**Category:**

Research Papers

**Sub-Category:**

Relativity Theory

**Date Published:**

February 19, 2021

**Keywords:**

Proper Velocity, Coordinate Velocity, Relative Motion

**Abstract:**

Since the time of Galileo, the same definition of velocity has been generally accepted. The definition (usually called Coordinate Velocity) is now shown to be secondary to a more fundamental measure of relative motion (usually called Proper Velocity). The method is that the transformation equations for Special Relativity are derived without introducing velocity or assuming a definition of velocity. For Inertial Frames K and K′, the transformation equations are: x′ = ax – bct, ct′ = act – bx, x = ax′ + bct′, ct = act′ + bx′ , a² = b² + 1; c is the velocity of light; a and b are constants. Four velocity measures are found. Coordinate Velocity, v, = x/ct or − x′/ct′ = b ∕ a = b/√(b² + 1). Proper Velocity, w, = x/ct′ or − x′/ct = b. Thus, v = w/√(w² + 1). The Transformation Equations for Proper Velocity replace b with w. They are x′ = ax – wct, ct′ = act – wx, x = ax′ + wct′, ct = act′ + wx′ , a² = w² + 1. The algebra shows v as a function of w, making w, Proper Velocity, the primary value. At slow velocities, Proper Velocity is an exact fit in the Galilean transformation.

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