The Elegant Universe: Superstrings, Hidden Dimensions, and the Quest for the Ultimate Theory

My layman's understanding, based on just having finished reading Brian Greene's "The Elegant Universe: Superstrings, Hidden Dimensions, and the Quest for the Ultimate Theory" [1], which was recently a Prime Reading selection (free to borrow for Prime Members), is that is that yes, it started out as one theory, with 10 dimensions, and then other forms were discovered, until they had 5 different string theories. That was the situation around 1985.

It's important to note that the equations of string theory (both when it was one theory and when it was 5 theories were beyond our ability to solve exactly. We could only approximate them, originally with things called "perturbation methods".

Perturbation methods involve solving something for the big influences, then adding in corrections to deal with smaller influences. For example, suppose you wanted to calculate the orbit of a small moon in a close orbit around a large planet. You could first calculate what the orbit would be in a universe that just has that planet and moon--we can do that exactly. Then you could add in the small differences that would be caused by their sun and other planets in their system--the perturbations caused by the sun and other planets.

If, however, you had a planet with two large moons, you might not be able to solve it for just the planet and one moon, then make small corrections for the other moon and the sun, because the influences of the other moon is not small. The exact solution for one planet and moon is just too far off from the final solution for the former to be tweakable into the later.

There's a thing called the "string coupling constant". Perturbation methods can only be used in the 5 string theories when the coupling constant is less than 1. Eventually they found out how to solve some problems in each of the theories even with coupling constants larger than 1, and to the surprise of most they found that the 5 theories could be split into 3 groups.

One group contained two of the 5 theories. A universe following one of those theories with a coupling constant of, say 0.5, would be identical to a universe following the other theory with a coupling constant of 2.0. The two theories are said to be duals of each other.

Another group contained just one theory. That theory was dual of itself. That is, a universe following that theory with a coupling constant of 0.5 would be identical to a universe following that theory with a constant of 2.0.

The final group contained the remaining two of the 5 theories. I'm having trouble remembering how those were connected.

Anyway, somewhere along figuring out that last group, it was found that low energy point-particle approximations of some of the string theories gave some of the 10-dimenensional supergravity theories that had been worked on before string theory to try to unify gravity and QM.

Then in 1995 Witten showed that if you took some of the string theories and go from low to high coupling constant, the physic you get has a low energy approximation that matches 11-dimensional supergravity.

Anyway, where they got to from there was that the 5 string theories had come out 10-dimensional due to the fact that they could only approximately solve the equations, and that string theory actually was an 11-dimensional theory, and the 5 string 10-dimensional theories (and 11-dimenensional supergravity) are just different perspectives on the one 11-dimensional theory that you get when you make certain approximations or take it to certain limits.

(I may have botched an arbitrarily large amount of the above, so caution is called for)

[1] https://www.amazon.com/Elegant-Universe-Superstrings-Dimensi...

tzs · 2018-02-28 · Original thread

The first book is one Einstein himself wrote to explain relativity to a general audience. There are some good versions of this on Project Gutenberg. Links below.

Here's how Einstein described this book:

> The present book is intended, as far as possible, to give an exact insight into the theory of Relativity to those readers who, from a general scientific and philosophical point of view, are interested in the theory, but who are not conversant with the mathematical apparatus of theoretical physics. The work presumes a standard of education corresponding to that of a university matriculation examination , and, despite the shortness of the book, a fair amount of patience and force of will on the part of the reader. The author has spared himself no pains in his endeavour to present the main ideas in the simplest and most intelligible form, and on the whole, in the sequence and connection in which they actually originated. In the interest of clearness, it appeared to me inevitable that I should repeat myself frequently, without paying the slightest attention to the elegance of the presentation. I adhered scrupulously to the precept of that brilliant theoretical physicist L. Boltzmann, according to whom matters of elegance ought to be left to the tailor and to the cobbler. I make no pretence of having withheld from the reader difficulties which are inherent to the subject. On the other hand, I have purposely treated the empirical physical foundations of the theory in a "step-motherly" fashion, so that readers unfamiliar with physics may not feel like the wanderer who was unable to see the forest for the trees. May the book bring some one a few happy hours of suggestive thought!

The book is called "Relativity: The Special and the General Theory".

Here is a copy of the 3rd edition in PDF and TeX made via OCR of the physical book [1].

Here is a copy that is available in HTML, MS Word, and TeX. I'm not sure what edition this is [2].

There's also a Kindle version of the 3rd edition on Amazon for $0.99 that is good. Books with math are often terrible on Kindle due to publishers sometimes doing the equations as small image files that are hard to read and ugly if you zoom them. This one, though, is specifically touted as being "with readable equations", and they are right.

Unless you actually want to read on a Kindle there is no advantage that I can see that it has over either of the Gutenberg copies I listed above. If you do want to read on a Kindle and are willing to cough up $0.99, here is the link [3].

Another book that goes over special and general relativity, in a way similar to what I gave in the prior comment (much of mine was ripped off from this, with my contribution just the probably introduction of errors) is Brian Greene's "The Elegant Universe" [4]. I grabbed this when it was free on Amazon Prime Reading a few months ago, and just recently started it. I'm only about 15% of the way through, but it has been quite good so far. The relativity material is only in the first couple of chapters, though, so if you aren't interested in the rest of the material it would probably not be worth it.

[1] http://www.gutenberg.org/ebooks/36114

[2] http://www.gutenberg.org/ebooks/5001

[3] https://www.amazon.com/gp/product/B004M8S53U

[4] https://www.amazon.com/Elegant-Universe-Superstrings-Dimensi...

dmix · 2017-06-02 · Original thread

Easily the hardest part of learning about string theory for me (via reading "The Elegant Universe" [1]) was grasping the idea of multiple other dimensions.

The book tried it's best to explain it by exploring a world starting with 1D and evolving to 3D, but it's still quite difficult to visualize, especially ones shaped like a "Calabi–Yau manifold" [2].

The one good thing I got out of learning about Calabi-Yau manifolds (and randomly reading another layman story involving Yau's clash with the guy who solved Poincaré conjecture) was a new interest in learning more about math and a getting a laymans grasp of topology.

I enjoyed the linked video, I was looking for a way to better understand 4+D in a way I could wrap my head around and an interactive game makes a lot of sense.

[1] https://www.amazon.com/Elegant-Universe-Superstrings-Dimensi...

[2] https://www.wikiwand.com/en/Calabi%E2%80%93Yau_manifold

ISBN: 039333810X