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Relativity of Distances
"No matter how fast you chase or flee light waves, they will always seem to approach you or recede from you at the speed c" - Matt Strassler
"Speed may be relative, but the speed of light waves, from everyone’s perspective, is always the same. Though this seems logically impossible, and common sense may protest at this seemingly absurd claim, the relativity of times and relativity of distances save the day" - Matt Strassler Self-referential? Waves in an Impossible Sea by Matt Strassler Basic Books, 2024 Extract: No less weird, though perhaps less nightmare-inducing, is what happens if you try to retreat from light waves that are already receding from you. They’ll seem to slow down. You’d naturally expect that if light is moving away from you to the south at the speed c, and you start moving north, then the distance between you and the light will grow at a speed faster than c. But that’s not the case— at least, not from your perspective. As you see it, the light will slow down in just such a way that the distance between you and the light still grows exactly at the cosmic speed limit. No matter how fast you chase or flee light waves, they will always seem to approach you or recede from you at the speed c. Bizarre as this may seem, Einstein’s point was that it’s required by Galileo’s principle. If light waves did anything else, you could use them to determine your own rate and direction of motion. If you’re moving steadily, light must behave just as though you’re not moving at all, and so the speed with which it approaches or recedes from you from any direction must always be the same. This is utterly different from sound. We describe “the speed of sound waves” as about one-fifth of a mile per second at sea-level pressure. But if all speed is relative, then what does this mean? Implicitly, we mean that sound’s motion is to be measured relative to its medium; sound waves move at one-fifth of a mile per second relative to the air. But from the perspective of someone at our galaxy’s center, viewing the sound waves traveling from you to me as carried along with the Earth and its atmosphere, those same sound waves would instead be moving along with us at a speed of roughly 150 miles per second. Only observers who see the atmosphere around them as stationary will view any and all nearby sound waves as moving at the standard speed of sound. But by “the speed of light waves,” we must mean something else. We can’t mean light’s speed relative to the luminiferous aether, because speed relative to an amotional medium has no meaning and can’t be measured. Indeed, we mean the waves’ speed as measured by any and all observers. Speed may be relative, but the speed of light waves, from everyone’s perspective, is always the same. Though this seems logically impossible, and common sense may protest at this seemingly absurd claim, the relativity of times and relativity of distances save the day. They precisely compensate for each other whenever we use our own rulers and our own clocks to measure the motion of a light wave. This all sounds like something out of science fiction or a dream. But its reality is something our cell phones take for granted as they guide us through unfamiliar towns. GPS navigation requires extremely precise timing, and the differences between Einstein’s formulas and Newton’s older ones are too large to ignore. If you disputed Einstein, you’d soon end up in the wrong neighborhood or driving off a cliff. Unlike gravitational waves or electromagnetic waves, the waves of many other elementary fields move below the speed limit. That’s true for the Higgs field, for instance. |