Monday, January 7, 2013

Relativity (specifically time dilation)

Recently a buddy of mine started dating a girl with two kids (aged 8 and 10... I think). We had them over for dinner a little while ago and as they were leaving they asked a question that brought up relativity (dont remember the exact question unfortunately...) I gave a quick quick answer, but I don't think I did it justice and would like to do a full blown "how to explain stuff to your kids" answer (also because I havnt posted here in a while)

I remember the crux of their question being time dilation, so I'll try to focus on that for now, and maybe post more in the future on the other aspects of it.

I would start by using the "light clock analogy" (I didn't feel like animating this myself, so I found a copy off google images)

(depending on the age) I'm sure you've heard E=MC^2 and if not, its one of the most well known physics equations from Albert Einstein (one of the most known scientists of all time). E stands for energy, M stands for mass, and C stands for the speed of light (which is very very very fast)

Lets find out what that all means!

Energy is the stuff that allows anything, to do anything. Every time you stand up? your body is using energy stored in itself to do that. When you turn on the lights, energy from the electricity is making them work. When you see something on fire, the heat and light that comes from the fire is energy that was stored in the wood.

Mass is the amount of "junk" something has. A simplified way to think about mass is using weight (this only works if everything is on the same planet because two identical baseballs on the earth, and on the moon weigh differently, but the have the same amount of stuff. This is because the moon's gravity is pulling down less.) We are both on earth, and I weigh more than you, so I have more mass. A giant bag of feathers may be bigger than a bowling ball, but because it weighs less, it has less mass. (Mass is not the same as weight, I will explain another time a little better, but this is close enough for now)

The Speed of light is SUPER CRAZY VERY FAST. Its 670,616,629 miles per hour.  Typical bikes can go 10-20 miles per hour. The moon is 238,900 miles away, that means if there was a road (with gravity and air) it would take you one year, and 4 and a half months to bike there. Light takes 1.24 seconds to get to the moon. Its the fastest thing possible in the universe.

The thing that got Einstein thinking about relativity is the fact that the speed of light cant be sped up. Most everything else in the universe can be sped up. If you throw a ball forward 20 miles an hour while you are in a car going 20 miles an hour the ball looks like its going (about) 40 miles an hour to someone standing on the side of the road (its not exactly 40 miles an hour, but close enough, we can look into this more in the future). If you hold the ball in your hand, it doesn't look like its moving at all, but if you are in a car going 20 miles an hour, its actually going 20 miles an hour relative to someone watching on the side of the road.

Here is where relativity comes in. If you noticed I said "relative to". Relative to means "compared to". Pretty much everything in the universe can be looked at differently depending on who is looking at it. A car looks pretty big close up, but if you are far away it looks very tiny. If you are in a car going fast, a house that is standing still, looks like its going past you very fast even though its standing still compared to the earth.

The weird thing about light though, is no matter where its coming from (even if its on a car going a MILLION miles an hour) light always goes the same speed. (We have tested this in almost every way possible and we always find this to be true) Its always the same speed no matter what. This causes some problems that I will show you.

Look at this light "ping pong" clock. Imagine you can slow down time to look at light, and imagine you have 2 mirrors with a bit of light bouncing back and forth between them forever.

Notice how the clock on the left and the clock on the right are not in sync? This is because the clock on the right is moving, and because of that it has a longer distance to travel. Take our a ruler and measure to verify for yourself.

The clock on the right is actually slower (it takes longer for the light to bounce back and forth between the same mirrors) than the clock on the left. This shows that the faster you go, the more time slows down for you (but only you) You don't normally notice this because light is so fast, so the amount of time that is slowed down by going as fast as humans can isn't really noticeable. But we tested this by sending a very accurate clock up in space in a spaceship that was going around the earth (this is called orbiting) very fast. After a while when it came back down, we compared the clock to another very accurate clock we kept on earth, and it was off by 0.007 (not a lot, but enough to prove Einstein right!)

So we know this works, but WHY is the speed of light a constant? I don't like to answer why questions in science because it implies purpose and a pre-defined goal. The speed of light is one of the things that we found out through testing a lot of stuff. There could be a hidden mechanism that prevents light from going faster than its current speed, but for right now we don't know.

There is a lot we still don't know today, and that's what makes science exciting. It seems like every time we figure something out, two more questions pop up that we cant answer. Its like a puzzle that keeps making new puzzles. :)

So the moral of this story is that faster you go (the closer to the speed of light you are) the more time will slow down for you, and the more everyone else around you will look to be going faster.

(Just wanted to point out, that there was a typo in the statement: "The clock on the right is actually slower (it takes longer for the light to bounce back and forth between the same mirrors) than the clock on the right." that an anonymous comment caught, thanks!)


  1. Please can you analysis in my web site ? Thanks.

    1. what do you mean by analysis? What specifically did you want me to do with your website?

  2. loved how you explain time dilation. very easy to grasp compared to other sites. Thanks a bunch!

    1. Thanks! If there is anything else you'd like explained in this manner, feel free to add suggestions :)

  3. Can you explain dimensions in this manner too? Thanks.

  4. I want to cite your information for a project I am writing, and I would like to give credit where credit is due.

  5. Thanks Man!.i gonna put you up in our site!

  6. This is by far the best explanation I have seen of time dilation.

  7. Thank you. There is one question I have always had regarding this explanation.
    In kinematics we 'consider' the horizontal and vertical distances separate. Such as dropping a bullet vs shooting a bullet; they both hit the ground at the same time because the vertical distance is the same for each bullet even though the total distance is not. Why is the same not true in the mirror example? Light is traveling the same vertical distance in both clocks.

    1. This is because you are actually considering "gravity" as the driving velocity in your "bullet" example.

      While a shot bullet does in fact have a lot more velocity/distance traveled, its a drop in the bucket compared to light.

      Any examples using "normal speeds" in analogies will not work due to this.

      If you replaced the "bit of light" in my analogy above, with a "bouncy ball" or something going at a "non-light" speed, the analogy wouldn't work as obviously (due to how small of a difference the time-dilation would be)

      We took an atomic clock on some commercial airplanes in 1971, and flew them around the world twice. When they compared the clocks (one on the ground, one that flew east, on that flew west) they disagreed on the current time (due to the time dilation)

      But it required atomic clocks, and they only differed by nano seconds.