Why do we say that light travels at a speed?

Question

According to Einstein's theory of relativity, the more speed something has the slower that time passes for it; and presumably when traveling at the speed of light, time stops entirely. So this means that when a photon is created, the rest of existence virtually pauses until the photon ceases to exist, and then the rest of existence begins again. If time is stopped while the photon exists, then what are we measuring when we measure light? In order to measure the actual photon, we would need to take the measurement while time was standing still. Speed requires time, so why do we say that light travels at a speed?

Answer 1

It's simpler than you think. When we measure the velocity of light we are simply measuring how much distance light travels per second. For example if we send a very short laser pulse to a reflector on the Moon and wait for it to return we find it covers the 768,934 kilometer round trip in about 2.56 seconds. This is measured in the Lunar Laser Ranging Experiment.

You're quite correct that time dilation tends to infinity as the relative velocity tends to $c$, but we don't care what's happening in the rest frame of the fast moving object. When we measure a velocity we measure the time in our frame and the distance in our frame.

Answer 2

If I (on the Earth) and you (on a very fast rocket) measure the time that takes you to travel a certain distance we would not agree. Still, nothing forbids me to compute your velocity using my measures of time and distance. The interesting point is that if your rocket is made of photons, even a third person trying to chasing you will agree with my measured speed. This happens because of the combination of time dilation and length contraction (the person moving with respect to me sees a shorter distance, but his time also goes slower, both of the same factor $\gamma$), he will always agree with me unless he reaches your photonic speed somehow braking relativity. That is just how relativity works: time is not absolute, speed of light is!

Answer 3

what are we measuring when we measure light?

When considering "(average) speed of light (in vacuum)", or rather primarily: "(average) speed of a signal front" this means the quotient of

• the distance of a signal source and a receiver between each other (i.e. under the condition that these two participants had been at rest with respect to each other), divided by

• the duration of the signal source from its signal indication, until its indication simultaneous to the reception indication of the receiver (or equally the duration of the receiver from its indication simultaneous to the signal indication of the source, until it's (the receiver') reception indication).

By the definition of (how to measure) distance between two participants who were and remained at rest with respect to each other as $$c/2 \text{ ping duration},$$ where $c$ is foremost some symbolic parameter which is distinct from Zero,
therefore the value of the "(average) speed of a signal front" can be directly calculated and obtained as $1 ~ c$; or for short: $c$. (That is to say there is no reasonable measurement involved at all, but the result value is obtained as a theorem.)

According to Einstein's theory of relativity, the more speed something has the slower that time passes for it;

That's an unfortunate, imprecise, improper statement. Let's better say that geometric and kinematic relations between participants (such as speed, or curvature) must be accounted for, in order to compare their individual durations to each other.

The details of how to carry out such comparisons can of course be derived; beginning with comparisons between participants who move "uniformly" (straight, and with constant average speeds) with respect to each other. As a consequence, some non-zero value of duration can not be attributed to a signal front "itself".

Addendum:

To address the title question:

Why do we say that light travels at a speed?

Strictly, we don't say that "light travels", which might suggest some particular "path, or curve" being "travelled along"; but rather that signals had been "exchanged" (between some particular source and receiver), without any further presumption of geometry, but in order to establish geometric relations (involving that source and receiver, and perhaps additional identifiable participants) in the first place.