Answer: Rather than a complicated answer you can do a thought experiment to understand time dilation and from there you’ll understand how it affects you.
So imagine you’re on a train moving REALLY fast, like, Japanese Shinkansen fast. And while you’re on the train moving really fast, you point a torch out the window and move it 1m up, then 1m down, up and down and up and down. From your perspective the torch just goes up and down and if we say it takes 1s each way, we’d say it’s moving up and down at 1m/s, right?
So now imagine you’re a bystander, standing on the side of the tracks when the train goes past and watching the torch go up and down. From the bystanders perspective the torch goes up and down but it’s also moving sideways so it makes a diagonal zig zag path; But remember for the person on the train it’s going up and down, not zig zagging!
This means that the bystander watching the torch follow its zig zag path, has watched the torch cover more distance but because it wasn’t going any faster and as far as they could tell, it took the same amount of time, that leaves time as the only variable that could have changed because the people in our thought experiment experienced it differently. And that’s how we prove time dilation exists.
As far as each person is concerned, time stays the same for them, but if a bystander is looking at them, the bystander will see the first person cover more distance without going faster which they can only do if time has slowed down to allow them more “time” to cover that extra distance. Time has dilated.
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