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 earth has mass and is moving, but it’s minimal enough that we can pretend these have no effect. We will pretend that the airport where you start is in an inertial reference frame. Inertial reference frames are usually easier to deal with, except when it comes to time dilation because it’s impossible to tell one inertial reference frame from the other which leads people into unintuitive (seemingly contradictory) conclusions.
Luckily, however, one of you gets in a plane which experiences significant acceleration. While accelerating (and decelerating), you are not in an inertial reference frame. This means we have a way point in the sand that makes it easier to compare. We can guarantee there is something about your experience which differs from your twin’s. Namely, time dilation.
While you are accelerating, your clock will slow down compared to anyone in an inertial frame of reference, but not to you. Your clock is your source of truth. Your body slows down, your metabolism slows down, your heart rate slows down, the clock ticking on the shelf slows down, even the very slight rusting of the fuselage between repairs slows down. From your perspective, everything is normal because it all slows down together. You can’t measure any change in clock speed.
This means, if your twin measures the plane moving for two ticks of his clock, your slower clock might actually only tick once. (The exact ratio, of course, depends on speed and duration of acceleration). So your brother aged 2 seconds during the flight, but you only aged 1 second. Your twin is now older than you by one second.
Remember the other side of time dilation is length contraction. So from your twin’s perspective, you are going a certain speed. That is a certain distance in a certain amount of time. Miles per hour means miles÷hours. From your perspective, you can measure your speed by looking out the window and seeing how much earth you fly over in how much time. Remember, it takes less time for you because your clock is slower… However, the earth will appear to shrink by the same factor. You will travel less distance in less time, but they cancel out perfectly and you measure the same speed.
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