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Mikael Karimäki

Planck Momentum, the Human-Sized Fundamental Quantity and Possible Window to Physics in the Planck Regime

Planck units are fundamental physical units, defined using only a few fundamental constants, such as the speed of light, the gravitational constant, and the reduced Planck constant. Using them we get the Planck units of time, length and mass: t_P = 5.391×10^-44 s, l_P = 1.616×10^-35 m, m_P = 2.177×10^-8 kg.

From these, we get the Planck units for other physical quantities such as area, volume, and energy. Now, the Planck time and the Planck length are incredibly small when compared to anything found in particle physics, whereas the Planck mass, is much bigger, and corresponds to an energy far beyond anything achievable using particle accelerators.

So, it would seem that the Planck units fall beyond the limits of anything that humans can perceive, or even beyond the range of experimental physics. There is one exception, however. If we calculate the Planck unit of momentum, we get p_P = 6.525 kg m/s. Remarkably, this falls within the range of day-to-day human experience. The size of the Planck momentum may also offer a way to probe the Planck regime experimentally. It is possible to produce macroscopic quantum systems with Planck momentum (or mass). Since, e.g., a Bose-Einstein condensate forms a single quantum-mechanical whole, it is possible that when two such systems interact, a measurable resonance phenomenon appears, which gives us a peek into the otherwise unreachable area of experimental physics in the Planck regime.

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