Special Relativity for Beginners

Special relativity is actually pretty easy to understand. There's the odd bit here and there that bends your head a bit, but there's only one formula to learn, and it's only applied in three situations, one or two of which you can ignore. General Relativity, on the other hand, is a whole new kettle of fish. That's really tricky stuff full of tensors and stuff, but we're not going there. So long as our spacecraft are going in a straight line at a constant velocity, we don't have to. Nothing really strange happens when spacecraft accelerate, it just makes the maths hard. There's other stuff in there too which links up gravity. I'll touch on that, because it's kind of important in some cases.

No doubt you are aware that the speed of light is the fastest speed you can go and when a spacecraft travels at nearly the speed of light time slows down, so the crew only experience a short time, but come back to find thousands of years have passed on Earth. In addition to those, the mass of the spacecraft appears to increase and it appears to get shorter.

Einstein started from two postulates:

• The speed of light is the same for all observers.
• The laws of physics are the same if you are moving as when you are not.

Imagine you are driving your car at 1 metre per second slower than the speed of light, and you switch on the headlights. What do you see? Because the speed of light is the same for all observers, you see just the same thing you would see if you were stationary. An car 300 metres in front of you would be illuminated within a microsecond. Meanwhile, a stationary observer would see the light travelling just 1m/s faster than you and taking five minutes to get to the car in front. Obviously something has to give. What to you is one microsecond, to someone else is five minutes. That is time dilation. If your time is T, and the observer's time is T', then

(1)
\begin{align} T' = T \times ( \frac {1} {\sqrt{1 - \frac {v^2} {c^2}}}) \end{align}