Temperatures, Energies, and Lengths

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Theoretical physicists tend to use units of length, energy, and temperature interchangeably. Energy is related to temperature through the expression E = kT, where k is Boltzmann's constant, so high energies correspond to high temperatures. Length and energy have a very direct relationship in quantum mechanics. The energy of a particle is related to its wavelength when it is described as a wave. The proton is a good example—its mass gives an energy (when multiplied by c2, the speed of light squared), which is roughly the binding energy of the quarks inside it, and its mass also gives a size (when Planck's constant, h, is divided by the mass times c), which is related to a scattering cross section area in proton-proton scattering. The size and binding energy of the atom don't quite match up because the electron is going less than a hundredth of the speed of light. As for gravity, the important thing to note is that the current collider energies (the LHC line) is much, much smaller than the energy associated with quantum gravity (the "Planck scale"). Thus, it is very difficult to imagine how one would ever directly test theories of quantum gravity. The scale in the diagram above is logarithmic, so each tick mark is separated by a factor of 100,000. (Unit: 2)