4 D ec 2 00 7 Clock rates , clock settings and the physics of the space - time Lorentz transformation

A careful study is made of the operational meaning of the time symbols appearing in the space-time Lorentz transformation. Four distinct symbols, with different physical meanings, are needed to describe reciprocal measurements involving stationary and uniformly-moving clocks. Physical predictions concern only the observed rate of a clock as a function of its relative speed, not its setting. How the failure to make this distinction leads to the conventional predictions of spurious 'relativity of simultaneity' and 'length contraction' effects in special relativity is explained. The purpose of this paper is to discuss the physical consequences, for measurements of space and time intervals, of the Lorentz transformation a (LT): x ′ = γ[x − vt] (1) t ′ = γ[t − vx c 2 ] (2) y ′ = y (3) z ′ = z (4) where γ ≡ 1/ 1 − (v/c) 2 and c is the speed of light in vacuum. For this it is necessary to establish the exact operational correspondence between the mathematical symbols representing space-time events (x,y,z,t) and (x ′ ,y ′ ,z ′ ,t ′) in two inertial frames S and S' and actual clock readings and measured spatial intervals. In the LT (1)-(4) the Cartesian spatial axes of S and S' are parallel and the frame S' is in uniform motion, relative to S along the common x, x ′ axis, with velocity v. In order apply the LT to any experiment, the times t and t ′ must be identified with those recorded by clocks at rest in either S or S'. The simplest experiment that can be conceived will use just one clock in each frame, say, C and C'. Using these clocks two different, but reciprocal, experiments may be performed. The two clocks may be viewed from S, or they may be viewed from S'. In order to describe these experiments, four physically distinct time symbols are required: τ , t ′ , τ ′ and t. The symbols τ (τ ′) a The Lorentz Transformation (1)-(4) was first given by Larmor in 1900 [1]. The same transformation appears in 1904 in Lorentz's last pre-relativity paper [2]. The latter paper was cited in 1905 by Poincaré [3] who first introduced the appellation 'Lorentz Transformation'. Einstein independently derived the transformation in the same year [4]. See Ref. [5] for a discussion of historical priority issues