In this thought experiment, my twin brother and I are both turning 20 at the airport.
At midnight on our birthday, we are both exactly age 20 years.
He stays put while I get on a 777 and fly around the world. The flight takes me 24 hours and so he waits 24 hours. I arrive and we are both age 20 years plus 24 hours.
If I instead get on an SR-71 and fly around the world at 3x speed of the 777, the flight takes me 8 hours so he waits 8 hours. I arrive and we are both age 20 years plus 8 hours. Clearly, we are both younger in this scenario than the first one.
If I got onto a super plane flying at 0.99x light speed and fly around the world, the flight takes me 1 second. Since I’m so fast, he should also only wait one second. Intuitively, I’m back and we’re both 20 years and 1 second old.
But my understanding of time dilation is that I’m 20 years and 1 second old when I’m back, but he would be much older since I was almost going at light speed.
Why is that? My flight and his wait time should both be much much shorter since I was flying much much faster.
In: Physics
The example you’re giving is making some bad assumptions. I think you’re getting hung up on some specific things:
1. You’re hooked on the distance you travel. Distance doesn’t mean anything. It might be a fun fact “how far did you travel?” but it’s not important. Time dilation is actually about *how long a moving observer spends at their speed*.
2. You’re making the assumption that at 0.99c, time dilation would do something crazy and your brother would be years older when you get back. You’re looking for a smoking gun, but there isn’t one.
In scenario one, it’s 24 hrs vs 24 hrs. Speeds are low, so no notable time dilation. A 777 flies around 950 km/hr, or 0.26 km/s.
In scenario two, it’s 8 hrs vs 8 hrs. Again speeds are low compared to light, no notable time dilation. An SR-71 flies at about 1 km/s.
You got hung up on the fact that “in the time it takes to go around the world”, 8 hrs have passed. We’re both younger. Younger than what? Than if it took 24 hrs to do the same task. We might as well standardize it to 24 hrs. You make **three** flights around the world. You both observe 24 hours difference. In reality, you experienced 0.999999999994 x 24 hrs. This isn’t showing up on a stopwatch though. It’s 0.02 nanoseconds.
When you’re flying around at 0.99c, you’re travelling at 296,794.5 km/s. In one second you make 7.42 trips around the world. At 0.99c, the Lorentz factor for time dilation is about 7.1, meaning that you will experience time 7.1x slower than your brother (i.e. he will age 7.1x faster than you). If you only fly like that for 1 second, that’s 7.1s for your brother. Your watches could tell you that. Pretty cool.
But lets standardize it for *time spent* flying. If you spend 24 hrs flying at 0.99c, then your brother is going to age 7.1x more than you. You’re going to land and be one day older, and he’ll be 7 days older.
7x isn’t very exciting, and it’s why you’re not seeing that smoking gun. While 0.99c is wicked fast, it’s not movie-script-crazy. You were looking for some smoking gun that says your brother is going to be 5 years older or something while you were only doing a single trip around the world.
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