Okay. I've come up with a different way to explain time dilation:
Imagine you're racing your car in the salt flats. There's a start and a finish line, but the racetrack is very wide; it's the salt flats, so there's no curb and no shoulder.
Now imagine your car only goes 60mph. If it's 10 miles between the start and finish lines, it'll take you 10 minutes to complete the race. But if you don't drive straight, but drive at a diagonal, it'll take you a little longer. Some of your constant speed of 60mph isn't being applied in the start-finish direction, it's being applied in the side-to-side direction. The more diagonal you drive, the more side-to-side you're going, and the longer it takes you to complete the race.
This works because you car only goes 60mph. No more, no less, so there's no way for you to make up lost time. The 60mph is constant, how you apply it to the two dimensions in the example (side-to-side and start-finish) is up to you.
Now, this is the leap that Einstein made: The speed of light is constant, and everything is always moving at the speed of light. Everything. But now we're not talking two dimensions; we're talking four. Up-down, left-right, forward-back (our regular 3D world) and, for the fourth dimension:
Time.
Rather than time slowing down, think of it this way: The more of the total speed you're allowed (the speed of light) that you apply to motion in the three spatial dimensions, the less you have available to move through time. And as you move through time more slowly, you age more slowly, your watch ticks more slowly, everything happens more slowly.
As it stands now, most of our lightspeed allotment is applied toward motion through time, so increasing our speed through space a small amount, as in the Mt. Everest example, takes very little away from our motion through time.
If a car goes 120mph around a racetrack, and it takes 30 seconds to complete a lap, as measured by a stationary bystander, the driver will clock that very same lap, from aboard the racecar, as having taken 29.99999999999952 seconds. A little difference, because in the bigger picture, he was only taking a little more of his lightspeed allotment and applying it toward motion than the bystander.
But if the car went 99.5% of the speed of light, the time dilation increases to a factor of ten. At this speed, if the bystander measures 30 seconds for a lap around the track, the driver measures only 3.
And since photons are the only things that move, through space, at the speed of light, it means that there's nothing left over to use as motion through time.
Light, then, doesn't move through time at all--it never gets any older. Light emitted from the big bang is the same age today as it was then.
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