ABSTRACT
The motion in space-time of a classical particle (that is to say, non-quantum mechanical) is described by four functions of time: https://www.w3.org/1998/Math/MathML" display="inline"> x μ = x μ ( t ) https://www.w3.org/1999/xlink" xlink:href="https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003436263/11a1814b-c2ab-4d89-be15-80efb520b7b3/content/math2_1.tif"/> . We consider the interval which separates two positions very close together in time and its invariant length: https://www.w3.org/1998/Math/MathML" display="block"> Δ x μ = ( c Δ t , v ⋅ Δ t ) Δ s = ( Δ x ⋅ Δ x ) = ( 1 − v 2 c 2 ) ( c Δ t ) 2 . https://www.w3.org/1999/xlink" xlink:href="https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003436263/11a1814b-c2ab-4d89-be15-80efb520b7b3/content/math2_2.tif"/>
