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On September 26th, 1905, Albert Einstein published his seminal work (among many in that year, which has since come to be known as the Annus Mirabilis or ‘Miracle Year’ for Einstein) On the Electrodynamics of Moving Bodies. Here, he developed his theory on special relativity. This theory discusses the relationship between space and time, and challenges the previous understanding of physics, known as Newtonian mechanics. This worksheet will take you through the different features of this theory and primarily will focus on the theoretical parts of it (no need to know complicated maths!).

We will explore the theory using thought experiments which Einstein himself was very fond of. This will help us understand the theory without having to do much complicated mathematics. Although, if you find this interesting and want to have a crack at the mathematics, go forth and do so!

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There are two main principles that make up special relativity: 

1. The laws of physics are identical in all frames of reference which have no acceleration. 

2. The speed of light (which will be given the sign ‘c’ from now) will be the same in vacuum for any person viewing light no matter how either light or the observer moves.  

Before we go about explaining these two, let us define some of our terms: 

Frames of reference: a physical concept, a way of understanding how physical objects observed relate to an observer. So, you might have the movement of your hands as part of your frame of reference. 

Acceleration: is how fast the speed of an object with respect to direction (velocity) changes. So, if you have a car going straight, how fast it changes speed in going straight is its acceleration. 

Speed of Light: how fast light travels over a distance. In a vacuum, it goes at this speed – 299,792,458 metres per second 

Vacuum: is a space with no physical matter within it.

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The first principle originates from the work of Galileo Galilei. It makes a simple claim: the laws of physics stay the same when there is no acceleration. However, Einstein developed this idea further, asking what kind of frames of reference exist?  

There was a belief – which is needed for Newtonian mechanics to work – that there must be an absolute frame of reference from which all objects all act upon.  

Imagine the universe to be like a table. All the different particles and objects are moving above the table, relative to it, but these objects cannot leave the table. Everything moves relative to the table. This table acts as the absolute frame of reference that all objects move with respect to. 

Some physicists believed that there was an absolute frame of reference and it was called ‘the aether’. This was influenced by another form of mechanics called Electromagnetism, developed by James Clerk Maxwell, suggesting that there are waves which travel through vacuums. And, as said earlier, vacuums have no matter – so how can anything travel through it? Their answer was to propose the existence of an aether, some substance which allows light/electromagnetic waves to travel through.

Einstein sought to criticise this view with special relativity. Experimentally, the aether was already under question due to the Michelson-Morley Experiment — from Eric Weisstein’s World of Physics (wolfram.com) which showed that the existence of the aether was to be held suspect.  

With special relativity, Einstein proposed that the principle of relativity takes precedence over any absolute frame of reference. Any moving frame of reference will observe the same laws of physics.

The second principle is that light remains at the same speed in a vacuum, no matter what the motion of either the light itself or the observer looking at the light. Let’s bring in a thought experiment: 

Imagine you are chasing a beam of light. What happens as you approach the beam? You view it as a field at rest, despite it still going up and down. Yet this contradicts the normal understanding of light – how can you see it rest? Experience tells us we can only see if light comes into our eyes. Furthermore, Maxwell has shown that light remains at this same speed in a vacuum no matter what.

What then must be the conclusion of this? 

How does it support the conclusion of Einstein?  

Here’s another famous thought experiment as well:  

In this experiment there are two observers M and M’, M is on the embankment whilst M’ is on the train. As the train passes by the embankment at velocity (v), lightning strikes points A and B at the same time. M will see the lightning strike A and B at the same time. M’, however, will see the lightning strike B first and then strike A since the train is heading B’s direction.

Finally, we have discussed this issue without the maths – but if you are interested in some of the mathematics that goes behind these problems, check out this video by Sixty Symbols: 

Special Relativity was not the end of the road for Einstein, you could say it was the beginning of his career. There are two major problems for Einstein, however. Special relativity is ‘special’ and only deals with cases which do not have acceleration. It doesn’t deal with any cases outside of that!

And even with this, there is a second problem. We have been dealing with thought experiments and theoretical understandings of physical laws but how well does this translate to what happens in the real world? 

Further Reading

Einstein’s Theory of Special Relativity | Space
This talks about how special relativity relates to the famous equation: E = mc²   

On the Electrodynamics of Moving Bodies (1920 edition) – Wikisource, the free online library Einstein’s famous paper where he first described Special Relativity