# Q & A: How Time Dilation Occurs

Q:
do you know" why" time slows down if you are travelling near the speed of light? relative to someone who is not. is it because when time or light leaves you at say 1oclock it shoots out in all directions ,so if you are traveling at near the speed of light you are catching that light up ?
- derek (age 34)
glasgow
A:
Dear Derek,

That is certainly an interesting question! And yes, your reason that we "catch up" with the light is indeed one of the oddities that can only be resolved if time slows down.

This is how it happens:

The speed of light is always a constant to any observer, and let's call it c. What's so significant about that? It is actually very odd. Imagine a person, say Mary, in a rocket moving at v meters/second. She is holding a flashlight pointed to the front, and she turns it on. So to Mary, light rushes off away from her at a staggering speed c. This makes sense, because to Mary, light has to travel at speed c. Now imagine that John is standing still and looking at Mary's flashlight. According to John, the light does not rush of at a speed of (c + v)meters/second, but just c!

Something must be wrong – a ball thrown forward by a passenger in a car must move faster than one thrown by a stationary guy because the car is moving. But light does not behave like ordinary objects. According to both Mary and John, light travels at speed c, no more and no less.

So how does the fact that time slows down come into the picture? According to Einstein's Theory of Relativity, it turns out that both time intervals and distances depend on the motions of the observer. To John, Mary's spaceship is shorter (in its direction of movement) and Mary's watch ticks slower, i.e. her time passes at a slower rate. Interestingly, to Mary, John's "distances" are also shorter and his watch also ticks slower. This is because of the fact that both Mary and John's points of view are equivalent – both are moving relative to the other, and no point of view is more "special" than the other. After accounting for these effects of what we call time dilation and length contraction, light moves at the same speed for both observers.

demonstrates the concept neatly.

Hope this helps!

- Mae

(published on 12/16/2010)

Q:
Well, according to the twins paradox, Mary is suppose to age slower than John because shes moving near C relative to John. But if relative to Mary John is travelling near c and relative to Mary John's clock ticks slower as you previously stated, isn't John suppose to age slower than Mary? So in the end, who does age slower???
- Anonymous
A:
So long as they continue in fixed relative motion, there's no objective way to say. Say at time t=0 they started at the same age and the same place. Later on, each wants to see how much the other has aged. They get a picture of the other sent to them. The picture looks young, but they have to make some allowance for the time it took to send the picture, since it was taken a while ago. After making that allowance, each concludes that the other was still not aging as fast as they themselves were. However, each says that the other did not make a big enough allowance, since according to them the relative speed of the light and the other observer was less than c. they each have a consistent account, equally good.

In order to make a comparison that everyone will have to agree on, we have to get John and Mary back to the same place at the same time. Then we can take a picture and everyone in any frame can look and see who aged more. That means that one or both of John and Mary have to change their motion, i.e. accelerate. Say that it's John who fires his rocket engines and accelerates back toward Mary. He no longer is using a non-accelerating frame, so our old rules describing how things look from his point of view don't apply. Mary's frame is ok. She says John isn't aging fast enough, so she must be right. We conclude that John's acceleration back toward Mary must make him see her as aging faster. We can get quantitative about this, figuring out how things look from accelerating frames.

If we then add one more principle, that one can't distinguish between the effects of gravity and acceleration, then we have the ingredients for General Relativity.

Mike W.

(published on 05/08/2011)