By Bertrand Russell

First released in 1925, Bertrand Russell’s *ABC of Relativity* used to be thought of a masterwork of its time, contributing considerably to the mass popularisation of technology. Authoritative and available, it offers a notable introductory advisor to Einstein’s conception of Relativity for a normal readership. the most definitive reference publications of its type, and written through one of many 20th century’s so much influential philosophers, *ABC of Relativity* is still as appropriate this day because it used to be on first publication.

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14) More generally, the coordinates {x, y, z} of the interval between any two points in 3-dimensional space (a vector) change when the coordinate system is rotated in 3 dimensions, but the separation r of the two points remains constant r2 = x2 + y 2 + z 2 = constant . 13 A wheel. 14 A spacetime wheel. 14 shows a spacetime wheel. The diagram here is a spacetime diagram, with time t vertical and space x horizontal. A rotation between time t and space x is a Lorentz boost in the x-direction. As the spacetime wheel boosts, a point on the wheel describes an invariant hyperbola.

You continue to watch your twin through a telescope. How much time elapses on your twin’s wristwatch, as seen by you through the telescope, during the twin’s journey back from Alpha to Earth? How much time passes on your own watch as you watch (through the telescope) the twin journey back from Alpha to Earth? What is the ratio of these two times? Express your answers first in terms of ℓ, v, and γ, and then in years. 28 Special Relativity 9. During the journey back from Alpha to Earth, your twin likewise continues to look through a telescope at the time registered on your watch.

Mass is rest mass m, a scalar, not to be confused with energy. 12 Photon energy-momentum The energy-momentum 4-vectors of photons are of especial interest because when you move through a scene at near the speed of light, the scene appears distorted by the Lorentz transformation of the photon 4-vectors that you see. A photon has zero rest mass m=0. 51) p n p n = − E 2 + p 2 = − m2 = 0 . 52) Its scalar energy-momentum squared is thus zero, Consequently the 3-momentum of a photon equals its energy (in units c = 1), p ≡ |p| = E .

### ABC of relativity by Bertrand Russell

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