# Speed of Light Question

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1. May 6, 2015

### ScienceGuy30

Hello everyone! Recently my work has been more involved with high energy physics. I have been looking into some things, and I would like help with an understanding of the speed of light. So far, the main ideas I have seen have been thought experiments, with minor (if any) direction to experimental verification. I have two points, that if clarified, would help with my understanding.

1) One thought experiment that keeps coming up as an example is the light clock. The main idea is that a beam of light is reflecting off two mirrors, which can be interpreted as a clock. The thought experiment takes the same clock and gives it a transverse velocity (perpendicular to the direction of travel of the light in the clock). In the reference frame of the light clock, the period seems to be straightforwardly the same. However, looking in as an observer, the light clock will move in both the x and y directions. They go on to say that the time is distorted to allow for light to travel at "c". I do not see how the new speed does not become c'=sqrt(c^2+V_perpendicular^2) in the observer reference frame.

2) It is known that particles can exceed the speed of light in a medium (incurring Cerenkov losses along their path). What is the actual process for why the light is slowing down? Is it related to the light being absorbed and re-emitted from the particles in the medium (thus slowing it down?) or is it intrinsic to the mass actually interacting with the photons (or something else)? If the light is being absorbed and re-emitted, then we should see the lengthening of the pulse of light as it travels through a medium (I am basing this off nuclear absorption cross-sections for photons).

2. May 6, 2015

### Staff: Mentor

You just gave the answer in your previous sentence. In the frame in which the light clock is moving, the light travels a distance $\sqrt{x^2 + y^2}$ from one mirror to the other, where $x$ is the distance the clock as a whole moves and $y$ is the distance between the mirrors. The light takes a time $\sqrt{x^2 + y^2} / c$ to travel this distance, according to this frame, so its speed remains $c$.

Note that the above result is not dictated by theory; it's dictated by experiment. We use the theory of special relativity, in which the speed of light is invariant and moving objects appear time dilated, because that is the theory that matches experiments.

These aren't really two different ways the light slowdown could happen; they're just two different descriptions of the same process. Mass interacting with photons is photons being absorbed and re-emitted.

I don't know whether this is observed experimentally or not, but it's worth checking.

3. May 6, 2015

Dispersion.