There are several distinct but very closely interrelated uses of the term "coherence" in physics. For example,Pure States
The first two of these share in common that a quantum wavefunction informs the evolution of a physical system as a whole, perhaps nonlocally. The second two have in common that given systems exhibit patterning, so that information about one part of a system provides information about other parts.
- 'Pure states' are coherent
- Many-particle states may exhibit macrosopic quantum coherence
- Classical coherence is also important
"A quantum coherent state thus maximizes both global cohesion and also local freedom! Nature presents us with a deep riddle that compels us to accomodate seemingly polar opposites..."
Mae-Wan Ho, The Rainbow and the Worm
Coherence is important to the physics of nonlocality,computation,
Macroscopic Quantum Coherence
For example, the fundamental picture of a particle in quantum mechanics is that all of the alternative possibilities open to the system co-exist as a 'superposition' in a 'pure state' which is said to be coherent. (The process which converts a pure to a mixed state is known as 'decoherence'.) In this sense one can say of the two-particle singlet state considered by EPR and Bell that"The two particles are, as it were, entangled with each other in a pure or coherent state." (Ho, 1993)
cf. Mandel's "Coherence and indistinguishability"
A second, intimately related form of coherence involves multiple particles that that share a quantum state which is governed by a macroscopic wavefunction - this typically has the name 'quantum coherence', and typically involves the spaciotemporal organization of the multiparticle system. (This is closely related to what is called 'Bose-Einstein condensation'.)"What is quantum coherence? This refers to circumstances when large numbers of particles can collectively cooperate in a single quantum state..."
Examples of quantum coherence in many particle, macroscopic systems include superfluidity, superconductivity, and the laser.
Of these three paradigm systems, the former two (superfluidity and superconductivity) are basically equilibrium systems, whereas the the laser is our first example of an open system which achieves coherence by energetic pumping - this latter idea is of the greatest importance for understanding the general implications of coherence. The laser functions in thermal environments (eg. room temperature) and there are are other, perhaps many other, nonequilibrium possibilities for coherence to exist and endure at macroscopic and thermally challenging scales, as for example, Frohlich has shown...
When systems undergo phase transitions (e.g. boiling) they may become ordered...