 1887 - 1961, contributed to the developing theoretical basis of quantum mechanics in the 1920s with Schrodinger's Equation, which is a basis for the description of wave mechanics. To some extent this was in competition with the work of Bohr and Heisenberg, which focused more on a 'particle' approach (known as the Copenhagen interpretation). Later the two approaches were reconciled.

Arthur Holly Compton, 1892 - 1962, discovered the Compton effect, in which the collision of a photon with an electron provides direct evidence of wave-particle duality (early 1920s).

Wolfgang Ernst Pauli, 1900 – 1958, extended quantum mechanics with his exclusion principle and the theory of nonrelativistic spin, for which he received a Nobel prize. The exclusion principle states that two identical fermions (particles with half-integer spin) cannot occupy the same quantum state simultaneously.

Werner Heisenberg, 1901 - 1976, published in 1925 a paper establishing much of the theoretical basis of quantum mechanics; he described the 'uncertainty principle' in 1927, according to which energy travels on the basis of a probability distribution. Attempts to measure a given packet of energy result in the 'collapse' of the probabilistic wave function into a particle; but you can measure only one of the particle's key attributes, position or momentum, not both. Heisenberg's actual words were (translated): "The more precisely the position is determined, the less precisely the momentum is known in this instant, and vice versa." Ever since there has been discussion (unresolved) as to whether the act of measuring a particle actually changes the physical characteristics of the particle or merely seems to do so to the measurer.

One of the results of the theoretical work of the 1920s was the reaffirmation of the principle of 'locality', i.e. that a material object can only be affected by forces acting immediately upon it. But it became clear to Einstein in the early 1930s that the theory of quantum mechanics implied the existence of 'entanglement', a state that comes about when one particle divides into two: the 'entangled' particles, even when at a distance from one another, can affect one another's properties. Thus, measuring the spin of one particle (causing 'collapse' of the wave function) instantaneously affects the spin of the other, entangled particle.

Bell's Theorem

Einstein was unhappy with the direction that quantum theory was taking ("God does not play dice with the universe" was one famous remark, and after quantum entanglement had been demonstrated, he called it "spooky action at at distance"). Along with co-workers Boris Poldolsky (1896 - 1966) and Nathan Rosen (1909 - 1995), the three stated the 'EPR Paradox', being either that entanglement implies non-locality, or that there are 'hidden variables' attached to the entangled particles, the latter being the explanation preferred by Einstein. The paradox remained unresolved until in 1964 John Stewart Bell posited Bell's Theorem, whose subsequent experimental validation (eg Aspect et al, 1982) has largely demolished the idea of 'hidden variables' and established 'non-locality' as a key principle of quantum mechanics.

Although Bell's Theorem is widely accepted as having been validated, there remain some loopholes, of which the most significant are the 'detection' loophole and the 'locality' loophole. Proofs of Bell's theorem depend on the detection and measurement of photons, and it is experimentally very difficult to detect a high proportion of the photons being generated. As long as some photons escape detection, there is a theoretical possibiity that the escapees are different from the ones that are caught (in effect, that there is an undiscovered hidden variable). The locality loophole results from the possibility that one measurement could 'contaminate' another measurement; thus the only way to avoid it is to complete each next measurement before the previous one could have been communicated (at the speed of light, evidently).

A further loophole is concerned with 'freedom of choice': if in fact the results of an experiment were determined in advance (by God or the universe or whatever) then a fair sample of photons will be impossible to achieve. Such theories are known as 'superdeterministic' and in their nature are hard to disprove. For what it is worth, Bell himself rejected superdeterminism as being highly implausible.

In the 50 years since Bell published his inequality, experiments have come ever closer to closing all three loopholes. Giustina et al (2013) state:

'. . . we use photons and high-efficiency superconducting detectors to violate a Bell inequality closing the fair-sampling loophole, i.e. without assuming that the sample of measured photons accurately represents the entire ensemble. Additionally, we demonstrate that our setup can realize one-sided device-independent quantum key distribution on both sides. This represents a significant advance relevant to both fundamental tests and promising quantum applications.

'We note that with our experiment, photons are the first physical system for which each of these three assumptions has been successfully addressed, albeit in different experiments.'

A further recent experiment which closes the fair-sampling and detection loopholes, although not the location loophole, is reported by B G Christensen et al. (2013).

In 2015, an experiment conducted by a team led by Ronald Hanson of Delft University of Technology, with a report published in the October edition of Nature, claimed to have firmly closed both the 'detection' and the 'locality' loopholes.

Says the report:

'The researchers started with two unentangled electrons sitting in diamond crystals held in different labs on the Delft campus, 1.3 kilometres apart. Each electron was individually entangled with a photon, and both of those photons were then zipped to a third location. There, the two photons were entangled with each other — and this caused both their partner electrons to become entangled, too.'

The experiment generated 245 pairs of entangled electrons over nine days, clearly violating Bell's inequality, in a way that closed both loopholes at once: because the electrons were easy to monitor, the detection loophole was not an issue, and they were sufficiently separated to close the communication loophole in addition.

The researchers, like most others, express themselves as being unconcerned about the 'freedom of choice' loophole.

Non-locality is therefore a done deal, to all intents and purposes, and physicists are faced with the fact that there is a 'field' (call it what you will, a space, a medium) in which the supposedly immutable laws of physical science do not operate. Quantum scientists have been saying this through their mathematics for the best part of a hundred years, yet mainstream scientists have always managed to wriggle out of the consequences. Now there is no wriggle-room left!

So far, quantum mechanics has been successful at providing a theoretical basis both for classical mechanics and electromagnetic effects, and for all of the 19th and 20th century irregular results which contradicted the classical scheme of things. What it has not done is to make the universe comprehensible to humans, whether they be milkmaids, masters of the universe or research physicists.

As regards the impact of quantum mechanisms on biological evolution, a certain amount of progress has been made in linking the two. We do have at least one well-described example of the use of quantum effects in organic cell assemblies, and a number of speculative possibilities, some of which have been given a thorough theoretical and/or mathematical basis.

Photosynthesis

Gregory Engel et al (2007) studied the mechanism of photosynthesis in the Fenna-Matthews-Olson bacteriochorophyll complex, found in green sulphur bacteria, and demonstrated the role of quantum coherence in improving the performance of energy transfer from a light-harvesting antenna to the central reaction centre. The quantum coherence (i.e. continuation of the state of entanglement) is much longer lived than might have been expected.

In 2012 Engel and Elad Harel published a paper extending the work on quantum involvement in photosynthesis to a study of the light-harvesting complex of purple bacteria, showing that quantum effects help to optimize the transfer of energy among variously available pathways. Once again, quantum coherence was long-lasting, even at room temperature.

In 2014 O'Reilly and Olaya-Castro examined energy transfer by light-gathering macro-molecules of a type frequently found in cyanobacteria, some algaes and higher plants, employing molecular vibrations at room temperature which cannot be described using classical physics. These quantum effects can be prompted upon incoherent input of excitation, and the authors suggest that 'investigation of the non-classical properties of vibrational motions assisting excitation and charge transport, photoreception and chemical sensing processes could be a touchstone for revealing a role for non-trivial quantum phenomena in biology'.

Yasser Omar of the University of Lisbon has reported (2014 and 2016) on the existence of quantum coherence in energy transport phenomena in photosynthetic complexes at room temperature. Curiously, the efficiency of transport varied inversely with the degree of order in the structures studied: very symmetrical structures experienced low levels of transport efficiency, whereas more disordered structures saw more efficient transport even though the degree of coherence might be lower.

Dr Omar explains that the efficiency of the energy transfer process is helped by a quantum phenomenon known as the superposition principle, which means that the energy is able to travel down every route towards the plant’s reaction centre at the same time.

‘Our project is trying to understand how come these quantum effects can be there when they shouldn’t be, because you would expect all the environmental effects would kill the quantumness,’ he said.

By using a combination of experimentation and theoretical models, the team has found that quantum effects are preserved in photosynthesis precisely because of the disorder created by the natural vibrations of molecules in the plant.

Biology

Although quantum biology was a known field of research by the middle of the 20th century, it has not attracted as much attention as some other disciplines. However, there are now signs of life in quantum biology, some of which are described below, see e.g. Lambert (2013).

In 1999, Al-Khalilib and McFadden published a biological cell model which showed the feasibility of accounting for the phenomenon of adaptive mutations (which appear to contradict the established rules of neo-Darwinian evolutionary biology) through the operation of quantum effects at cell level. They demonstrate that quantum coherence can be maintained over biologically significant periods of time (multiple seconds), and that a mutating DNA cell with quantum coherence can exist in a superposition with the external environment while it, so to speak, 'tests' possible mutations against the environment (employing the reverse quantum Xeno effect) until a point at which the cell decoheres (the superposition collapses) leaving an adaptive mutation. This work is discussed more fully in Chapter Four, Evolution Revisited.

A paper by Johann Summhammer, leader of the Experimental Quantum Physics and Solar Cells Group at Vienna University, written in 2006, proposed a model for quantum-assisted cooperation between two insects, in one case two ants pushing an object and in another two butterflies looking for each other. His mathematical analysis of how such cooperation might work on the basis of quantum entanglement concludes that both tasks can be performed up to twice as effectively if quantum effects are employed, without there needing to be any communication as such between the two animals. The writer admits that his analysis is heavily over-simplified, and merely wishes to establish that the employment of quantum-based effects can provide a survival advantage in general terms.

Tieyan Si (2010) described a mathematical model of the working of individual muscle fibres from water insect Lethocerus Maximus in which a quantum chain of molecular level motors is proposed as a more satisfactory explanation for the force-velocity relationship than classical physics can provide.

In 2012, Summhammer et al modelled ion channels that conduct electrical membrane signals in the nervous system, building potentials that propagate along the membranes. The model shows that alkali ions can become highly delocalized in the filter region of proteins at warm temperatures, so that quantum effects result in faster and more selective transmission of ions. Say the authors: 'Our results provide the first evidence that quantum mechanical properties are needed to explain a fundamental biological property such as ion-selectivity in trans-membrane ion-currents and the effect on gating kinetics and shaping of classical conductances in electrically excitable cells'.

Quantum tunneling, generally, refers to the fact that a particle can sometimes surmount a potential barrier which ought to defeat it because its probabilistic wave function includes a low probability of its existence on the other side of the barrier. It has been described in a number of scientific disciplines, and in particular in quantum biology, in which it is said to account for the otherwise unexpected speed of enzyme-driven physiological reactions taking place at room temperature. See, e.g., Nagel et al (2012).

Quantum effects are also thought to be important in the process of phototransduction, used in the retina of the eye to convert incoming photons into visual signals, something that happens at an extremely rapid rate. See for instance Sia et al (2014).

Biological Magnetic Compass

Hans Briegel, (2009), a professor of theoretical physics at the University of Innsbruck, and colleagues Jianming Cai and Gian Giacomo Guerreschi have studied the role of quantum effects in avian navigation, establishing a theoretical basis for how entanglement could persist in a cyclic organic environment, although the work has been attacked by some other researchers. Birds are thought to be able to 'vizualize' magnetic maps as an aid to navigation, and quantum effects could improve the efficiency of the mechanism. 'Radical pairs' (pairs of transient radicals created simultaneously, with correlated electron spins) are thought to be involved in the process, and the theory suggests that at least in relatively short-lived pairs, entanglement probably plays a major role.

In later work, Briegel et al (2012) showed that entanglement can persist despite, and apparently because of, extremely 'noisy' environments, which suggests to them that long-term entanglement is feasible in complex biological assemblies.

Ritz (2011) surveys the then-current state of research into birds' magnetic compass, concluding that while the biophysical basis of this compass remains unknown, there is a growing body of evidence in support of a quantum-based radical-pair mechanism as the basis for the compass.

A biological compass needle has been described In work reported in November, 2015, by a team of Chinese researchers led by Xie Can (see Qin). Studying fruit flies (drosophila), they found a rod-shaped complex of proteins that can align with Earth’s weak magnetic field. It was known previously that fruit flies' magnetic orientation depended on a protein named 'Cry', short for cryptochrome; however, on its own, Cry cannot determine orientation; the Chinese researchers say that they have found a protein in fruit flies, known as CG8198, and termed MagR that both binds to iron and interacts with Cry with which it forms a nanoscale ‘needle’: a rod-like core of CG8198 polymers with an outer layer of Cry proteins that twists around the core. The needle orients itself in the Earth's magnetic field.

After identifying MagR in Drosophila, Xie and his colleagues screened the genomes of several other animal species, finding genes for both Cry and MagR in virtually all of them, including in butterflies, pigeons, robins, rats, mole rats, sharks, turtles, and humans. “This protein is evolutionarily conserved across different classes of animals (from butterflies to pigeons, rats, and humans),” Xie wrote.

In 2016, Czech researchers published a study (see Bazalova et al) showing that a Cry protein mediates directional magnetoreception in the retina of cockroaches.

A coherent theory of the involvement of quantum phenomena in geolocation is not yet extant, but the work described in this section and the last one is highly suggestive of a prominent quantum role in the workings of the eye across a wide range of species both in relation to vision as such and also in relation to magnetic geolocation.

Bioluminescence

Fritz-Albert Popp, born 1938 has specialized in the study of biophotons. Dr. Popp became an Invited Member of the New York Academy of Sciences and an Invited Foreign Member of the Russian Academy of Natural Sciences (RANS). Popp is the founder of the International Institute of Biophysics in Neuss (1996), Germany, an international network of 19 research groups from 13 countries involved in biophoton research and coherence systems in biology. His work provides a basis for theories of communication between bodies of cells (including organs and independent organisms) based on the emission of photons, which have quantum characteristics as well as obeying Maxwellian wave theory. Biophoton emission and 'delayed luminescence' are closely but not uniquely linked to cell division.

In daphnia magna, for example, photon emission is shown to be the mechanism for controlling the density of animals at an optimal level, while in dinoflagellates (fireflies) the synchronization of flickering between two separate colonies is shown to result from bioluminescence effects, especially since it still takes place even when there is a considerable degree of separation between the colonies.

Popp and his colleagues (2003) describe an organism as a macroscopic quantum system; they propose that the molecules of the organism form part of a unified, coherent radiation field in which biophotons can be treated as being emitted by the organism as a whole. Cancerous growth of a cell assembly can be seen as a failure of coherence to match emission levels.

While Popp's views have some experimental foundation, they are disputed by many researchers in the field, who prefer a biochemical explanation for the emission of photons.

Quantum Computing

Although it would not be right to say that quantum computing is already a reality, a vast amount of research is being thrown at the possibility of it, both in academia and in the research labs of the sorts of large company that might employ it, if one day it existed in commercially useful form. A particularly interesting collaboration is between Google and Professor John Martinis (UCSB), with the explicit goal of creating commercializable quantum computers. Martinis and his group at UCSB have published multiple papers on related subjects, e.g. Fowler (2014), dealing with error detection in qubit assemblies. Google collaborator, Canadian company D-Wave, claims to have constructed a 512-qubit quantum computer.

Quantum computing employs qubits in place of the bits used in classical computing. A qubit resides in an atom, an ion, a photon, or possibly an anyon, and has quantum superposition. Typically, it is entangled with one or more fellow qubits, and it is this assembly of entangled qubits that can function as a computer. In principle, the values of all the entangled components change instantaneously when one of them changes, and measuring the 'output' of the assembly, being the sum of the probabilities of a specified set of qubit states, gives an extremely rapid result. There are plentiful technical problems to solve, notably that of maintaining the coherence of entangled qubits and their individual superpositions without using temperatures close to absolute zero, and the difficulty of measuring the state of a qubit without causing its wave function to collapse.

One particular aspect of quantum computing that has received a great deal of attention is so-called 'teleportation', in which the state of a qubit is transferred to a remote, enangled qubit. An observer of the remote qubit can therefore know the state of the original qubit. However, the process still requires the transfer of accompanying information by classical methods. There is a large literature, e.g. Xiao-Hui Bao et al (2012).

The Unresolved Quantum Questions

The major problems raised by quantum mechanics, sketched out above, can be said to be those of wave/particle duality, the measurement problem, and the fact of non-locality, none of which have physical explanations that are in any sense related to the existing body of scientific knowledge.

This has not stopped philosophers and others from coming up with theories to explain quantum mechanics, and some of these theories will be examined at a later stage of this work.

References

Al-Khalilib, Jim and McFaddena, Johnjoe, (1999) A quantum mechanical model of adaptive mutation, Biosystems Volume 50, Issue 3, June 1999, Pages 203–211, at http://www.researchgate.net/profile/Johnjoe_Mcfadden/publication/12899582_
A_quantum_mechanical_model_of_adaptive_mutation/links/09e4150fa9e345efc4000000.pdf, accessed on June 26, 2015

Aspect, Alain, Dalibard, G Roger (1982) Experimental test of Bell's inequalities using time-varying analyzers, Physical Review Letters 49 #25, 1804 (20 Dec 1982)

Bazalova, O, et al (2016) Cryptochrome 2 Mediates Directional Magnetoreception in Cockroaches, Proceedings of the National Academy of Sciences, vol. 113 no. 6, pp 1660–1665, doi: 10.1073/pnas.1518622113

Bell, John Stewart, (1964), On the Einstein Podolsky Rosen paradox, Physics 1 #3, 195 (1964)

Bohr, Niels, (2008), Nielsen, J. Rud, ed. Volume 3: The Correspondence Principle (1918–1923). Niels Bohr Collected Works, Elsevier, Amsterdam

Briegel, H J, Cai J, Popescu, S and Guerreschi, G G, (2011) Persistent dynamic entanglement from classical motion: How bio-molecular machines can generate non-trivial quantum states, New J. Phys. 14, 053043 (2012)

Briegel, H J, Cai J and Guerreschi, G G, (2009) Quantum control and entanglement in a chemical compass, Phys. Rev. Lett 104, 220502 (2010)

Christensen, B G, et al, (2013) Detection-Loophole-Free Test of Quantum Nonlocality, and Applications, Phys. Rev. Lett. at http://prl.aps.org/abstract/PRL/v111/i13/e130406

Compton, Arthur H, (1923) A Quantum Theory of the Scattering of X-rays by Light Elements, Phys. Rev. 21, 483 – Published 1 May 1923

Einstein, Albert, (1905) Über die Entwickelung unserer Anschauungen über das Wesen und die Konstitution der Strahlung (On a Heuristic Viewpoint Concerning the Production and Transformation of Light), Verhandlungen der Deutschen Physikalischen Gesellschaft 7, 482–500 (1909); Physikalische Zeitschrift 10, 817–826 (1909) (with 'Discussion'); in Collected Papers, Vol. 2 (Ref. [1]), pp 564–582, 585–586, and translation volume, pp 379–398

Einstein, Albert, Podolsky, Boris, Rosen, Nathan (1935) Can quantum-mechanical description of physical reality be considered complete? Physical Review 41, 777 (15 May 1935)

Engel, G S, et al (2007) Evidence for wavelike energy transfer through quantum coherence in photosynthetic systems, Department of Chemistry & QB3 Institute, University of California, Berkeley, California 94720, USA, Nature April 12, 2007, 446(7137): 782-6

Fowler, Austin G, Sank, D, Kelly, J, Barends, R and Martinis, John M, (2014) Scalable extraction of error models from the output of error detection circuits, at http://arxiv.org/pdf/1405.1454v1.pdf, accessed on June 27, 2015

Giustina, Marissa, et al., (2013) Bell violation using entangled photons without the fair-sampling assumption, Nature 497, 227–230

Hanson, Ronald, et al (2015) Loophole-free Bell inequality violation using electron spins separated by 1.3 kilometres, Nature 526, 682–686 (29 October 2015) doi:10.1038/nature15759

Harel, E and Engel, G S, (2012) Quantum coherence spectroscopy reveals
complex dynamics in bacterial lightharvesting complex 2 (LH2)
, The James Franck Institute and Department of Chemistry, University of Chicago; PNAS Direct Submission

Heisenberg, Werner (1927), Über den anschaulichen Inhalt der quantentheoretischen Kinematik und Mechanik (On the physical content of quantum theoretical kinematics and mechanics), Z. Phys. 43 (3–4): 172–198

Lambert, Neill, Yueh-Nan Chen, Yuan-Chung Cheng, Che-Ming Li, Guang-Yin Chen and Nori, Franco (2013) Quantum biology, Nature Physics 9, 10–18 (2013) doi:10.1038/nphys2474, at http://www.nature.com/nphys/journal/v9/n1/full/nphys2474.html, accessed on June 30th, 2015

Lenard, Philipp, (1906) Über Kathodenstrahlen (On Cathode Rays), Leipzig, 1906; 2nd ed., Leipzig, 1920

Mohseni, M, Omar, Y, Engel, G S, Plenio, M B (Editors, 2014) Quantum Effects in Biology, Universität Ulm, Germany, ISBN: 9781107010802

Nagel, Z D, Meadows, C W, Dong, M, Bahnson, B J and Klinman, J P (2012) Active Site Hydrophobic Residues Impact Hydrogen Tunneling Differently in a Thermophilic Alcohol Dehydrogenase at Optimal vs. Non-Optimal Temperatures, Biochemistry 2012 May 22; 51 (20): 4147–4156.doi:10.1021/bi3001352

Novo, L, Mohseni, M, Omar, Y, (2016) Disorder-Assisted Quantum Transport in Sub-Optimal Decoherence Regimes, Scientific Reports 6:18142 | DOI: 10.1038/srep18142

O'Reilly, Edward J. and Olaya-Castro, Alexandra, (2014) Non-classicality of the molecular vibrations assisting exciton energy transfer at room temperature, Nature Communications 5, Article number: 3012 doi:10.1038/ncomms4012, at http://arxiv.org/pdf/1301.6970.pdf, accessed on June 25, 2015

Pauli, Wolfgang, (1945) The Exclusion Principle and Quantum Mechanics, Nobel Lecture, December 13, 1946, Nobel Lectures, Physics 1942-1962, Elsevier Publishing Company, Amsterdam, 1964

Planck, Max, (1900) Entropie und Temperatur strahlender Wärme (Entropy and Temperature of Radiant Heat), Annalen der Physik 1(4): 719-37

Popp, F-A, (2003) Properties of biophotons and their theoretical implications, International Institute of Biophysics, Neuss, Germany, Indian Journal of Experimental Biology, 41, 391-402 (2003)

Qin, S, et al (2015) A Magnetic Protein Bio-Compass, Nature Mater. http://dx.doi.org/10.1038/nmat4484

Ritz, Thorsten, (2011) Quantum effects in biology: Bird navigation, Procedia Chemistry 3 (2011) 262–275, at http://ac.els-cdn.com/S1876619611000738/1-s2.0-S1876619611000738-main.pdf?_tid=2ce8985e-1bd3-11e5-9887-00000aab0f26&acdnat=1435303131_734b3fb4bcec26222861f4b5ab765a07, accessed on June 26, 2015

Schrödinger, Erwin, (1926) An Undulatory Theory of the Mechanics of Atoms and Molecules, Physical Review 28 (6): 1049–1070

Sia, P I, Luiten, A N, Stace, T M, Wood, J P M and Casson, R J (2014) Quantum Biology of the Retina, Clin Experiment Ophthalmol. 2014 Aug; 42(6): 582-9. doi: 10.1111/ceo.12373. Epub 2014 Aug 7.

Summhammer, J, (2006), Quantum Cooperation Of Two Insects, Vienna University of Technology, Atominstitut, Vienna, arXiv:quant-ph/0503136v2 Jan 30, 2006

Summhammer, Johann, Salari, Vahid and Bernroider, Gustav, (2012) A Quantum-mechanical description of ion motion within the confining potentials of voltage gated ion channels, Journal of Integrative Neuroscience 11, No.2 (2012), 123-135, at http://arxiv.org/pdf/1206.0637v1.pdf, accessed on June 26, 2015

Tieyan Si (2010), One dimensional chain of quantum molecule motors as a mathematical physics model for muscle fibre (Max-Planck-Institute for the Physics of Complex Systems), MIT Technology Review 2010, at http://arxiv.org/pdf/1004.3120v2.pdf, accessed on June 26, 2015

Xiao-Hui Bao, Xiao-Fan Xu, Che-Ming Li, Zhen-Sheng Yuan, Chao-Yang Lu and Jian-Wei Pan (2012) Quantum teleportation between remote atomic-ensemble quantum memories, PNAS December 11, 2012 vol. 109 no. 50, DOI: 10.1073/pnas.1207329109, at arXiv:1211.2892, accessed on June 27, 2015

 
 
BACK TO PREVIOUS CHAPTER | BACK TO TABLE OF CONTENTS | ON TO NEXT CHAPTER
 
 
Copyright 2016 M G Bell. The material contained on this site is the intellectual property of M G Bell and may not be reproduced, transmitted or copied by any means including photocopying or electronic transmission, without his express written permission.