An expanding wave of light.

[geordief]

If an expanding wave of light is viewed as a sphere which increases in size and propagates away from the source, is it fair to say that a portion of the wave actually moves at 2c with respect to a corresponding portion of the wave expanding in the opposite direction?

 

Is that true and does anything follow from that observation?

 

Or is it not true and is this an example of how relativistic speeds do not add linearly ?

 

Or is it perhaps an example of ,as I have heard the idea that you cannot use light as a frame of reference?

[Sriman Dutta]

You have to consider the spherical wave's two opposite wave fronts as two separate objects travelling at speeds c.

So for any one of the observers, observed velocity = (c+c)/(1+c^2/c^2) = 2c/2 = c.

That's how the system works ( as far as I have understood the concept, I'm a novice in this field).

[Janus]

If an expanding wave of light is viewed as a sphere which increases in size and propagates away from the source, is it fair to say that a portion of the wave actually moves at 2c with respect to a corresponding portion of the wave expanding in the opposite direction?

 

Is that true and does anything follow from that observation?

 

Or is it not true and is this an example of how relativistic speeds do not add linearly ?

 

Or is it perhaps an example of ,as I have heard the idea that you cannot use light as a frame of reference?

Any observer will measure one all points of the expanding wave moving at c relative to the center of the expanding sphere. Thus by their measurement, two fronts on opposite sides of the sphere are moving at 2c relative to each other.

This is true regardless of what velocity any of the observers have with respect each other, and in addition, each of these observers will measure that they are at rest with respect to the center of this expanding sphere of light.

This true until you try and consider how things look like from the perspective of something traveling along with the wave front itself, at which point you get nonsense answers. This is what is meant by not being able to use light as a frame of reference. You can't get meaningful answers once you try to consider the view of something traveling at c.

 

The non-linear nature of velocity addition comes up in the following way. Imagine you have a spaceship traveling at 0.5c relative to you and it fires a light beam to the front and back. By its measurement both light beams travel out at c relative to the ship at c. To get how fast each light beam travels relative to you as you measure things, you use the relativistic velocity addition theorem.

in one direction it is (0.5c+c)/(1+0.5c©/c^2) = c and in the other is is (0.5c-c)(1-0.5c©/c^2)=c. This is like I mentioned earlier, you both measure the light as traveling away at c from a point that is at rest with respect to yourself.

 

This formula is better illustrated when all the velocities involved are less than c. So let's take our ship and have him fire a projectile at 0.75c in the forward direction. By its measurement, the projectile is traveling at 0.75c in one direction relative to itself, while you are traveling at 0.5c in the other. For him the difference in speed between you and the projectile is 1.25c.

You, however, measure the projectile speed as being (0.5c+0.75c)/(1+0.5c(0.75c)/c^2 = 0.909c relative to you. conversely, someone traveling along with the projectile will measure you as moving at 0.909c relative to them.

 

The fact that the ship considers your and the projectiles speed with respect to each other is not a violation of Relativity, as this is being measured from a frame that is not at rest with respect to either you or the projectile. The c speed limit is for speeds relative to the one doing the measurement.