Discovering Relativity for Yourself by Lilley

By Lilley

Learning Relativity for your self explains Einstein's idea of Relativity to readers who're daunted by way of the normal mathematical method of that profound thought. For two decades Sam Lilley taught this topic to adults without technological know-how heritage. Now he has written an evidence of the idea that calls for no earlier wisdom of arithmetic or physics past a capability to do simple math. the 1st sector of the publication makes use of not more than mathematics and a bit easy geometry to introduce the various major recommendations of the idea, in addition to discussing a magnificent experimental try out, which comes down strongly in its favour. whilst ultimately extra development calls for use of algebra and different mathematical innovations, those are conscientiously defined in a manner that makes them available to absolute rookies, utilizing many new and unorthodox tools.

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15 give ˆ αα (1 − cos θ ) = 1 − cos θ. e. 17) where γ −2 = 1 − V 2 . 17) gives n · vˆ = γ (1 + V ) and n · vˆ = γ (1 + V cos θ). 16), we get the required result: cos θˆ = cos θ + V . 20) Note that θˆ < θ for V > 0, that is, according to Speedy, Vega is closer to the polestar. Indeed, if v → 1 then θˆ → 0. 1), if the frequency of light from Vega is ω according to Earthy, what will it be according to Speedy? Since p is proportional to n , n · v = 1 and p · v = ω, we have p = ωn . The frequency according to Speedy is thus given by ωˆ = ωn · v.

3 shows, it has a natural extension to other types of displacements. We say that PQ and P Q are equivalent if the timelike displacements O P and OQ are equivalent to O P and O Q . Physically, O is a possible spacetime meeting point of two observers whose world lines pass through P and Q, respectively. All displacements can thus be partitioned into equivalence classes where, for example, the equivalence class v = {O P } represents the class 27 28 THE GEOMETRY OF FLAT SPACETIME of all displacements equivalent to O P.

We shall not assume that the clocks are correlated in any way – this would almost be tantamount to introducing absolute time – nor shall we assume that our observers carry rulers or yardsticks. Such pieces of apparatus are not particularly useful for measuring distances on a astronomical scale. Using his clock, an observer can assign a number, t( p), called the proper time, to each point p on his world line, where t( p) is the reading on his clock when he occupies p. Note that each individual observer has his own proper time and, as yet, we have defined no relationship between the proper times of different observers.

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