# "The Elegant Universe" by Brian Greene

Notes from Kindle

## Table of Contents

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## ¶Highlight on page 140 | Location 2136-2141 | Added on Thursday, December 29, 2016 1:10:45 PM physics

unlike-colored quarks (red with green, green with blue, or blue with red) are also identical. In fact, the data support something even more striking. If the three colors—the three different strong charges—that a quark can carry were all shifted in a particular manner (roughly speaking, in our fanciful chromatic language, if red, green, and blue were shifted, for instance, to yellow, indigo, and violet), and even if the details of this shift were to change from moment to moment or from place to place, the interactions between the quarks would be, again, completely unchanged. For this reason, just as we say that a sphere exemplifies rotational

## ¶Bookmark on page 173 | Location 2641 | Added on Saturday, December 31, 2016 8:07:40 PM physics

just something about point particle interation as strings (the X-letter like tube)

## ¶Highlight on page 182 | Location 2789-2791 | Added on Sunday, January 1, 2017 10:00:57 PM physics

bearing any resemblance to our world. Subsequently, though, close examination of this theorem, based on insights of a number of physicists revealed precisely one subtle loophole: The Coleman-Mandula result did not exploit fully symmetries sensitive to something known as spin.

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By 1971 or so, physicists showed that the answer to this question was yes. Although the full story is quite involved, the basic idea is that when spin is considered, there is precisely one more symmetry of the laws of nature that is mathematically possible. It is known as supersymmetry.3 Supersymmetry cannot be associated with a simple and intuitive change in observational vantage point; shifts in time, in spatial location, in angular orientation, and in velocity of motion exhaust these possibilities. But just as spin is "like rotational motion, with a quantum-mechanical twist," supersymmetry can be associated with a change in observational vantage point in a "quantum-mechanical extension of space and time." These quotes are especially important, as the last sentence is only meant to give a rough sense of where supersymmetry fits into the larger framework of symmetry principles.4 Nevertheless, although understanding the origin of supersymmetry is rather subtle, we will focus on one of its primary implications—should

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Since none of the superpartner particles has ever been detected, you would be justified to take Rabi's remark from Chapter 1 regarding the discovery of the muon one step further, declare that "nobody ordered supersymmetry," and summarily reject this symmetry principle. For three reasons, however, many

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moon with a margin of error no greater than the thickness of an amoeba. Although numerical adjustments of an analogous precision can be made within the standard model, many physicists are quite suspect of a theory that is so delicately constructed that it falls apart if a number on which it depends is changed in the fifteenth digit after the decimal point.5

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not sure what did I like here

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particular class of six-dimensional geometrical shapes can meet these conditions. They are known as Calabi-Yau spaces (or Calabi-Yau shapes) in honor of two mathematicians,

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there is not much room for a large object like your hand to move—it all averages out so that after sweeping your arm, you are completely unaware of the journey you took through the curled-up Calabi-Yau dimensions.

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Holes in Calabi-Yau shapes have impact on vibrational patterns of strings

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This realization has led string theorists to examine the physics resulting from a sample of possible Calabi-Yau shapes. Even here, however, life is not completely smooth sailing. The approximate equations that string theorists currently use are not powerful enough to work out the resulting physics fully for any given choice of Calabi-Yau shape. They can take us a long way toward understanding, in the sense of a ballpark estimate, the properties of the string vibrations that we hope will align with the particles we observe. But precise and definitive physical conclusions, such as the mass of the electron or the strength of the weak force, require equations that are far more exact than the present approximate framework.

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Appaprently book got good basic explanations for Calabi-Yau figures

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values such as 1/5, 1/11, 1/13, or 1/53, among a variety of other possibilities. These unusual charges can arise if the curled-up dimensions have a certain geometrical property: Holes with the peculiar property that strings encircling them can disentangle themselves only by wrapping around a specified number of times.18

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By using Einstein's E = mc2 relating mass to energy, we can also say that the energy bound in a wound string is proportional to the radius of the circular dimension. (Unwrapped strings also have a tiny minimum length since if they didn't, we would be back in the realm of point particles. The same reasoning might lead to the conclusion that even unwrapped strings have a minuscule yet nonzero minimum mass. In a sense this is true, but the quantum-mechanical effects encountered in Chapter 6—remember The Price Is Right, again—are able to exactly cancel this contribution to the mass. This is how, we recall, unwrapped strings can yield the zero-mass photon, graviton, and the other massless or near-massless

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significantly from the value 1 (meaning, again, 1 times the Planck length), then one of our operational definitions proves extremely difficult to carry out while the other proves extremely easy to carry out. In essence, we have always carried out the easy approach, completely unaware of there being another possibility.

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According to the light string modes, the universe is large and expanding; according to the heavy modes it is tiny and contracting.

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By carefully examining a huge sample set of Calabi-Yau spaces that they had generated by computer, they found that almost all came in pairs differing precisely by the interchange of the number of even and odd holes. I told him that I was still seated—that Plesser and I had found the same result. Candelas's and our work turned out to be complementary; we had gone one step further by showing that all of the resulting physics in a mirror pair was identical, whereas Candelas and his students had shown that a significantly larger sample of Calabi-Yau shapes fell into mirror pairs. Through the two papers, we had discovered the mirror symmetry of string theory.7

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something about mirror Calabi-Yau spaces?

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not sure what was interesting here..

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illustration how M-theory connects Type I, IIB, IIA, Heterotic-0, Heterotic-E, Supergravity

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not sure what was interesting here..

## ¶Highlight on page 378 | Location 5791-5793 | Added on Sunday, June 25, 2017 2:52:18 PM physics

He found another solution to Einstein's equations in which the very early universe undergoes a brief period of enormously fast expansion—a period during which it "inflates" in size at an unheralded exponential expansion rate. Unlike

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One overarching lesson we have learned during the past hundred years is that the known laws of physics are associated with principles of symmetry.