Reading for Sep 26

For next week’s class, please read:-

• the first part of chapter 2 of Greene: pp23-46
• the following plain-language summary of topics for next week

Newton and Gravity / Einstein and Special Relativity

Next week we will begin discussing gravity in some detail, by introducing Isaac Newton’s incredible insight of over three centuries ago that the very same gravity force is responsible for the motions of celestial bodies and for the motions of human scale objects like baseballs on Earth. We describe the inverse-square behaviour of Newton’s Law of Universal Gravitation.

Newton’s theory of gravity is very powerful, with the ability to explain observations like Kepler’s Laws of planetary motion (planets move in elliptical orbits, and each orbit sweeps out equal area in equal times). Newton’s gravity is precise enough to land humans on the Moon.

One weakness of Newton’s gravity theory, however, is that it assumes that the speed of transmission of gravity is infinite. This gives rise to nasty causality problems, which is part of what drove Einstein to refine Newton’s theory of gravity by formulating Relativity. Newton’s theory also predicts a deflection of light by gravity that is experimentally incorrect; Einstein’s refinement got it right.

Einstein’s fundamental insight was that the speed of light is invariant – the same in all frames of reference. This deceptively simple looking proposition is amazingly deep, in that it forces us to rethink our conventional, low-speed-based, intuition about how velocities should add and about how every observer should measure the same time. In fact, as Einstein showed theoretically and decades of experiments have shown since, time is relative (not absolute) and velocities which are a significant fraction of the speed of light do not add simply.

We demonstrate how time dilation works in a very simple example. By drawing a straightforward diagram and using simple trigonometry without any  equations, we show that – because the speed of light is the same in all reference frames – clocks look like they are running slow to an observer in relative motion.

We also set up and explain the famous Twin Paradox. In particular, we explain that it is the acceleration of the astronaut twin that breaks the apparent symmetry between the twins. The astronaut twin ages less quickly than the homebody. This kind of theoretical prediction of Relativity has been exhaustively tested in the laboratory and found to work perfectly. So it is real life, not “just a theory”!