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Why do we say that light travels at a speed?

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?