Maximum particle energy, 1.22 * 10^19 GeV, is where gravity has quantum effects and makes space and time discontinuous. Field theory no longer applies. Space is foam-like and loops and distorts, due to spin, and has no dimensionality.
Particles have phase-space waves. Particle momentum varies directly with particle-wave wavelength. Wavelength varies directly with time. Because momentum uncertainty times length uncertainty must be less than Planck constant, by the uncertainty principle, at maximum particle energy, quantum length unit {Planck length} is 1.6 * 10^-33 centimeters (1.6 x 10^-35 meters). Because space-time is no longer continuous, phase-space waves cannot have frequency greater than 10^43 Hz and wavelength less than 10^-35 meters.
Planck length depends on gravity strength and so gravitational constant g, electromagnetism strength and so light speed c, and action quantum Planck constant h: (h-bar * g / c^3)^0.5, where h-bar is Planck constant h divided by (2 times pi). h is the quantum of action, and h-bar is the quantum of angular momentum, so Planck length is the quantum of length. Planck length is distance light travels in Planck time.
Planck area quantum is 10^-66 cm^2. Planck volume quantum is 10^-99 cm^3.
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Date Modified: 2022.0224