see Aharonov–Bohm effect in wikipedia

The Aharonov–Bohm effect is a quantum mechanical phenomenon in which an electrically charged particle is affected by an electromagnetic field even in such regions of space, where the electric and magnetic field intensities vanish. In other words, despite the magnetic field and electric field are zero, experimental measurements show that particles are in some way still impacted by the field. The New Scientist magazine proclaimed Aharonov-Bohm effect to be one of the "seven wonders the quantum world". This effect was first predicted by Werner Ehrenberg and Raymond E. Siday in 1949, later published by Yakir Aharonov and David Bohm in 1959 [1], confirmed experimentally by Robert G. Chambers in 1960 (solenoid magnet experiment), by Akira Tonomura et al in 1986 [2] (toroidal magnet experiment), a general review can be found in [3]. The magnetic AB-effect takes place at magnetic fields produced by a long solenoid or at toroidal magnetic fields. Sometimes, it is denoted as A-vector potential [4].

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There exists also an electric version of the AB-effect, takes place at electric scalar potential (cylindrical capacitor).

 image from [1]

The AB-effect is related to a number of paradoxes, related e.g. to a “hidden” relativistic mechanical momentum [3], rotating objects and spins [5], the well-known Graham-Lahoz experiment [6] and others.

Macroscopic Aharonov–Bohm effect

Despite the AB effect has a quantum nature, there are many macroscopically measurable phenomena, produced by the AB effect. Experimental tests demonstrated the AB effect at L-band frequencies, where a longitudinal vector potential wave propagation across 1.5 meters out to a range of 25 meters and beyond was measured [7]. Authors in [8] reported the AB-phase shift for a macroscopic system. Several works also compared the AB effect — on the macro-scale and the macro-scale — contrasted to each other here in their manner of detection of the static curl-free vector potential [9]. Generally a large number of publications are related to the macroscopic Aharonov-Bohm effect and discuss its theoretical as well as application sides.

Biological impact of the A vector potential

As indicated by the current research, A vector potential is biologically active. For instance, the experiments are performed on viability of bacteria E. coli measured in terms of bioluminescence [10], obility of infusoria, rate of sugar fermentation in yeast cells [11]. Modifications of several physical characteristics of water (UV absorbtions spectrum and state of a silica admixture) was also discovered [11]. The AB effect and the impact of A vector potential is frequency considered in the context of alternative medicine [12]. Generally the effect of weak magnetic fields and A vector potential are closely related to each other in several biological works, e.g. impact of weak magnetic fields on plants [13] or investigation of biological mechanisms [14].

References

[1] Y. Aharonov, D. Bohm, Significance of Electromagnetic Potentials in the Quantum Theory, Phys. Rev., Vol. 115, No. 3, 1959 (link to the journal) (link to the .pdf paper)

[2] Akira Tonomura, Nobuyuki Osakabe, Tsuyoshi Matsuda, Takeshi Kawasaki, Junji Endo, Shinichiro Yano and Hiroji Yamada, Evidence for Aharonov-Bohm effect with magnetic field completely shielded from electron wave. Phys. Rev. Lett. 56, 792–795, 1986 (link to the journal) (link to the .pdf paper)

[3] Herman Batelaan and Akira Tonomura, The Aharonov–Bohm effects: Variations on a subtle theme, Physics Today, Vol. 62 (8), 38, 2009 (link to the jounal) (link to the .pdf paper)

[4] R M Collins - Soviet research on the A-vector potential and scalar waves (link to the .pdf paper)

[5] Yakir Aharonov, Daniel Rohrlich, Quantum Paradoxes, Wiley-VCH, 2005 (link to the book in google)

[6] G. M. Graham, D. G. Lahoz. Observation of static electromagnetic angular momentum in vacua, Nature, 285, 154, 1980 (link to the journal)

[7] Robert K. Zimmerman Jr., Macroscopic Aharonov–Bohm Effect At L-Band Microwave Frequencies, Modern Physics Letters B, 25:09, 649-662, 2011 (link to the journal)

[8] Adam Caprez, Brett Barwick, and Herman Batelaan, Macroscopic Test of the Aharonov-Bohm Effect, Phys. Rev. Lett. 99, 210401, 2007 (link to the journal) (link to the .pdf paper)

[9] Ram K Varma Curl-free vector potential observation on the macro-scale for charged particles in a magnetic field compared with that on the micro-scale: the Aharonov–Bohm effect, 2012 Phys. Scr. 86 045009 doi:10.1088/0031-8949/86/04/04500 (link to the journal)

[10] Ivan Rampl, Lukáš Palko, Pavel Hyršl, Libor Vojtek , Pulsed Vector Magnetic Potential Field Existence, World Journal of Condensed Matter Physics, Vol.2 No.4, November 2012 (link to the journal) (link to the .pdf paper)

[11] E. M. Trukhan, Impact of weak electro-magnetic fields on biological activity of water phase, Computer Research and Modeling, vol. 1, no. 1, pp. 101–108, 2009 (link to the .pdf paper)

[12] W. Smith, Quanta and Coherence Effects in Water and Living Systems, The Journal Of Alternative And Complementary Medicine Volume 10, Number 1, 2004, pp. 69–78 (link to the .pdf paper)

[13] Belyavskaya NA. Biological effects due to weak magnetic field on plants. Adv Space Res. 2004;34(7):1566-74 (link to the journal)

[14] Lednev, V. V. (1991), Possible mechanism for the influence of weak magnetic fields on biological systems. Bioelectromagnetics, 12: 71–75. doi: 10.1002/bem.2250120202 (link to the journal)

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