# Planck Units: Mass and Length

1. Aug 18, 2009

### Dmitry67

I was always puzzled by the fact that while almost all Planck units are extreme (very high or very low), Mass and Energy are exception from that rule. Planck mass is in the ‘middle’ of the spectrum, and it divides the mass spectrum into 2 parts:

• For small masses/energies m << Mplanck we can define a wavelength corresponding to the energy (E=hv). The higher energy – the shorter wavelength.
• For big masses we can define Schwarzschild radius Rs which is proportional to mass (and as I noticed in Black Hole physics scientists think in Rs units, substituting R with M). So, the higher energy – the longer wavelength.

So the same length corresponds (in Planck’s sense) to 2 masses: one light and one heavy. And there is also a correspondence (mapping) of heavy masses into light masses and vice versa. Assuming that Planck units are natural such mappings must be important, but so far I haven’t heard anything about it.
This is really weird. Any thoughts? (or URLs?)

2. Aug 18, 2009

### Finbar

This is confusing but you really just need to think about what different physical mass/length scales are. You need to differentiate between the A) total energy of the system B) the typical energy scale of the system. Its only when B) is approaches the Planck scale that we need to start caring about Planck scale physics. In terms of black holes you can think of A) as the mass of the black hole M and B) as the temperature T of the black hole. Large Black holes M>>m_p have T<<m_p where small black holes M~m_p will have a temperature T~m_p.