As most of you know by now, I’m working on my next book. While I haven’t come up with a particularly snappy title yet, the general theme will be symmetry, and how it gives rise to physical laws and how simple assumptions (that every particle of a given type is the same, for example) can give rise to some surprising results. I’m going to include a few of my more popular “Ask a Physicist” columns but for the most part, this will be in a similar tone, but largely new material.

Anyway, unlike with the User’s Guide, I decided to do an experiment. I won’t exactly post this in real time, but I did want to share some key points in the process with you guys, and if people had thoughts or ideas, or questions, I’d be able to incorporate them in the book.

So let’s start with my current draft of the table of contents. It looks long-ish, but the idea is to keep individual chapters short enough for people to digest the material in one sitting. Bold face indicates a particular symmetry to be discussed. I have subsections for these chapters, but I’m not prepared to reveal that much of my hand at this time. The idea is that, like the User’s Guide, each chapter and subchapter will have a question leading into it.

I’d love hearing any thoughts that people have. Feel free to email me or just post a comment below.

And of course, if you can’t wait the several years that it will take to finish writing and publish this (and I should point out that I haven’t yet tried to sell this to a publisher), I should remind you that I have another very excellent book available. You should read that in the meanwhile.

- If someone replaced you with an exact duplicate, would anyone notice?

**Particle Replacement** - Why is it dark at night?

**Isotropy of Space** - Can I build a shrink ray?

**Scale Invariance (not a symmetry)** - Is antimatter really so dangerous?

**Charge Conjugation** - How do you identify a parallel universe evil twin?

**Parity,Time, CPT** - Does Entropy increase with time or does it make time?

**Time Invariance (on a macro scale)** - Why are Past, Present, and Future our only Options?

Dimensionality of Spacetime - Noether’s Theorem
- Galilean Relativity
- Special Relativity

**Lorentz Invariance** - General Relativity
- Spin
- The vacuum
- Electromagnetism

**U(1)** - The Electroweak Model

**SU(2)** - The Strong Force

**SU(3)** - Some failed unification schemes

**e.g. SU(5)** - Symmetry Breaking
- Supersymmetry (though this will likely span several chapters)

I’m looking forward to reading your comments.

**-Dave**

An excellent start to what looks like a good book. I’ll offer a few suggestions that may or may not have place in your book (depending on scope and accessibility):

1] Renormalization group (RG) theories the idea that the system in study is self-similar at multiple scales which gives predictions on critical exponents. This comes up quite a bit in stat-mech when you can take the limit of large N.

2] Real-world graph theory models with scale invariance. For example, consider the Erdős–Rényi graphs vs the Barabási–Albert ones. Both are generated via some random process, but the BA graphs possess an inherent symmetry at all scales which leads to many interesting theorems. You can guess which one are more prevalent in the real world.

3] Finite simple groups and their connections to physics. Plus, no book about symmetry would be complete with a brief nod to the Monster Group.

4] The symmetry found in many problems with boundary conditions. There is beauty and elegance in the special functions like the spherical harmonics and Bessel’s. Naturally the pure solutions only arise when there is some kind of inherent symmetry, but that’s the whole point isn’t it?

Good suggestions, and I’ll see what I can work in. I’m already in danger of not being able to provide a sufficiently lucid non-technical description. Let me see where I can shoehorn some of these in. And thanks.