Volume 5: Pages 121-125, 1992
Light Kinematics in Galilean Space‐Time
Jacques Trempe 1
1425 Orchard Avenue, Otterburn Park, Quebec J3H 1P9 Canada
A new theory of light propagation is introduced by showing that the Lorentz transformation is applicable in Galilean‐invariant space‐time. The distance of a point on an ellipse to a focus, or its projection on the major axis, is given in terms of the distance to the other focus and its projection using eccentricity as the sole parameter. This form of the equation of an ellipse is then shown to be a Lorentz transformation, proving that the Lorentz transformation is a pure geometrical transformation of spatial coordinates, with no inherent relationship to space‐time. The transition to kinematics is made by considering an ellipse, or ellipsoid, expanding with time. The expanding surface can be interpreted as the propagation of a signal with velocities C and C′ in two different frames of reference with relative velocity V, having their origins at the foci of the expanding ellipse. Einstein interpreted the Lorentz transformation in a space‐time system where the speed of a light signal is constant in all frames of reference. The present paper shows that the Lorentz transformation, a purely geometrical relation of spatial distances, can also be applied to the propagation of a light signal in an invariant (Galilean) space‐time, where the velocities C and C′ are functions of the relative velocity V of the reference frames. To determine which of the two interpretations corresponds with the real world, an experiment is proposed in which the one‐way velocity of light between a moving source and a receptor is measured directly.
Keywords: relativity, invariants, Galilean space‐time, light propagation, signal velocity, speed of light, kinematics, Lorentz transformation, Lorentz transformation applicable in invariant Galilean space‐time
Received: November 16, 1990; Published Online: December 15, 2008