The Velocity Addition Formula
Velocity Addition Formula Updated: December 8, 2025 On the Electrodynamics of Moving Bodies Einstein-EDoMB-1905-Section §5 https://www.fourmilab.ch/etexts/einstein/specrel/www/ Einstein: Relativity, The Special and the General Theory, 1920, Chapter VI page 19, Chapter XIII page 45 https://www.google.com/books/edition/Relativity/n8QKAAAAIAAJ?hl=en&gbpv=1 Both sources show the velocity-addition-formula as it is today. Shown: V = ( v + w ) / ( 1 + vw/c² ) #### Lorentz Transforms Lorentz Transforms – subtraction, per 1905 Sections §3 and §4: x′ = gamma • ( x – vt ) t′ = gamma • ( t – vx / c² ) Lorentz Transforms – addition, from modern textbooks: x = gamma • ( x′ + vt′ ) t = gamma • ( t′ + vx′ / c² ) #### Textbook derivation of the v-a-f Halliday & Resnick, 10th Edition, Chapter 37-4. Precursor to numerator ( v + w ) in the v-a-f is the spatial Lorentz Transform. Two problems: 1) The LT’s of 1905 are subtractive, not additive. 2) The spatial LT is addition or subtr...