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
Time dilation goes together with length contraction. Basically, whether we as the observer are moving or not, we don’t know. We only know that an object is moving relative to us. So in your example, despite you flying around the world in the airplane, you don’t actually know that. To your frame of reference, you are hovering in standstill in the airplane, while it is the world that actually zooms by. To your brother’s frame of reference, he is standing still on the ground, while it is the earth that actually zooms by.
Objects with relative velocity have length contraction, in the direction of travel. So for example when your brother looks at your airplane, he sees the airplane zooming by, but the airplane appears shorter. Meanwhile, you in the airplane think that you are hovering in standstill, with the earth zooming by, but objects on the earth appear squished with smaller distances in length.
Now, there is also time dilation. According to special relativity, the amount of time lapse is not agreed upon by different observers of different frames of reference (observers of different velocity relative to each other).
>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.
So this is where the misconception happens. Time dilation and length contraction are tied together by a very simple set of algebraic equation: Time A = Constant * Time B. Say your brother is on the ground measuring with a stopwatch. He measures that Time A elapsed from takeoff to landing. For you traveling in the airplane, you measure that Time B has elapsed. The constant is related to the speed of the airplane where constant = 1 occurs when the airplane is moving at 0 speed, and constant = infinity occurs when the airplane is moving at the speed of light (the constant is an exponential speed measurement, relative to the speed of light).
So based on this equation, because you are going so extremely fast, you and your brother will disagree on how much time has elapsed from takeoff to landing. Your stopwatch will display less time than your brother.
Less intuitively, we can also speak of this in terms of length contraction, which from your standpoint the earth is squished and feels like you traveled less distance than what we know the earth’s distance to actually be from the stationary observer. To me this is less intuitive of an explanation.
>Why is that? My flight and his wait time should both be much much shorter since I was flying much much faster.
The constant in that equation works in such a way that no matter who’s speed, everyone will agree that the speed of light is 3e8 m/s. That’s just the way it is. Within a single frame of reference (a frame of reference are all objects traveling at the same speed relative to each other. Meaning, they all appear stationary to one another), then the laws of physics are the same for all off them. But only for the people within that frame of reference.
Second, the speed of light is the same for everybody, *regardless of their speed*. That’s kind of hard to wrap your head around, but that’s just the way it is. So, as a result of this, because you and your brother are moving at different speeds relative to each other, the two of you can’t agree on events that appear synchronized, and you also can’t agree on how much time has passed, or how much distance you have traveled. The only thing you can agree on is what the speed of light is.
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