Forces of Nature by Professor Brian Cox & Andrew Cohen

Author:Professor Brian Cox & Andrew Cohen [Cox, Professor Brian]
Language: eng
Format: epub
ISBN: 9780008210038
Google: eovIjwEACAAJ
Amazon: 0008210039
Publisher: William Collins
Published: 2017-03-09T00:00:00+00:00

Spacetime calculations

Monet and the aviator

We can use Einstein’s two postulates to show why it is that the aviator and Monet measure different intervals of time between any pair of events. This is surely one of the most bizarre ideas ever to come out of a human being’s head. It is all the more bizarre for being demonstrably correct. The argument is surprisingly simple. First let us imagine a special type of clock – at the end we will show that the argument must work for any type of clock, but for now we will consider a ‘light clock’. A light clock is made up of two parallel mirrors with a beam of light bouncing back and forth between them. Suppose that the two mirrors are a distance d apart. If light travels at a speed c it will take a time t=2d/c for the light to travel from one mirror to the other and back again, as determined by someone who is holding the clock (more formally, we might say ‘by someone who is at rest relative to the clock’). Let us refer to the person holding this clock as (and here we will not bother exercising our imagination) ‘person A’. Now let’s introduce a second person: ‘person B’. If person A and person B are both at rest relative to each other then both will clearly agree on how long the light clock takes to tick (let’s call one tick of the clock the time it takes for the light to make one round-trip, i.e. t=2d/c). Pre-Einstein, and according to common sense, we’d say that the clock takes this time t to tick, regardless of what it is doing or who is doing the measuring. But that is wrong, as we are about to show.

To see how time is not absolute, let’s put person A and their clock on a train (Einstein often used trains to explain his theories), and person B on the platform. Now let us consider how the clock is understood by person B. The top illustration shows the path taken by the light as it makes one tick of the clock.

According to person B, the clock moves a distance equal to υt’ in one tick, where υ is the speed of the train and t’ is the duration of the tick. At this stage we will resist the temptation to say that t’ (the time of one tick of the light clock according to person B) is equal to t (the time of one tick according to person A). From the figure we can see the path that the light beam traces out as it moves up and down. Obviously, the light travels further according to person B than it does according to person A. Using Pythagoras’s Theorem, the distance the light travels according to person B is whilst for person A it is just 2d (notice that it would be just 2d for person B if υ=0, i.e. if the train isn’t moving). The

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