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The Issinski resonance (IR) is a nuclear magnetic resonance of hydrogen atoms in oceanic waters polarized by the Earth's magnetic field and triggered by lightning discharges. It is a large-scale natural phenomenon of quantum nature that involves up to a hundred kilotons of synchronously precessing protons per oceanic lightning event.

Potential applications of this phenomenon are remote real-time spectral imaging of the Earth's oceans and atmosphere, environment monitoring, and experimental testing of quantum gravity.

As of 2024, the IR is a theoretically predicted phenomenon that has only limited experimental evidence. In particular, IR explains radio atmospheric tweeks and whistlers as an electromagnetic emission from protons precessing at Larmor frequency. A widely accepted alternative theoretical formulation for such radio signals is an electromagnetic resonance in the Earth's surface-to-ionosphere cavity.

Description

Protons - hydrogen atoms that form water molecules, are spin-⁠1/2⁠ particles and demonstrate magnetic resonance effects. Within 20 km radius from the lightning strike zone and 100 meters deep waters below it, a total amount of 10 kg of hydrogen atoms will be presented. Two other factors required for resonance to occur: a constant magnetic field as a polarizing force and an excitation signal to inject energy into the system. In the case of IR, the Earth's background magnetic field acts as the constant hydrogen polarizing force, and a lightening discharge acts as the excitation signal. A similar resonance effect is expected for electrons in the Earth's upper atmosphere layers.

Resonance natural frequency

In the presence of the Earth's background magnetic field of strength ${\displaystyle B}$, spin-⁠1/2⁠ particles will precess at Larmor cyclic frequency ${\displaystyle \nu }$ defined by the formula:

${\displaystyle \nu =-{\frac {\gamma }{2\pi }}B}$

where ${\displaystyle \gamma }$ is the particle's gyromagnetic ratio. For protons, it is equal to

${\displaystyle {\frac {\gamma _{p}}{2\pi }}=\mathrm {42.577\,MHz{\cdot }T^{-1}} \,\,}$

Earth's magnetic field ranges approximately from 25 μT near equator to 65 μT at the poles. This translates to the resonance frequencies from 1 kHz to 2.7 kHz for protons respectively.

For the electrons, the gyromagnetic ratio is

${\displaystyle {\frac {\gamma _{\mathrm {e} }}{2\pi }}=\mathrm {-28\,024\,MHz{\cdot }T^{-1}} \,\,}$

which corresponds to the resonance frequency 1.8 MHz in the 65 μT magnetic field. It should be noted that for electrons in the upper atmosphere layers, the Earth's dipole magnetic field will decrease approximately as ${\displaystyle 1/R^{3}}$, where ${\displaystyle R}$ is the distance from the Earth's center. For example, at altitudes equal to 10 Earth's radiuses, the magnetic field will become about 1000 times weaker.

Size of an event

Amount of the precessing protons involved in a resonance event can be estimated from an electromagnetic radiation that they produce at large distances at registering radio equipment. According to the classical electrodynamics, a system with a total magnetic moment ${\displaystyle M}$ oscillating at an angular frequency ${\displaystyle \omega }$ will emit waves with electric field amplitude ${\displaystyle E}$ at a distance ${\displaystyle r}$ defined by the formula:

${\displaystyle E={\frac {Z_{0}}{4\pi }}{\frac {\omega ^{2}}{c^{2}}}{\frac {M}{r}}}$

where ${\displaystyle Z_{0}}$ is the vacuum impedance and ${\displaystyle c}$ is the speed of light. A system consisting of ${\displaystyle N}$ polarized protons with ${\displaystyle \mu _{p}}$ magnetic moment each will have the total magnetic moment ${\displaystyle M=N\mu _{p}}$. Hence for known distance to the event and the electric field strength ${\displaystyle E}$ at the receiver, the number of protons ${\displaystyle N}$ involved can be estimated by:

${\displaystyle N={\frac {4\pi c^{2}}{Z_{0}\mu _{p}}}{\frac {rE}{\omega ^{2}}}}$

For the typically observed electric field amplitude of 30 μV/m at a distance 2000 km, this leads to the estimate of 10 particles or 10 kg of protons involved.

Relation to Schumann resonances

While both Schumann and Issinski resonances are generated by lightning discharges, they have different physical nature. Schumann resonances are electromagnetic resonances in the cavity formed by the Earth's global shape and the ionosphere, and can be described by Maxwell's equations of classical electrodynamics. Issinski resonances are of quantum nature, typically localized within an area of less than 100 km, and are not affected by the Earth shape or the ionosphere presence.

Absorption vs Emitting

For an external observer, the IR may look either as absorbing electromagnetic signals, or as emitting them. In accordance with the energy conservation law, protons will always first absorb electromagnetic waves. The absorption process will convert electromagnetic energy of photons into an energy of protons. Then the protons will slowly loose their energy by further transforming it both into a heat and by emitting electromagnetic waves at the resonance frequency.

When the external electromagnetic signal is a continues in time noise, the resonance will absorb a narrow spectral portion of the source noise, convert some portion of it into the heat, and then return the remaining energy back to the source signal. This will look as a narrow-band signal absorption for the external observer.

If, however, the source signal is a short high-intensity pulse, the energy of the pulse will be stored by the proton and then slowly emitted in a form of electromagnetic waves at the resonance frequency, long time after the source signal had disappeared. This will look to the observer as the resonance is emitting its own signals.

Applications

For most of the applications of IR, the location and phase of each individual resonance event will be required. With sufficiently large number of electromagnetic sensors registering IR signals around the globe, a solution of the inverse problem will lead to the recovery of the 3d positions of the resonance sources and their timing. With the typical observable resonance quality factor around 30 and the radiated electromagnetic wave length of 150 km, the proton resonance location and phase accuracy limited by about 5 km.

Measuring Earth's magnetic field

From the Larmor frequency of either proton or electron, one can recover the surrounding magnetic field with a high accuracy, and at the elevations far above the Earth surface.

Experimental tests of quantum gravity

Protons involved in IR phenomenon have sufficient mass to produce gravitational strain up to 10 in the existing gravitational wave observatories for ${\displaystyle 1/r}$ propagating gravity effects. At LIGO, typical noise floor in the 1kHz to 2 kHz range is about 10 per a single oscillation event. With statistical accumulation of 10 oscillation events per one year, this sensitivity threshold improves 10 times and becomes 10. If a single polarized proton creates an asymmetrical gravitational field linked to its polarization, then it can be potentially measured with up to 1% accuracy by analyzing cross-correlation between precessing protons in the Earth’s oceanic waters and data from LIGO, Virgo, and KAGRA gravitational wave detectors network.

Atmosphere 3d spectroscopic imaging

Magnetic resonance effects from water molecules and free electrons in the atmosphere can be potentially used to remotely observe its properties. Once the resonance position is resolved, the densities will follow from the resonance amplitudes.

Large-scale NMR phenomenon

IR can be used to study nuclear magnetic resonances at the scales far beyond than achievable in laboratory conditions.

History

Quantum precession of hydrogen atoms forming the Earth's oceans and polarized by the Earth's magnetic field was theoretically predicted by Canadian scientist A. Issinski in 2023 while searching for massive quantum sources to experimentally test effects of quantum gravity. One of the initial approaches was to use naturally occurring magnetite deposits in the upper Earth crust which may have up to 100 kg of electrons polarized by the Earth's magnetic field and excite them by a man-made radio frequency source. This approach would however require a multi-megawatt power source and significant efforts to create. Natural phenomena such as thunderstorms and more abundant sources such as hydrogen were then reconsidered.

References

1. ^ Issinski, A. (2023-05-12). "Earth Natural Magnetic Resonances in Quantum Gravity Experiments". Zenodo (CERN). doi:10.5281/ZENODO.7949353.
2. ^ Issinski, A. (2016-08-28). "Electromagnetic field records taken August 2016 near Stewart BC, Canada".
3. Simões, Fernando; Pfaff, Robert; Berthelier, Jean-Jacques; Klenzing, Jeffrey (2011). "A Review of Low Frequency Electromagnetic Wave Phenomena Related to Tropospheric-Ionospheric Coupling Mechanisms". Space Science Reviews. 168. doi:10.1007/s11214-011-9854-0. ISBN 978-1-4614-5676-6.
4. Griffiths, David J.; Schroeter, Darrell F. (2018). Introduction to quantum mechanics (3rd ed.). Cambridge: Cambridge University Press. ISBN 978-1-107-18963-8. OCLC 1030447903.
5. "proton gyromagnetic ratio over 2 pi in MHz/T". NIST. 2022.
6. "electron gyromagnetic ratio in MHz/T". NIST.
7. ^ Landau, Lev D; Lifshitz, Evgeny M (1975). The Classical Theory of Fields. Vol. 2 (4th ed.). Butterworth-Heinemann. ISBN 978-0-7506-2768-9.
8. Jackson, John D (1999). Classical Electrodynamics (3rd ed.). ISBN 978-0-471-30932-1.
9. "LIGO Livingston sensitivity (based on first three months of O3) (aligo_O3actual_L1.txt, 974.7 kB)". 2022.