The Velocity Addition Formula
Velocity Addition Formula Updated: April 25, 2024 On the Electrodynamics of Moving Bodies Einstein-EDoMB-1905 https://www.fourmilab.ch/etexts/einstein/specrel/www/ Section §5 presents the velocity-addition-formula used today. Shown: V = ( v + w ) / ( 1 + vw/c² ) Section §5 has very little derivation. Einstein: Relativity, The Special and the General Theory, 1920 https://books.google.com/books?id=n8QKAAAAIAAJ Section 13, Theorem of the Addition of the Velocities, page 45. Section 11, The Lorentz Transformation, Galileans, page 40. See also: A Stubbornly Persistent Illusion: The Essential Scientific Works of Albert Einstein, compiled by Stephen Hawking. Contains both EDoMB-Section §5 and RSGT Section 13. We use uppercase V per 1905 rather than uppercase W per 1920. ++++ MINUS-sign and PLUS-sign Shown next: MINUS-sign Lorentz Transforms of EDoMB-1905-Section §3. x′ = gamma × ( x – vt ) t′ = gamma × ( t – vx / c² ) Shown next: PLUS-sign transforms of modern textbooks. x = gamma × ( x′ + v