# What Planck units are limits?

Some Planck units, like time, length, or temperature, describe a physical maximum or minimum, at least approximately: you can't get hotter than the Planck temperature, measure anything smaller than Planck time or length, etc. Others, like the Planck charge, Planck momentum, or Planck energy, seem to have no associated maxima. Which units are of what type, and is there a reason that some are limits while others are in the 'middle' of a spectrum of possibilities? Are there limits to physical units which are distinct from the associated Plank unit?

• You can get hotter than the Planck temperature, but it's just that modern physics is not able to acceptably describe that regime. Also things like the Planck length aren't quite a minimum length. We could easily tell that a photon had a wavelength below the Planck length if its energy was over $77000YeV$ or about 7 times the Planck energy. Problem is modern physics mostly isn't valid at that energy scale either. – Jim Feb 17 '15 at 17:19
• @JimdalftheGrey: I tried to handwave away the small constant factors with "approximately". But I'm just looking for a general explanation here, within current understanding. – Charles Feb 17 '15 at 17:21
• And the Planck mass is somewhere around the mass of a single biological cell, just going to show that Planck units are mostly numerology. – user10851 Feb 17 '15 at 18:18

Planck units are constructed in such a way that all fundamental constant are equal to one, so they set a scale where the speed of light, the planck constant and the gravitational constant are relevant in their description, this would imply we would presumably need a quantum theory of gravity to explain phenomena in that setup. Since we no have such theory, many physicist think they mark a boundary to our current understanding of nature. We can not say for sure, for example, if lenght is defined below planck length, since length is a property of space itself, and using Einstein theory, it's closely related to gravity, which we don't know how behaves in quantum regimen. Of course, these ideas are speculative, but are the things we expect to find, we don't know what exactly happen at that scales.

Planck units are partly bound by the theory that they're defined in (they're electrodynamic and unrationalised).

The planck units fall in the crossing point of the upper and lower cosmological bounds.

The upper scale is based on the 'black hole' condition, where the escape velocity of a ball of matter is c or greater. In this scale, L ~ M ~ T ~ Q, so the largest mass that can be placed in a sphere can be thought of as a giant sausage of constant size, stretching across the diameter of the sphere. The maximum charge is then a surface feature etc.

The lower scale is set by the 'electrostatic limit', $mc^2 = e^2/4\pi\epsilon r$. This limit equates to putting all of the available energy of a particle into electrostatic self-capacitance, supposing it has a quantum of charge.

The actual crossing point for these scales is at the 'Stoney Point', which is not far from the planck point. The planck point supposes that $mcr = \hbar$ is the lower limit, some 137 higher than the stoney line.

Real matter is set by the 'springyness' of atoms, runs from the scale of the Bohr atom up to star-size matter. Here L :: T, L^2 :: Q, and L^3 :: M (ie density, velocity and surface charge are constant).