Answer to Question #290323 in Mechanics | Relativity for Arnica

Question

. List some ways our day-to-day lives would change if the speed of light were only 30 m/s.

Answer 1

No long range communication: having a conversation with someone who isn’t close at hand will result in really annoying delays. It would be like those satellite interviews, only in person. To send a message to someone on the other side of the world would take at least 5 days and 4 hours at the speed of light.

Leave your watch at home: The act of walking around would cause you to lose about half a second for every mile you walk, which isn’t to bad. But if you started moving around in a car at highway speeds (65 mph), then you could expect to lose about 17 seconds for every mile you travel.

“Super Speed”: One of the slick things about traveling at relativistic speeds is that, although you can only pass things at up to 100mph, you can actually cover more distance than the 100mph speed limit might imply. There are two ways to look at this.

From your point of view the world around you undergoes length-contraction. So, for example, at about 87mph you would see the world contracted by a factor of 2. So while you’d see things pass by at 87mph, you’d be eating up distance as though you were traveling at 174mph (2 x 87mph).

From everyone else’s point of view, you’re traveling through time slower. At 87mph they’d see your watch ticking at half the usual rate, so the trip will only take half the time it should.

Pretty colors: Even at running speed there would be enough relativistic doppler shift to change the colors around you. If you were driving past a yellow field of grain, it would appear blue in front of you and fade to deep red as it passed behind you.