Talk:Phase velocity

vg*vp = c*c

I removed this:

For light, group velocity and phase velocity are related by the formula

$v_{\mathrm {g} }v_{\mathrm {p} }=c^{2}$

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)

See "differentiation of the dispersion relation (1155) yields eq.(1160)" in [2], and also this quote in [3]: "the product of the group velocity and phase velocity of the GPS signals is equal to the speed of light squared". fgnievinski (talk) 15:27, 16 May 2016 (UTC)

It's only true in what is known as a cold electron gas, which apparently models the ionosphere at certain frequencies.--Guy vandegrift (talk) 21:52, 16 May 2016 (UTC)

I can confirm that vg*vp is quite far off from c^2 for visible light passing through glass. --Steve (talk) 02:54, 17 May 2016 (UTC)

@Guy vandegrift and Sbyrnes321: Thanks for your input. Would you object to this sentence: "For the ionosphere at radio frequencies (and other cold plasmas), the following relation holds: $v_{\mathrm {g} }v_{\mathrm {p} }=c^{2}$." Thanks. fgnievinski (talk) 10:36, 17 May 2016 (UTC)

Not my article, but would rather prefer a short section on phase velocity for a few well known waves: glass, cold plasma, deep water waves, and perhaps whistlers. Adding one equation for the ionosphere is like allowing Pluto to be a planet: If you let Pluto in there are a lot of others waiting to join the club. But as I said, I am not involved with that article...just saying. I am not a Wikipedian but a Wikiversarian. Why don't you write a Wikiversity article? --Guy vandegrift (talk) 13:33, 17 May 2016 (UTC)

References

Older discussions

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

---

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)

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)

Cherenkov Radiation

Do think that Pavel Alekseyevich Cherenkov should be mentioed with reguards to the faster than light phenomena of electromagnetic waves in a dialectric ? Cherenkov Radiation

~~pendodecahedron 12:27 10 May 2007

Pic?

Is there any way someone could do an animated gif or similar to demonstrate what the topic is about? I think it would help its ability to be understood. --El Pollo Diablo (Talk) 09:38, 5 June 2008 (UTC)

Fourier transformation and Fourier space

Man,,, you are all wrong here. Phase velocity is related to the ---velocity of propagation of the wave in the Fourier space of frequencies --- that is why Phase velocity can be greater then c!speed of light! Because it is not related to the real velocity of propagation of mass and energy.

what is right for sure is that Vf . Vg = c^2 , where Vg is the group velocity, and that is the velocity related to the propagation of mass , information,,, whatever..

that is it ! Trust me! I have exam about this Tomorrow!  : ) See you

I think the article have to be change and a analised taking into account the Fourier transformation and Fourier space, that is completely related to the development of the ideas about phase velocity. —Preceding unsigned comment added by 193.49.162.11 (talk) 22:35, 26 April 2009 (UTC)

velocity/speed

I have reverted the velocity -> speed change. WP is not a tool for language reform, and phase velocity is the usual formulation.

The objection seems to be the usual line about "velocity is a vector and speed is a scalar", which is all very well for high-school physics, because students at that level are apt to confuse the vector and scalar meanings, and this arbitrary word-choice helps them keep it straight. However it does not really reflect scholarly usage. Velocity is used frequently in contexts where only the magnitude is important. Etymologically this makes perfect sense; the Latin root (I'm assuming it's velox) presumably means only "fast", not "fast in a direction". --Trovatore (talk) 21:34, 5 June 2010 (UTC)

It looks to me like the so called "phase velocity" is the velocity of what might be called a "carrier wave" in that it only carries the basic wave frequency of oscillation of the carrier medium without any additional information. That's like the carrier frequency on a current carrier telephone system. And the "phase velocity" is a dot that is always associated with the same phase value location of a single wave of the carrier wave. Then the Group variation of the intensity level of the carrier wave may be considered to be a modulation factor, which is imposed on the carrier wave in such a manner as to become the main factor controlling the amplitude of the individual carrier waves, even to the point of periodically eliminating their amplitude at the carrier wave null points. In a Current carrier Telephone system the carrier wave is eliminated by a filter, and only the group wave is passed on to the recipient.WFPM (talk) 18:01, 1 November 2010 (UTC)SeePower line communication

Someone theoretically adept asked me: Is it possible to go faster than light? He cited this Wiki page. He pointed my attention toward the green dot's procession forward. To answer him I quote from a section called PROLOG in IEEE Proceedings, October 2010, page 1773, from a paper called A Systemized View of Superluminal Wave Propagation, by Withaychumnankul, Fischer, Ferguson, Davis, and Abbott: "...analytical studies estimated...if...an electromagnetic pulse traveled a sufficiently short distance through a dispersive medium, it could conceivably travel faster than the speed of light. This was later confirmed by measuring the phase information of a laser beam, which found group velocities exceeding the speed of light. Significantly, it was observed that the superlumenality in these instances did not violate the fundamental principle of causality for three reasons. First, the peak of the transmitted pulse is not causally related to the peak when it is received. Second, the energy of the emerging pulse never exceeds that of the corresponding pulse in vacuo. Finally, the speed of the transmitted propagating wave itself never exceeds the speed of light. The tail is more attenuated than is the leading edge, in the way that the pulse shape remains the same. This results in a superluminal group velocity." Jeffreagan (talk) 21:26, 24 January 2018 (UTC)

y, y´, y´´ Add introduction in relation to derivatives.

This topic would be fastly easier to grasp if you would pertain to using derivatives in the introduction, instead of memorized nomenclature in relation to long dead individual. You aren´t going to resurrect those dead by using their names in physics.

Take any equation of the form y=f(x). y´=f´(x) is the first derivative, which is defacto the tangent line to the curve at that location. That tangent has an angle, and that angle is the phase of the ´particle´ at that location as that particle moves through the trajectory described by that equation.

Defacto, for any equation y=f(x), the integral of that equation, makes y=f(x) the tangent line change (the phase), of that integral.

A good question in relation is, is the constant in any equation of importance, or is it negligible in that it soley pertains to an operating point differenciation (IE: [f(x+Δx)-f(x)]/Δx is the derivative function and in that function, the constant does not add information at all). Given that that is true, must the phase have that constant included, or would that be overloading that equation? — Preceding unsigned comment added by 201.209.204.34 (talk) 11:48, 13 July 2013 (UTC)

Wave velocity

Female 2405:201:C01F:4459:4168:55A7:5EDF:865 (talk) 14:18, 2 January 2023 (UTC)