Talk:Group velocity

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The group velocity of a wave is the velocity with which the overall shape of the wave's amplitude (known as the envelope of the wave) propagates through space.

I have NO idea what this means! "overall shape of ...amplitude" ? I thought amplitude was a number (scalar). Even if its a vector, tensor or other function, the claim (implicit) that it has a "shape" which propagates is unhelpful gobble-de-gook.

What about talking about wave composition? or "repeating units" (as in poly-"mers")

Amplitude is indeed a scalar, but is it not necessarily constant. Consider shining a flashlight onto a wall. The brightness is high inside some circle, but outside the circle it is low and eventually vanishes. So if you were to plot the amplitude as a function of the position on the wall, it would look like some radially symmetric hill (high in the middle, low in the ends). That is what people mean when they talk about shape, except that they are talking about the shape as a function of time rather than a function of wall position. —Preceding unsigned comment added by 140.180.174.115 (talk) 14:11, 8 December 2007 (UTC)

Contents

[edit] inconsistency with dispersion

The article here claims that:

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

v_g v_p = c^2 \,

where:

vp is the phase velocity
c is the speed of light in a vacuum.

but dispersion (optics) gives phase velocity:

v = \frac{c}{n}

and group velocity

v_g = c \left[ n - \lambda \frac{dn}{d\lambda} \right]^{-1}.

which imply that:

v_p v_g = c^2 \left[ n (n - \lambda \frac{dn}{d\lambda}) \right]^{-1} \not= c^2.

Something is wrong here. i don't see why \left[ n (n - \lambda \frac{dn}{d\lambda}) \right] should be equal to one. Boud 13:52, 13 September 2005 (UTC)

  • I agree, it doesn't seem right. I've removed that equation, pending a cite. --Bob Mellish 22:05, 4 October 2005 (UTC)
  • That formula is specific to (hollow metal-pipe) waveguides. --catslash 20:56, 3 September 2007 (UTC)

[edit] picture of group velocity

Leo-

Can someone please post a picture or a trailer where the group velocity is different from the phase velocity, like how the travelling wave would look in the transverse point of view?
Try http://krypton.mnsu.edu/~7364eb/Math113/groupvelocity.html unsigned
I tried to make a gif, but its a bit large. I think i need to cut out half the frames.. but i'm too lazy right now. Fresheneesz 03:34, 12 September 2006 (UTC)

[edit] "Faster than light"

For whom feels inclined, I think a section on discussing the numerous experiments that claim "faster than light" but end up measuring group velocity is warranted. It seems these keep cropping up. Cburnett 00:28, 18 August 2007 (UTC)


"However, superluminal communication is not possible in this case, since the signal velocity remains less than the speed of light."

The first paragraph culminating in this claim is illogical and self-contradictory. It amounts to predjudicing in favour of the theory of velocity-absolutism.

If the group velocity can propagate faster then light so can information and obviously so. Anyone who claims otherwise is being self-evidently idiotic.

The article starts off talking about how normal waves move. And then an inference is made that some implications don't hold when its waves of light. But the inference is arbitrary. And so the claim ought not be made. Since its fitting a square peg in a round hole in an ideologically motivated effort to support relativity.

Its an unnecessary importing of tribalism and politics into physics. —Preceding unsigned comment added by 122.148.183.191 (talk) 02:21, August 26, 2007 (UTC)

It is you who is the self-evident idiot--obviously, the notion of a signal, as described by Brillouin in his famous book, must be a discontinuity in the light wave. And because discontinuities contain infinitely high frequency components, the discontinuity must travel at c (the speed of light in vacuum)--the material cannot respond to such high frequency content and is effectively transparent. Perhaps a little reading before posting a comment is in order, eh? —Preceding unsigned comment added by 128.112.50.49 (talk) 01:18, 7 December 2007 (UTC)


To be honest I guess I understand the comment above in the sense that "physicists and scientists" sometimes basically copy paste arguments they have seen made by others without following whether there are any mistakes in the derivations. However, for that reason I consider that rather than politics it is the fact that the subject is hard enough to understand by itself thatleads people to make such claims. To be honest I even find hard to understand basic textbooks and I think it is due to the authors having done the same as others, basically copy paste an argument. In short, I think I also read in "Concepts of modern Physics" something about all this and then the author says that sending information via group velocity is imnpossible even though it is true that group velocity is faster than light. I will give it a look later to see what it actually says.

[edit] the animated graphic

In the nice animated image, the red dot moves three times as fast as the green dot! Can someone produce a new image? (Could just change "twice" to "three times", but then it doesn't represent deep water waves!). The fact that it overtakes two green dots does not prove it goes twice as fast: it depends also on their relative densities (no. of spots in the image)! Simplifix (talk) 08:52, 20 March 2008 (UTC)

I see what you mean, and will work on it. Crowsnest (talk) 09:00, 20 March 2008 (UTC)
A new animation has been uploaded, to correct the problem. Thanks for pointing the error out! Crowsnest (talk) 09:19, 20 March 2008 (UTC)

Thanks for correcting it. It's a nice image. Simplifix (talk) 11:19, 17 April 2008 (UTC)

[edit] Missing reference for measurement of group velocity of matter wave functions

I think there should be a reference for the sentence: "Quantum mechanics has very accurately demonstrated this hypothesis, and the relation has been shown explicitly for particles as large as molecules." in the section "Matter wave group velocity", because this is quite a strong statement. —Preceding unsigned comment added by Cholewa (talk • contribs) 13:42, 17 April 2008 (UTC)