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:
“The hotel was once where things coalesced, where you could meet both townspeople and travelers. Not so in a motel. No matter how you build it, the motel remains the haunt of the quick and dirty, where the only locals are Chamber of Commerce boys every fourth Thursday. Who ever heard the returning traveler exclaim over one of the great motels of the world he stayed in? Motels can be big, but never grand.”
—William Least Heat Moon [William Trogdon] (b. 1939)
“And his wish is intimacy,
Intimater intimacy,
And a stricter privacy;
The impossible shall yet be done,
And, being two, shall still be one.
As the wave breaks to foam on shelves,
Then runs into a wave again,
So lovers melt their sundered selves,
Yet melted would be twain.”
—Ralph Waldo Emerson (1803–1882)
“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)