The mathematical basis for the earlier reported spectrum of discrete electromagnetic field (EMF) frequencies that were shown to affect health and disease is substantiated and generalized in the present paper. The particular EMF pattern was revealed by a meta-analysis of, now, more than 500 biomedical publications that reported life-sustaining as well as life-decaying EMF frequencies. These discrete eigenfrequency values can be related to supposed bio-resonance of solitons or polaron quasi particles in life systems. Bio-solitons are conceived as self-reinforcing solitary waves that are constituting local fields, being involved in intracellular geometric ordering and patterning, as well as in intra- and inter-cellular signalling. Literature search, revealed very similar frequency patterns for wave resonances of nucleotides in aqueous solution, for a candidate RNA-catalyst, as well as for sound-induced vibrations evoked in thin vibrating membranes. This collective evidence points at a generalized biophysical algorithm underlying complexity in nature, evidently manifest in both animate and non-animate modalities. The detected EMF eigenfrequencies could be arithmetically scaled according to an adapted Pythagorean tuning. The mathematical analysis shows that the derived arithmetical scale exhibits a sequence of unique products of integer powers of 2, 3 and a factor .？This generalized semi-harmonic frequency spectrum may reflect a discrete pilot-wave structure that can be interpreted as a, so called, hidden variable in Bohm’s causal interpretation of quantum field theory.
References
[1]
Wigner, E.P. (1960) The Unreasonable Effectiveness of Mathematics in the Natural Sciences. Richard Courant Lecture in Mathematical Sciences Delivered at New York University, May 11, 1959. Communications on Pure and Applied Mathematics, 13, 1-14. https://doi.org/10.1002/cpa.3160130102
[2]
Tegmark, M. (2014) Our Mathematical Universe. Knopf. ISBN 978-0-307-59980-3.
[3]
Penrose, R. (2014) On the Gravitization of Quantum Mechanics 1: Quantum State Reduction. Foundations of Physics, 44, 557-575. https://doi.org/10.1007/s10701-013-9770-0
[4]
Barrow, J.D. (2003) The Constants of Nature: The Numbers that Encode the Deepest Secrets of the Universe. ISBN 0375422218.
[5]
Tegmark, M. (2008) The Mathematical Universe. Foundations of Physics, 38, 101-150. https://doi.org/10.1007/s10701-007-9186-9
[6]
Meijer, D.K.F. (2012) The Information Universe. On the Missing Link in Concepts on the Architecture of Reality. Syntropy Journal, 1, 1-64. https://www.researchgate.net/publication/275016944_Meijer_D_K_F_2012_The_Information_Universe_On_the_Missing _Link_in_Concepts_on_the_Architecture_of_Reality_Syntropy_Journal_1_pp_1-64
[7]
Meijer, D.K.F. and Geesink, J.H. (2017) Consciousness in the Universe Is Scale Invariant and Implies the Event Horizon of the Human Brain, NeuroQuantology.
[8]
Penrose, R. (1998) Quantum Computation, Entanglement and State Reduction. Philosophical Transactions of the Royal Society A, 356, 1927-1939. https://doi.org/10.1098/rsta.1998.0256
[9]
Meijer, D.K.F. and Raggett, S. (2014) Quantum Physics in Consciousness Studies. The Quantum Mind Extended, Quantum Mind. http://quantum-mind.co.uk/wp-content/uploads/2014/11/Quantum-Ph-rev-def-2.pdf
[10]
Geesink, J.H. and Meijer, D.K.F. (2017) Bio-Soliton Model that Predicts Non-Thermal Electromagnetic Frequency Bands, that either Stabilize or Destabilize Living Cells. Electromagnetic Biology and Medicine, 36, 357-378. https://doi.org/10.1080/15368378.2017.1389752
[11]
Geesink, J.H. and Meijer, D.K.F. (2016) Quantum Wave Information of Life Revealed: An Algorithm for EM Frequencies that Create Stability of Biological Order, with Implications for Brain Function and Consciousness. NeuroQuantology, 14, 106-125. https://doi.org/10.14704/nq.2016.14.1.911
[12]
Huffman, C.A. (2013) Reason and Myth in Early Pythagorean Cosmology. In: A History of Pythagoreanism, Cambridge University Press, Cambridge.
[13]
McKirahan, R. (2012) Philolaus on Number. Proceedings of the Boston Area Colloquium in Ancient Philosophy, 27, 211-232. https://doi.org/10.1163/22134417-90000137
[14]
Huffman, C.A. (1993) Philolaus of Croton: Pythagorean and Presocratic. Cambridge University Press, Cambridge.
[15]
McKay, J.Z. and Rehding, A. (2011) The Structure of Plato’s Dialogues and Greek Music Theory: A Response to J. B. Kennedy. Apeiron, 44, No. 4. https://doi.org/10.1515/apeiron.2011.021
[16]
Cifra, M., Fields J.Z. and Farhadi, A. (2010) Electromagnetic Cellular Interactions. Progress in Biophysics & Molecular Biology, 105, 223-246. https://doi.org/10.1016/j.pbiomolbio.2010.07.003
[17]
Meijer, D.K.F. and Geesink, J.H. (2016) Phonon Guided Biology: Architecture of Life and Conscious Perception Are Mediated by Toroidal Coupling of Phonon, Photon and Electron Information Fluxes at Discrete Eigenfrequencies. NeuroQuantology, 14, 718-755. https://doi.org/10.14704/nq.2016.14.4.985
[18]
Fröhlich, H. (1968) Long-Range Coherence and Energy Storage in Biological Systems. International Journal of Quantum Chemistry, 2, 641-649. https://doi.org/10.1002/qua.560020505
[19]
Meijer, D.K.F. and Geesink, J.H. (2017) The Folding of Life Proteins: Being a Guest in a Multi-Scale Landscape; On the Role of Long- and Short Range Electromagnetic Pilot Mechanisms, in an Evolutionary Context. Biological Physics, Research Gate.
[20]
Melkikh, A.V. and Meijer, D.K.F. (2017) On a Generalized Levinthal’s Paradox: The Role of Long- and Short Range Interactions on Complex Bio-Molecular Reactions, Including Protein and DNA Folding. Progress in Biophysics and Molecular Biology, 132, 57-59. https://doi.org/10.1016/j.pbiomolbio.2017.09.018
[21]
Fröhlich, H. (1988) Biological Coherence and Response to External Stimuli. Springer, Berlin, Heidelberg, New York. https://doi.org/10.1007/978-3-642-73309-3
[22]
Belyaev, I.Y. (1998) Cell Density Response of E. coli Cells to Weak ELF Magnetic Fields. Bioelectromagnetics, 19, 300-309. https://doi.org/10.1002/(SICI)1521-186X(1998)19:5%3C300::AID-BEM4%3E3.0.CO;2-5
[23]
Müller, H. (2009) Fractal Scaling Models of Resonant Oscillations in Chain Systems of Harmonic Oscillators. Progress in Physics, April.
[24]
Shiramatsu, S., Ozono, T. and Shintani, T. (2015) A Computational Model of Tonality Cognition Based on Prime Factor Representation of Frequency Ratios and Its Application. Creative Commons Attribution 3.0 Unported License.
[25]
Chew, E. (2007) Out of the Grid and Into the Spiral: Geometric Interpretations of and Comparisons with the Spiral-Array Model. Tonal Theory for the Digital Age, Computing in Musicology, 15.
[26]
Singh, V. (2008) Bohm’s Realist Interpretation of Quantum Mechanics. arXiv:0805.1779v1 [quant-ph]
[27]
Peat, F.D. (1997) Infinite Potential: The Life and Times of David Bohm. American Journal of Physics, 65, 1027. https://doi.org/10.1119/1.18717
[28]
Bohm, D. (1952) A Suggested Interpretation of the Quantum Theory in Terms of “Hidden” Variables. I. Physical Review, 85, 166-179. https://doi.org/10.1103/PhysRev.85.166
[29]
Geesink, J.H. and Meijer, D.K.F. (2018) Favourable and Unfavourable EMF Frequency Patterns in Cancer: Perspectives for Improved Therapy and Prevention. Journal of Cancer Therapy, 2018, 9.
[30]
Lambert, N., Chen, Y., Cheng, Y., Li, C., Chen, G. and Nori, F. (2013) Quantum biology. Nature Physics, 9, 10-11. https://doi.org/10.1038/nphys2474
[31]
Huelga, S.F. and Plenio, M.B. (2013) Vibration, Quanta and Biology. Contemporary Physics, June 2013.
[32]
Arndt, M., Juffmann, T. and Vedral, V. (2009) Quantum Physics Meets Biology. HFSP Journal, 3, 386-400. https://doi.org/10.2976/1.3244985
[33]
Rozzi, C.A., Falke, S.M., Spallanzani, N., Rubio, A., Molinari, E., Brida, D., Maiuri, M., Cerullo, G., Schramm, H., Christoffers, J. and Lienau, C. (2012) Quantum Coherence Controls the Charge Separation in a Prototypical Artificial Light-Harvesting System. Nature Communications, 4, Article Number: 1602.
[34]
Cohn, R. (1997) Neo-Riemannian Operations, Parsimonious Trichords, and Their “Tonnetz” Representations. Journal of Music Theory, 41, 1-66. https://doi.org/10.2307/843761
[35]
Chew, E. (2013) Mathematical and Computational Modelling of Tonality: Theory and Applications, Ser. International Series in Operations Research & Management Science, Vol. 204, Springer, New York.
[36]
MacDonnald Cornford, F. (1997) Plato’s Cosmology: The Timaeus of Plato, Translated with a Running Commentary, Indianapolis, (London, 1935).
[37]
Huffman, C. (2005) Archytas of Tarentum: Pythagorean, Philosopher and Mathematician King. Cambridge University Press, Cambridge.
[38]
O’Connor, J.J. and Robertson, E.F. (2011) Archytas of Tarentum. The MacTutor History of Mathematics Archive.
Rasch, R.A. (1983) Description of Regular Twelve-Tone Musical Tunings. The Journal of the Acoustical Society of America, 73, 1023-1035. https://doi.org/10.1121/1.389150
[41]
McClain, E.G. (1978) The Pythagorean Plato: Prelude to the Song Itself. Nicolas-Hays, York Beach, ME.
[42]
Parncutt, R. (2012) Harmony: A Psychoacoustical Approach. Springer, New York.
[43]
Duffin, R.W. (2006) How Equal Temperament Ruined Harmony and Why You Should Care. W.W. Norton, New York.
[44]
Timaios, P. (1888) The Timaeus; Edited with Introduction and Notes by R.D. Archer-Hind.
[45]
Hopkin, B. (1996) Musical Instrument Design: Practical Information for Instrument Design. Sharp Press, Dover, p. 160.
[46]
Wolf, D.J. (2003) Alternative Tunings Alternative Tonalities. Contemporary Music Review, Abingdon, UK.
[47]
Tobey, F.A. (2017) Feeling for Harmony: The 3-Semester Music Theory Course for Earlham College. http://legacy.earlham.edu/~tobeyfo/musictheory/Book1/home1.html
[48]
Barker, A. (2007) The Science of Harmonics in Classical Greece. Cambridge University Press, Cambridge. https://doi.org/10.1017/CBO9780511482465
[49]
Henry, M. (2016) Hofmeister Series: The Quantum Mechanical Viewpoint. Opinion in Colloid & Interface Science, 23, 119-125. https://doi.org/10.1016/j.cocis.2016.08.001
[50]
Wohlin, A. (2016) Numerical Analysis of 3/2-Relations in the Genetic Code and Correlations with the Basic Series of Integers 5-0, Biomedical Genetics and Genomics.
[51]
Négadi, T. (2011) The Multiplet Structure of the Genetic Code, from One and Small Number. [arxiv.org/pdf/1101.2983]
Tang, M., Huang, Q., Wei, D., et al. (2015) Terahertz Spectroscopy of Oligonucleotides in Aqueous Solutions. Journal of Biomedical Optics, 20, Article ID: 095009. https://doi.org/10.1117/1.JBO.20.9.095009
[54]
Nardecchia, I., Torres, J., Lechelon, M., et al. (2017) Out-of-Equilibrium Collective Oscillation as Phonon Condensation in a Model Protein. arXiv:1705.07975v1 [cond-mat.soft]
[55]
Davydov, A.S. (1977) Solitons and Energy Transfer along Protein Molecules. Journal of Theoretical Biology, 66, 379-387. https://doi.org/10.1016/0022-5193(77)90178-3
[56]
Levin, F.R. (2016) Philolaus. Oxford University Press, Oxford. http://www.oxfordmusiconline.com.ccl.idm.oclc.org/subscriber/article/grove/music/21585
[57]
Einstein, A., Podolsky, B. and Rosen, N. (1935) Physical Review, 47, 777-780. https://doi.org/10.1103/PhysRev.47.777
[58]
Bell, J. (1964) On the Einstein Podolsky Rosen Paradox. Physics, 1, 195-200. https://doi.org/10.1103/PhysicsPhysiqueFizika.1.195
[59]
Fremling, M. (2013) Coherent State Wave Functions on a Torus with a Constant Magnetic Field. Journal of Physics A: Mathematical and Theoretical, 46, No. 27. https://doi.org/10.1088/1751-8113/46/27/275302
[60]
Keppler, J. (2013) A New Perspective on the Functioning of the Brain and the Mechanisms behind Conscious Processes. Frontiers in Psychology, 4, 242. https://doi.org/10.3389/fpsyg.2013.00242
[61]
Marcus, P.S., Pei, S., Jiang, C.H. and Hassanzadeh, P. (2013) Three-Dimensional Vortices Generated by Self-Replication in Stably Stratified, PRL. Physical Review Letters, 111, Article ID: 084501. https://doi.org/10.1103/PhysRevLett.111.084501
[62]
Brenner, M.P. and Zeravcic, Z. (2014) Self Replicating Colloidal Clusters. Proceedings of the National Academy of Sciences of the United States of America, 111, 1748-1753.
[63]
Mandelbrot, B.B. (2016) The Fractal Geometry of Nature. Goodreads.
[64]
Vitiello, G. (1995) Dissipation and Memory Capacity in the Quantum Brain Model. International Journal of Modern Physics B, 9, 973. https://doi.org/10.1142/S0217979295000380
[65]
England, J.L. (2013) Statistical Physics of Self-Replication. The Journal of Chemical Physics, 139, Article ID: 121923. https://doi.org/10.1063/1.4818538
![\"\"](\"Edit_dbc5a13f-6bd9-486e-8f7b-3fed5aafbca4.bmp\")
.？This generalized semi-harmonic frequency spectrum may reflect a discrete pilot-wave structure that can be interpreted as a, so called, hidden variable in Bohm’s causal interpretation of quantum field theory.
