Questions tagged [phase-velocity]
133 questions
36
votes
3 answers
In superluminal phase velocities, what is it that is traveling faster than light?
I understand that information cannot be transmitted at a velocity greater than speed of light. I think of this in terms of the radio broadcast: the station sends out carrier frequencies $\omega_c$ but the actual content is carried in the modulated…
Approximist
- 1,203
32
votes
4 answers
$\lambda=\frac{2h}{p}$ instead of $\lambda=\frac{h}{p}$?
I am studying quantum physics and there is something I don't understand:
I know that for any particle $E=hf$ (Einstein relation) and
$v=\lambda f$ ($v$ is the speed of the particle).
I also know that the kinetic energy is $E_k=\frac{mv^2}{2}$.…
snickers
- 527
16
votes
6 answers
Understanding group velocity
Group velocity as a concept in Classical Waves confuse me. It's very easy to point out visually, like in this really helpful graphic here. Okay, it's the speed of the moving bulge, which, notably moves opposite to the phase velocity.
I see what it…
sangstar
- 3,280
11
votes
1 answer
Phase and Group Velocity of Electromagnetic Waves
Moving charges produce oscillating electric and magnetic fields -we have an electromagnetic wave.
In terms of moving charges or at the level of charges, what is phase velocity and group velocity of an electromagnetic wave?
What is the origin of…
Spaceman Spiff
- 163
10
votes
1 answer
Seeming violation-wave travelling faster than speed of light
Consider the basic relation $$E=\sqrt{(pc)^2+(mc^2)^2}.$$
Every particle possesses a wave nature and it depends on the situation in which one among the two is perceptible...
Consider a particle with rest mass $m$. If we consider the speed of…
8
votes
2 answers
What really is the speed of light in a medium/vacuum, group or phase velocity?
While reading about refractive index 2 terms popped up, group velocity which alway slows down in a medium and phase velocity which may exceed speed of light. Say in a complete vacuum and using laser with only 1 frequency as an example, which of the…
user6760
- 13,214
8
votes
4 answers
Does radiation force depend on group velocity or on phase velocity?
What is the radiation force $F$ due to a beam of photons of power $P$ undergoing perfect reflection? Is it
$$a) F = 2 P / c$$
or
$$b) F = 2 P / v_g$$
where $v_g$ is the group velocity
?
Note that $v_g$ varies spatially in waveguides and in…
Andrew Palfreyman
- 1,719
7
votes
2 answers
Deriving group velocity
At the introduction to quantum mechanics, phase $v_p$ and group $v_g$ velocities are often presented. I know how to derive $v_p$ and get the equation:
$$
\scriptsize
v_p=\frac{\omega}{k}.
$$
What I don't know is how to explain a derivation of a…
71GA
- 2,633
7
votes
7 answers
Information relationship to Special Relativity
How do we write mathematically that "information" cannot go faster than light? And along a similar line of thought, how do we relate "information" with special relativity. Lastly, what is the relationship between Special Relativity and the fact…
mcFreid
- 2,671
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7
votes
3 answers
Controllable faster-than-light phase velocity
This is not another question about faster-than-light travel or superluminal communication. I totally appreciate the speed limit capped by physical laws (or theories.)
Just curious, since there is no limit for phase velocity, is there any way to…
skywaddler
- 1,515
6
votes
3 answers
How to calculate the phase and group velocity of a superposition of sine waves with different speed and wavelength?
This might seem like a trivial question but it is not for me. So, I was reading on group and phase velocities from A.P. French where he calculates the phase and group velocities for a superposition of sine waves of different speed and wavelength. I…
Tachyon209
- 813
6
votes
5 answers
Group and phase velocity - why can the latter be faster than light?
The phase velocity can be faster than light. Some argue that the phase velocity doesn't convey information, but this doesn't convince me.
We can emit a wave of a single one frequency. Then it will move in the space, but the group velocity will be…
marmistrz
- 565
5
votes
1 answer
What is the mechanism of the Askaryan effect?
(Quoted largely from Wikipedia): Askaryan radiation, known otherwise as the Askaryan effect, is a phenomenon which occurs when a particle traveling faster than the phase velocity of light in a dense dielectric produces a shower of secondary charged…
10GeV
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5
votes
1 answer
anticausal group velocity?
https://en.wikipedia.org/wiki/Anomalous_dispersion claims:
Recently, it has become possible to create gases in which the group
velocity is not only larger than the speed of light, but even
negative. In these cases, a pulse can appear to exit…
Arnold Neumaier
- 46,304
5
votes
1 answer
Fermat principle: which index of refraction?
I am somewhat puzzled by a common formulation of the Fermat principle (light travel time), because it contains index of refraction related to phase velocity while light travel time through a slab of glass, for instance, should be IMO described by…
Leos Ondra
- 2,265