Matter Wave Phase
In quantum mechanics, particles also behave as waves with complex phases. By the de Broglie hypothesis, we see that
Using relativistic relations for energy and momentum, we have
where E is the total energy of the particle (i.e. rest energy plus kinetic energy in kinematic sense), p the momentum, the Lorentz factor, c the speed of light, and β the speed as a fraction of c. The variable v can either be taken to be the speed of the particle or the group velocity of the corresponding matter wave. Since the particle speed for any particle that has mass (according to special relativity), the phase velocity of matter waves always exceeds c, i.e.
and as we can see, it approaches c when the particle speed is in the relativistic range. The superluminal phase velocity does not violate special relativity, as it carries no information. See the article on signal velocity for details.
Read more about this topic: Phase Velocity
Famous quotes containing the words matter, wave and/or phase:
“It seems to me that upbringings have themes. The parents set the theme, either explicitly or implicitly, and the children pick it up, sometimes accurately and sometimes not so accurately.... The theme may be “Our family has a distinguished heritage that you must live up to” or “No matter what happens, we are fortunate to be together in this lovely corner of the earth” or “We have worked hard so that you can have the opportunities we didn’t have.””
—Calvin Trillin (20th century)
“Wind goes from farm to farm in wave on wave,
But carries no cry of what is hoped to be.
There may be little or much beyond the grave,
But the strong are saying nothing until they see.”
—Robert Frost (1874–1963)
“This is certainly not the place for a discourse about what festivals are for. Discussions on this theme were plentiful during that phase of preparation and on the whole were fruitless. My experience is that discussion is fruitless. What sets forth and demonstrates is the sight of events in action, is living through these events and understanding them.”
—Doris Lessing (b. 1919)