Jose Wudka

Illustrated Special Relativity Through Its Paradoxes: A Fusion of Linear Algebra, Graphics, and Reality

J Depillis Illustrations. Paperback. Book Condition: New. Paperback. 384 pages. Dimensions: 10.0in. x 7.0in. x 0.9in.This accessible work, with its plethora of full-color illustrations by the author, shows that linear algebra --actually, 2x2 matrices --provide a natural language for special relativity. The book includes an overview of linear algebra with all basic definitions and necessary theorems. Since Einstein acknowledged his debt to Clerk Maxwell in his seminal 1905 paper introducing the theory of special relativity, we fully develop Maxwells four equations that unify the theories of electricity, optics, and magnetism. Using just two laboratory measurements, these equations lead to a simple calculation for the frameindependent speed of electromagnetic waves in a vacuum. (Maxwell himself was unaware that light was a special electromagnetic wave. ) Before analyzing the paradoxes, we establish their linear algebraic context. Inertial frames become ( 2-dimensional vector spaces ) whose ordered spacetime pairs ( x , t ) are linked by line-of-sight linear transformations. These are the Galilean transformations in classical physics, and the Lorentz transformations in the more general relativistic physics. The Lorentz transformation is easily derived once we show how a novel swiveled line theorem, ( a geometric concept ) is equivalent to...

Measuring the Speed of Light

Conceptually the experiment is very simple: measure the time t it takes to send a pulse of light from a source to a detector a distance d away. The speed of light is simply t d c / = . The obvious problem is that c is very large, about 3×10 8 m/s, so the travel time is very small. You might manage to fit a 3m long apparatus in the lab, but even this means the time will be about 10ns, which is just at the resolution limit of a good oscilloscope. If you want to determine c to 1% accuracy (a modest goal) you’ll need timing resolution of 100ps, which is very ambitious. Clearly, a more subtle measurement technique is required.