# Special Relativity

Curriculum Connections: Special Relativity is part of the Ontario curriculum but it is missing in many other places. However, most physics curricula look at kinematics, addition of velocities and frames of reference and that's what special relativity is all about. The lesson on relativistic momentum uses the magnetic force on charged particles - F= qvB - and centripetal force - F = mv^2/r - to establish that momentum does not equal mv.

1) Spacetime Diagrams: Part I
This lesson introduces the students to Minkowski spacetime diagrams - a really powerful visualization tool. A French version is now available thanks to Laure Ghia (Hamilton.)

2) Spacetime Diagrams: Part II
This lesson extends the ideas of Part I and gets a bit more mathematical.

3) Relativistic Momentum
This lesson uses a 15-minute video and data from TRIUMF - home of the world's largest cyclotron - to establish the formula for relativistic momentum.

4) Everyday Einstein: The GPS and Relativity
This is a free resource from the Perimeter Institute and can be used in many places in high school including geography. It deals with the GPS, which is an application that uses special and general relativity. Worksheet 3 is the most relevant for a unit on special relativity. It shows how even at satellite speeds is important.

# General Relativity

Curriculum Connections: General Relativity is not usually an explicit part of the high school curriculum. However, if you are supposed to teach frames of reference, then it is easy to justify looking at Parts 1 and 2 below. Your students want to know about black holes and the big bang and you can`t do that without courved space, so really owe it to them to do parts 3 and 4.

1) General Relativity: Gravity Slows Time (60 minutes)

This lesson takes Everyday Einstein: The GPS and Relativity, a great resource from Perimeter Institute, as the starting point to explore general relativity. It focuses on the activities and questions of Worksheet 5 in the Teachers Guide. This is a lesson about accelerated frames of reference and what led Einstein to the equivalence principle and the prediction that gravity slows time.

2) General Relativity: Gravity Curves Light (60 minutes)

The questions in this sheet review and extend the implications of the inertial and non-inertial frames of reference. Then it uses the equivalence principle to predict that a beam of light will bend in a gravitational field. It also shows that the equivalence principal can’t deal with non-uniform gravitational fields and tidal forces. A full treatment of gravity needs the concept of curved spacetime, which is the topic of the next lesson.

3) General Relativity: Gravity Curves Spacetime (60 minutes)

This lesson has students work in small groups with a guided inquiry sheet and a variety of physical models (ballons, stretchy fabirc etc.) to explore the effects of curved spacetime. It benefits from, but does not require, that students learn about slowed time and curved light.

4) General Relativity: Gravity Causes Black Holes (60 minutes)

Dark stars were predicted ìn 1783 using Newtonian gravity. Black holes are something similar but wildly different predicted by general relativity. This lesson has students compare the predictions of the two models and look at the evidence for black holes.

NEW!!! The version of this that was done at the STAO conference 2010 can be found here: PowerPoint Slides, Part 1:Equivalence Principle Worksheet, Part 2: Curved Spacetime Worksheet.

Thanks to Tim Langford for his editorial skills. Thanks to Philip Freeman of B.C. for lots of insight into making general relativity accessible to high school students.