Wednesday 11 February 2015

Special Relativity for everyman (or woman) - 4. What is this mysterious thing we call Relativity?

What is this mysterious thing we call relativity?

Relativity is a term almost guaranteed to bring a blank look to the face of most of the population. It also brings a certain uneasiness to many scientists. Something that is acknowledged and respected, yet with an air of foreboding, a foreboding that comes from a lack of confidence in our understanding of it.

Why?

Just what is this thing called Relativity?

It has the reputation of being mathematically complex, and esoteric. That it can only be understood in the abstract realms at the boundaries of science. Despite this, it is in fact very simple.

Imagine two passengers sitting in trains on opposing platforms in a station. Each will see the other as stationary. Until one of the trains starts to move. Then, for a moment, each passenger is convinced that his train is moving. He automatically assumes that what is outside the window is stationary. Only the one train is moving relative to the railway track; yet each train, and the observer within it, is moving relative to the other train.

Take this a step further and imagine two trains passing one another. Observers seated on those trains will each measure the same speed for the other train, relative to themselves for each observer will deem their own train stationary and the other to have all the movement.

In fact we can expand this to say: If, relative to system K, K' is a uniformly moving co-ordinate system devoid of rotation, then natural phenomena run their course with respect to K' according to exactly the same general laws as with respect to K. This statement is called the principle of relativity (in the restricted sense).

(The secret is to imagine one train is stationary, taking all measurements relative to that train. The other train is then moving with velocity v relative to the stationary train.
Yet in the same way, if we were to take the second train as stationary then the first train would no longer be stationary but would be travelling with velocity -v with respect to the now stationary second train.

And it this been with us from the distant realms of history, before being defined in those terms by Galileo. First when man learned to sail the seas, using maps to Navigate by and reckoning in the winds and currents obtaining in the seas. Then similarly in the days of aviation, accounting for winds and weather systems, right up to the modern day, when the need to account for the velocity of the orbiting satellites used in GPS navigation brought new challenges to be catered for. Challenges predicted by the genius of Einstein and his follow pioneers.

In one chapter of his little book, Einstein described: 'the theorem of the addition of velocities employed in Classical Mechanics'. In it he stated that a man walking with velocity w along a train travelling at velocity v, would be travelling with velocity, v + w, relative to the track. He termed this the Galileian Transformation.

Essentially, relativity is about how the locations and measurements from one observer's perspective are transformed to become those of another observer, moving with respect to the first.

At low speeds, simple Relativity, where Relative measurements can be calculated using simple addition and subtraction, Gallilei Transformations, is all we need. Such calculations being sufficiently accurate for all practical purposes. But Einstein went on to point out, that using light shining along the railway track instead of the man, the speed of the light relative to the train would be c ± v. This, of course, is contrary to the many experimental measurements that have all shown that the speed is in fact 'c'.

Thus the need for a new theory of relativity was born and that new theory was Einsteins Theory of Special Relativity.


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