Unraveling the Mysteries of the Universe's Hidden Dimensions

Too difficult for the average reader. If you're looking to learn about particle physics this is not the place to start. Although she tries
to explain with analogies and she does a very good job,the concepts are still too dificult for the layman. One needs to study and reread the book then perhaps some of the concepts can be grasped.

I enjoy keeping up with developments in physics, reading Brian Greene's and Lee Smolin's books for and against string theory, for example. But it has been awhile since I have thought deeply about particle physics. So I was excited to see how this area of physics has progressed, especially with such innovative and potentially testable ideas presented in Lisa Randall's Warped Passages. What is especially attractive about Professor Randall's book is that she has explained the many physical ideas presented, while mind-bending, so clearly and thoughtfully. Rarely when reading a non-fiction book do I come away with such a feeling of good will toward the author. I applaud Dr. Randall for letting us amateurs in on such a fantastic story of physical reality as she weaves in her Warped Passages book. Bravo!

This is a great book to understand extra dimensions, string theory, etc.

If one lived in a one dimensional or two dimensional world,She uses simple examples to explain three dimensions. This is the way she operates throughout the text to help us understand the concepts for the various theories. Take it slow. Go back and reread to mesh it all together.

Just one word fits this book: extraordinary... Lisa Randall succeeds in clearly explaining, for the average Joe, bleeding edge particle physics (and cosmology) research and theory, as well as physicists' hopes and dreams, without using one formula. She brilliantly continues the work of Michio Kaku (Hyperspace, Parallel Worlds) and Brian Greene (The Elegant Universe, The Fabric Of The Cosmos). Her comparisons, metaphors and quotes are both suggestive and funny. When you reach the last page, you understand that only the book ends, but not the story. And, like the author, you can hardly wait for the CERN's next microscope, sorry, accelerator, and hope that Randall will explain the next chapter.

Lisa Randall of Harvard is one of the most imaginative popularizers of modern physics, who has the mind of a brilliant physicist combined with the imagination of a poet. With Randall, these two talents are not a zero sum game, the two talents actually synergize in her writing. As an example, her book, Warped Passages, manages to tackle the elusive issue of how to deal with higher dimensions in string theory and trace its implications through the world of modern physics by the use of her imaginative concept of bulk dimensional domains. These are regions of full higher-dimensional space.

Such a concept is an alternative to the somewhat convoluted (to my mind) Kaluza-Klein solution for the higher dimensional domains of strings, in which the higher dimensions are wrapped around the
lower dimensional axes

Although not mentioned by Randall, because it seems to be unknown to the community of string theorists, another possible solution to the higher-dimensional problem is to realize that strings do not inhabit physical space, they inhabit mental or quantum space
(the timeles spaceless domain of Plato's Mind). Then the solution to the higher higher dimensional problem is to relegate strings l to the mental space of Leibniz's dual-aspect, monadic, mental-physical or quantum-physical universe. In that quantum space, which is not physical but mental, and is also timeless and spaceless, an infinite number of mental or quantum dimensions is opened up so that the regions of bulk domain can be dispensed with. For details on Leibniz's dual aspect universe, one has to consult his Monadology.

-Ever since Hume, science has imprisoned us in the dark cave of materialism and blind empiricism
and needs to restore us to the quantum sunlight of plato (plotinus) -- see my website
[...] or search in Google with a search term such
as Clough platonic theory of mind Site: [...]

Lisa Randall has written a sometimes breezy and often vague book that specializes in sentiments like: If this is true, then all these other things might be true, too!

Her expositions of Newton, Einstein and others do not compare favorably with her many predecessors. Her primers on gravity and relativity are memorable for their opacity. She has succeeded in being new and different, but not clearer and better.

A reader interested in modern physics would be well advised to read Nobel Prize winner Robert Laughlin's book, "A Different Universe: Reinventing Physics from the Bottom Down." It is smarter and more insightful. His concept of emergence is very important.

OK, I haven't read a book about physics/cosmology for a quite long time.

Not since I read Stephan's "Brief History of Time".

I found the book by Ms.Randall very interesting and intellectually stimulating.

Although I have already known many of theories and facts she discussed in the first 2/3 of the book, reading recap of well-known topics is good; She is a teacher after all and I would appreciate her writings to refresh my memory.

The most interesting part is, of course on the page 454, Ms.Randall's friend Nathan Seiberg (scientist of 21st century) confessed that he is almost certain that space and time are illusions.

Now that takes us back to Herr Immanuel Kant!

Prof. Kant said that Space and Time do not exist as thing itself.

It is only a format that human brain recognizes outside world.

Simply put, such things like Space and/or Time do not exist; those are mere measuring scales given to miserable rats like us a priori (to find cheese?)

According to Kant, causality is only a function of brain.

"After you study my science, you will not be bothered by foolishness such as infinite space and time" he said.

I believe that science, religion, and the paranormal are not mutually exclusive. I see no basic divide separating Albert Einstein, the concept of intelligent design, and Edgar Cayce or the Michael Spirits. I believe they are all looking for the same thing - the truth. Of the three, I would consider theoretical physics to be the most outrageous with its multiple universes, hidden dimensions, alternate realities.

The intellectually "correct" view would be that science is the only acceptable path to the truth, and that religion and spiritualism are utter nonsense. I consider that a form of snobbery, and a very popular one. The line "You have no evidence" is so often used by the science snobs, and yet there is no evidence of so much in today's science. For example, there is no evidence that an amoeba is capable of "evolving" into anything more complex than another amoeba, so how do we get from amoebas to trees to geese to humans? Not a shred of evidence that an amoeba can do that. Not a shred of evidence that much in theoretical physics is true. It's all a game of "what if" and of internal consistency. Show me the little dimensions. Show me the alternate universes. There's no evidence that they exist. But they might. So don't be a snob and don't complain that there is "no evidence" of life after death or of a designer. The "no evidence" argument is over-used. No, there's no evidence, but then again, there's no evidence to disprove things either, so you either think or you don't, and you can stuff the snobbery.

Personally, I think that "dark matter", "dark energy", "multiple dimensions", "alternate universes", and "life after death" might all be related. Think about it. There is no evidence either way, but I think it all dovetails together well. Don't be a snob about it. You don't have the answers. Don't pretend you do.

What if "dark matter" includes other dimensions and alternate universes? What if other dimensions include heaven? What if "dark energy" includes the energy of our souls, of us, in the afterlife? Are you married to the idea that death means complete obliteration? You have no evidence either way, so why be so attached to one possibility and dismissive of another? Is it just snobbery? Or perhaps just a lack of imagination? Or an unwillingness to risk the disapproval of your teachers? Or your own desire to sit comfortably with the right people, the academics, as you throw scorn at all the ignorant people who have the nerve to think differently?

A very boring read. I am a scientist myself. Physics is not my field and I wanted to broaden my horizon... it did not work. Just give me a Sam Harris, a Richard Dawkins or a Malcom Gladwell.
EDIT: fixed typos: boaded -> broaden (yeah, I was asking for that response of yours, Steve)

Gravity is the weakest forces of all the four forces of our universe, because, according to the author, it is concentrated in another spatial dimension of the universe, and these extra dimensions could be infinitely large. The summary of this book is as follows: We live in a three-dimensional pocket of higher dimensional space, also called branes. It is like a bead on a wire that can only move along one dimension, a brane may restrict our motion to three dimensions although other dimensions exist around it. The theory of supersymmetry also explains the hierarchy problem by postulating that every fundamental particle has a heavier partner, but the theory currently predicts particle interactions that don't occur in nature. The author predicts that if extra dimensions exist, particles could be separated to prevent unwanted interactions, and that gravity could be concentrated somewhere in an extra dimension. The force's strength becomes exponentially weaker further from the gravity brane. The model consists of a pair of universes, four-dimensional branes (three space and one time), thinly separated by a five-dimensional space called the bulk. The mathematical solutions for this setup suggested that the space between the branes is warped, and objects could grow larger or smaller (less massive or more massive) as they moved back and forth between two branes, a direct result of higher gravitational force. The fifth dimension could be so warped that the number of dimensions you see would depend on where you are in the bulk. In addition, gravity is as strong as the other forces, because it is much stronger on one brane than the other. Therefore our universe is located on a brane where only weak gravitational force is felt. This idea of the author is not new since string theorists, Arkani-Hamed, Divali and Dimopoulos (group A.D.D.) suggested that if one or two of the curled-up extra dimensions of string theory had sizes as big as a tenth of millimeter, then gravity would be similarly diluted and weakened thus explaining the hierarchy problem.

There is increasing perception among some leading physicists like Ed Witten that space and time could be illusions, or it is perhaps made of simpler yet undiscovered physical parameters. We are still long way to clearly understand the concept of space and time, but the author's theory may be a step in the direction of advancement. However, one of the major problems of this theory is that it is all talk (theoretical) but no substance (no experimental evidence). We have to wait a little longer after the LHC data is completely analyzed and understood.

The book is very well written and easy to understand; the author has explained the relevant physical concepts in a simple and lucid manner; highly recommended.

1. The Elegant Universe: Superstrings, Hidden Dimensions, and the Quest for the Ultimate Theory
2. A First Course in String Theory

Why would anyone let another's review determine if they would buy this book? Opinions are like bellybuttons: everyone has one and everyone's is different. I can see reading objective reviews of concrete objects (planes , trains and automobiles) but a book? I bought the book with a scant background in Physics of any kind, and I thought it was great because it took a very complex subject and made it understandable. But buy it yourself and determine for yourself. Some people hate Robert Frost's poetry, some love it...why would I let either opinion sway me?

Jim Morrison may have noted that people are strange, but I don't think he realized that on the most basic level, everything is strange. Beyond the cells that make us up, beyond the molecules and atoms, and beyond the protons, neutrons and electrons, is a host of exotic particles that both make up matter but also give us clues into the fundamental nature of everything.

Lisa Randall's book Warped Passages is a tour through this weird landscape, one in which we see semi-familiar particles like quarks, photons and neutrinos, and more alien things like gluons, gluinos and sleptons. Beyond all these are the strings that vibrate in different fashions in rolled-up dimensions so tiny that they are undetectable.

Or are they? Much of Warped Passages deal with attempts to experimentally determine if these hidden dimensions exist, and if they do, what it means to our theories of matter and energy. Right now, however, much of what Randall discusses is only theoretical. It may make sense (at least if you've done graduate work in physics), but it is still unproven.

When you get down to the quantum level, things behave in a way that often contradicts what would seem rational on the human scale of perception. As a result, the concepts in this book are not always easy to understand; in fact, the deeper you get into the book, the more mind-bending it gets. Randall does well-enough with a rather difficult subject: if you have the interest and the patience, Warped Passages can be a rewarding experience.

Speaking as both a scientist and science educator Warped Passages in by far the most impressive of the numerous books I have read on higher dimensional space and particle physics! Professor Randall’s writing style is both illuminating and colorful especially in her use of analogies and metaphors in explaining her “model building approach” to particle physics vs. the more ethereal methods of string theory. As compared to other books on the subject once I open it I have a hard time putting it down! I highly recommend this exciting and dynamic book from the lay reader through the professional scientist, and especially science educators as it
is an outstanding resource on the subject.

"The postulated braneworlds are a theoretical leap of faith, and the ideas they contain are speculative. However, as with the stock market, riskier ventures might fail but they could also reward you with greater returns." Sound familiar science fans? This popular apologetic pitch for strings/branes has been written quite a few times over the past two and a half decades. Lisa Randall's Warped Passages stands with the best of the several I've read, but the risky market of her analogy is more connectable to the physical world than are `braneworlds', whose "greater returns" continue to have no physical home beyond such happy sounding analogies and the professional commitments of Ed Witten's disciples.

The story of string/branes cannot be well told without expositing the history of theoretical physics. Newton's brilliant and far reaching understanding of gravitation and his promising but limited grasp of particles and of relativity, eventually had to give way to the deeper understandings introduced by Planck and Einstein, and advanced by Bohr and Heisenberg. But even with its tremendous and ongoing successes, quantum theory has always suggested that it is not a complete picture of nature. George Gamow, one of the principle `completers' of quantum physics had expected a deeper view of nature to begin to appear forty years ago. But nature's deepest secrets have remained beyond our grasp. String theory promised access to `the mind of God' -- borrowing Hawking's famous hyperbole of nearly 25 years ago (which he had borrowed from Einstein, and which Einstein had borrowed from Kepler) -- reducible to elegant mathematics. But string theory became many string theories, which became M theory, which became braneworlds theory, the mathematics became less elegant and the theory abjured from what most would be willing to call the scientific method and from the logical principle of economy commonly referred to as Okham's Razor. There could be no conceivable greater violation of Okham's principle than braneworlds theory, which demands 10 to the 500th power, or more, possible ensembles of non-examinable and unknowable `worlds'. This is a very far cry from "elegant".

Randall offers that there *might* be *possible* future experimental results that *could* be more consistent with braneworlds theory than other possible results, this is as much of an olive branch as the strings/branes speculation can hold out to the real world of scientific falsifiability. It's okay to be unimpressed. At this point, I think it should be mandatory.

Randall's book is well organized and well presented, and if you're looking for an exposition on braneworlds that is thorough at an accessible `entry level', this book will be better than most. On the one hand, I'd like to rate her book at 4 or 5 stars, based on style and presentation. But the intractable problems remain with the open-ended, extra-scientific speculations that she is pitching. Like Leonard Susskind, another ardent apologist for strings/branes, Randall cannot avoid constant admissions that the entire field of study is as speculative as ever, and may prove to be a wasted effort. In the end, this is as much as can be honestly said of strings/branes. We may call strings/branes a conjecture, but it fails to amount to a theory unless that word is dispossessed of its normal meaning.

With 25 years of strings/branes to scrutinize, it is apparent that it is a topic better fitted to mathematical and theological studies than to theoretical physics. It is not fitted to experimental physics at all.

The impetus, i.e., the pressure, to pursue strings/branes, is understandable on several levels. But Randall's early chapter references to Edwin Abbott's 19th century classic `Flatland', a little book treating dimensions, is as powerful as the strings/branes conjecture gets (Flatland is clearly more modest and more persuasive). I give Lisa Randall credit for her attempted honesty and nearly ubiquitous caveats: "Today, we can't say whether or not the obstacles facing the theory are `insuperable' or not . . ." (pg 297), and, "no one has yet found a way to solve many of the most important questions . . ." (pg 453); with these necessary admissions reappearing every few paragraphs throughout much of the book. The profound secrets of nature are indeed arresting, but strings/branes speculations have NOT presented us with any verifiably real knowledge of nature. Nor is it apparent how strings/branes could ever do so. After dominating research for 25 years, it seems that strings/branes cannot bring us anything as physically concrete as Abbott's Flatland did nearly 125 years ago. Regarding the growing mathematical *inelegance* of braneworlds, as well as the scientific irrelevance of the speculation, I recommend mathematician Peter Woit's important book, Not Even Wrong.

In the mid 1600's Sir Isaac Newton established the classical view of the physical world. It took almost three hundred years for the chinks in the theory to reach the point where Einstein published his theory of relativity. That theory didn't exactly replace the Newtonion world, but extended it dramatically. Now it's been a bit more than a hundred years and holes in the theory have appeared justifying a bunch of new theories that explain areas where Einsteinian theory doesn't work.

This book explains the newest theories of multi-dimensional string and supersymmetry theories, some of which are the result of her own work.

The surprising thing about the book is not that she has been working to develop these theories, but that she is able to explain them so well to those of us unlikely to read 'Physical Review,' the main trade journal.

These newest theories don't have simple analogies like the apple hitting Newton's head, or Einstein's famous equasion relating energy and mass. But there is nothing that says that the universe has to be simple. The world of theoretical physics is alive and doing very well. Dr. Randall is helping it to move along, and trying to help the rest of us move along with it.

Writing about advanced topics in modern physics for the layman is almost always an exercise in futility. Attempting to provide meaningful explanations of notions requiring sophisticated mathematics like differential geometry, topological groups and Lie algebras for someone who can't balance a chequebook is worse than ridiculous.

Some books in this genre do succeed in some fashion. Penrose's magnificent "The Road to Reality" actually teaches much of the relevant maths before launching into a discussion of the physics. Gamow's entertaining "Thirty Years that Shook Physics" both teaches and conveys some of the immense excitement surrounding the birth and early development of quantum theory. Even Glashow's amusing reminiscences in "Interactions" serve to show that doing physics is great fun. Unfortunately, Prof. Randall's work shares none of these worthy qualities.

The author's plodding prose (She lectures in the same style) is only part of the problem. The pedestrian pace is further slowed by silly, pointless vignettes at the beginning of each chapter that describe the irrelevant adventures of two laymen trying (unsuccessfully) to understand the properties of higher spatial dimensions. Worse, the early chapters are endlessly repetitive and rambling without being informative.

Once we get past the first, largely irrelevant, eighty or so pages, a good portion of the book is devoted to a rather tiresome history of twentieth century physics, from the special and general theories of relativity and quantum mechanics through the standard model to supersymmetry and string theory. This may be of value to some but, as observed previously, many more coherent and stimulating versions exist. And those versions do not have egregious errors such as attributing the notion of "electron waves" to Niels Bohr in 1913 when, in fact, it was the subject of Louis de Broglie's 1924 Ph.D. dissertation. Less important, but still annoying, is Prof. Randall's reference to the "theory of general relativity" as opposed to the "general theory of relativity".

The real purpose of the book does not become apparent until Prof. Randall launches herself into a self-congratulatory explanation of topics related to her own research. While an informed reader could make sense of this, of course, the absolute layman will, at best, achieve only the unjustified illusion of understanding.

The message here is clear. If you want to understand modern physics, do the work. Learn the maths first. You can't run if you can't stand.

Lisa Randall is described in the cover notes as the first woman to hold a tenured professorship in the Princeton physics department, the first woman theoretical physicist to gain tenure at MIT, and the first woman theoretical physicist to gain tenure at Harvard. With credentials like those, she obviously knows her physics. So the only real question is, can she write readably on the subject. And I think she can -- mostly. I certainly understand more about modern concepts like string theory, supergravity, and the ideas of 10- and 11-dimensional spacetimes that physicists are using now than I did before reading the book. While some points are still not clear, it is hard to tell whether this is because they are too complex for anyone but a practicing physicist to understand or because Prof. Randall still hasn't explained them thoroughly enough. And I'm willing to give her the benefit of the doubt there.

Her format derives, it seems, from the type of book that George Gamow wrote describing relativity and quantum mechanics using the adventures of the fictional character, Mr. Tompkins. One difference is that, in this book, the story is a relatively minor part and the physics takes up the bulk of the book, the reverse of Gamow's books. In fact, one can probably ignore the story and get most of what Prof. Randall has to say. Though it is somewhat interesting to follow her characters, Icarus and Athena Rushmore (and she obviously chose her characters' names with care; Icarus is a devil-may-care type who dies in an accident while Athena, his younger sister, is the smart one who loves owls! I wonder if Randall intends Athena to represent herself.)

I mostly liked the book; as I say, I don't think I understand _everything_ yet, but I know a lot more than I did before I opened the book. If you have an interest in the subject matter of this book, I recommend that you read it.

The author starts this book with a review of physics starting with classical mechanics, through electromagnetism, quantum mechanics, relativity, and the Standard Model for particle physics. There are only two equations in the text, both familiar to many people: Newton's F=ma, and Einstein's E=mc2. Others, including Maxwell's equations, have been placed in the math section at the back of the book. (Thank you. I make my living working with radio waves, good old 19th century physics.) Also in the math section is the author's elegant five-dimensional space-time metric.

The story gets really interesting in the last one hundred or so pages with descriptions of extra-dimensional models. These models provide insight into the mystery of gravity. Why is it so weak compared to the other three forces? In the last quarter of the book the author's enthusiasm and joy for revealing the secrets of the universe is apparent. We live in a universe that appears to us to be four dimensional, three of space and one of time. However, the universe may have five, ten, eleven, or another number of dimensions. There is occasional humor, although some may be unintended. When asked whether the universe has ten or eleven dimensions, Professor Randall replies that there is a duality in the two. You use the one in which the calculations are easier! Sometimes it is hard to know when physicists are joking.

What good is all this? One hundred years ago, no one could have imagined that we could not have in-car navigation without knowing relativity theory, or that quantum mechanics would be needed to bring us the greatest triumph of human civilization, the iPod. No one can say where this new physics will lead.

I recently learned that the author and I went to high school together. Actually, we were together in all dimensions except one - time. Four of five, nine of ten, or ten of eleven, is pretty good. However, we do live in the same cultural time period. There are references in the book to Jefferson Airplane, Pink Floyd, and Suzanne Vega (the Mother of the MP3). I have to admit that there was one concept in the book that I found too difficult to understand. How can a native New Yorker become a Red Sox fan?

Others have commented on Lisa Randall's accomplishments. She is the first female theoretical physicist to be tenured at Harvard. What time period is Harvard living in? Judging by the remarks of their recent president about women in science, they must be at least one hundred years in the past. Randall has to be an order of magnitude better than her male counterparts to have the job. She may just be the smartest person on the planet. Read the book. At the very least you will be able to add some new phrases to your conversation: Planck scale, symmetry breaking, brane, and gauge boson.

I had to read Warped Passages for the second time to get a good comprehension of its ideas. It has been almost 40 years since I studied physics in college. I had heard the buzz words like quarks and branes but had no understanding. Now I feel connected to particle physics and string theory. I am excited about the new theories and what we hope to learn in the next few years at CERN.

Warped Passages is well written. The short stories about Ike and Athena which begin most chapters give a good mind set to follow the concepts presented in each chapter. I found some discussions like that about supersymmetry to be a bit daunting. Hence, I had to read the book twice. I am sure that I will reread at least some of it a third time.

Although I am an engineer and have a background in mathematics, I have not kept up with particle physics over the years. I feel that Warped Passages has brought me up to date. Lisa Randall does an excellent job in giving credit to other ideas and to those who helped her do her research. Her forthrightness makes the book very credible.

Scientists, experts and those with years of experience and training sometimes have problems grasping the complex, and compressing it into something understandable for the rest of us. Not so with Lisa Randall. Her obvious love of her subjecct matter bubbles across the pages and infects the reader with the same sense of discovery, awe, and entertainment that she obviously feels. She manages to explain what some idiots claim is unexplainable, teaching, providing examples and offering a glimpse into the workings of the universe.

This book makes for a very pleasant addition to anyone interested in learning about our world.

Given her deft way with words, her ablity to explain without becoming ponderous or lecturing, I would love to see Ms. Randall on a forum with a group of Intel Design or Creationist fundies and watch her do her magic. An unbiased audience would quickly see which position was arrived at through hard work, brilliant minds and creating problem solving. This book makes a great gift for adults, yet the way she eases the path to understanding our complex universe, this would also be a great gift for teens.

Brava, Ms. Randall. We anxiously await your next work.

I really appreciate Lisa Randall's ability to bring complex ideas down to within grasp of the typical educated reader. She does an excellent job explaining concepts and offering analogies. Individuals who enjoy books like Brian Greene's The Fabric of the Cosmos: Space, Time, and the Texture of Reality or Michio Kaku's Parallel Worlds: A Journey Through Creation, Higher Dimensions, and the Future of the Cosmos will really appreciate this book.

Sure, Lisa speculates a bit, but who wouldn't? She's truly excited about her work and the opportunity to share that excitement with her readers. It's true that some of her ideas will become testable upon completion of the Large Hadron Collider in Geneva, Switzerland. It will be exciting to follow the research and see where the data leads. I'd encourage anyone with an interest in high energy physics to read this book!

Already having an extensive science background and an interest in cosmology, physics and astronomy for years, I found Lisa Randall's book incredibly provocative and fascinating. (I was also delighted to discover a WOMAN in this field predominantly filled with male physicists...) Honestly, it may be a little over the head of someone with little or no science background, unless, of course, they were highly motivated and interested in the subject to begin with. I would put it right up there with Brian Greene's works (The Elegant Universe, etc.) in that it makes the subject very relevant to everyday existence as well as existential questions. (As an aside, I would also supplement your reading with viewing the DVD, "What the (Bleep)? Down the Rabbit Hole" to contemplate string theory's possibility of connecting science to spirituality...)

A great general-audience book on modern physics--string theory, particle physics, relativity, etc. While informative and well-written, Dr. Randall at times takes simplifying analogies too far, such that the reader is left wanting a more in-depth explanation of the science itself.

Having said that, I feel like this book has prepared me to tackle Briane Greene's works, and I would recommend it for anyone looking for a good introduction to this subject matter.

Professor Randall of Harvard has written a truly monumental book for physics and for those interested in science. She has brilliantly bridged the knowledge gap between the scientist and the layperson. With this book, she dispels forever the ridiculous notion that women are somehow less equipped to do science at the highest level. As a theoretical physicist, her work is perhaps the most quoted in recent history - proof that her discoveries, which opens up fresh new thinking, are among the most significant in the history of science.

Warped Passages is a book that showcases Professor Randall's skills as a "model builder" in theoretical physics. Using the logic of model building, she deftly wove a tale of how past discoveries finally led to her out-of-the-box insight to use the fifth dimension to explain some of the more vexing modern day problems in physics. She demonstrated for us that with warped space, we may not even see a fifth dimension of infinite size.

The book is full of creative analogies to help us understand what the human mind is not equipped to grasp - extra dimensions. It is written simply, elegantly and clearly. Even if you find the more esoteric concepts difficult to understand at a deeper level as I do, she has included at the end of each chapter bullets of key concepts that anyone can understand. After reading the book, you will find yourself able to discuss at dinner parties the more important discoveries in physics such as general relativity, quantum mechanics and extra dimensions with the confidence of a trained physicist. You will also want to learn more about the latest advances in physics. Whether you have a Ph.D. in physics or are someone with a passing interest in science, you will find this book useful, interesting, informative and exhilarating. You will be infected by her obvious enthusiasm in physics and mathematics. Professor Randall has done a great service for the advancement of science and the recruit of students into physics. As a bonus, you will see glimpses of her humanity, humor and wit.

This is an exciting time in the history of physics. With this book, you will see why Professor Randall is the chief architect of what makes it exciting.

Very disappointing. Poorly written. I wanted a detailed explanation of the new thoughts in physics and got a droll tedious lecture on physics. It was painful to plod through the entire book.

Don't ...

This is a very educational book for lay readers interested in science, particularly in physics, to know the current scientific understanding of particle-physics and our universe. The author, a Harvard professor of physics, writes at the end of the book: "If, instead, other extra-dimensional models describe the universe, energy will disappear into extra dimensions and we'll ultimately detect these dimensions through the resulting unbalanced energy accounting." I am sure, however, that the author knows the tale of "the missing 21 grams" (which has been also an unaccountable energy loss from "our brain?") of Dr. Duncan MacDougall published in 1907, but just does not take it seriously, maybe because it is too big a loss for her to be true, compared with the loss of gravitons from "our brane."

I recently read "Warped Passages" and wanted to take this opportunity to thank and congratulate the author for it. The "dance" between experimentalist and theorist is as elegant as any you will see on "Dancing with the Stars". The highly communicative and refreshing style of this book immensely helped my understanding of the still evolving, state-of-the-art issues addressed. As a particular side note, I must say I also enjoyed the symmetry of a rock musician on a shared airplane flight spontaneously asking the author for an explanation of a 10- versus 11-dimension universe and her use of rock lyrics to introduce the theme of each chapter.

Clearly, there is an appetite among the wider public for highly readable, science books like "Warped Passages". I also believe such books serve a vital need in the US to stimulate and excite young people about pursuing careers in math, science and engineering. As a society, we have not done enough in this area. We have made up for this deficiency by importing the best and brightest students from around the world. In turn, such graduates have often remained here to contribute to the scientific and engineering strength of our country and its economy. However, the scientific and economic climates around the world have improved to the point where we can no longer depend so much on benefiting from this "brain drain". Domestic availability of books such as "Warped Passages" and others is necessary to the future well being of our country.

In fact, the author inserted several clearly indicated, sidebar summary descriptions of a range of physics topics which relate to and impinge upon the main thrust of her book. I found these helpful to my broader understanding of her main points and the context in which she makes them. For those who wish to explore in more depth these related issues, I also recommend "The Whole Shebang, A State of the Universe(s)Report" by Timonthy Ferris, "Deep Down Things, The Breathtaking Beauty of Particle Physics" by Bruce Schumm, "The Quantum World, Quantum Physics for Everyone" by Kenneth Ford, "Quantum Reality" by Nick Herbert, and "Relativity" by Albert Einstein (Nothing like getting it straight from the horse's mouth!). Each offers very clear descriptions and explanations of the topic at hand, with a minimum of jargon and mathematics.

Lastly, I want to encourage the author to write a "sequel" to "Warped Passages", probably in no more than five years. By that time, substantive first results from the new Large Hadron Collider (LHC) will be available and theories will have been further confirmed, pruned, refined and created to continue the "dance".

The hypothetical hyperspace wherein Strings supposedly dwell entrances many gifted physicians. In Randall's model, which she describes, some extra dimensions, or passages, can remain hidden even even if they stretch to infinity. However String theory has not told us since more than 20 years much about the key usolved problem: why does the Universe has dark energy? Randall is enthusiastic narrator, but her boosterish presentation will seem awfully familiar to anyone who has read "The Elegant Universe", and she never seriously grapples with the shortcomings of Strings mentioned above (to find more shortcomings check "Hiding in the Mirror" by Lawrence Krauss). Large Hadron Collider, due hopefully to come on line in 2007 will yield definitive evidence (or rather not according to many sceptics) for particular large extra "D"/String model. Until then, treat "Warped Passages" sections related to Strings/Branes (past page 276) as an interesting well written science fiction brain exercise. As for particle physics and related symmetries (first half of Randall's book)- "Symmetry and the Beautiful Universe" by Lederman and Hill is superior.

Physics is hard to write about, but a good popular physics book can be worth its weight in gold. Lisa Randall, who is a leading theoretical physicist, has shown she has that rare gift of being able to master mathematics/science and writing/communication by putting together this wonderful book. I found Randall's basic description of extra dimensions alone to be worth the price of the book and enjoyable reading that gets me excited about the idea. I found the discussion of different approaches to solving the current dilemmas in theoretical physics to be refreshing. Overall her writing style is enjoyable and I highly recommend this book.

You will not be disappointed: Lisa Randall's passion for her research is well reflected in this book. I read it almost like a 'who dunnit' thriller so I will not spoil your fun by giving away too much details, but, having read quite a few similar books, this one really stands out in the crowd.

All the familiar characters of modern day physics, like quantum mechanics, relativity theory, particle physics, supersymmetry, string theory and braneworlds come on stage. They are properly introduced to the reader in separate chapters, which each start with a little intermezzo to give you a feel for how the story will go on. It serves both as an appetizer and gives you a moment to reflect before indulging in the next scenes.

This all builds up to the last chapters, where all these characters seem to play a part in a mysterious plot: hiding the evidence for extra dimensions !!
Then you will discover that Lisa Randall has quite a few tricks up her sleeve to push these characters to reveal the truth they so cleverly conceal from us in our everyday four-dimensional world. By introducing several different higher-dimensional models of our universe, she interrogates them one by one. That's hard and arduous work, that's for sure, but you get the exciting impression that they will give in and that answers are laying just around the corner. The author makes a quite convincing story so far and finally asks the reader with the same disarming honesty this question: "Extra dimensions: Are you in or are you out?"

Many questions have yet to be completely answered, but I for one am certainly in...

Don't worry, you won't need a formal background in physics or mathematics to fully appreciate this book. After each chapter the main points are summarized with bullets, as easy reminders without interrupting the natural flow of the story. No formulae are presented in the main text, but in the back however is a math notes section where some subjects are further explained. So if you are a newbie, an amateur physics buff (like me) or even a professional physicist, I am sure the enthusiasm and fun with which the author tells this fascinating story will take you on a rewarding and intellectually challenging adventure !!

As one who enjoys struggling with modern concepts in physics - and causing mental meltdown in the attempt - I must commend "Warped Passages", a book I have thoroughly enjoyed, though I would never be arrogant enough to say I have understood. Despite John Gribbin's review in the Sunday Times, Dr Randall's writing style is both clear and charming . One suggestion would be that her next book include a bit more of the exotic mathematics which, I am sure, her editor required her to omit. Lisa Randall is a breath of fresh air in the realm of sharing the frontiers of physics today with those of us whose vocations place us in different places. I can heartily recommend this fine book to anyone with an interest in contemporary theoretical physics.

I have read many books written for the public about modern physics. What I really like about the best of them is that they give a new perspective on some aspect of physics that is much different from what anyone else has written.

Lisa Randall's Warped Passages is among the best. Her descriptions of the issues and the promises of extra dimensions were far better than any others I have read. For me it was also an introduction to the differences between model building and string theory. And a very lucid introduction.

As with most of these type of books, she gives an overview of the ideas behind quantum theory and general relativity. Like the best of these, some of her perspectives are particularly enlightenly. Her descriptions of the weak force and of the problems with the scale differences among the forces were both prime examples of this.

I do not believe that it is an either/or choice when deciding whether to read one of these books by the top physicists. We are incredibly fortunate to have available to us such accessible information. So many of them are good and worth the time to read.

I have also read, and recommend,

Brian Greene's The Fabric of the Cosmos and The Elegant Universe

(the former gives what I found really nice perspectives on special relativity)

A. Zee's Fearful Symmetry which is the best ever description of the link between the laws of conservation and symmetry

Heinz Pagels The Cosmic Code

Bob Phillips

Stilwell, KS

Anybody who has an interest in leading-edge ideas of cosmology and particle physics should read this book. Prof. Randall, along with colloberator Prof. Sundrum, developed the theory of warped 5th dimension that could explain some of the most intractable problems of fundamental physics while opening up a big can of revelations. If proven correct, this could very well be the biggest discovery in physics of the 21th century. There is nothing like reading this amazing development from the one who developed it. She offers an unique and powerful perspective.

On the short side, I wish the editors could have more time to improve clarity and draw more compelling diagrams. I am sure Prof. Randall next book, which could very well come after experimental test of her theory at the Large Hadron Collider, will be better edited complete with beautiful illustrations.

For now, just go ahead get this book and enjoy what I know is a landmark book.

There is nothing like the thrill of hearing about the latest developments in a field from a leader in that field, and Lisa Randall is that. This is a book that explains some of the biggest questions in physics today (offering some possible answers, as well), and it is written for the ordinary reader to understand it. Leavened with humor, helpful diagrams, and the perspective of a woman who clearly lives to probe the mysteries of our universe(s), the book is designed to transmit to us her excitement about the discoveries she describes. Short of a brain transplant, she does everything possible to make clear to the non-scientist a host of arcane concepts. The book has a whole different tone from so many of these pop science books that I‚ve picked up and then put down a short time later because I‚m just not getting it. Warped Passages has a down-to-earth (no pun intended), humane, personal feeling to it, even though it‚s chock full of information, so it draws the reader in and makes him or her feel capable of understanding these momentous concepts. Randall actually makes it fun. Which allowed me to feel like I was, indeed, sharing her adventures in extra dimensions with her. Without having to do the math. An excellent read.

I found Lisa Randall's "Warped Passages . . ." to be an extremely accessible book for the layperson because of its clarity and balanced emphasis on each of several competing and non-competing modern physics theories.

Each of the several layperson-friendly books on physics that I have read contains an introductory set of chapters on which the main premise of the particular book is based. In terms of understandability, some are fair, others are adequate, and others are quite good. For example, I found such chapters in Brian Greene's "The Elegant Universe" to be quite good. However, Lisa Randall's "Warped Passages . . ." contains exceptionally clear introductory chapters. This clarity not only demonstrates her command and understanding of these early parts of her book, it also effectively expresses her humility and implicit acknowledgment of the incompleteness of the various competing theories that make up her life work. This intellectual honesty lends credibility and therefore ease of understanding to her mode of expression. For example, unlike Brian Greene, who seems to prefer "string theory" and its progeny over all competing theories (for reasons which frustratingly fade away in inverse proportion to the number of pages in his book), Lisa Randall takes a comprehensive and perhaps therefore a more objective approach to each theory she discusses.

The history of modern physics from the late 19th century through today is replete with partial "sub-theories," each of which form the foundations (and limitations) of quantum mechanics and the theories of relativity. If such history is to be any guide, Lisa Randall's "weigh and consider several theory" approach to explain the nature of space, time, energy, and matter is not only sound, but necessary, not only to diversify intellectual and fiscal resources in an economic sense, but also to build the most scientifically robust model possible.

I have a limited physics background and began this book thinking the prime purpose was to receive an explanation of string theory, multiple dimensions and membrane theory. It achieved its purpose. In addition, it magnificently delineated the history of this field's development, plus liberal recognition of her colleagues involvement in pursuing these endeavors (despite some being theorists and some experimentalists).

Professor Randall's writing has a continuity of development in concise, lucid, complete, and very clever terms. Terminology is kept simple and (thank goodness) mathematics eliminated. Inclusions of real life analogies helps breakdown the complex into the understandable.

The author's personality, as demonstrated by the book, shows that even physicists are people ... She climbs rocks, communes with nature, appreciates pop-culture, hangs-out in coffee shops and enjoys conferences in beautiful locales. And, best of all, she has a delicious sense of humor (ironic closing at books-end: what is a dimension?) All this and she does not let her intellect get in the way of clarity in describing to the layperson (me) of strings that rock `n' roll, minuscule curlicue dimensions, and wimpy gravity (my characterization).

In summary, I now have a greater appreciation and understanding of this realm of science. It is a magnificent, multifaceted book in revealing science, scientists and one scientist's personality.

Maybe in Professor Randall's sequel (Warped Passages, the Next Generation ?) she can explain: Is time a black sheep dimension among the spatial dimensions? How does one particle communicates attraction and/or repulsion? What about variable speed of light or gravity?

Now I am impatient for the results of bashing those energetic particles together and letting the shower's fall where they might. Let the fireworks begin, thank you Doctor Randall.

The last ten years or so have witnessed an upsurge of interest in an old idea: that there are extra dimensions of space, somehow hidden from our view. Lisa Randall's book provides an insider's view of this revolution in our understanding of spacetime, presented in a way that anyone can understand.

Randall herself has been a leader in extending our picture of extra dimensions, authoring (with Raman Sundrum) a paper that Stephen Hawking called "the best paper of the year." Here she starts with an introduction to the very idea of the dimensions of spacetime, followed by a primer on the foundations of relativity and quantum mechanics, before finishing with a compelling account of how ideas from string theory, cosmology, and particle physics came together to offer new scenarios for branes and extra dimensions. Reading this book will teach you a lot of physics, but also give you an idea of how cutting-edge research actually gets done.

A reviewer below complains that the book can be difficult in places. The truth is, physics is difficult, and some of these ideas are truly mind-bending. We can either gloss over them, or take them seriously; Randall's book takes them seriously, providing explanations that are clear and understandable to any non-experts willing to engage with the material. The expert's view given here provides a perspective that simply isn't available anywhere else. As a theoretical physicist myself, I'm very glad to see this book on the market, and hope as many people as possible will read it.

One of the characteristics of a great textbook or an interesting popular book on a scientific topic is excellent exposition that explains difficult concepts before they are used further in the book. Good exposition can prevent the misuse of technical terms, or help explain something conceptually by analogy that might be inherently mathematical.

Near the beginning of this book, Lisa Randall explains the meaning of the what physicists and mathematicians mean by a "space." In particular, she distinguishes between a set of points and a set of points with the additional structure of a metric on it such that distances can be computed. This explicit idea of a metric is often overlooked by physics students, and many assume that a space automatically "includes" a way to measure intervals. In this book, the metric as added structure is presented in a clear way that someone of no mathematical background can understand and recall while proceeding through the book. Defining the basics also helps when new ideas arise. If the reader knows that a set of points and a metric to compute distances are separate entities, the idea of a topological space without a metric will be easier to grasp conceptually.

As an example of the importance of exposition, take the idea of an "observer" from high school physics and the treatment of special relativity. My high school physics book did not really state what an "observer" was when the word was being used regularly in the book. By the time we reach high school, we know enough about the real numbers to understand a 4-tuple, so why not define an "observer" as a point in spacetime? We can extend the idea of Euclidean geometry to think of an observer in spacetime as a point (x^0, x^1, x^2, x^3). We can use the Lorentz formulae to perform computations while only understanding conceptually that the geometry is different, and that the time coordinate has a different nature than the spatial coordinates because of the negative sign. The goal at this level should be for general understanding rather than the details of a 4-D manifold over which a Lorentzian metric is defined. The concepts are derived from the exposition, and bad exposition leads to bad conceptual understanding.

Some other examples in relativity where exposition can speed progress along include ideas such as "inertial observer", "curved space", "symmetry", and even the idea of what a theory is. Inertial observers are usually explained in books as "frames in which the observers are not accelerated", but this leaves the reader with a lot to wonder about. It is perfectly possible to present the worldline of an accelerated observer in a spacetime diagram, so a reader might well ask how this can be if SR applies only to unaccelerated objects. Authors could remove a lot of potential ambiguity by handling details like this at the point where they explain inertial frames. On the idea of "curved spaces", most popular books allow the lay reader to continue to believe that a curved space must be something like:

{x,y in R | d(x,y) does not equal 'straight line' value}

If the idea of a space and a metric has been explained, as Randall has in this book, the type of misperception above can be avoided since readers know the type of space is determined by the metric, and the metric must be defined before you discuss the idea of "straight line." The author handles the idea of "symmetry" probably as well as it can be explained without appeal to groups. Most authors of popular science ignore this, and the omission leaves lay readers without a good understanding of what a symmetry is. The idea of symmetry is usually poorly covered by scientists writing for a general audience. A few pictorial examples of symmetry groups (see J. Fraleigh, circa 1976), or a mention of how some mathematical operations leave a result unchanged goes a long way.

As other reviewers have mentioned, Lisa Randall does a delightful job of explaining by analogy the ideas that have to precede higher dimensions and SUSY, and the rest of the unification effort that we would all like to know more about. One example could be "isotropy." We can probably think of it conceptually as a property that changes independently of direction, and this definition will not lead us into false understanding at beginning levels. Only when we get to the level of detail needed for GR at the level of Wald do we see the need to be far more precise with the definition of isotropy, but Randall realizes that we need the concept before we need the details.

One reviewer detracted from the book claiming that too much of the book was "mired in mystery" (my paraphrase), but this was an area where I thought the author did a particularly good job since there are many mysteries that are hard to explain in words. Take the quadratic equation from high school. We learn to derive it and solve word problems with it, we factor higher order polynomials by guessing roots and reducing the order such that we can apply the quadratic formula. The central idea is that we can isolate the independent variable and express it in terms of the coefficients to obtain the general solution for an arbitrary quadratic equation. Then we wonder whether such a general solution by radicals exists for higher order equations, and we learn that the answer is "yes" for the cubic and quartic, but the quintic is provably insoluble by radicals in the general case. Probably no one could foresee that the general solutions by radicals would stop at the 4th order equation - David Hilbert did not - and it would be practically impossible to explain to someone not versed in modern algebra why there is no general solution to the quintic. The best you can do is to say: "the mathematics work out that way." This is one of the mysteries of our discipline, and when Randall comes across an idea that is nearly impossible to explain conceptually, she chooses to admit that some things are mysteries rather than offer an analogy that misleads or forces the reader to try to understand something that does not reflect the underlying science. Rather than a defect, I see this as a benefit. Some ideas simply derive from the model that we have constructed, and may not have a simple verbal explanation. As Feynman liked to say in such cases: "no, since we can't prepare a freshman lecture on it, we have to admit that we don't really understand it." This is a better path to follow than to translate the ideas unconsciously in our head into something that we "understand" but that is incorrect. Let us keep our mysteries.

Textbooks written with this same coherence and awareness of the audience would be most welcome. The author would assuredly maintain the talent that some science writers have of knowing the value of exposition and definition. Robert Wald is an example of an excellent textbook author. His exposition and definitions clarify the technical manipulations that are to follow. As an example, many GR textbooks define a tensor by its transformation properties, but this does not give the first-time reader an idea of what a tensor is, only how it transforms. Why not far rather define it as a geometric object that maps 1-forms and vectors in R? Then discuss its transformation properties. This is the manner of Wald, and I imagine Randall would handle it in similar fashion. Other GR authors (d'Inverno) state firmly that defining a tensor will be discounted in favor of learning how they transform, but this evades the entire idea that general relativity is a geometric treatment of gravitation, and the geometric objects need to be defined to understand the theory. My view is that having good definitions where possible, even if they are conceptual only, is the best way to begin understanding complicated physics, and Lisa Randall does this in the present book in a way that is interesting for a lay reader and even useful to readers who have had some exposure to the topics being discussed.

One of the final benefits to the lay readers is that they will derive an idea of what exactly a theory is and is not, and how models are built. If someone says: "I have this theory that there is a parallel universe that we can cross over into and experience a strong nuclear force that does not increase with

separation", then a reasonable question would be: "well what is the parallel universe to start with? are you talking about multiply-connected sets?" Many lay readers will learn in this book that a "theory" might be right or wrong, but it will have some predictive power or promise of predictive power, and they will learn that the goal of most scientific endeavor is to generalize to the greatest extent possible. We would ultimately like to start with a few axioms, and derive all the observed results in Nature from these axioms/postulates.

If you are looking for an accessible book that gives you as much of the motivation and explanation as possible in an intro book on higher dimensions, this text offers clarity of expression, satisfying analogies, and the contented feeling that you have learned something. You will not think you are missing the conceptual points because the anologies are bad. If you asked Randall how to fit a 15 meter rope (pretend 1 dimension) onto a wall of 10 meters, she might tell you to bend the rope up and down repeatedly in waves with care not to crumple it (to avoid singularities) until it fit on the wall. She would not (in this book) start telling you about topologies and homeomorphisms. You will understand the idea behind higher dimensions and embeddings, and can choose to look further into the matter if that is your wish.

Happy reading.

When you read anything stating that "physicists now believe..." you are heading into confusion. Okay, for example, physicists now believe there are as many as 11 dimensions or even more. I am going to state right now, there are only 3 dimensions, and time doesnt exist, as it has been proven to be totally flaky by relativity theory. Sure, you can use time in physics in ways that put it into relationship with the three spatial dimensions, but, if you are going to call time a dimension, you are redefining the original term, "dimension," which was specifically defined as being for measuring lengths of extension in space as linear measures. When time was added into the mix, basically given "equivalence" with the three spatial dimensions, this was bound to lead to trouble, because, if we call time a dimension (when it is not a dimension, if we have already identified dimensionality as being the extension of linear spatial measurements) then we have already warped the fundamental ground rules we started with, the definition of what dimensionality actually is. Time does seem related to space, because when we travel or move objects in space, it does take time to do this. But to then say that time is a "dimension" places time itself into the schema of observation, as being something it is not, i.e., time is not a dimension, rather, it is a measure that can be made of duration of events happening in space, a space of three dimensional axes only, such as length, breadth and depth. Events have been defined as having 3 dimensions of space, and one of time; an instantaneous event then acts as its own "time zero" and a spacetime interval is defined as a distance and time traveled by a person or object, from one spacetime location to another spacetime location; this brings us to the fact that when two events can be connected by a single ray of light, then the spacetime interval between them is zero; they are simultaneous. So, when time is used in physics, it disappears at the speed of light, regardless of the spatial separation between two events in spacetime. An event is described as having three spatial coordinates which give the distance from some specified zero point in a coordinate system or lattice of grid lines; the same event has a particular time of occurrence as observed also from the zero point chosen. So within the three dimensional grid, to measure and time events, the time axis is added as a time reference axis. It is then called a "dimension," but again, when we have assigned a certain meaning to a dimension as indicating an objects location and/or extension in 3D space, to now place time into the same coordinate system simply redefines what is meant by dimensionality, because dimensionality was originally designated as being extension in length, breadth, and depth, and nothing else. In other words, dimensionality was originally defined and designated as being extension in space, and could not be related to time, except by ad hoc and imprecise, opportunistic of some sort of time axis being placed into the lattice grid or reference frame of the 3D system as originally defined. Time itself is dimensionless, although, we can measure time as being "extension" or duration between two distinct events, this measure is an arbitrary linkage of the 3D reference frame of spatial dimension, with the added "arrow of time" used in an arbitrary way and set as an equivalent dimension "analogous" to the three spatial dimensions. This was an arbitrary and seemingly very useful method, i.e., setting up a 4D reference frame so that time can be a "dimension" with a precise "axis" within the system, but "dimensionality," of length, breadth and depth, did not originally incorporate time. The three spatial dimensions measure or illustrate only spatial extent; dimensionality itself, so designated, relates to the three spatial dimensions, and not to any measurement or illustration of the "distance" (interval) between two "events," such measurement or illustration being "beyond" dimension, because, for example, in 3D space there are no "events" at all; an event is a construct in physics incorporating "dimensionality" (3D extensions) with an arbitrarily placed time axis being granted "dimensionality" itself, when it has none, being nonspatial. This is a seemingly minor discrepancy in definitions of the ground rules of dimensionality, but time is dimensionless if dimension is spatial, which is (by definition) the true situation. Then later in physics when these concepts develop into relativity theory and the theorized added dimensions of physics, we are already working with flawed theory; relativity shows that space and time are somehow one and the same, when in fact, they are not. If they are taken to be one and the same, it would have to be because at the outset, when we assigned dimensionality to the three dimensions of space, the dimensions being, by definition, spatial dimensions, then violated our own definition of dimensionality, to allow the dimensionless time axis to become an analogous dimension placed within the 3D space, sharing the same zero point origin, we have already made the mistake that relativity had to uncover by complex analysis, that space and time--if defined as being equivalent dimensions--are equivalent dimensions. Then time is shown to "warp" so that if two spacetime events can be connected by a single light ray, the spacetime interval between the two events is zero. This points up the problem: If we take time as being equivalent to space, we are taking time as being a dimension, when in fact it is dimensionless (because the three dimensions of space are length, breadth, and depth--and time has zero extension in space--so it is, by our original definition of dimensions, dimensionless). But due to the fact that we had arbitrarily set time as being an equivalent reality with space, and we set time as having its own axis, giving it extent and duration in spacetime, effectively making it into a new spatial dimension, even though it is dimensionless, we had set up the ground rules and theoretical construct from the beginning, to make time into a new space dimension, something it could never be.

A very beautiful book explaining in simple terms the most recent ideas physicists have about our Universe. Some times is very technical but very well explained without going into the mathematical intricateness, easy to follow. At the end you "will be an expert in many dimensions" theories.