QuantumPhysics.dvi

Instead of Joules (J), one often uses electron-volts (eV) to express energy; the two are related

by 1eV = 1. 60219 × 10 −^19 J. All other dimensionful constants are either artifacts of the

units used (such as the Boltzmann constantkB, which converts temperature to energy by

kBT) or composites (such as Stefan-Boltzmann’s constantσ=π^2 kB^4 / 60 c^2 ̄h^3 ).

Usingcto convert a frequencyνinto a wavelengthλbyλ=c/νand vice-versa, and ̄h

to convert frequency into energyEbyE=hν and vice-versa, all length scales, times and

energies may be converted into one another. Finally, with the help ofEinstein’s relation

E=mc^2 , we may also convert a rest massm into an energyE. It is therefore common

practice to describe masses, times and length-scales all ineV.

The role of Newton’s gravitational constantGNis actually to set an absolute scale (the

so-called Planck scale) of energyEP, (and thus of mass, length, and time), whose value is

EP= ( ̄hc/GN)^1 /^2 = 1. 22 × 1019 GeV. This energy scale is very much larger than the highest

energies reachable by particle accelerators today (only about 10^3 GeV), and corresponds to

and energy where quantum effects in gravity become strong. In this course, gravitational

effects will always be neglected.

1.3 Scales

The orders of magnitude of the length scales of the known world areas follows,

Object size inm

known Universe 1026

Milky Way 1021

Earth’s orbit around Sun 1011

Earth 107

human 1

grain of salt 10 −^4

wavelength of visible light 5 × 10 −^7

atom 10 −^10

Lead nucleus 10 −^14

strong interaction scale (mass of the proton) 10 −^15

weak interaction scale (mass ofW±/Z) 10 −^17

Planck length 10 −^34

Quantum mechanics is crucial to understand physics at atomic scales and smaller, but

may also govern certain larger objects. The macroscopic structure of a neutron star, for

example, is quantum mechanical. To date, there appear to be no compelling experimental

results that vitiate the validity of quantum mechanics at all length scales.