# Further misunderstanding of coherence

Comment on “Macroscopic Quantum Coherence in Patient-Practitioner-Remedy Entanglement: The Quantized Fluctuation Field Perspective” [eCAM Advance Access published online on May 14, 2008].

## Submitted 8^{th} July 2008, online 11^{th} July 2008

Alex Hankey (1) has written to support and defend Lionel Milgrom (2,3), but does so in his own terms of “quantum fluctuation fields” in biological systems (4) rather than Milgrom's model (often referred to as a metaphor (5)) of patient-practitioner-remedy entanglement (6) via “weak” quantum theory (7). Quantum fluctuation fields are supposed to demonstrate quantum coherence on a macroscopic scale, but the reasoning behind this is flawed; in any case, a link between these two models is not to be taken for granted (8,9).

Neumann et al. (10) have recently reported that they have achieved entanglement between two ^{13}C nuclei in a diamond lattice (controlled via their coupling to an electron in a nitrogen-vacancy defect) and that the quantum correlated state persists for 3–5 milliseconds at room temperature, similar to the spin-spin relaxation time of the electron spins (6 ms). A quantum correlated state involving three spins (the two ^{13}C nuclei plus an electron) persisted for less than 2 μs, because interaction with other spin impurities shortens the relaxation times of the electron's spin (11). This represents the reality of quantum correlations in solid matter at room temperature - persistence of an entangled state of two of three particles for milli- or microsecond timescales (respectively) represents a breakthrough. It is a long way from the kind of “macroscopic quantum coherence” which Hankey writes about (1). Hankey insists that coherence can be maintained over macroscopic distances in quantum systems at high temperature:

“All quantum field theories in solid state physics provide examples where this kind of assumption is made at a primal level, since the low energy forms of their various quanta are assumed to extend over the whole lattice being considered. Theoretically that is infinite in thermodynamic systems, and, practically, over a whole crystal, or whatever kind of domain is appropriate to the exciton under consideration, be it phonon, electron, magnon or other.”

Solid state physicists use Bloch waves to describe electrons in a crystal - they are made up of normal plane waves multiplied by a function with the periodicity of the crystal. Plane waves are eigenstates of momentum and are of course infinite in extent but no actual particles really have such well-defined momentum. In a thin semiconducting layer at low temperature (of the order of 1 K) it may be possible to see weak localization (12,13), which causes a slight increase in resistance when the charge-carrying particles (electrons or holes) become trapped in quantum-coherent loops. This coherence persists on a timescale called the dephasing time, which at 1 K (-272°C) in a good-quality sample may be of the order of a few picoseconds (14) and coherence may be maintained over length scales of around a micrometre. The dephasing time decreases as temperature increases. At 1 K the momentum relaxation time (the time it takes the particle to change direction significantly) is also just a few picoseconds, and due to the uncertainty principle this sets a limit on how well-defined the momentum can be. Far from extending “over the whole lattice being considered” the wavepacket of the charge-carrying particle in this example extends for about 1 μm at 1 K and only gets smaller as the temperature increases. Recently, Billy et al. (15) have observed a localization length of almost 0.6 mm in a one-dimensional Bose-Einstein condensate of rubidium-87.

Incidentally, an exciton is a bound electron-hole pair, not a general term for phonons, electrons, magnons or whatever (although the electron-like quasiparticles which pass for electrons in a crystal may be considered as *excitations* of the Fermi sea, for example).

The Mössbauer effect (16,17) is the emission of a gamma ray by an atom in a solid, in which the crystal as a whole recoils a tiny amount (instead of the emitting atom recoiling alone by a relatively large amount, thus reducing the energy of the emitted gamma ray). It relies only on the fact that there is a significant probability (for gamma rays of relatively low energy) that the recoil, which involves just the atom which emitted the gamma ray, will not excite even the lowest-energy vibrational modes (phonons) of the solid (18). It happens because the tiny momentum kick from the emission of the gamma ray involves just one atom, and the low-energy phonons which can take that sort of momentum have very long wavelength so involve lots of atoms. I struggle to understand how this means that the system undergoes “a quantum interaction as a coherent whole”. It is actually the failure to interact which means the momentum kick is not lost to phonons and is therefore taken up by the entire crystal.

Regarding David Chalmers (19) it seems that Chalmers’ dismissal of Penrose's “nonalgorithmic processing” actually invalidates Hankey's “putting together” (20) of Penrose and Chalmers (21). Chalmers has already considered Penrose's ideas on conciousness and quantum gravity (22), and even if they were right (which is somewhat controversial, to say the least (23,24,25)) they are not what Chalmers was looking for in his “innocent version of dualism”. He is not particularly interested in general quantum mechanics either, which seems to further negate what Hankey is trying to suggest (and probably what Milgrom is trying to suggest, or at least what Hankey is trying to suggest about what Milgrom is trying to suggest). Chalmers also dismisses vitalism and therefore the “life force” which would be “equated with quantized instability fluctuations” (4). In any case, the non-trivial quantum effects (23) which Hagan et al. discuss (22) would take place in microtubules of diameter 25 nm and coherence might last for 0.01–0.1 milliseconds, although Tegmark calculated times of less than 0.1 ps (24). We are still a long way from macroscopic time- and length-scales.

Regarding phase transitions and the critical point (26), Hankey writes

“As the temperature

Tapproaches the critical temperatureT_{c}from above, the increase in specific heat means that extra heat energy is lost; implying that systems of critical fluctuations have anomalously low energy/heat content. This translates into low entropy content, since, bydq=TdS, heat changedqis directly related to entropy changedS.”

The third law of thermodynamics states that minimum entropy *S* of a system is to be found at the absolute zero of temperature. The entropy only increases as the internal energy *q* and therefore the temperature *T* is increased, by *dq* = *CdT* (where *C* is the heat capacity and is almost always positive). The high value of the specific heat at the critical temperature *T*_{c}
means that to increase the *T* through *T*_{c} requires an anomalously large input of heat energy. This translates via *dq* = *TdS* to a large increase in entropy. Hankey seems to imply that a low-entropy state exists at *T*_{c}, but since entropy is a state function this cannot be true, and systems of critical fluctuations do not have anomalously low energy/heat content. It is just that a system at a temperature just below *T*_{c} has quite a low energy/heat and entropy content compared to a system just above *T*_{c}.

This would already seem to render most of Hankey's further reasoning untenable. The correlation length does become very large at the critical point, but this is not related to low entropy and it certainly has nothing to do with macroscopic *quantum* coherence. This is because the correlation length in a statistical mechanical sense is not directly related to the phase correlation length in a quantum mechanical sense. Spins, for example (26), correlate because they line up in each other's magnetic fields, not because there is some quantum phase interaction. (If the long-range correlation were quantum mechanical in nature then we would only be able to understand it by creating a wavefunction which contained all the particles' spin states combined in a non-trivial way; this is not usually necessary, unless *T*→ 0 (27).)

In conclusion, the link between coherence of some property near the critical point and coherence of the quantum phase is spurious and nothing to do with low entropy; Hankey's “quantized fluctuation fields” (4) do not seem to have anything to do with Milgrom's hypothesis of patient-practitioner-remedy entanglement (2,6) based on “weak” quantum theory (7) to explain what is only the placebo effect (28), apart from the vague appeal to quantum theory. Milgrom's work is not physics and neither for that matter is Hankey's.

## References

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This document was translated from L^{A}T_{E}X byH^{E}V^{E}A.

draust.wordpress.com)Do you suppose by any chance Hankey is the person that reviews Lionel's efforts? And vice versa? The US expression is, I believe, "tag team".

After all, even at serious journals, a main source of names for referees tends to be those who publish papers in the journal. And when the pool of pseudo-quantum wafflers is so small...