The Earth as a resonator

Lightning strikes somewhere on Earth around fifty times a second. Each stroke radiates electromagnetic energy over a wide band, including extremely low frequencies with wavelengths of thousands of kilometres. At those frequencies the conducting ground and the conducting lower ionosphere, some 60–90 km up, form the two walls of a spherical waveguide that wraps around the whole planet. Waves that travel all the way round and arrive back in step reinforce one another, so the cavity resonates.

In 1952 the German physicist Winfried Otto Schumann calculated the resonant frequencies of an idealised cavity of this kind (Schumann 1952). The resonances were first clearly observed by Balser and Wagner in 1960 (Balser and Wagner 1960). For a lossless thin shell of radius $R$, the frequencies are

$$f_n = \frac{c}{2\pi R}\sqrt{n(n+1)}, \qquad n = 1, 2, 3, \dots$$

import math

# Schumann's ideal (lossless) Earth–ionosphere cavity:
#   f_n = c / (2π R) · √(n (n + 1))
c, R = 2.998e8, 6.371e6
OBSERVED = [7.83, 14.3, 20.8, 27.3, 33.8]          # Hz, typical observed peaks
f0 = c / (2 * math.pi * R)
print(f"c / 2πR = {f0:.2f} Hz")
for n, obs in enumerate(OBSERVED, start=1):
    ideal = f0 * math.sqrt(n * (n + 1))
    print(f"n = {n}: ideal {ideal:5.1f} Hz, observed ≈ {obs:4.1f} Hz, ratio {obs / ideal:.2f}")

lam = c / OBSERVED[0]
print(f"wavelength at 7.83 Hz ≈ {lam / 1e3:,.0f} km; Earth's circumference ≈ {2 * math.pi * R / 1e3:,.0f} km")
# c / 2πR = 7.49 Hz
# n = 1: ideal  10.6 Hz, observed ≈  7.8 Hz, ratio 0.74
# n = 2: ideal  18.3 Hz, observed ≈ 14.3 Hz, ratio 0.78
# n = 3: ideal  25.9 Hz, observed ≈ 20.8 Hz, ratio 0.80
# n = 4: ideal  33.5 Hz, observed ≈ 27.3 Hz, ratio 0.82
# n = 5: ideal  41.0 Hz, observed ≈ 33.8 Hz, ratio 0.82
# wavelength at 7.83 Hz ≈ 38,289 km; Earth's circumference ≈ 40,030 km

The ideal formula gives 10.6 Hz for the fundamental, but the observed peak is near 7.8 Hz, and all the modes are lower by about a fifth to a quarter. The difference is physics, not error: the ionosphere is not a perfect conductor, and its finite, height-dependent conductivity lowers the frequencies and broadens the peaks (Nickolaenko and Hayakawa 2002). The spacing still follows the $\sqrt{n(n+1)}$ pattern roughly, and the wavelength of the fundamental is close to the Earth’s circumference, as the simple picture suggests.

The fundamental at 7.8 Hz lies near the brain’s alpha band, and this coincidence has led to claims that the brain is “tuned” to the Earth or that devices emitting 7.83 Hz restore a natural rhythm. Chapter 6 of The Default Mode Network, the Entropic Brain and Neural Oscillations, the previous book in the 5D Library, showed how hard it is to entrain brain rhythms even with stimuli delivered directly to the eyes and ears; a field of a picotesla, far weaker than the fields from household wiring, offers no plausible route. This book makes no claim that Schumann-frequency devices have any effect on health.

Earthing

“Earthing” or “grounding” means connecting the body electrically to the ground, by walking barefoot on soil or by sleeping or sitting on a conductive mat or sheet wired to the earth connection of a building’s electrical system. Its proponents say that the Earth’s surface supplies free electrons that reduce inflammation and improve sleep and many other aspects of health.

The part that physics can check is what grounding does to the body’s electric potential. A person in a building is capacitively coupled to the mains wiring around them and also to the ground; together these form a voltage divider.

import math

# A person lying in bed near mains wiring: a capacitive voltage divider.
f, V_mains = 60.0, 120.0       # US mains, as in the measurements reported by Applewhite
C_couple = 1.6e-12             # F, wiring-to-body coupling (chosen to give ~1.3 V)
C_body = 150e-12               # F, body-to-ground capacitance
w = 2 * math.pi * f

V_float = V_mains * C_couple / (C_couple + C_body)
print(f"ungrounded body: ≈ {V_float:.2f} V (reported: 1.24–1.32 V)")

# Grounded through a resistance R (pad, wiring and a ~100 kΩ safety resistor):
for R in (1e3, 100e3):
    Zc = 1 / (w * C_couple)                 # the coupling capacitor sets the current
    I = V_mains / Zc
    print(f"grounded via {R / 1e3:5.0f} kΩ: current {I * 1e9:.0f} nA, body ≈ {I * R * 1e3:5.2f} mV")
print("reported with a grounding pad: about 0.01 V")
print(f"the current is ≈ {0.5e-3 / I:,.0f} times below the 0.5 mA threshold of perception")
# ungrounded body: ≈ 1.27 V (reported: 1.24–1.32 V)
# grounded via     1 kΩ: current 72 nA, body ≈  0.07 mV
# grounded via   100 kΩ: current 72 nA, body ≈  7.24 mV
# reported with a grounding pad: about 0.01 V
# the current is ≈ 6,908 times below the 0.5 mA threshold of perception

The simple divider reproduces the measured voltages: about 1.3 V floating, a few to ten millivolts when grounded. The current flowing to ground is less than a ten-thousandth of what a person can feel (International Electrotechnical Commission 2005). So grounding really does change the body’s electrical environment, by draining static charge and reducing a small induced alternating voltage. What remains unproven is that this change has the health effects claimed. A floating potential of a volt is harmless, and nobody has shown a physiological mechanism by which removing it would reduce inflammation.