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
> 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.
The age difference is always *proportional* to the journey time. So, the thing you have to keep in mind about those “Twin Paradox” examples is that their trip timeframes are on the order of decades whereas your scenario’s trip timeframe was only a second.
To your brother, your 0.99c journey around the Earth takes ~1 second by his wristwatch; so he ages by ~1 second. At those speeds, however, your time/aging “slows” by a factor of Sqrt[ 1-0.99^2 ]=0.141 and so your wristwatch only registers 0.141 seconds from start-to-finish.
The difference between 1 second and 0.141 seconds means that he aged ~7x faster than you did.
Your example is just unusual in that those additional 0.859 seconds don’t *feel* like the kind of thing we use language like “much older than” for; but if you did 1-billion laps (i.e. ~1-billion seconds = ~32 years) then your brother aging 32 years to your aging 4.5 years would start to feel “much older than”.
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