Saturday, August 11, 2018

The Speed of Light and Time Dilation

So light is fast.  But its speed isn’t necessarily special.  It just travels at the highest speed the universe allows.  Photons (the particles of light) have no mass so, like all things without mass, they have nothing to slow them down.  So off they go as fast as they can!  Why is there a universal speed limit?  The answer to this is, like other questions about the fundamental nature of the universe and laws of physics, we simply could not exist in a universe with infinite speeds.  There are two things that would go wrong for us:  1. It would take infinite energy to give something mass and so things with mass (like us) couldn’t exist.  2. Time (or to be more precise, really, space-time) wouldn’t exist.  Light travels at the fastest speed a signal can be sent in our universe.  Because we have a finite signal speed it means that events have distance and time between them.  This is quite odd to say, but an infinite speed of light or infinite signal speed would mean that there are not distances and times between events.  How would a particle with infinite speed actually behave?  A signal (or particle) with infinite speed would exist everywhere in the universe at once.  These particles would never take any amount of time to go anywhere and would never need to travel anywhere because they all would already be everywhere forever.  So while such a universe could exist we wouldn’t be around to observe it.  Nothing, really, would be around. 

Because the speed of light is always at the fastest possible speed the universe allows this has a weird byproduct: light’s speed is not relative to the observer.  It is always the same.  Here’s a little more detail about what that means and following, a little about why that’s weird.  Imagine someone on a train car going 100 km/h, you’re standing still watching the train car go by.  Now imagine they throw a ball at 50 km/h.  From their perspective the ball is going 50 km/h.  But from your perspective the train and the ball add their speeds together and the ball is going 150 km/h.  For most moving objects in the universe you have to measure their speed from a particular frame of reference.  That is, are we measuring the ball’s speed from your frame or from the person who is throwing the ball?  We will get different answers depending on which frame we decide to measure from.  But because light always goes at the maximum speed allowed by the universe, this does not happen for light.  Let’s go back to the train car only this time the person on board has a flashlight.  They’re traveling along again at 100 km/h.  They turn on the flashlight.  From their perspective the photons exiting the flashlight are going c (the speed of light, about 300,000 km/s). From your perspective the photons are traveling?  Also c, exactly the same speed.  Not c + 100 km/h.  

Here’s the weird thing…at least weird from our day to day experience:  the fact that light travels at the universal speed limit and its speed doesn’t change based on any frames of reference leads to time being experienced differently when travelling at different speeds.  Let’s go back to the train car.  This time, imagine there are mirrors inside the car and a beam of light bouncing between them.  The light beam is bouncing straight back and forth and takes some very small amount of time to make one bounce.  This is what it might look like, the back bars being the mirrors and the blue bar being the light beam:

Now, let’s set the train car moving.  Now the light beam must bounce at a diagonal and travel a slightly longer distance in order to “catch up” with the moving car.  Here’s what this looks like, again, the black bars are the mirrors, spaced out to show the movement of the train car:

Just like with the ball thrower, with most objects the train will just impart its speed on the object and we will see it go faster to keep up with the moving train across the slightly longer diagonals.  But here’s where things get weird.  Remember that light cannot go any faster and that it always goes at the speed c regardless of frame of reference (so its speed is the same if you are observing from outside the train or on the car).  If the speed can’t increase it seems we may be stuck with a problem: the light has to travel a longer distance in the same amount of time but it simply can’t because the speed of light is conserved no matter what.  Here’s the punchline: instead of adjusting the speed of light, the universe adjusts how much time passes for each frame of reference.  From outside the train time on the train actually slows down so the light has enough time to get back and forth from mirror to mirror.  From inside the train time appears to move at a normal rate.  But from outside, time is moving slower.

This is the phenomenon known as time dilation.  We don’t really start to see significant effects until we get pretty close to the speed of light but this happens every time you move with respect to someone/something else.  Every time you get in a car, train, plane, skateboard, bicycle, heck even walking, time slows down for you just a little bit.  So be wise, friends.  Choose something productive to do with all your extra nanoseconds. 

Some references:


Cox, Brian and Jeff Forshaw.  Why Does E=MC2?  Boston: Da Capo Press, 2009.