# Greater than c

1. Dec 15, 2004

### 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/

2. Dec 15, 2004

### ZapperZ

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

Zz.

3. Dec 15, 2004

### marlon

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

4. Dec 15, 2004

### KingNothing

Hey ZZ, can you explain phase velocity?

5. Dec 15, 2004

### da_willem

phase velocity is the velocity at wich 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.

6. Dec 15, 2004

### Staff: Mentor

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).

7. Dec 15, 2004

### 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 travelled 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 travelled a distance of 1. So the edge of the lit region has averaged over twice the speed of light.

8. Dec 15, 2004

### 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.

9. Dec 15, 2004

### marlon

great example ceptimus...

this is one to remember...

regards
marlon

10. Dec 15, 2004

### rbj

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

11. Dec 15, 2004

### Tide

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!

12. Dec 15, 2004

### 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

13. Dec 15, 2004

### 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.

14. Mar 6, 2005

### spacetime

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

15. Mar 14, 2005

### 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.

16. Mar 15, 2005

### da_willem

No they won't!

17. Mar 15, 2005

### 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.

18. Mar 15, 2005

### Andrew Mason

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

19. Mar 15, 2005

### Andrew Mason

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

20. Mar 15, 2005

### Staff: Mentor

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.

Last edited: Mar 15, 2005