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I'm not a physicist but I'm interested in unified theories, and I do not know how to start learning about it. What would be a good book to read to start learning about this topic?

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I'm not sure if this is going to be on topic here, but for now I just edited it to be one of our book recommendations. We'll see what the community thinks about its on-topicness. –  David Z Sep 26 '12 at 17:36

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As a theory of everything includes a theory of all particular things, it would be good if you start by learning about the theories that need to be unified. This means first

  • some quantum mechanics,
  • something about classical electromagnetism,
  • something about special anf general relativity, then
  • some quantum field theory,
  • something about quantum electrodynamics,
  • something about the standard model.
So you should look at the recommendations for introductions to these subjects available at our Book recommendations.

Unless you are content with such books as ''The elegant universe'' http://en.wikipedia.org/wiki/The_Elegant_Universe where you learn the buzzwords without a deeper understanding.

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The book Out of this world written by Stephen Webb is a good introduction if you have really no idea what modern fundamental physics is up to. It is the one that made me excited about this stuff for the first time several years ago, and the excitement still holds on :-).

It gently starts by explaining why symmetries are important in physics, followed by an overview about QM and GR, what particle physics generally is about, and the standard model. Then the key ideas behind GUTs (Grand Unified Theories), supersymmetry, and extra dimensions leading to supergravity as a first unified theory including gravity, get introduced. The second part focuses on explaining string and M-theory (other approaches are shortly mentioned too) and some topics, such as black holes, the holographic principle, and cosmology that can be addressed by it.

The book builds up the wisdom it explains in a logical and systematic manner and it is written in a absorbing style that made it difficult for me to put it away. Historical notes about when which ideas and concepts are discovered by whom are included and the way the narrator tells the story made me think that these are all nice people who do awesome and cool things when reading it for the first time.

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These sorts of questions are hard to answer unless there is some understanding about the level of math and physics the asker actually has. Probably one of the most irritating aspect about trying to learn physics is that there is a lot of literature out there that completely ignores any discussion of the Lagrangian and Hamiltonian which are so fundamental to physics formulations (in fact I have an entire college physics text that doesn't use either term once, which is mind numbing and infuriating in retrospect, and I even had a physics grad argue blue in the face that the Hamiltonian was not $\mathcal{H}=T+V$). If a person has not been exposed previously to these concepts, then it is very difficult to have a coherent conversation about physics let alone the Theory of Everything.

Assuming you have at least this level of introductory understanding, the next place I would start is to get an understanding of algebra, lie groups and the standard model. The best introductory paper I have ever read is A Simple Introduction to Particle Physics by Robinson, Bland, Cleaver and Dittman of Baylor University. I would focus especially on Part II - Algebraic Foundations.

The reason this is critical is that although the Theory of Everything is not some sort of crude algebra (despite attempts by some to make it so), modern physics is understood in the language of algebra, and even more importantly a supersymmetry algebra which makes us of Grassmann numbers for the fermionic fields.

Another good introductory text which is worth exploring is the book Lie Groups, Physics and Geometry by Robert Gilmore. I would pay special attention to chapter one, as there is an excellent discussion of why the general polynomial of degree 5 or more can not be solved using radicals. It also gives an excellent initial expose about Lie groups and their classification as simple vs. solvable.

In any case, if you want to master Theories of Everything, it is the language of algebra that needs to mastered first.

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I particularly like the links to the Robinson et al. paper and the book about Lie groups and geometry for myself +1, but I'm not sure if this is what the asker had in mind too, since these resources are rather technical ... –  Dilaton Sep 27 '12 at 16:24
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@Dilaton Probably true, I am just to the point where I think people need to be realistic in the level of effort they are going to have to invest in order to get a good understanding to discuss TOE's. Most popular discussions really barely touch on some of the more difficult concepts. Algebra is really not too difficult, its just that we don't introduce it early enough in the curriculum for people to make the mental connections. –  Hal Swyers Sep 27 '12 at 18:50
    
of course, the hamiltonian is T + V, but I would argue that that is a horrible definition to use for the Hamiltonian--fundamentally, it is the Legendre transformation of the lagrangian, replacing time derivatives with their canonical momenta. –  Jerry Schirmer Oct 30 '12 at 13:18

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