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
You’re assuming a constant flow of time in your scenarios, but constant time is a misunderstanding caused by the fact that most everyday objects are not traveling fast enough to experience time dilation in a meaningful way.
In all three cases, your assumptions are wrong.
As you are moving relative to your twin, your experience of time is no longer identical to his. Specifically, time will move slower for you than it does for your brother, in all scenarios. The amount by which it changes is tiny over the scales you’re talking about, but it is there.
On your 777 flight, your time will be a few millionths of a second off from your brother’s. This, by the way, has been experimentally measured and confirmed. We have clocks that are sensitive and precise enough to measure differences on this scale, and when taken on trans-Atlantic flights the clocks that were flying ticked a slight bit less than the clocks on the ground.
And obviously, as you speed up, your time will dilate further and further. It still isn’t going to dilate to the point where you’ll notice it without an incredibly precise clock – you need to move much faster for time dilation to be noticeable on human scales. But in all cases, there will be measurable dilation.
Incidentally, the GPS satellites are moving fast enough that they have to correct for relativistic effects in order to remain accurate.
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