The Transition to the Appearance of a Classical World
- The Analogy between v / c → 0 and h → 0 is flawed.
- v / c can go to zero.
- But h never changes.
- Appearance of Classical World When We Have A Large Number of Particles
(or Large Quantum Numbers - the Correspondence Principle)
- When the Mass is Large, and has Stable Information, Two Things Happen
- With many particles, we can average over the phases,
off-diagonal terms are negligible
- With many particles, m is large
- h> is now small compared to m
- We Can Rewrite the Heisenberg Indeterminacy Relation
- ΔpΔx ≥ h/2π
- Replace p with mv, divide by m
- ΔvΔx ≥ h/2πm
- The Appearance of Classicality Is When h / m Approaches Zero!