phase
'phase' is a bit like an outsider in the Grand National. a horse which has hardly been noticed emerges during the race as a serious contender. When physics started, who could have guessed that 'phase' would turn out to be such a key concept -- a winner, even?
The word has had an interesting evolution. From Greek phasis an appearance, it started its career in English in connection with the moon. The moon changes its appearance every month, going through a cycle which lasts 29 days, roughly 4 quarters of 7 days each. (Ever wondered where the 7-day week came from?) The 'phase' of the moon is how one refers to the momentary appearance of the moon, knowing that a day earlier, and a day later, that appearance was and will be somewhat different.
Subsequently, the word was applied to stages of other developments, those undergone by living creatures, for example. In the general use of the word, the development need not be a cyclical one (as it is in the case of the moon).
In the world of physics, there are 2 main uses of the word that I can think of.
Chemical/thermodynamic: meaning the different physical states of a substance. most obviously water, which can exist as water, ice or steam. These are the different 'phases' of water, liquid solid and gas. again, the transformation of the substance can be cyclical (e.g. in a steam engine, as idealized by Carnot) but need not be. yet the transformation is always somewhat superficial, in that it can be reversed, by the addition or removal of heat.
its use in the theory of wave motion. think to start with of the motion of a pendulum, swinging from side to side. there are many points of similarity with the cyclic transformation of the moon. the motion is cyclic, with a definite period of repetition. it is natural to describe the state of the pendulum bob at any given moment (as to both position and momentum), as the 'phase' of the motion. As before, one is conscious that 'phase' is not an altogether static concept, but is always changing from one moment to another. In a sound wave, each little volume of air undergoes pendulum-like oscillations, back and forth along the line in which the sound is propagating. In a wave travelling along a plucked string, each element of the string swings like a pendulum from side to side. In each case the wave has a phase, which now differs from place to place in the air (or along the string). The phase describes where a particular element of the medium (be it air or string) has got to in its cycle of movement. For example:
- furthest forward (=new moon)
- mean position, moving backwards (=first quarter)
- furthest back (=full moon)
- mean position, moving forwards (=third quarter).
As mentioned, the concept of phase has become more and more important in physics. Its 'apotheosis' occurs in the concept of wave function (in quantum mechanics). A wave function is 'nothing but phase'. It is merely 'the stage of development of a cyclical process' but where the substance of the process has dissolved into thin air, exactly like the Cheshire Cat in Alice's Adventures in Wonderland.