## Einstein’s Special Theory of Relativity

We started our study of Einstein’s special theory of relativity this week.  Special relativity is tricky get your head round, so I’ve put together a collection of videos that help to explain the ideas we’re going to consider.  Let’s start with a video about the speed of light.

The next video follows Einstein’s thought process as he worked through his special theory of relativity.

special relativity from mr mackenzie on Vimeo.

When I walked around the room throwing the tennis ball, I showed that what I saw as purely vertical motion looked to you like the curved path of a projectile.  For me (the moving observer) and you (the stationary observer), the ball appeared to travel different distances.  Extending this situation to a ray of light, as in the video, we need to consider two aspects of special relativity, time dilation and length contraction.  The speed of light can only be constant for all observers if something happens to time and length (distance) when considering fast moving objects.

We’ll look at time dilation first.

### time dilation

Here is another take on special relativity and the twins paradox

…and the Glesga Physics version

### length contraction

This video has helpful examples to explain length contraction.

Sometimes it’s easier to imagine we’re a stationary observer watching a fast moving object go whizzing past.  For other situations, it’s better to put yourself into the same frame of reference as the moving object, so that everything else appears to be moving quickly, while you sit still.  The muon example in this video shows how an alternative perspective can work to our advantage in special relativity.

Another way to think about this alternative frame of reference is that it’s hard to measure distances when you yourself are moving really quickly.  Think about it, you’d get tangled up in your measuring tape like an Andrex puppy.

###### image: trotonline.co.uk

It would be far easier to imagine you’re the one sitting still and all the objects are moving relative to your position, as if your train is stationary and it’s everything outside that’s moving.  That keeps everything nice and tidy – including your measuring tape.  Got to love Einstein’s postulates of special relativity.

## evidence that special relativity is real

For the past two weeks, we’ve been looking at equations that describe time and distance changing according to speed. It’s been quite heavy on theory and maths with no supporting evidence to suggest Einstein’s ideas were correct.  I want to address that lack of evidence by pointing you to some practical work that had been carried out before Einstein’s theory was developed and by introducing measurements that scientists are still making today.

### The speed of light is the same for all observers

Einstein’s Special Theory of Relativity was published in 1905 but I want to go back to an experiment carried out 1887, the Michelson-Morley experiment.  Throughout the 19th century, scientists believed that waves needed some form of matter through which to travel.  From your National 5 knowledge, you know that electromagnetic radiation, such as light or radio waves, can travel through the vacuum of space where there is an absence of matter but this was not known way back then.  Instead, scientists believed that the Earth was moving through a mysterious substance called the ether (also known as the aether).

At the time, it was believed that Earth moved through the ether, so a stationary observer on Earth should be able to measure the relative speed of the ether as we moved through it.  Michelson and Morley devised an experiment where light beams were directed in different directions and brought back together to produce something called interference (we shall study interference in the Particles & Waves unit).  The idea was that there would be a change in the speed of light when it had to move against the direction of the ether and, through relative motion, they could determine the speed of the ether.

It was a total flop!  They found that the speed of light was the same in all directions.  It was only later, when Einstein was looking for ways to prove that the speed of light was the same for all observers, that the importance of the Michelson-Morley experiment became apparent.

This video summarises the evidence nicely.

### You can’t prove that time and distance change according to speed

Actually we can.  The upper atmosphere is constantly bombarded with very high energy particles from space, mostly protons.  These particles are called cosmic rays.  When cosmic rays collide with atoms at the edge of our atmosphere, many different subatomic particles are produced.  We will meet these particles at the start of the Particles & Waves unit.  The particle we’re interested in just now is one called the muon (μ).  Muons are similar to electrons, but about 200 times heavier.

###### image by Los Alamos National Lab

The trouble is that muons can’t exist for very long, they have a very short half-life (think back to National 5 radioactivity).  In fact, the half-life of a muon is so short that we should never be able to detect the muons produced in the upper atmosphere with a particle detector at ground level, yet we can detect them.  Lots of them!

###### video from the exploratorium

There are two ways in which Special Relativity explains why we can detect muons.  The explanation depends whether you are in Earth’s frame of reference, in which case the time dilation explanation is appropriate, or the muon frame of reference, where the length contraction explanation is appropriate.  This video from minute physics explains the situation quite well.

For the more curious among you, there is a comparison of the two different frames of reference on the hyperphysics site, with a simulator where you can vary muon parameters and distances to see how the outcome changes.

## introducing special relativity…

We’ve been looking at Einstein’s special theory of relativity this week.  Special relativity is tricky get get your head round.  Let’s start with a video about the speed of light.

We watched this video in class, it follows Einstein’s thought process as he worked through his special theory of relativity.

special relativity from mr mackenzie on Vimeo.
We need to consider two aspects of special relativity, time dilation and length contraction.  We’ll look at time dilation first.

### time dilation

A Tale of Two Twins from Oliver Luo on Vimeo.

another take on special relativity and the twins paradox

…and the Glesga Physics version

### length contraction

This video has helpful examples to explain length contraction.

Sometimes it’s easier to imagine we’re a stationary observer watching a fast moving object go whizzing past.  For other situations, it’s better to put yourself into the same frame of reference as the moving object, so that everything else appears to be moving quickly, while you sit still.  The muon example in this video shows how an alternative perspective can work to our advantage in special relativity.

Another way to think about this alternative frame of reference is that it’s hard to measure distances when you yourself are moving really quickly.  Think about it, you’d get tangled up in your measuring tape like an Andrex puppy.

###### image: trotonline.co.uk

It would be far easier to imagine you’re the one sitting still and all the objects are moving relative to your position, as if your train is stationary and it’s everything outside that’s moving.  That keeps everything nice and tidy – including your measuring tape.  Got to love Einstein’s postulates of special relativity.