Length contraction
Another consequence of the speed of light being fixed is that length must also change. At very high speeds, again within 10 per cent of the speed of light, the length of a moving object seen by a stationary observer shortens.
The cartoon illustrates a fictional cyclist moving close to light speed towards two stationary observers.
The cyclist appears contracted - but only in the dimension she is moving in.
The contracted length \(l\textquotesingle\) (from the point of view of the stationary observer) can be calculated using this equation:
\(l\textquotesingle=l\sqrt{1-\frac{v^{2}}{c^{2}}}\)
Where \(l\) is the proper length observed by the cyclist herself.
Example
The fastest moving man-made object is the four metre long Voyager space probe. It is travelling at 17 260 ms-1. The length as seen by observers on Earth is the contracted length, \(l\textquotesingle\).
\(l\textquotesingle = 4\times \sqrt{1-\frac{17260^{2}}{(3\times 10^{8})^{2}}}\)
\(l\textquotesingle = 4\times \sqrt{1-3.3100844444 \times 10^{-9} }\)
\(l\textquotesingle = 4 \times 0.99999999834\)
\(l\textquotesingle = 3.9999999933798m\)
So the four metre long craft has only shortened by just under 7 nm travelling as the highest speed mankind has managed.
To give an idea of size, the smallest smoke particle is 10 nm. Relativistic effects are generally not noticeable in our experience.
Question
Would the astronauts aboard a near-light speed spacecraft notice each other to be thinner?
No. As the observer and the fellow-astronaut are both moving at the same speed they will both appear normal.
