This summer we’ll see Bureau 42’s first summer school session, which covers graduate level quantum physics with grade school math. I had a blast writing it, and will probably write more educational columns in math, physics, and more. (Summer school topics have already been chosen through 2015, featuring contributions from multiple site authors.) Well, not all topics warrant the full summer course treatment, and cover only single lessons at a time. Those will be posted at random intervals right here. Here’s the first topic: turning repeating decimals into fractions. The algorithm can be followed and applied by just about anybody, though the explanation will be easier to deal with if you’re comfortable with high school math. I am also willing to take requests if there’s something you want to learn. I’m not omniscient, but if it’s math and/or physics, I can probably manage it.
I don’t know if it’s on the list, but as I’ve love a lesson on why we believe that the speed of light is a constant that can’t be crossed. I get the whole ‘can’t measure faster than that’ angle, but I don’t see why not being able to be measured means it can’t happen.
Short version: It’s not just a measurement limitation. The rate at which time flows varies from observer to observer. As a side effect, uniform kinetic energy increases do not lead to uniform increases in velocity. This leads to an exponential increase in the energy required to accelerate a body, with a light speed limit.
Think of it this way: every observer, regardless of their own motion, will measure the speed of a photon as the speed of light. (Let’s assume this is all happening in vacuum.) Now imagine you are an observer chasing a photon. You increase your speed, but from your perspective, that photon is still moving faster than you by lightspeed. You speed up again, but it’s still going faster than you by lightspeed. In fact, there is no way to continuously accelerate yourself until you move at the same speed as the photon. An observer who hasn’t accelerated will agree that the photon is moving at lightspeed, and that the photon is faster than you. He or she will not agree on the amount of time elapsed, or the distance you have traveled.
Long version: join us for our Summer School course in 2012, where I will teach key aspects of both the special and general theories of relativity in the span of nine lessons. Each lesson will have two parts. Part 1 will be entirely non-mathematical; these parts will be written and proofread first to ensure completeness. Part 2 of each lesson will include all of the math associated with the topics covered in part 1. Bureau 42 readers will have the choice to download versions of each lesson either with or without the math. Some of the math required for later lessons will be covered in our Summer School course in 2011.
I read this many years ago and highly recommend it:
The Einstein Theory of Relativity: A Trip to the Fourth Dimension by Lillian R. Lieber
Pleasantly surprised to find it’s still available (on Amazon)