Summary

The universe has many secrets. It may hide additional dimensions of space other than the familier three we recognize. There might even be another universe adjacent to ours, invisible and unattainable . . . for now. Warped Passages is a brilliantly readable and altogether exhilarating journey that tracks the arc of discovery from early twentieth-century physics to the razor's edge of modern scientific theory. One of the world's leading theoretical physicists, Lisa Randall provides astonishing scientific possibilities that, until recently, were restricted to the realm of science fiction. Unraveling the twisted threads of the most current debates on relativity, quantum mechanics, and gravity, she explores some of the most fundamental questions posed by Nature-taking us into the warped, hidden dimensions underpinning the universe we live in, demystifying the science of the myriad worlds that may exist just beyond our own.

Preface and Acknowledgements

vii

I. Dimensions of Space (and Thought)

Introduction

(149)

1 Entryway Passages: Demystifying Dimensions

(20)

2 Restricted Passages: Rolled-up Extra Dimensions

(19)

3 Exclusive Passages: Branes, Braneworlds, and the Bulk

(13)

4 Approaches to Theoretical Physics

(21)

II. Early Twentieth-Century Advances

5 Relativity: The Evolution of Einstein's Gravity

(31)

6 Quantum Mechanics: Principled Uncertainty, the Principal Uncertainties, and the Uncertainty Principle

115

(35)

III. The Physics of Elementary Particles

7 The Standard Model of Particle Physics: Matter's Most Basic Known Structure

150

(29)

8 Experimental Interlude: Verifying the Standard Model

179

(11)

9 Symmetry: The Essential Organizing Principle

190

(13)

10 The Origin of Elementary Particle Masses: Spontaneous Symmetry Breaking and the Higgs Mechanism

203

(18)

11 Scaling and Grand Unification: Relating Interactions at Different Lengths and Energies

221

(19)

12 The Hierarchy Problem: The Only Effective Trickle-Down Theory

240

(16)

13 Supersymmetry: A Leap Beyond the Standard Model

256

(21)

IV. String Theory and Branes

14 Allegro (Ma Non Troppo) Passage for Strings

277

(26)

15 Supporting Passages: Brane Development

303

(18)

16 Bustling Passages: Braneworlds

321

(13)

V. Proposals for Extra-Dimensional Universes

17 Sparsely Populated Passages: Multiverses and Sequestering

334

(17)

18 Leaky Passages: Fingerprints of Extra Dimensions

351

(11)

19 Voluminous Passages: Large Extra Dimensions

362

(23)

20 Warped Passage: A Solution to the Hierarchy Problem

385

(29)

21 The Warped Annotated "Alice"

414

(4)

22 Profound Passage: An Infinite Extra Dimension

418

(15)

23 A Reflective and Expansive Passage

433

(13)

VI. Closing Thoughts

24 Extra Dimensions: Are You In or Out?

446

(9)

25 (In)Conclusion

455

(4)

Glossary

459

(13)

Math Notes

472

(9)

Permissions

481

(2)

Index

483

Supplemental Materials

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Excerpts

Warped Passages
Unraveling the Mysteries of the Universe's Hidden Dimensions

Chapter One

Entryway Passages: Demystifying Dimensions

You can go your own way.
Go your own way.
-- Fleetwood Mac

"Ike, I'm not so sure about this story I'm writing. I'm considering adding more dimensions. What do you think of that idea?"

"Athena, your big brother knows very little about fixing stories. But odds are it won't hurt to add new dimensions. Do you plan to add new characters, or flesh out your current ones some more?"

"Neither; that's not what I meant. I plan to introduce new dimensions -- as in new dimensions of space."

"You're kidding, right? You're going to write about alternative realities -- like places where people have alternative spiritual experiences or where they go when they die, or when they have near-death experiences?* I didn't think you went in for that sort of thing."

"Come on, Ike. You know I don't. I'm talking about different spatial dimensions -- not different spiritual planes!"

"But how can different spatial dimensions change anything? Why would using paper with different dimensions -- 11 X 8 instead of 12 X 9 , for example -- make any difference at all?"

"Stop teasing. That's not what I'm talking about either. I'm really planning to introduce new dimensions of space, just like the dimensions we see, but along entirely new directions."

"Dimensions we don't see? I thought three dimensions is all there are."

"Hang on, Ike. We'll soon see about that."

The word "dimension," like so many words that describe space or motion through it, has many interpretations -- and by now I think I've heard them all. Because we see things in spatial pictures we tend to describe many concepts, including time and thought, in spatial terms. This means that many words that apply to space have multiple meanings. And when we employ such words for technical purposes, the alternative uses of the words can make their definitions sound confusing.

The phrase "extra dimensions" is especially baffling because even when we apply those words to space, that space is beyond our sensory experience. Things that are difficult to visualize are generally harder to describe. We're just not physiologically designed to process more than three dimensions of space. Light, gravity, and all our tools for making observations present a world that appears to contain only three dimensions of space.

Because we don't directly perceive extra dimensions -- even if they exist -- some people fear that trying to grasp them will make their head hurt. At least, that's what a BBC newscaster once said to me during an interview. However, it's not thinking about extra dimensions but trying to picture them that threatens to be unsettling. Trying to draw a higher-dimensional world inevitably leads to complications.

Thinking about extra dimensions is another thing altogether. We are perfectly capable of considering their existence. And when my colleagues and I use the words "dimensions," and "extra dimensions," we have precise ideas in mind. So before taking another step forward or exploring how new ideas fit into our picture of the universe -- note the spatial phrases -- I will explain the words "dimensions" and "extra dimensions" and what I will mean when I use them later on.

We'll soon see that when there are more than three dimensions, words (and equations) can be worth a thousand pictures.

Warped Passages
Unraveling the Mysteries of the Universe's Hidden Dimensions. Copyright © by Lisa Randall. Reprinted by permission of HarperCollins Publishers, Inc. All rights reserved. Available now wherever books are sold.

Excerpted from Warped Passages: Unraveling the Mysteries of the Universe's Hidden Dimensions by Lisa Randall
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