I want to like this book more than I do.

As a general matter, this is exactly the sort of science book we need more of. As you can probably guess from the title, Why Does E=mc^{2}? sets out to explain Einstein’s theory of relativity, and does an excellent job of it. It presents a clear and concise explanation of the theory for a non-scientific audience, using no math beyond the Pythagorean Theorem.

I picked this up partly as research of a sort– if there is ever a How to Teach Physics to Your Dog 2: Canine Boogaloo, the most obvious topic for it would be relativity, which I mention a few times, but don’t discuss in any detail. I was thinking about how that would work, and picked this up to see how they went about explaining things. I don’t think I’ve encountered a better explanation of the physics, which they explain entirely with a geometric picture of spacetime, that makes a great deal more sense than most of the mathematical approaches I’ve encountered in my professional education.

And yet…

While explaining relativity with no math more than the Pythagorean theorem is impressive, something about the way they do it ended up annoying me. On the few occasions when they do use math, the parts with the equations are preceded by a paragraph or so reassuring the reader that while math is about to occur, they don’t really need to worry about all the details, and can just skip ahead if they find the math too scary. Then they present some equations, followed by a paragraph or so congratulating the reader for being a brave soldier and making it through the scary math. It starts to seem a little patronizing after a while.

And then, after all the folderol about how the Pythagorean theorem isn’t really all that scary, they go and dump the Standard Model Lagrangian on the reader. They don’t do anything with it, other than describing the various terms in a very vague and qualitative way, but it seems like a bit much given the rest of the text.

There are a few other mis-steps, most notably a running joke about Thales of Miletus that goes on too long, and starts to get a little creepy. The end result was to sort of undermine what is otherwise a really excellent explanation.

Now, it should be noted that I am very much not the target audience for this book. And it’s entirely possible that I am subconsciously using these elements as a source of annoyance to justify continuing to think about the possibility of a HtTPtYD2:CB (as it would be hard for Emmy and me to do a better job on pure physics grounds). I don’t think I can reliably assess how this book would work for its intended audience of people who have no science background to speak of. It might be that the sections I found annoying are genuinely soothing to them, and make the explanations work better for them.

And, as I said, the explanations, stripped of the annoying bits, are outstanding. So I definitely recommend it to people who would like a better understanding of how relativity, particularly special relativity, works in modern physics. Just, you know, when you get to the bits where they tell you how the next bit has some math, and you can skip it if you like? Skip those bits.

Did they go into the historical tangents on who wrote

E = mc^2 before Einstein, or came so very close as with Lorenz and Poincare’?

Or why he first wrote

E^2 – (pc)^2 = (m_0 c^2)^2 = m_0^2 c^4

or why he was truncating the power series:

= m_0 c^2 [1 + (1/2) (v/c)^2 + (3/8) (v/c)^4 + (5/16) (v/c)^6 + …]

Just wondering…

Does the parallel mirror time clock analysis still work if you rotate the mirrors so the planes of the mirrors are oriented perpendicular to the direction the train is travelling???

If it doesn’t, why not?

I have been struggling with the maths on page 127.

Can any one explain it to me?

The key phrase is “it can also be written as dt/gamma.”

Well, I have spent a few hours trying to get delta s/c to equal dt/gamma and have not been successful.

Am I missing something?

Just work with the right-hand side of the definition of Ds/c. Factor a (cDt)^2 from both terms under the square root, giving you a cDt outside the square root, and leaving 1-(Dx/cDt)^2 inside. Dx/Dt is equal to v, so that’s really a square root of (1-v^2/c^2) and you’re just about done.

Thanks Chad

That’s great. I haven’t got much time this evening so will look at it at greater length tomorrow.

But doesn’t your approach leave us with Ds/c= cDt/gamma rather than Dt/gamma?

Steve

There’s a c in the denominator of the original equation, that cancels the c that you factor out from the square root.

Thanks a lot Chad.

I was just going to say I spotted the c (even after a glass of wine!).

I understand it now.

Thanks very much for your help. Much appreciated.

I agree with you, the Thales thing is a little overdone.

Steve

On p.77 of ‘Why does E=mcÂ²’, I fail to grasp why the minus-sign version of the Pythagorean distance equation is considered as a possible solution to calculating the distance in spacetime. Could anyone please shed any light on why this is so ?

Also, ref momentum vector in time direction, p.131-133, top p.133, “Don’t be confused by the fact that we multiplied by c…….included term Â½mvÂ² rather than Â½mvÂ²/cÂ²”. If we take gamma = 1 + Â½(vÂ²/cÂ²) from top p.132 and put into gamma x mc from bottom of p.131, we would get conserved energy E = mc + Â½mvÂ²/c, the second bit being divided by c (not cÂ²) – please explain why it’s Â½mvÂ²/cÂ². So if mass is stationary, E would equal mc (not mcÂ²), which would mean a factor of c less energy produced !? A monumental difference from simply choosing to not multiply by c, ref bottom p.131, which is apparently done pure and simply to give the kinetic energy term Â½mvÂ²) Please help with my confusion !

Same question as Steve K: on page 133 multiplying by c does not cancel the cÂ² in Â½mvÂ²/cÂ². What are we missing here?

I picked this up to see if it was worth recommending / giving to people. I found exactly the same things annoying . The whole standard model part was ludicrous. The other thing that annoyed me was the constant references to Manchester and other vaguely northern things – all a bit twee. Sad because the explanations that were there were quite good. Overall, I think there’s certainly space for a better entry into the field.

I found this book almost excellent. Yes, you have to think about it a bit. E.g. Minowski (hyperbolic) space isn’t flat so it looks like the solution doesn’t work when viewed on a 2d diagram. Maps of the globe suffer from 3d to 2d distortion so this isn’t all that surprising. I also thought you needed a bit more maths than Pythogoras. E.g. page 127 where I’ve inserted my own 10 stage “bit of mathematical manipulation”. I’d have liked to have seen an appendix with such mathematic manipulations explained. However, I’m really pleased that the authors didn’t shy away from including the maths. Overall I think it’s an extemely good book and I’ll be looking for more by the same authors.