Tuesday, July 20, 2010

Causal Dynamical Triangulations


Causal dynamical triangulation (abbreviated as "CDT") invented by Renate Loll, Jan Ambjørn and Jerzy Jurkiewicz, and popularized by Fotini Markopoulou and Lee Smolin, is an approach to quantum gravity that like loop quantum gravity is background independent. This means that it does not assume any pre-existing arena (dimensional space), but rather attempts to show how the spacetime fabric itself evolves. The Loops '05 conference, hosted by many loop quantum gravity theorists, included several presentations which discussed CDT in great depth, and revealed it to be a pivotal insight for theorists. It has sparked considerable interest as it appears to have a good semi-classical description. At large scales, it re-creates the familiar 4-dimensional spacetime, but it shows spacetime to be 2-d near the Planck scale, and reveals a fractal structure on slices of constant time. These interesting results agree with the findings of Lauscher and Reuter, who use an approach called Quantum Einstein Gravity, and with other recent theoretical work. A brief article appeared in the February 2007 issue of Scientific American, which gives an overview of the theory, explained why some physicists are excited about it, and put it in historical perspective. The same publication gives CDT, and its primary authors, a feature article in its July 2008 issue.

Contents

Explanation

It is widely accepted that, at the very smallest scales, space is not static but is instead dynamically-varying. Near the Planck scale, the structure of spacetime itself is constantly changing, due to quantum fluctuations. This theory uses a triangulation process which is dynamically-varying and follows deterministic rules, or is dynamical, to map out how this can evolve into dimensional spaces similar to that of our universe. The results of researchers suggests that this is a good way to model the early universe, and describe its evolution. Using a structure called a simplex, it divides spacetime into tiny triangular sections. A simplex is the generalized form of a triangle, in various dimensions. A 3-simplex is usually called a tetrahedron, and the 4-simplex, which is the basic building block in this theory, is also known as the pentatope, or pentachoron. Each simplex is geometrically flat, but simplices can be "glued" together in a variety of ways to create curved spacetimes. Where previous attempts at triangulation of quantum spaces have produced jumbled universes with far too many dimensions, or minimal universes with too few, CDT avoids this problem by allowing only those configurations where cause precedes any event. In other words, the timelines of all joined edges of simplices must agree.

Derivation

CDT is a modification of quantum Regge calculus where spacetime is discretized by approximating it with a piecewise linear manifold in a process called triangulation. In this process, a d-dimensional spacetime is considered as formed by space slices that are labeled by a discrete time variable t. Each space slice is approximated by a simplicial manifold composed by regular (d-1)-dimensional simplices and the connection between these slices is made by a piecewise linear manifold of d-simplices. In place of a smooth manifold there is a network of triangulation nodes, where space is locally flat (within each simplex) but globally curved, as with the individual faces and the overall surface of a geodesic dome. The line segments which make up each triangle can represent either a space-like or time-like extent, depending on whether they lie on a given time slice, or connect a vertex at time t with one at time t+1. The crucial development, which makes this a relatively successful theory, is that the network of simplices is constrained to evolve in a way that preserves causality. This allows a path integral to be calculated non-perturbatively, by summation of all possible (allowed) configurations of the simplices, and correspondingly, of all possible spatial geometries.

Simply put, each individual simplex is like a building block of spacetime, but the edges that have a time arrow must agree in direction, wherever the edges are joined. This rule preserves causality. This is the crucial piece that this theory provides, which was missing before. When we join the pieces only in this way, the simplicial manifold evolves in a more orderly fashion than with earlier theories, and eventually creates the observed framework of dimensions. CDT builds upon the earlier work of Barrett and Crane, and Baez and Barret, which demonstrates the feasibility and utility of this approach, but by introducing the causality constraint as a fundamental rule (influencing the process from the very start) Loll, Ambjørn, and Jurkiewicz created something different and exciting. Where others had regarded causality as an emergent property, they made it one of the primary ingredients of their "soup".

Advantages and Disadvantages

By far the greatest advantage of this theory is that it derives the observed nature and properties of spacetime from a minimal set of assumptions, and needs no adjusting factors. The idea of deriving what is observed from first principles is very attractive to physicists, as it often indicates a concept that is close to the truth, or offers powerful tools for investigating the nature of reality. Since it allows us to probe the character of spacetime both in the ultra-microscopic realm near the Planck scale, and at the scale of the cosmos, CDT can give us many insights into the nature of reality. This is its strength.

The disadvantageous aspect of this theory is that it relies heavily on computer simulations to generate results. The term Monte Carlo simulation has a bad connotation, in this regard. Some feel that this makes CDT a less "elegant" solution to the problem of creating a completely successful quantum gravity theory. Also, it has been argued that discrete time-slicing may not accurately reproduce all possible modes of a dynamical system. However, research by Markopoulou and Smolin demonstrates that the cause for those concerns may be limited. Therefore, many physicists still regard this line of reasoning as promising.

Related theories

CDT has some similarities with loop quantum gravity, especially with its spin foam formulations. For example, the Lorentzian Barrett-Crane model is essentially a non-perturbative prescription for computing path integrals, just like CDT. There are important differences, however. Spin foam formulations of quantum gravity use different degrees of freedom and different Lagrangians. For example, in CDT, the distance, or "the interval", between any two points in a given triangulation can be calculated exactly (triangulations are eigenstates of the distance operator). This is not true for spin foams or loop quantum gravity in general.

Another approach to quantum gravity that is closely related to causal dynamic triangulation is called causal sets. Both CDT and causal sets attempt to model the spacetime with a discrete causal structure. The main difference between the two is that the causal set approach is very general, whereas CDT assumes a specific relationship between the lattice of spacetime events and geometry. Consequently, the Lagrangian of CDT is constrained by the initial assumptions to the extent that it can be written down explicitly and analyzed (see, for example, hep-th/0505154, page 5), whereas causal-set theory is not nearly as completely developed at this point.

See also

References

Early papers on the subject:

External links

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Andrew Thomas of Swansea Performs First Successful Triangular Cellular Automata Experiment

Dr. Andrew Thomas, PhD. Electrical Engineering, performed the first successful experiment on March 12, 2009 of a repeating Triangular Cellular Automata in his flat at Swansea in Wales, based on the square-based Game of Life by John Conway. The first (and still simplest, for squares) repeating GoL automata was invented by Bill Gosper based on a challenge by Conway and is now known as Gosper's Gliding Gun. Thomas' accomplishment is similar, based on a challenge by yours truly, who invented the idea of triangular GoL.

This is the first known and currently only known experiment of its kind ever performed, that is to say on a triangular version of Conway's Game of Life.

Here is Thomas' notebook page document:



The purpose of this post to to alert others to its existence, in the hope that it will aid further research into Causal Dynamical Triangulations, which in turn it is hoped will provide better knowledge, at least on the theoretical side, of what is actually happening in Reality on the smallest Planck scale of length.

Also, it looks to be quite fun just to play around in one's spare time.

Sincerely,

Steven Colyer
Amateur Applied Mathematician (MathoMcPhysicist)

BSME, Rutgers, 1979, Pi Tau Sigma
MBA, Rutgers, 1989

July 20, 2010
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Bill Gosper

First picture: Bill Gosper. Second picture and lone animation: Gosper's Gliding Gun, from cellular automata and John Conway's "The Game of Life".



Ralph William Gosper, Jr., (born 1943) known as Bill Gosper, is an American mathematician and programmer from Pennsauken Township, New Jersey.[1] Along with Richard Greenblatt, he may be considered to have founded the hacker community, and holds a place of pride in the Lisp community. Perhaps his most profound contribution is that he was the first person to realize the possibilities of symbolic computation on a computer as a mathematics research tool, whereas computer methods were previously limited to purely numerical methods. In particular, this research resulted in his work on continued fraction representations of real numbers, and for more famously, developing Gosper's algorithm for finding closed form hypergeometric identities. Because his mathematics is largely self-taught and a number of his completely original formulas have inspired professional mathematicians to write papers developing them into full fledged theories, he has been considered a modern day Ramanujan.

Gosper enrolled in MIT in 1961, and received his bachelor's degree in mathematics from MIT in 1965. After taking a course on programming in his second year with John McCarthy, Gosper became affiliated with the MIT AI Lab. His contributions to computational mathematics include HAKMEM [1] and the MIT Maclisp system. He also made major contributions to the Macsyma computer algebra system at MIT, later working with Symbolics and Macsyma, Inc. on the greatly improved commercial versions.

He became intensely interested in the Game of Life shortly after John Horton Conway had proposed it. Conway conjectured on the existence of infinitely growing patterns, and offered a reward for an example. Gosper was the first to find such a pattern (specifically, the Glider gun), and won the prize. Gosper was also the originator of the hashlife algorithm that can speed up the computation of Life patterns by many orders of magnitude.

In the 1970s Gosper moved to California for a three year stint at Stanford, where he lectured and helped Donald Knuth write volume II of The Art of Computer Programming.

Since that time, he has worked at or consulted for Xerox PARC, Symbolics, Wolfram Research, the Lawrence Livermore Laboratory, and Macsyma Inc.

Gosper has created numerous packing problem puzzles, such as "Twubblesome Twelve".

See also

Notes

  1. ^ Bill Gosper, Vintage Computer Festival. Accessed January 3, 2007.

External links

from Wikipedia
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Monday, July 19, 2010

John Horton Conway


John Horton Conway (born 26 December 1937, Liverpool, England) is a prolific mathematician active in the theory of finite groups, knot theory, number theory, combinatorial game theory and coding theory. He has also contributed to many branches of recreational mathematics, notably the invention of the cellular automaton called the Game of Life.

Conway is currently professor of mathematics at Princeton University. He studied at Cambridge, where he started research under Harold Davenport. He has an Erdős number of one. He received the Berwick Prize (1971),[1] was elected a Fellow of the Royal Society (1981),[2] was the first recipient of the Pólya Prize (LMS) (1987),[1] won the Nemmers Prize in Mathematics (1998) and received the Leroy P. Steele Prize for Mathematical Exposition (2000) of the American Mathematical Society.

Contents

Biography

Conway's parents were Agnes Boyce and Cyril Horton Conway. John had two older sisters, Sylvia and Joan. Cyril Conway was a chemistry laboratory assistant. John became interested in mathematics at a very early age and his mother Agnes recalled that he could recite the powers of two when aged four years. John's young years were difficult for he grew up in Britain at a time of wartime shortages. At primary school John was outstanding and he topped almost every class. At the age of eleven his ambition was to become a mathematician.

After leaving secondary school, Conway entered Gonville and Caius College, Cambridge to study mathematics. He was awarded his BA in 1959 and began to undertake research in number theory supervised by Harold Davenport. Having solved the open problem posed by Davenport on writing numbers as the sums of fifth powers, Conway began to become interested in infinite ordinals. It appears that his interest in games began during his years studying at Cambridge, where he became an avid backgammon player, spending hours playing the game in the common room. He was awarded his doctorate in 1964 and was appointed as College Fellow and Lecturer in Mathematics at the University of Cambridge.

He left Cambridge in 1986 to take up the appointment to the John von Neumann Chair of Mathematics at Princeton University. He is also a regular visitor at Mathcamp and MathPath, summer math programs for high schoolers and middle schoolers, respectively.

Conway resides in Princeton, New Jersey.

Achievements

Combinatorial game theory

Among amateur mathematicians, he is perhaps most widely known for his contributions to combinatorial game theory (CGT), a theory of partisan games. This he developed with Elwyn Berlekamp and Richard Guy, and with them also co-authored the book Winning Ways for your Mathematical Plays. He also wrote the book On Numbers and Games (ONAG) which lays out the mathematical foundations of CGT.

He is also one of the inventors of sprouts, as well as philosopher's football. He developed detailed analyses of many other games and puzzles, such as the Soma cube, peg solitaire, and Conway's soldiers. He came up with the Angel problem, which was solved in 2006.

He invented a new system of numbers, the surreal numbers, which are closely related to certain games and have been the subject of a mathematical novel by Donald Knuth. He also invented a nomenclature for exceedingly large numbers, the Conway chained arrow notation. Much of this is discussed in the 0th part of ONAG.

He is also known for the invention of the Game of Life, one of the early and still celebrated examples of a cellular automaton.

Geometry

In the mid-1960s with Michael Guy, son of Richard Guy, he established that there are sixty-four convex uniform polychora excluding two infinite sets of prismatic forms. They discovered the grand antiprism in the process, the only non-Wythoffian uniform polyhedron. Conway has also suggested a system of notation dedicated to describing polyhedra called Conway polyhedron notation.

He extensively investigated lattices in higher dimensions, and determined the symmetry group of the Leech lattice.

Geometric topology

Conway's approach to computing the Alexander polynomial of knot theory involved skein relations, by a variant now called the Alexander-Conway polynomial. After lying dormant for more than a decade, this concept became central to work in the 1980s on the novel knot polynomials. Conway further developed tangle theory and invented a system of notation for tabulating knots, nowadays known as Conway notation, while completing the knot tables up to 10 crossings.

Group theory

He worked on the classification of finite simple groups and discovered the Conway groups. He was the primary author of the Atlas of Finite Groups giving properties of many finite simple groups. He, along with collaborators, constructed the first concrete representations of some of the sporadic groups. More specifically, he discovered three sporadic groups based on the symmetry of the Leech lattice, which have been designated the Conway groups.

With Simon Norton he formulated the complex of conjectures relating the monster group with modular functions, which was named monstrous moonshine by them.

Number theory

As a graduate student, he proved the conjecture by Edward Waring that every integer could be written as the sum of 37 numbers, each raised to the fifth power, though Chen Jingrun solved the problem independently before the work could be published.[3]

Algebra

He has also done work in algebra, particularly with quaternions. Together with Neil James Alexander Sloane, he invented the system of icosians.[4]

Algorithmics

For calculating the day of the week, he invented the Doomsday algorithm. The algorithm is simple enough for anyone with basic arithmetic ability to do the calculations mentally. Conway can usually give the correct answer in under two seconds. To improve his speed, he practices his calendrical calculations on his computer, which is programmed to quiz him with random dates every time he logs on. One of his early books was on finite state machines.

Theoretical physics

In 2004, Conway and Simon B. Kochen, another Princeton mathematician, proved the Free will theorem, a startling version of the No Hidden Variables principle of Quantum Mechanics. It states that given certain conditions, if an experimenter can freely decide what quantities to measure in a particular experiment, then elementary particles must be free to choose their spins in order to make the measurements consistent with physical law. In Conway's provocative wording: "if experimenters have free will, then so do elementary particles."

Books

He has (co-)written several books including the ATLAS of Finite Groups, Regular Algebra and Finite Machines, Sphere Packings, Lattices and Groups, The Sensual (Quadratic) Form, On Numbers and Games, Winning Ways for your Mathematical Plays, The Book of Numbers, and On Quaternions and Octonions. He is currently finishing The Triangle Book written with the late Steve Sigur, math teacher at Paideia School in Atlanta Georgia, and in summer 2008 published The Symmetries of Things with Chaim Goodman-Strauss and Heidi Burgiel.

See also

Notes

  1. ^ a b LMS Prizewinners
  2. ^ List of Royal Society Fellows
  3. ^ Breakfast with John Horton Conway
  4. ^ This Week's Finds in Mathematical Physics (Week 20)

References

External links

Surreal numbers

In mathematics, the surreal number system is an arithmetic continuum containing the real numbers as well as infinite and infinitesimal numbers, respectively larger or smaller in absolute value than any positive real number. The surreals share many properties with the reals, including a total order ≤ and the usual arithmetic operations (addition, subtraction, multiplication, and division); as such, they form an ordered field.[1] In a rigorous set theoretic sense, the surreal numbers are the largest possible ordered field; all other ordered fields, such as the rationals, the reals, the rational functions, the Levi-Civita field, the superreal numbers, and the hyperreal numbers, are subfields of the surreals. The surreals also contain all transfinite ordinal numbers reachable in the set theory in which they are constructed.

The definition and construction of the surreals is due to John Horton Conway. They were introduced in Donald Knuth's 1974 book Surreal Numbers: How Two Ex-Students Turned on to Pure Mathematics and Found Total Happiness. This book is a mathematical novelette, and is notable as one of the rare cases where a new mathematical idea was first presented in a work of fiction. In his book, which takes the form of a dialogue, Knuth coined the term surreal numbers for what Conway had simply called numbers originally. Conway liked the new name, and later adopted it himself. Conway then described the surreal numbers and used them for analyzing games in his 1976 book On Numbers and Games.


From Wikipedia
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Friday, July 16, 2010

He's Ba-a-AK ! Eric Verlinde !



A Scientist Takes On Gravity

By DENNIS OVERBYE, The New York Times
Published: July 12, 2010

It’s hard to imagine a more fundamental and ubiquitous aspect of life on the Earth than gravity, from the moment you first took a step and fell on your diapered bottom to the slow terminal sagging of flesh and dreams.

But what if it’s all an illusion, a sort of cosmic frill, or a side effect of something else going on at deeper levels of reality?

So says Erik Verlinde, 48, a respected string theorist and professor of physics at the University of Amsterdam, whose contention that gravity is indeed an illusion has caused a continuing ruckus among physicists, or at least among those who profess to understand it. Reversing the logic of 300 years of science, he argued in a recent paper, titled “On the Origin of Gravity and the Laws of Newton,” that gravity is a consequence of the venerable laws of thermodynamics, which describe the behavior of heat and gases.

“For me gravity doesn’t exist,” said Dr. Verlinde, who was recently in the United States to explain himself. Not that he can’t fall down, but Dr. Verlinde is among a number of physicists who say that science has been looking at gravity the wrong way and that there is something more basic, from which gravity “emerges,” the way stock markets emerge from the collective behavior of individual investors or that elasticity emerges from the mechanics of atoms.

Looking at gravity from this angle, they say, could shed light on some of the vexing cosmic issues of the day, like the dark energy, a kind of anti-gravity that seems to be speeding up the expansion of the universe, or the dark matter that is supposedly needed to hold galaxies together.

Dr. Verlinde’s argument turns on something you could call the “bad hair day” theory of gravity.

It goes something like this: your hair frizzles in the heat and humidity, because there are more ways for your hair to be curled than to be straight, and nature likes options. So it takes a force to pull hair straight and eliminate nature’s options. Forget curved space or the spooky attraction at a distance described by Isaac Newton’s equations well enough to let us navigate the rings of Saturn, the force we call gravity is simply a byproduct of nature’s propensity to maximize disorder.

Some of the best physicists in the world say they don’t understand Dr. Verlinde’s paper, and many are outright skeptical. But some of those very same physicists say he has provided a fresh perspective on some of the deepest questions in science, namely why space, time and gravity exist at all — even if he has not yet answered them.

“Some people have said it can’t be right, others that it’s right and we already knew it — that it’s right and profound, right and trivial,” Andrew Strominger, a string theorist at Harvard said.

“What you have to say,” he went on, “is that it has inspired a lot of interesting discussions. It’s just a very interesting collection of ideas that touch on things we most profoundly do not understand about our universe. That’s why I liked it.”

Dr. Verlinde is not an obvious candidate to go off the deep end. He and his brother Herman, a Princeton professor, are celebrated twins known more for their mastery of the mathematics of hard-core string theory than for philosophic flights.

Born in Woudenberg, in the Netherlands, in 1962, the brothers got early inspiration from a pair of 1970s television shows about particle physics and black holes. “I was completely captured,” Dr. Verlinde recalled. He and his brother obtained Ph.D’s from the University of Utrecht together in 1988 and then went to Princeton, Erik to the Institute for Advanced Study and Herman to the university. After bouncing back and forth across the ocean, they got tenure at Princeton. And, they married and divorced sisters. Erik left Princeton for Amsterdam to be near his children.

He made his first big splash as a graduate student when he invented Verlinde Algebra and the Verlinde formula, which are important in string theory, the so-called theory of everything, which posits that the world is made of tiny wriggling strings.

You might wonder why a string theorist is interested in Newton’s equations. After all Newton was overturned a century ago by Einstein, who explained gravity as warps in the geometry of space-time, and who some theorists think could be overturned in turn by string theorists.

Over the last 30 years gravity has been “undressed,” in Dr. Verlinde’s words, as a fundamental force.

This disrobing began in the 1970s with the discovery by Jacob Bekenstein of the Hebrew University of Jerusalem and Stephen Hawking of Cambridge University, among others, of a mysterious connection between black holes and thermodynamics, culminating in Dr. Hawking’s discovery in 1974 that when quantum effects are taken into account black holes would glow and eventually explode.

In a provocative calculation in 1995, Ted Jacobson, a theorist from the University of Maryland, showed that given a few of these holographic ideas, Einstein’s equations of general relativity are just a another way of stating the laws of thermodynamics.

Those exploding black holes (at least in theory — none has ever been observed) lit up a new strangeness of nature. Black holes, in effect, are holograms — like the 3-D images you see on bank cards. All the information about what has been lost inside them is encoded on their surfaces. Physicists have been wondering ever since how this “holographic principle” — that we are all maybe just shadows on a distant wall — applies to the universe and where it came from.

In one striking example of a holographic universe, Juan Maldacena of the Institute for Advanced Study constructed a mathematical model of a “soup can” universe, where what happened inside the can, including gravity, is encoded in the label on the outside of the can, where there was no gravity, as well as one less spatial dimension. If dimensions don’t matter and gravity doesn’t matter, how real can they be?

Lee Smolin, a quantum gravity theorist at the Perimeter Institute for Theoretical Physics, called Dr. Jacobson’s paper “one of the most important papers of the last 20 years.”

But it received little attention at first, said Thanu Padmanabhan of the Inter-University Center for Astronomy and Astrophysics in Pune, India, who has taken up the subject of “emergent gravity” in several papers over the last few years. Dr. Padmanabhan said that the connection to thermodynamics went deeper that just Einstein’s equations to other theories of gravity. “Gravity,” he said recently in a talk at the Perimeter Institute, “is the thermodynamic limit of the statistical mechanics of “atoms of space-time.”

Dr. Verlinde said he had read Dr. Jacobson’s paper many times over the years but that nobody seemed to have gotten the message. People were still talking about gravity as a fundamental force. “Clearly we have to take these analogies seriously, but somehow no one does,” he complained.

His paper, posted to the physics archive in January, resembles Dr. Jacobson’s in many ways, but Dr. Verlinde bristles when people say he has added nothing new to Dr. Jacobson’s analysis. What is new, he said, is the idea that differences in entropy can be the driving mechanism behind gravity, that gravity is, as he puts it an “entropic force.”

That inspiration came to him courtesy of a thief.

As he was about to go home from a vacation in the south of France last summer, a thief broke into his room and stole his laptop, his keys, his passport, everything. “I had to stay a week longer,” he said, “I got this idea.”

Up the beach, his brother got a series of e-mail messages first saying that he had to stay longer, then that he had a new idea and finally, on the third day, that he knew how to derive Newton’s laws from first principles, at which point Herman recalled thinking, “What’s going on here? What has he been drinking?”

When they talked the next day it all made more sense, at least to Herman. “It’s interesting,” Herman said, “how having to change plans can lead to different thoughts.”

Think of the universe as a box of scrabble letters. There is only one way to have the letters arranged to spell out the Gettysburg Address, but an astronomical number of ways to have them spell nonsense. Shake the box and it will tend toward nonsense, disorder will increase and information will be lost as the letters shuffle toward their most probable configurations. Could this be gravity?

As a metaphor for how this would work, Dr. Verlinde used the example of a polymer — a strand of DNA, say, a noodle or a hair — curling up.

“It took me two months to understand polymers,” he said.

The resulting paper, as Dr. Verlinde himself admits, is a little vague.

“This is not the basis of a theory,” Dr. Verlinde explained. “I don’t pretend this to be a theory. People should read the words I am saying opposed to the details of equations.”

Dr. Padmanabhan said that he could see little difference between Dr. Verlinde’s and Dr. Jacobson’s papers and that the new element of an entropic force lacked mathematical rigor. “I doubt whether these ideas will stand the test of time,” he wrote in an e-mail message from India. Dr. Jacobson said he couldn’t make sense of it.

John Schwarz of the California Institute of Technology, one of the fathers of string theory, said the paper was “very provocative.” Dr. Smolin called it, “very interesting and also very incomplete.”

At a workshop in Texas in the spring, Raphael Bousso of the University of California, Berkeley, was asked to lead a discussion on the paper.

“The end result was that everyone else didn’t understand it either, including people who initially thought that did make some sense to them,” he said in an e-mail message.

“In any case, Erik’s paper has drawn attention to what is genuinely a deep and important question, and that’s a good thing,” Dr. Bousso went on, “I just don’t think we know any better how this actually works after Erik’s paper. There are a lot of follow-up papers, but unlike Erik, they don’t even understand the problem.”

The Verlinde brothers are now trying to recast these ideas in more technical terms of string theory, and Erik has been on the road a bit, traveling in May to the Perimeter Institute and Stony Brook University on Long Island, stumping for the end of gravity. Michael Douglas, a professor at Stony Brook, described Dr. Verlinde’s work as “a set of ideas that resonates with the community, adding, “everyone is waiting to see if this can be made more precise.”

Until then the jury of Dr. Verlinde’s peers will still be out.

Over lunch in New York, Dr. Verlinde ruminated over his experiences of the last six months. He said he had simply surrendered to his intuition. “When this idea came to me, I was really excited and euphoric even,” Dr. Verlinde said. “It’s not often you get a chance to say something new about Newton’s laws. I don’t see immediately that I am wrong. That’s enough to go ahead.”

He said friends had encouraged him to stick his neck out and that he had no regrets. “If I am proven wrong, something has been learned anyway. Ignoring it would have been the worst thing.”

The next day Dr. Verlinde gave a more technical talk to a bunch of physicists in the city. He recalled that someone had told him the other day that the unfolding story of gravity was like the emperor’s new clothes.

“We’ve known for a long time gravity doesn’t exist,” Dr. Verlinde said, “It’s time to yell it.”

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