Talk:Phase velocity

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The reference site says the group velocity can be greater than c, not the phase velocity. Probably someone should edit this.

I removed this:

For light, group velocity and phase velocity are related by the formula
vgvp = c2
where c is the speed of light in a vacuum.

Since I don't think it's right. Cite, please? -- Bob Mellish 20:40, 4 October 2005 (UTC)



The article currently states that "phase velocity of electromagnetic radiation may under certain circumstances exceed the speed of light in a vacuum." This sentence should be changed to something like "phase velocity of electromagnetic radiation may under certain circumstances exceed the speed of light in the medium of propagation", since propagation faster than the speed of light in vacuum is unphysical. I'll try to find references on this topic before I edit the entry extensively. -- Crosswalkcs 05:35, 31 August 2006 (UTC)

  • Nope. The phase velocity of light in a medium can routinely exceed c, that is, the speed of light in vacuum (not just the speed of light in the medium). It's not unphysical, since the phase velocity doesn't represent the speed that information or energy travels at. --Bob Mellish 19:55, 1 September 2006 (UTC)

DrBob is right, whats important to remember here is that the phase propagation appears to exceed c, not that any individual photon or propagation of information actually exceeds c. Whats required to understand how this is possible is a fundamental understanding of what is meant by phase. In electronics one often hears about phase being shifted in advance, and if you take that literally it makes it seem as if the circuit advancing the phase actually anticipates the arrival of current. Not so, obviously. Perhaps what is needed in order to make the article make a little more sense to the layman is a separation of where one is asked to consider the "crest" of the wave propagating faster than the speed of light. The mental picture I had upon reading this was of a light-wave surfer exceeding c... This is the age-old problem of visualizing something that is both a particle and a wave, and in this case its a whole lot easier to visualize as a photon which also happens to contain phase information. Zaphraud 17:51, 18 September 2006 (UTC)

  • Yes, after doing some reading I realize that I was mistaken; thanks to you guys for straightening me out. Apart from a sentence or two on the dispersion page, I was unable to find anything in greater detail about this phenomenon on Wikipedia. I wonder if it might be appropriate for somebody to elaborate more on this topic, whether it be on this page, the dispersion page, or somewhere else. Given that other velocities can exceed "c," it might even be worthwhile to create a new article on the subject. I'll leave that up to the experts. Crosswalkcs 05:13, 26 September 2006 (UTC)

[edit] Phase velocity of matter wave

According to many sources including the Feynman lecture on Physics III (Quantum Mechanics) and here, the following formulas should be correct instead of those currently in the article:

v_p = E/p = \hbar \omega / \hbar k = \omega/k,

where E is total energy, i.e. E = \gamma m_{rest}c^2 = m_{rest}c^2 + E_k = \sqrt{m_{rest}^2 c^4 + c^2 p^2}
and

v_g = \frac{d\omega}{dk} = v_{particle} = c^2 / v_p ,

which holds for both light wave and matter wave. --KasugaHuang 03:11, 4 January 2007 (UTC)

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