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11
votes
4answers
1k views

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 ...
6
votes
3answers
318 views

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 ...
5
votes
1answer
3k views

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 ...
4
votes
7answers
473 views

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 ...
3
votes
3answers
158 views

Why is the phase velocity used in the definition of the refractive index?

I'm aware of the so-called group index but why is the phase velocity used in the standard definition of the index of refraction? What advantage does this offer?
3
votes
1answer
283 views

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 ...
3
votes
2answers
2k views

Group Velocity and Phase Velocity of Matter Wave?

In quantum mechanics, what is the difference between group velocity and phase velocity of matter wave? How can it also be that phase velocity of matter wave always exceeds the speed of light?
2
votes
3answers
550 views

Two different mediums can have equal index of refraction?

In other words: given a certain medium, is light's phase velocity unique?
2
votes
2answers
917 views

Rotating mirror - Foucault's measurement of light speed

Some time ago I came across a secondary web source on measurement of light speed in water made by Foucault around 1850. I append its redrawn scheme below (light is reflected from the rotating mirror ...
1
vote
3answers
4k views

How do you find the velocity function of a mechanical wave?

With the form $y(x,t)=A\sin(kx-\omega t+\phi_0)$, there are two variables, How do I find the velocity? I don't know I can apply derivative with two variables.
1
vote
2answers
2k views

What does the velocity of a wave mean?

I know that the velocity of a wave is given by $v=\lambda f$ but what does this velocity represent in the physical sense. For instance, if I am told a car moves at a velocity of 5 $m/s$ I know that ...
1
vote
1answer
2k views

Deriving group velocity

At the introduction to quantum mechanic phase $v_p$ and group $v_g$ velocities are often presented. I know how to derive $v_p$ and get equation: $$ \scriptsize v_p=\frac{\omega}{k} $$ What i dont ...
1
vote
1answer
276 views

Why doesn't anomalous dispersion allow faster-than-light propagation?

It seems that the phase velocity of light could be greater than $c$, if $\sqrt{\epsilon \mu} < 1/c$, i.e. for anomalous dispersion. Are there examples of such media? For diamagnetics it seems ...
0
votes
1answer
195 views

Wavefronts and phase velocity faster than $c$

Lets assume we have parallel wavefronts in a glass of water: and we put an inclined rod on the water surface: related to a very small inclining, Vy velocity is greater or much greater then Vx ...
0
votes
1answer
73 views

How can we calculate (relativisticly correct) ratio $\lambda_e/\lambda_p$ if proton and electron have same speeds

This question is about group/phase velocities and also De Brogilie wavelength. What I would like to know is how to derive ratio $\lambda_e/\lambda_p$ ($\lambda_e$ and $\lambda_p$ are De Broglie ...
0
votes
0answers
39 views

Group velocity and phase velocity of a wave packet [on hold]

A wave packet in a dispersive medium is represented by the following equation, $$y(x, t) = \cos(1.0x - 5.0t)\cos(0.2x - 0.4t)\cos(0.1x - 0.2t).$$ Find the group velocity and the phase velocity ...
0
votes
0answers
25 views

Wave Packets, Group velocity, and Phase velocity [duplicate]

Mathematically, you find that the wave function of a particle $\Psi (x,t)$ moves with the same velocity as the velocity of the particle ($v_{particle} = v_{group}$). Is there a reason why the ...
0
votes
0answers
71 views

group and phase velocity of free particle [duplicate]

If Schrödinger wave equation is for matter waves then for a free particle Group velocity $V_g =2$ Phase velocity $V_p$ But matter waves satisfy the relation $V_g V_p = C^2$ where $V_p>C$ Does this ...
0
votes
0answers
23 views

Learning about group velocity, phase velocity and particle velocity [duplicate]

I am studying quantum physics and I would like to know a bit more in detail about group velocity, particle velocity and phase velocity. Can you guys suggest some books/online resources where I can ...