We kick off Episode 4 by describing how knowledge of Newton’s three laws of motion and Newton’s law of universal inverse-square gravitation aids astronomers in discovering planets orbiting other stars. The most important physics points in this story are (1) stellar recoil (like with a gun firing a bullet) and (2) blueshift/redshift, which is similar in some ways to the Doppler effect for sound, wherein frequencies are upshifted for sources approaching us but downshifted for sources moving away. This blue/redshift effect for light gets contributions from time dilation and from the motion of the source, and does not depend on any medium (EM waves travel just fine in vacuum). By focusing on spectral lines for emissions/absorption from gases like hydrogen, we show how astronomers deduce the planet/star mass ratio from observations of stellar radial velocity wobbles.

We then segue into a discussion of fundamental properties of photons. Photons are quanta of the EM field, i.e., indivisible packets of electromagnetic energy. We discuss how photon frequency f is related to photon energy E by the formula E=hf, where h is Planck’s constant. We display the entire EM spectrum of frequencies (or equivalently, wavelengths) – from gamma rays through X-rays and ultraviolet to the visible, infrared, microwave and radio bands.  We also explain the true relativistic relationship between energy, momentum, mass and the speed of light as we build up a conceptual outline of the ideas and thought processes that led Einstein to his famous theory of General Relativity. We emphasize how important Special Relativity was to the development of GR.

We also highlight the importance of Maxwell’s Equations, a beautiful synthesis of electromagnetic phenomena involving charges, currents, and electric and magnetic fields. We describe how Maxwell unified electricity and magnetism into one theoretical whole – an umbrella set of concepts that covers all electromagnetic phenomena. For art’s sake, we show off the equations.   We next emphasize the importance also of the Equivalence Principle, an idea that acceleration due to gravity is indistinguishable from acceleration from an on-board rocket. We finish our lead-up to GR with a description of Einstein’s new concept of spacetime, as a fabric warped by energy/momentum in a causal way, with gravitational disturbances moving at the speed of light. Particles just move the most natural way they can in this context, leading to curved paths like planetary orbits.

This sets the stage for our next episode (#5) developing the physics of black holes.  I hope you enjoy, and stay tuned!

Here is a PDF file of all my slides from Episode 4.

Newton’s theory of gravity is very powerful, with the ability to explain observations like Kepler’s Laws of planetary motion (like the fact that planets move in elliptical orbits, and that each orbit sweeps out equal area in equal times). One weakness of Newton’s gravity theory, however, is that it assumes 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 that light is unaffected by gravity, which turns out to be experimentally incorrect.

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.

Next, 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.

(I even give a page of equations describing a disarmingly simple way of computing relativistic velocity addition, for those who happen to enjoy wrangling equations. This one slide can easily be skipped.)

Here is a PDF file of my slides for Episode 3.