Forces of Nature by Professor Brian Cox

Author:Professor Brian Cox [Cox, Professor Brian]
Language: eng
Format: epub
Publisher: HarperCollins Publishers
Published: 2016-06-21T06:00:00+00:00

Spacetime calculations

Monet and the aviator

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.

Hyperbola.

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