Exploring the Speed of Light: Beyond the Beam of Light

[Lesnick]

Is the speed of light what they call the front velocity, the formost part of a beam of light?
If this is so the actual path of the electromagnetic wave must travel further than the distant traveled by the beam of light. So any point along the path of the wave must be traveling faster than the speed of light. Is this so or is it complete nonsense

 

[HallsofIvy]

I don't know what you mean by "the formost part of a beam of light". Nor do I have any idea how a "point along the path of the wave" can move at all!

 

[Lesnick]

Sorry i didi not express this very clearly, I'm a little unsure of the terminology.
According to my physics books A pulse of light has a phase velocity the speed of the ripples, group velocity the speed of the evelope and a front velocity the formost part of the pluse. The ripples or waves must travel futher because they are not traveling in a straight line

 

[russ_watters]

This is a common misconception caused by too-strict of an interpretation of the wave nature analogy of light. Light is not a wave in the way waves on the ocean are waves. And even if it were, the propagation speed of a wave is the speed in the direction of propagation, not the speed of a hypothetical point that is riding the wave. Remember, there is no physical thing in a water wave moving at the speed of the water wave. Individual water molecules travel in a circular pattern as the wave passes: they do not travel with the wave.

 

[sophiecentaur]

Why are they not traveling in a straight like? Take any point on the crest of a 'ripple' and that point will move ever-outwards in a straight line. But the energy will, of course, be spreading outwards in all directions on a curved wave FRONT.

 

[edguy99]

Sorry i didi not express this very clearly, I'm a little unsure of the terminology.
According to my physics books A pulse of light has a phase velocity the speed of the ripples, group velocity the speed of the evelope and a front velocity the formost part of the pluse. The ripples or waves must travel futher because they are not traveling in a straight line

I don't think it is correct to think of the phase velocity as not traveling in a straight line, but more the idea of a wave within a wave that is traveling at a certain speed.

You may have seen the image from http://en.wikipedia.org/wiki/Group_velocity that illustrates this, I think the green dot would be considered the "group velocity" or the "speed of light" as generally understood. Notice the red dot (phase velocity) seems to go faster...

One question I like to ponder: Perhaps the designer of this animation should have the red dot start on the "group wave" behind when it reaches the end of the "group wave", rather then move to the next "group wave"...

 

[sophiecentaur]

@Lesnick
Are you assuming some sort of 'side to side' movement here? There is no movement.

 

[watchphysics]

I appreciate the question you asked, and clearly this arises due to the analogy of wave and particle nature of light. But due to your question i came up with What's the oscillates of a electromagnetic wave? I found the answer that Electormagentic wave oscillates which doesnot require any medium to travel with. My problem is why does it oscillates. I don't see any significance that a eletromagentic energy needs oscillataion. Please let me know if i m thinking wrong?

-BP
http://watchphysics.com

 

[jambaugh]

Light, and other electromagnetic waves don't have to be pure frequency waves. With this in mind you may be better able to understand the speed of light by imagining a charged particle sitting at the origin for a long time. You find the electromagnetic field around the particle to be the static Coulomb E field. Now imagine you suddenly move the particle a short distance. The electromagnetic field doesn't suddenly change over all space at the same time but rather the change propagates outward at a speed, c.

We can break this down into the propagating changes in the E and B fields via Maxwell's equations. Changes in the B component induces changes in the E component and vice versa. But remember, though we write the E and B fields at a point as vectors these are not vectors indicating actual motion or displacements of anything through space, they have no spatial extent but rather indicate potential direction and magnitude of effect if a charge were to be at the given point. The EM field at a point affects the EM field at neighboring points in a way expressed by Maxwell's eqns so that it propagates at speed c. (And then with relativity we see all observers measure the same c in all directions... in vacuum)

Now with phase velocity and group velocity issues remember you are talking about waves of a certain type and we can break them down into sinusoidal components. A sinusoidal wave is one which is being emitted over infinite time so there is no issue of causal propagation faster than c.

The way I visualize e.g. faster than c phase velocities is with the giant scissor analogy. If you have a pair of very long scissors and try to close them at the handle your effect will propagate down the length at no more than the speed of light. The scissors necessarily deform and the crossing point must travel at < or = c. (it's more like two whips than a pair of scissors.)

To keep the scissors from deflecting you would need to position say rockets along the lengths with timers preset to go off so that the two halves begin moving all at once. Then the crossing point (where it cuts) can move at arbitrarily large speeds but it is clearly understood that this point is not a causal signal, it is simply an abstract point you define for a sequence of effects which were preplanned by the earlier causal signals you used to set the timers on the rockets.

You can look at either the phase or group velocities of a wave packet as being like the crossing point of the above scissors. They can move faster than c but only due to the cumulative effect of earlier causal signals which themselves propagated at or below c.