How can light have a speed when it devies what speed is?

Question

For us to measure any movement, the "something" has to have a different position to some reference frame. now speed is defined by the amount of changed position( which we can tell by the reference frame) inside a certain amount of time. now assuming light moves at a certain speed, now has a reference frame implied by the very definition of speed. Following this, anything that has displacement over time can so on measure different speeds depending on the frame. However the "speed of light" does not follow these same rules in logic, so my question would be why call it speed when it clearly devies what speed is supposed to represent?

Answer 1

You are quite wrong to say that light does not move relative to anything. If you and I stand together and flash a light, it moves relative to both of us at the speed c. If you walk at a metre per second in the direction of the light, then light moves at a speed c relative to me and at a speed c relative to you. The fact is that light moves at a speed c relative to everything, which is not the same as your claim that it moves relative to nothing.

The speed c is about a foot per nano-second. If you were to flash a light at a detector a thousand feet away, it would be detected after a microsecond. There is no conceptual difficulty in defining the speed relative to you- it is simply the distance travelled by the light in your frame divided by the time taken in your frame. If were to speed past you at 0.5c toward the detector just at the moment you flashed the light, the speed of light would be c relative to me too. In my frame the light would have travelled less than 1000 feet to reach the detector, and it would have taken less than a microsecond to do so- the distance and the time would both be reduced in my frame so that dividing the former by the latter would still be c.

Conversely, if I sped past you at 0.5c in the opposite direction just as you flashed the light, then in my frame the light would travel a longer distance to reach the detector and take a longer time, but again the ratio between the two would still give the same speed, c, in my frame.

So the speed of light is the same in every frame, and is simply the distance travelled in any given frame divided by the time taken in that frame.

Answer 2

This question really shouldn't receive down votes (punctuation notwithstanding) since it is entirely logical for Galilean relativity. You fire a laser pulse with wavenumber $\vec k$, and then just boost along $c\hat k$, et voila: the laser is stationary.

Of course Galilean relativity is wrong, and there are no reference frames at $c$, and we need to use Lorentz transformations.

Back to the question: distance over time. Say you fire the laser at

$$ E_0 = (ct_0=0, x_0=0) $$

and then detect at the end of your length $L$ table:

$$ E_1 = (ct_1 = cL/c = L, x_1=L) $$

and measure the speed:

$$ v_S = \frac{x_1-x_0}{t_1-t_0} = \frac{L}{L/c} = c $$

($S$ is the lab frame).

Now boost to a frame moving along $x$ at $v$:

$$ E_0 = (ct_0'=0, x'_0 = 0) $$ $$ E_1 = (ct_1' = c\gamma[t_1-\frac{vx_1}{c^2}], x'_1 = \gamma[x_1-vt_1]) $$ so $$ v_{S'} = \frac{x_1-x_0}{t_1-t_0} = \frac{\gamma L}{\gamma L/c} = c $$

No problem. Everyone agrees, $c$ is the limit.