Is Phase Velocity Greater than c in Spacetime?

[spacetime]

Phase velocity of a wave can exceed the speed of light in vacuum. But it does not convey an information transfer at a speed greater than c. I am not sure about this concept. Is phase velocity just a theoretical concept in certain circumstances?



spacetime
www.geocities.com/physics_all/

 

[ZapperZ]

Phase velocity of a wave can exceed the speed of light in vacuum. But it does not convey an information transfer at a speed greater than c. I am not sure about this concept. Is phase velocity just a theoretical concept in certain circumstances?



spacetime

Nope! Just look at the RF cavity or accelerating structures in particle accelerators. They run into this all the time.

Zz.

 

[marlon]

Phase velocity of a wave can exceed the speed of light in vacuum. But it does not convey an information transfer at a speed greater than c. I am not sure about this concept. Is phase velocity just a theoretical concept in certain circumstances?



spacetime
www.geocities.com/physics_all/

No info can be transeferred at speeds that are higher then c... Indeed due to entanglement, a wavefunction can describe a specific state when a measurement is performed at some other place on the entangeled state...the resulting "modification" in wavefunction due to this measurement will be "transferred" immediately. I mean if one observer measures an entangeled state, the wavefunction will describe the changed state and this goes along for the other observer's wavefunction as well. Yet no info can be extracted from this new state (ie the entangeled state AFTER one observer perofrmed a measurement) because the density-matrix of the two systems is the same. The only way that info can be gained is when there has been some communication between the two observers and this info-transfer must have speed lower the c because of special relativity...

regards
marlon

 

[KingNothing]

Hey ZZ, can you explain phase velocity?

 

[da_willem]

phase velocity is the velocity at which surfaces of constant phase move. So if you move along with a wave at it's phase velocity (if possible) the wave's shape looks the same (locally).

E.g. for the archetype 1D wave y(x,t)=Acos(kx-wt) (k the wavenumber 2pi/wavelength and w the angular frequency 2pi*frequency) you have to move at such a speed it's phase kx-wt is constant. so x=(constant)+wt/k and dx/dt=w/k is the phase velocity.

The group velocity is defined not as w/k but dw/dk. In the example this is the same as the phase velocity as w and k are constants. But in general w is a function of k and the group velocity depends on the wavelength. This is called dispersion and the relation between w and k is called a dispersion relation.

 

[russ_watters]

Think about closing a pair of scissors - the point where they touch moves as they close. With a big enough pair of scissors, you could get that point to move faster than C (theoretically).

 

[ceptimus]

Switch on a light in the centre of the ceiling of a 2 x 2 square room. The sphere of light expands from the bulb and touches the nearest point on a wall (distance 1). A bit later, the light has traveled the extra distance \sqrt{2} - 1 \approx 0.414 and reached the corners.

Now consider the edge of the lit region of the wall. In the time it takes light to travel 0.414 units, the edge of the lit region has traveled a distance of 1. So the edge of the lit region has averaged over twice the speed of light.

 

[Tide]

ceptimus,

Excellent example! I also like the one with the rotating lighthouse beacon projecting a light beam onto a distant horizon. If the rotation rate and distance to the horizon are great enough the spot will travel faster than light.

 

[marlon]

great example ceptimus...

this is one to remember...

regards
marlon

 

[rbj]

ceptimus,

Excellent example! I also like the one with the rotating lighthouse beacon projecting a light beam onto a distant horizon. If the rotation rate and distance to the horizon are great enough the spot will travel faster than light.

wouldn't the beam of light look like a spiral or a swirl from afar above the lighthouse? i do not see how the spot would be traveling arbitrarily fast unless the beam itself was infinite and then the spot *still* would not travel faster than light.

r b-j

 

[Tide]

wouldn't the beam of light look like a spiral or a swirl from afar above the lighthouse? i do not see how the spot would be traveling arbitrarily fast unless the beam itself was infinite and then the spot *still* would not travel faster than light.

r b-j

If you are an observer standing next to a wall at the distant horizon you will see a spot moving faster than light speed. It would exhibit some strange properties from your perspective!

 

[T.Roc]

ceptimus & tide

2x2 room: you have an observer (1) on the "sphere" perimeter, and one in the corner(2). Light from the bulb to (1), and from the bulb to (2) is measured at c. The photons illuminating the edge of the "sphere" are not the same ones to hit the corner. (the sphere does not move)

lighthouse: at the far reaches of the beacon, 360 observers taking measurements for you all report the speed of c from lighthouse to them. The light "cone" itself is not moving, with each degree of turn, new photons arrive at c.




TRoc

 

[Tide]

T.Roc,

I think those were the points we were making. No information or energy is being transmitted faster than c in any of the examples. In the case of the beacon, at a distance R from the source, the spot moves at the speed 2\pi R/T if the beacon takes time T to complete one full (uniform) turn. For suitable R and T this can be made to exceed c.

 

[spacetime]

Think about closing a pair of scissors - the point where they touch moves as they close. With a big enough pair of scissors, you could get that point to move faster than C (theoretically).

So, can't we transfer information through that meeting point?

 

[Danger]

Hi folks;
The scissors are strictly a thought device. You could never accelerate their closing enough. The tips would have to exceed "c" to get that closing rate.

 

[da_willem]

Hi folks;
The scissors are strictly a thought device. You could never accelerate their closing enough. The tips would have to exceed "c" to get that closing rate.

No they won't!

 

[KingNothing]

No. If you have two points of a scissors 1 inch apart that close at a fixed 1 inch per second, the speed at which the 'cutting point' of the two blades moves is directly proportional to the length of the blades, which in theory have no limitations.

 

[Andrew Mason]

No. If you have two points of a scissors 1 inch apart that close at a fixed 1 inch per second, the speed at which the 'cutting point' of the two blades moves is directly proportional to the length of the blades, which in theory have no limitations.

But the time that it takes for the hand to transmit the closing force from the handle to the tip cannot be less than L/c where L is the length of the scissor blade. So the time it takes for the 'cutting point' to reach the tip cannot be less than L/c.

AM

 

[Andrew Mason]

Switch on a light in the centre of the ceiling of a 2 x 2 square room. The sphere of light expands from the bulb and touches the nearest point on a wall (distance 1). A bit later, the light has traveled the extra distance \sqrt{2} - 1 \approx 0.414 and reached the corners.

Now consider the edge of the lit region of the wall. In the time it takes light to travel 0.414 units, the edge of the lit region has traveled a distance of 1. So the edge of the lit region has averaged over twice the speed of light.

My question is: how is this concept of 'phase velocity' for light different than the separation velocity of fast particles?

You seem to be saying that the separation velocity of two photons starting out from the lightbulb at the same time separate at a speed greater than c in the inertial frame of the lightbulb/observer.

The observer would also conclude the same thing about two high energy particles (with speeds greater than c/2) leaving the lightbulb location at the same time (in the inertial frame of the lightbulb/observer) and moving in completely opposite directions (ie. a more extreme case than the one you gave). But if we measure their relative speeds in the inertial frame of one of the particles, it becomes apparent that their separation speed is less than c.

AM

 

[russ_watters]

So, can't we transfer information through that meeting point?

No. Its just a point.

Danger, KingNothing - my thought experiment does not violate any laws of physics. Please note: I was not talking about the tips of the blades (which cannot close at >C relative to each other), I was talking about the intersection point of the blades. If you had a really long piece of paper, the cut would propagate at greater than C.

 

[kaos]

wouldn't that violate SR??the scissors wouldn't be rigid enough as the propagation of motion would still travel at less than c right? or the scissors should break apart

 

[pervect]

Just imagine setting up the two angled blades in motion.

|       /
|      /
|      /
|     /
|     /
|    /
|    /

The vertical blade on the left moves to the right at a high fraction of the speed of light.

The tilted blade on the right moves to the left at a high fraction of the speed of light.

Their intersection point moves at a "velocity" greater than 'c' upwards.

There is nothing paradoxical about this - the intersection point is not a physical object, as various people have tried to point out.

 

[kaos]

oh i get it its like the shadow thing...

a shadow can move faster than light because it doesn't involve mass being moved faster than c...

 

[Andrew Mason]

Just imagine setting up the two angled blades in motion.

The vertical blade on the left moves to the right at a high fraction of the speed of light.

The tilted blade on the right moves to the left at a high fraction of the speed of light.

Their intersection point moves at a "velocity" greater than 'c' upwards.

There is nothing paradoxical about this - the intersection point is not a physical object, as various people have tried to point out.

But in order for the blade to move with angular velocity, a force has to be transmitted along the entire length of the blade (ie. from one molecule to another from the handle to the tip). This cannot be transmitted faster than c. So. in reality. the intersection point cannot travel faster than c.

AM

 

[Danger]

Danger, KingNothing - my thought experiment does not violate any laws of physics. Please note: I was not talking about the tips of the blades (which cannot close at >C relative to each other), I was talking about the intersection point of the blades. If you had a really long piece of paper, the cut would propagate at greater than C.

Sorry if I wasn't clear in my statement. What I meant was that it could never be physically achieved. That's why I called it a thought device. You'd never have enough energy available to accelerate the mass of the scissors themselves.