Why would you experience time differently when moving at the speed of light?

The problem with the concept of time dilation - as well as the rest of relativity - is that it’s not very intuitive. We like things that are intuitive and we can wrap our heads around, but relativity is just not one of those things.

All of it is dependent upon the fact that the speed of light is constant regardless of the relative speed of the observer. This doesn’t match what we observe intuitively for massive objects. For example, if I’m on a train car moving at 20 km/h, and I throw a ball backward at that same speed, I will observe that ball moving away from me at 20 km/h. However, to a stationary observer, the ball will appear to drop straight down. Mythbusters did a demonstration of this effect with a soccer ball fired from a truck:

To an outside observer, the velocity of the ball is the combined velocity of the throw plus the motion of the car, therefore its velocity is zero.

Light doesn’t do this. If I shine a laser beam and had some way to track the speed of it, it would appear to move away at the speed of light ([math]c[/math]). However, no matter how fast I’m moving, when I fire off the laser beam, a stationary observer will also observe the laser beam moving at [math]c[/math]. This is counterintuitive and doesn’t “make sense” - how can light appear to move at the same speed, relative to observers moving at different speeds themselves? Weird as it is, it just does, and we have observational evidence that this is true, not just a wacky theory.

So what does that have to do with time dilation?

Let’s say we’re back on the train car, and this time I have a laser beam, and the side of the train car has a mirror on it. Facing the mirror, I fire off a laser beam and simultaneously start a stopwatch. When the laser beam has had a chance to bounce off the mirror and come back to me, I stop the timer, and write down how long it took.

Outside the train we have an observer who starts their stopwatch at the same instant the laser beam starts, and stops it when the laser beam returns from reflecting off the mirror. From their perspective, though, the train (and everything on it) is in motion, meaning the path the laser beam had to travel is longer.

Left, observer in the train sees the laser go the distance L, and back. Right, external observer sees the laser travel distance D and back to account for the forward motion of the train.

So far so good right? Here’s where it gets weird. Since the external observer sees the laser beam traveling at the speed of light, just like I do inside, from their perspective this event takes longer to unfold. Their stopwatch will show more travel time. Our stopwatches disagree, even though we witnessed the same event happening. I, as the observer on the train, experienced less time go by than you did on the outside - in effect, everything inside the train appears slowed down relative to you.

This only really matters if you’re going really fast, of course. In real terms, even on a very fast train, the difference in observations will be so small that we can’t really detect it. But it’s there, and the closer you get to the speed of light, the more exaggerated the effect.

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