# Astronomy 2: Special Relativity

Session 2012–2013

### Contents

Podcast
I make the lecture audio available as a podcast; see below for details.
Aims and Objectives
This is now the final version of the aims and objectives. It differs only marginally from the version distributed in October, by some slight rewordings.
Notes
The distributed lecture notes.
Tutorial questions
You are set four of these during the term; they count toward the final assessment. You can find these on Moodle.
Examples
Collected in-text examples, with solutions.
Scribbles
The scans of the in-lecture scribbles are available.
What's new

The PDF files below are intended to be printed out on a double-sided printer; the nearby links marked ss are for printing out on a single-sided printer, the links scr are versions intended to be read on-screen.

## Podcast

As an experiment, I'm making available audio versions of the lectures, that is, a podcast. Please do let me know how you get on. I'm interested in whether you use these recordings, how, when, why, where, plus any other feedback that occurs to you.

If you have any problems with the feed, or with the enclosed MP3 files, do let me know fairly urgently.

## Notes and contents

From this page you can download the notes for each of the four blocks of the Special relativity course. These four blocks are

Part 1: Introduction
Central ideas and definitions. Inertial frames. How to measure lengths and times, and how to synchronise clocks. [ one lecture: pdf, ss, scr ]
Part 2: The postulates
Introducing and justifying the two postulates which SR rests on. [ one lecture: pdf, ss, scr ]
Part 3: Spacetime and the Lorentz Transformation
The central mathematical tool. The Minkowski diagram and the idea of spacetime. The invariant interval. [ four lectures: pdf, ss, scr ]
Part 4: Relativistic kinematics
Momentum, energy and force. [ four lectures: pdf, ss, scr ]

In the lectures, I will presume that you have already printed out the relevant part, and at least looked over them. You will not need to, and indeed should not expect to, understand things first time, but this preliminary scan should give you an indication of what bits of the lecture you need to pay special attention to. Having said that, don't be in a rush to print out everything – as I spot typos or other infelicities, I will occasionally adjust the notes as distributed here.

If anyone needs, for example, large-print versions of the notes, I can produce those very easily.

The dangerous bend symbol introducing certain paragraphs is intended to indicate passages, or even whole sections, you might want to skip on a first reading. They typically contain technical detail for the curious reader, or subtle points which are interesting but might distract from the flow of the arguments, or even alternative ways of thinking about the material around them. Think of them as extended footnotes. The material in these paragraphs is not examinable, and I generally won't refer to it explicitly in the lectures.

## Other resources

Aims and Objectives
This is the final version of the aims and objectives for this year [pdf, ss, scr].
Quick questions
You can find these slides on Moodle.

### All in-text questions, with answers

I've gathered together into a single document, all the examples which appeared in the various parts of the course, at the same time amplifying or adding the notes for those examples.

Solving problems like these is very valuable, since it forces you to think through the sometimes rather tricky material which they illustrate. However, the questions are useful only if you work through them yourself, and so the notes added here are intended only to help you when you get stuck, to allow you to check the answer you've obtained, or to add further details. There is less than no point in looking at the answers before you've attempted the question yourself. You will think yes, that makes sense, I would have written that, and be filled with illusory confidence.

Available on Moodle

### How hard are these questions?

The example problems included in the lecture notes are pretty various. Some are quite easy (more or less testing whether you're awake, and probably indicating good problems to start with) and others hard (requiring considerable thought and painful algebra). As payoff, some are very valuable (ah, now I understand!) and others are drill.

I have an idea of roughly which problems are in which category, but (a) it's not really my opinion that matters, and (b) the report that last year's students said X is much more interesting and valuable to next year's students than anything I can say.

Can I ask you, therefore, if you could score each of the problems in the problem set, assessing them for (1) difficulty, and (2) value, in each case scoring from 0.0 (not) to around 2.0 (very). No more than one decimal place, please! Both dimensions here might be easiest to assess nearer revision time, so don't hurry to get these back to me -- some time near the exams would be great.

Questionnaire: on Moodle.

## Recent changes

There's an Atom feed for the files in this directory, so you can be promptly informed of when files change. That's here. Follow that link (your browser may do the Right Thing) or paste that URL into a blog reader.

• The reworked light-clock example on page 3-9 of the notes somehow ended up rather garbled, with a value for the speed v which didn't match the numbers for x2 and t2. There's a fixed version available: page 3-9.
• Not garbled, but incomplete: I've adjusted the text on pp3-19 and 3-20, to include a fuller description of the pole-in-the-barn paradox, with Minkowski diagrams which should make the various relevant events clearer. See page 3-19.
• I've also posted a version of the true/false quiz of the October tutorial, with answers and explanations. See PDF.
• Added a couple of pages of supplementary material, which principally includes a recipe for working throug relativity problems in a systematic way.
2013-02-22
Update webpage; allexamples to moodle
2013-02-13
Refine/clarify Aims and Objectives
2012-11-27
Release link to PDF of supplementary material
2012-11-05
Expand discussion of vectors, components, and relativistic force
2012-11-04
Release complete set of examples + notes
2012-10-18
Add true/false tutorial exercise
2012-10-17
Adjustment to p3-19 in the notes, with diagrams
2012-10-16
Release part4 notes
2012-09-24
Release part3 notes
2012-09-18
Update notes and web pages for 2012-13 session

Norman Gray
2013-02-24