# Small=high mass at quantum level, but big=high mass at classical level. Why?

by SteveinLondon
Tags: energy, mass.
 P: 10 At a classical physics level, physically big equates to big mass, but at the sub-atomic level, small seems to equate to big mass i.e. (short wavelength big mass relationship. "momentum=h/wavelength"). Any ideas why there is this complete contrast?
 P: 2,258 because all subatomic particles have (roughly) the same angular momentum (ħ) http://en.wikipedia.org/wiki/Bohr_model so radius is inversely proportional to mass
Mentor
P: 16,353
 Quote by granpa because all subatomic particles have the same angular momentum (ħ)
No they don't.

 P: 435 Small=high mass at quantum level, but big=high mass at classical level. Why? In classical physics you have an intuition that all objects have constant density. So bigger size with the same density yields bigger mass. In quantum physics "density" is not constant. You rather have some constant amount of something (aether, waves) and you squeeze it. The classical intuition would be that the mass of a squeezed body remains constant, but from special relativity you get that the energy of the body gets higher. And higher energy means higher mass. Those two approaches can be considered at the same time. You get then the balance between classical and quantum physics. This yields the definition of Planck mass and the Bekenstein bound.
P: 4,603
 Quote by SteveinLondon At a classical physics level, physically big equates to big mass, but at the sub-atomic level, small seems to equate to big mass i.e. (short wavelength big mass relationship. "momentum=h/wavelength"). Any ideas why there is this complete contrast?
It is not so much classical vs quantum, but rather one vs many particles. For one quantum particle, smaller length x means more energy e, as you said. But if you have MANY (say N) such small particles at DIFFERENT positions, then total energy and total length scale like
E=Ne
X=Nx
so bigger N means both bigger E and bigger X.
P: 10
 Quote by Demystifier It is not so much classical vs quantum, but rather one vs many particles. For one quantum particle, smaller length x means more energy e, as you said. But if you have MANY (say N) such small particles at DIFFERENT positions, then total energy and total length scale like E=Ne X=Nx so bigger N means both bigger E and bigger X.
But if you use DeBroglie's wave/particle formula on a large object, say a rock, you get momentum=h/wavelength, so a big rock, at the same speed as a little rock, has bigger momentum yet smaller wavelength - yet it's made up from more than one particle.
 P: 194 Becuase on a quantum-level, the universe isn't intuitive?