Unified space-time starts to make sense if we think that the speed of light is a relationship between the distance traveled over time.
Because the speed of light can't change, your laser beam won't go any faster. The measurement of distance and time must be changed instead, depending on the state of motion. This leads to effects known as "space contraction" and "time dilation."
As you work at your desk, you move through time, but not through space. A cosmic ray moves over vast distances at nearly the speed of light but takes little time.
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