D’Inverno – Introducing Einstein’s Relativity problems

Here are my solutions to various problems in Ray D’Inverno’s textbook Introducing Einstein’s Relativity. The book does give answers to most problems at the back, but it doesn’t provide the working behind them in most cases, so I’ll post my own modest attempts here.

After some consideration, I’ve decided to repost this index to the solutions. I understand that some folks may be concerned that I am providing ‘free’ answers to problems that some students have been assigned as homework, but there are several points that should be made:

  • There are already many web resources (including physics blogs, tutorial sites and other pages where solutions are provided) available that provide answers to problems, so I’m not providing solutions that aren’t available elsewhere. What I am providing, hopefully, are background explanations of the theory that expands on, or describes in a different way, material found in the textbook. Judging by comments I have received, many people find these explanations helpful, and that is my main goal.
  • If a teacher is concerned about students copying answers from the internet, s/he should consider making up their own problems. I did this for the courses that I taught in my 25 years as a university lecturer. For a field as rich as physics, it shouldn’t be too difficult to come up with original problems.
  • If you’re a student seeking to copy solutions, you should realize that you won’t learn much unless you make a genuine effort to solve the problem on your own first. Remember that in most universities, the majority of the marks for a course are obtained from exams, and if you sit an exam without having worked out problems on your own beforehand, your chances of passing are pretty low. In my experience as a teacher myself, I found that most students realize this and do make a genuine effort to learn the material on their own.

Chapter 2 – The k-calculus

2.2, 2.3, 2.4, 2.52.6

Chapter 5 – Tensor algebra

5.1, 5.2, 5.3, 5.4, 5.5, 5.6, 5.7, 5.8, 5.9, 5.10, 5.11, 5.12, 5.13, 5.14, 5.155.16 (i-iv), 5.16 (v)

Chapter 6 – Tensor calculus

6.1, 6.2, 6.3, 6.46.5, 6.6, 6.7, 6.8, 6.9, 6.10, 6.11

14 thoughts on “D’Inverno – Introducing Einstein’s Relativity problems

  1. Julian Ingham

    Cheers mate this is really helpful! There are very few places on the web which talk you through textbook problems like this. Really looking forward to chapter 7!

  2. Howard

    I think there may be an error in 5.2 in the inverse transformation matrix.
    For partial d(theta)/dx and partial d(theta)/dy you have (x^2+y^2)^1/2 I think it should be (x^2+y^2)^-1/2. I am nervous about suggesting this ‘cos it’s a long time since I differentiated anything but my result, after substituting r, theta and phi gives the same result as in the back of the book.

    1. growescience

      you point out where in the post you’re referring to? I’ve checked it and can’t find any mistakes. In the 3-d Jacobian, I use

      displaystyle  frac{partialtheta}{partial y}=frac{y/zsqrt{x^{2}+y^{2}}}{1+left(x^{2}+y^{2}right)/z^{2}}
      which I believe is correct.

      1. Anonymous

        I think I may have misinterpreted your expression. I read the numerator as


        if I read it as


        it’s the same as my result.

  3. Sean

    Due to health problems, my school education came to a sudden halt. So I have no math skills beyond the bare bone basics, and I have no physics education either. Thus I find all this math darn confusing and I could not understand relativity, never mind any relativity problems. So I thought it would be best to discover Special Relativity on my own, and do so by stating from scratch. I succeeded, and I independently derived the basic SR equations, including the Lorentz transformation equations. It was an easy breezy task. See http://www.youtube.com/watch?v=KKAwpEetJ-Q&list=PL3zkZRUI2IyBFAowlUivFbeBh-Mq7HdoQ if interested in a new view of SR.


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