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.2009 Mar 17;106(11):4219-24.
doi: 10.1073/pnas.0806273106. Epub 2009 Feb 26.

Weak, strong, and coherent regimes of Fröhlich condensation and their applications to terahertz medicine and quantum consciousness

Affiliations

Weak, strong, and coherent regimes of Fröhlich condensation and their applications to terahertz medicine and quantum consciousness

Jeffrey R Reimers et al. Proc Natl Acad Sci U S A..

Abstract

In 1968, Fröhlich showed that a driven set of oscillators can condense with nearly all of the supplied energy activating the vibrational mode of lowest frequency. This is a remarkable property usually compared with Bose-Einstein condensation, superconductivity, lasing, and other unique phenomena involving macroscopic quantum coherence. However, despite intense research, no unambiguous example has been documented. We determine the most likely experimental signatures of Fröhlich condensation and show that they are significant features remote from the extraordinary properties normally envisaged. Fröhlich condensates are classified into 3 types: weak condensates in which profound effects on chemical kinetics are possible, strong condensates in which an extremely large amount of energy is channeled into 1 vibrational mode, and coherent condensates in which this energy is placed in a single quantum state. Coherent condensates are shown to involve extremely large energies, to not be produced by the Wu-Austin dynamical Hamiltonian that provides the simplest depiction of Fröhlich condensates formed using mechanically supplied energy, and to be extremely fragile. They are inaccessible in a biological environment. Hence the Penrose-Hameroff orchestrated objective-reduction model and related theories for cognitive function that embody coherent Fröhlich condensation as an essential element are untenable. Weak condensates, however, may have profound effects on chemical and enzyme kinetics, and may be produced from biochemical energy or from radio frequency, microwave, or terahertz radiation. Pokorný's observed 8.085-MHz microtubulin resonance is identified as a possible candidate, with microwave reactors (green chemistry) and terahertz medicine appearing as other feasible sources.

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Conflict of interest statement

The authors declare no conflict of interest.

Figures

Fig. 1.
Fig. 1.
Fröhlich's model for a driven system ofZ = 3 oscillators connected to a thermal bath. Red- energy input into each system oscillator at rates, blue- energy losses to the bath with a rate proportional to φ, and green- energy redistributions within the system at a rate proportional to χ.
Fig. 2.
Fig. 2.
Regions in which strong Fröhlich condensates can be observed. For linear dispersion andZ = 25 modes, the condensation index η is colored in plots as a function of the ratio of the energy input to the bath relaxation,s/φ, and the ratio of the rate of energy redistribution to bath relaxation, χ/φ. (A) single plot at a band-Center vibration frequency to temperature ratio of ℏω0/kT = 0.1 and band-narrowness parameter ω10 = 0.04 extracted fromB. (B) All results. Superimposed on each plot is a hatched region indicating system temperatureTS/T > 5/3 (500 K if the bath temperature isT = 300 K); such regions are certainly not accessible in a biological environment.
Fig. 3.
Fig. 3.
Regions in which at least weak Fröhlich condensates can be observed. For linear dispersion andZ = 25 modes, the condensation-induced enhancement factorn1/n1χ = 0, depicting the ratio of the number of quanta in the lowest-frequency mode to that expected if the source energy is evenly dispersed, is shown as a grid of plots akin to those in Fig. 2. For each plot, the abscissa is the ratio of the energy input to the bath relaxation,s/φ, whereas the ordinate is the ratio of the rate of energy redistribution to bath relaxation, χ/φ. White regions indicate regions with n1/n1χ = 0; much lower values should give experimentally observable effects. Superimposed on each plot is a hatched region indicating biologically inaccessible regions with system temperatureTS/T > 5/3 (500 K if the bath temperature isT = 300 K).
Fig. 4.
Fig. 4.
Dynamics of the Wu–Austin Hamiltonian in the wide-band low-frequency limit (ω10 = 0.12, ℏω0/kT = 1/15), showing the change in the average kinetic energy in modes 1 (the mode undergoing Fröhlich condensation), 2, 3, 12, and 25 forZ = 25 system oscillators; the instantaneous kinetic energy in mode 1 is also shown (thin line). Other parameters are: linear frequency dispersion,ZB = 430 bath modes atT = 300 K (hence ω0 = 10.425 cm−1, ω1 = 1.251 cm−1),ZI = 200 source modes atTI = 96,000 K, α/k = 150 μK, β/k = 150 μK, γ/k = 750 μK.
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References

    1. Fröhlich H. Long-range coherence and energy storage in biological systems. Int J Quantum Chem. 1968;2:641–649.
    1. Fröhlich H. Bose condensation of strongly excited longitudinal electric modes. Phys Lett A. 1968;26:402–403.
    1. Fröhlich H. Long range coherence and the action of enzymes. Nature. 1970;228:1093. - PubMed
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    1. Miller PF, Gebbie HA. Laboratory millimeter wave measurements of atmospheric aerosols. Int J Infrared Millimeter Waves. 1996;17:1573–1591.

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