COLLEGE OF ARTS AND SCIENCES Department of Mathematics and Statistics

# Mathematics Colloquium: "Linear Algebra as a Natural Language for Special Relativity and Its Paradoxes"

2015-10-22

4:10pm Neill 5W

John dePillis

USING BASIC LINEAR ALGEBRA as a natural language of special relativity, and assuming very little knowledge of physics, we present a novel linear-algebraic derivation of the Lorentz transformation. Through the geometry of Minkowski diagrams, we analyze properties and paradoxes of special relativity.

A BASIC ASSUMPTION of special relativity (SR) is that the speed of light in a vacuum is the same for all observers regardless of their speeds or the speed of the light source. Consequences of this simple axiom are profound. For example, rods in motion shrink in the direction of motion, and clocks in motion always run slower than stationary clocks.

The TWIN PARADOX: One twin leaves Earth in a fast rocket ship and after fifty years, say, returns to Earth, having aged only 30 years. But if each twin is in symmetric motion relative to the other, why do the twins age at different rates?

RIGIDITY and TIME REVERSAL Rigid systems are incompatible with SR usually because the motion of some rigid systems force certain particles to travel faster than the speed of light. However, we show in the bug-rivet paradox that rigidity can also cause time reversal in the sense that effect occurs before its cause.