I find it amusing that Einstein, who revolutionized time by making it relative, only implies it in his famous formula E=mc^2. Energy is timeless, so is mass, but c, which stands for the speed of light, needs time to have a quantity. It travels this distance in that time.
What really happens is that the light changes location, being constantly on the move. It was there, now it's here. And it went this way. That's just as true for any object in the universe. Planets move, galaxies move, continuously. Time is a way of describing change, but it isn't the change. The movement is. Time is a tool by which the observer can measure the change.
Light is again odd in this perspective, since time ceases to exist at its speed. If you could travel at the speed of light, time would stretch out infinitely. You would remain in the instant forever. That makes it impossible for you to at all perceive that you exist. So, light has no subjective existence. It only exists to us observers, traveling at a lesser speed.
So, with Einstein's formula as well as with other methods, we measure time by an entity that is timeless by nature.
Anyway, Einstein was far from the first to realize the relativity of time. That's how we all experience it. Sometimes it's slow, sometimes fast, and sometimes we forget about it completely, as if it ceased to exist for a while. The Wormhole episode mentioned how time goes faster the older we get, even presenting a formula for it. Alas, I know that.
What we relate to, and the whole universe with us, is change. If nothing changed, it would be like no time. Existence would be completely immeasurable. In all practicality, it would not exist.
The complexity of the universe as we experience it allows for countless changes. Every situation is in some way unique, separable from every other event. The sun rises and sets, day after day, but the view is never identical.
We live in a cosmos where its parts interact in patterns so complicated that no pattern is repeated. It's caused by what's called entropy, but I prefer the word disorder. Cracks in the uniformity increase. That causes change, which gives us the ability to perceive time passing.
Choosing time as a measure of change, we jump to conclusions about the universe. Because time consists of a past and a future, we search for a beginning and an end. Change in itself makes no such demand. We also expect some kind of continuity and consistency – again, that's nothing change in itself postulates.
Everything changes. Time, too. Maybe there could suddenly be a change of change, so that it stopped. If so, there would be no way of observing it.
The idea of change being a core ingredient in the world is well-established in ancient Eastern thought. It's even the title of one of the oldest Chinese books, I Ching, The Book of Change, traditionally used for divination. If you want to understand what might happen, you must start by accepting that everything changes, whether you like it or not. Be consoled by the fact that if there were no change, we wouldn't be.
Time is a line from the past to the future, but we really have no other experience of it than the moving point on the line that is the present. At any given moment, we are in the present, with both the past and the future elsewhere. That's how we experience it. Time is not a boat ride, but a stream passing us as we stand firmly in the middle of ourselves.
I look in the mirror and can compute, although with some difficulty, that I've grown older. Well, my face has. But me, I'm the same. It doesn't happen to what's really me, whatever that is. Time is no illusion, but it's not an adequate description of what we go through in our lives. It's just one way of looking at it.