Bats, echolocation, and a Newtonian view of Einstein's Special Relativity

Abstract:

Einstein's 1905 Special Relativity (SR) is a foundational theory of 20th century physics. While perhaps unintuitive and certainly surprising initially, it has a beauty and elegance which connects to a rich and interesting variant of Euclidean geometry.

In this talk we present a simple but novel introduction to SR and the associated geometry, showing that the mathematical framework actually resides already in Newtonian mechanics, and could possibly have been discovered any time after 1700 if physicists had asked themselves the question: how would two (mathematically inclined) bats compare time and position measurements??

The unique abilities of bats to hunt their prey using (sonor) echolocation is one of the more remarkable aspects of the world of mammals. We will show that by adopting a `bat-centric' point of view, and thinking about sound--not light!--as the source of physical measurement information, many of the standard pillars of SR, including Lorentz transformations, length contraction, time dilation, Einstein's interval, and the twin paradox arise simply and naturally.

Mathematically only some first year linear algebra is required. Holy Albert, Batman!