Special relativity

The fact that we spend our lives moving quite slowly compared to the speed of light is the reason we find some of the phenomena of relativity difficult to believe.

All of the changes that occur at close to light speed have been experimentally demonstrated – they are not science fiction.

When Albert Einstein carried out thought experiments to predict motion close to the speed of light he realized that the speed of light in a vacuum was actually a physical constant and could not change. It is given the symbol c and is approximately 3 \times 10^{8}ms^{-1}

As the speed of light remains constant, this means that everything else has to change at these speeds.

Mass, length and time must all be redefined at speeds greater than 90 per cent of light speed (approximately 2.7 \times 10^{8}ms^{-1}).

Time dilation

Research the "Twin Paradox" and you will discover how an astronaut returns from a high speed space journey apparently younger than his (or her) twin who observed the journey from Earth.

Both clocks keep time accurately in their own frame of reference but the 'paradox' comes from the comparison due to the relative motion - hence relativity.

The earthbound observer measures a longer or 'dilated' time due to the movement of the astronaut's clock that has kept time accurately on the moving spacecraft. Even the astronaut's biological age does not progress as quickly as the earthbound twin but this effect is only noticeable at speeds close to the speed of light. To remember which is the dilated time the aide memoire "moving clocks appear to run slowly" can be useful.

Relativity of time on earth and space

The numerical example below shows that the extent of dilation of time depends on how fast the astronaut is moving using the relationship:

t\textquotesingle = \frac{t}{\sqrt{1-\frac{v^{2}}{c^{2}}}}

This gives the result for t\textquotesingle, the dilated time - in this example the time observed on earth.

The time t on the top of the equation is the time observed by the astronaut travelling at speed v and is sometimes referred to as the 'proper time' in relativity.

The Russian Cosmonaut Sergei Avdeyev spent 747 days (64 540 800 seconds) aboard the Space Station Mir which travels at 7600 ms-1. Calculate how much time Sergei 'extended' his life by.

First put in the known numerical values:

t\textquotesingle = \frac{64,540,800}{\sqrt {1- \frac{7600^{2}}{(3\times 10^{8})^{2}}}}

When calculating this equation it is best to use the brackets facility on a calculator or to work outwards.

Start off with the \frac{v^{2}}{c^{2}} term and work through stage by stage.

t\textquotesingle = \frac{64,540,800}{\sqrt{1-6.41\times 10^{-10}}}

Which then gives:

t\textquotesingle = \frac{64,540,800}{0.9999999996795}

Remember to take the square root.

t\textquotesingle = 64,540,800.0207s

In other words after over two years being the fastest human being, Sergei only experienced 21 milliseconds less than colleagues on Earth.

Note in these examples since there is such a small difference we need to use a much larger number of significant figures than is usual.

Question

In considering relativity we think of ourselves at rest. Is this strictly true and if not, why not?

Certainly not. The Earth is spinning and we move at up to 1000 miles per hour depending on our latitude.

Earth orbits the Sun at approximately 60 000 miles per hour. Add to this the orbital speed of our Sun in the Milky Way galaxy and the movement of the galaxy in the universe and we are definitely not still on this wider scale.

However as an observer we are the reference frame and so can consider ourselves stationary.