Gematria – Wikipedia, the free encyclopedia

**Gematria** /ɡəˈmeɪ.tri.ə/ (Greek: meaning *geometry*) is an Assyro-Babylonian-Greek system of code and numerology later adopted into Jewish culture that assigns numerical value to a word or phrase in the belief that words or phrases with identical numerical values bear some relation to each other or bear some relation to the number itself as it may apply to nature, a person’s age, the calendar year, or the like.

Similar systems, some of which were derived from or inspired by Hebrew gematria, have been used in other languages and cultures.

The best-known example of Hebrew gematria is the word Chai (“alive”), which is composed of two letters that (using the assignments in the *Mispar gadol* table shown below) add up to 18. This has made 18 a “lucky number” among Jews, and gifts in multiples of 18 are very popular.[1]

https://en.wikipedia.org/wiki/Gematria

(The author of this post takes the opposing view, that “later adopted into Jewish culture” is the reverse of historical record. Bones of Contention lays out the historical evidence for how information was translated generationally, from the beginning. It’s wrong-headed to assume a cave man evolution to “civilization”. Rather, high civilization is the mark of the ancient archeological record. And considering that Adam walked with God, for an unspecified amount of time. Years? Decades? Millenia? Coupled with the centurian life spans. Vast knowledge reserve would have been collectively passed down generationally. Hence, the blessing passed on to those who bless the man of God.

Gen 12:1-3

Now the LORD had said unto Abram, Get thee out of thy country, and from thy kindred, and from thy father’s house, unto a land that I will shew thee:

And I will make of thee a great nation, and I will bless thee, and make thy name great; and thou shalt be a blessing:

And I will bless them that bless thee, and curse him that curseth thee: and in thee shall all families of the earth be blessed.)

**32 (number) – Wikipedia, the free encyclopedia**

32 (thirty-two) is the natural number following 31 and preceding 33.

**In mathematics **[edit]

32 is the smallest number n with exactly 7 solutions to the equation φ(x) = n. It is also the sum of the totient function for the first ten integers.

The fifth power of two, 32 is also a Leyland number since 24 + 42 = 32.

As with every power of two, 32 has an aliquot sum one less than itself: the prime 31. 32 is the first member of the 31-aliquot tree.

32 is the ninth happy number.

32 = 11 + 22 + 33

**Astronomy** [edit]

Messier 32, a magnitude 9.0 galaxy in the constellation Andromeda which is a companion to M31.

The New General Catalogue object NGC 32, a star in the constellation Pegasus

The Saros number of the lunar eclipse series which began on June 11, 1691 BC and ended on August 9, 375 BC. The duration of Saros series 32 was 1316.2 years, and it contained 74 lunar eclipses.

**In music** [edit]

The number of completed, numbered piano sonatas by Ludwig van Beethoven

**In religion** [edit]

In the Kabbalah, there are 32 Kabbalistic Paths of Wisdom.

One of the central texts of the Pāli Canon in the Theravada Buddhist tradition, the Digha Nikaya, describes the appearance of the historical Buddha with a list of 32 physical characteristics.

The Hindu scripture Mudgala Purana also describes Ganesha as taking 32 forms.

**In sports** [edit]

In chess, the total number of black squares on the board, the total number of white squares, and the total number of pieces (black and white) at the beginning of the game.

**In other fields** [edit]

Thirty-two could also refer to:

The number of teeth of a full set of teeth in an adult human, including wisdom teeth

The size of a databus in bits: 32-bit

The size, in bits, of certain integer data types, used in computer representations of numbers

IPv4 uses 32-bit (4-byte) addresses

ASCII and Unicode code point for space

The code for international direct dial phone calls to Belgium

In the title Thirty-Two Short Films About Glenn Gould, starring Colm Feore

Article 32 of the UCMJ concerns pre-trial investigations. Such a hearing is often called an “article 32 hearing”

Sometimes considered to be the occult opposite of number 23

The caliber .32 ACP

The number of pages in the average comic book (not including the cover)

The number of the French department Gers

The traditional 32 counties of Ireland

https://en.wikipedia.org/wiki/32_(number)

**SACRED GEOMETRY AND THE ART OF SCRIPTURAL WRITING**:

The Genesis Formula, the Vesica Piscis, the Flower of Life, The Kabbalistic Tree of Life and the Star of David

Copyright by William John Meegan

Presented with author’s permission

Sacred Geometry and the Art of Scriptural Writing – World Mysteries Blog

4. THE KABBALISTIC TREE OF LIFE & THE STAR OF DAVID

The Kabbalistic Tree of Life can only be envisaged by the researcher listing the thirty-two (32) times that the word ELOHYM is listed in the text of the first chapter of Genesis along with the accompanied word that each use is associated with (see chart below). The pattern of the 32-Elohyms is found to be exactly that which is found in the traditional Kabbalistic Tree of Life: 10-Serirahs (10-times the word ‘said’ is used), 3-Mother letters (3-times the word ‘made’ is used), 7-Double letters (7-times the word ‘saw’ is used) and 12-Single letters (there are various words used totaling 12). It was not difficult to locate the apex of the Kabbalistic Tree of Life once the thirty-two (32) ELOHYMS were placed into a circle sequentially: 1-32.

http://blog.world-mysteries.com/ancient-writings/sacred-geometry-and-the-art-of-scriptural-writing/

**Tree of Life**

The symbol of the Tree of Life may be derived from the Flower of Life. The Tree of Life is a concept, a metaphor for common descent, and a motif in various world theologies and philosophies. This has historically been adopted by some Christians, Jews, Hermeticists, and pagans. Along with the Seed of Life, it is believed to be part of the geometry that parallels the cycle of the fruit tree. This relationship is implied when these two forms are superimposed onto each other.

The Tree of Life is most widely recognized as a concept within the Kabbalah, which is used to understand the nature of God and the manner in which he created the world ex nihilo. The Kabbalists developed this concept into a full model of reality, using the tree to depict a “map” of creation. The tree of life has been called the “cosmology” of the Kabbalah.Some believe the Tree of Life of the Kabbalah corresponds to the Tree of Life mentioned in Genesis 2:9.

http://blog.world-mysteries.com/science/the-flower-of-life/

**A Head Full of Dreams** – Wikipedia, the free encyclopedia

A Head Full of Dreams is the seventh studio album by British rock band **Coldplay**.

https://en.wikipedia.org/wiki/A_Head_Full_of_Dreams

Sacred Geometry in Superbowl 50 | Spirit Science

The Super Bowl Halftime show is the most viewed event of the year, and in this 50th year we saw a presentation of many sacred symbols that begged for a more spiritual analysis. […]

He comes onto the stage onto a massive, bright flower of life. The ancient symbol is not only featured on their latest album cover, it is also found on each of the band members [Coldplay] and wherever else it might be squeezed in. Also on stage we have a prominent bell next to the drummer. It is a special bell known as the Ghanta. This is a bell you ring coming into a temple that is made to sound like an extended “Om.”

http://thespiritscience.net/2016/02/18/sacred-geometry-in-superbowl-50/

The Geometry of Football by: Bill Marinis by on Prezi

https://prezi.com/-pvwgynoa0ez/the-geometry-of-football-by-bill-marinis/

Vesica piscis – Wikipedia, the free encyclopedia

https://en.wikipedia.org/wiki/Vesica_piscis

Lest it not be lost on the reader.

The “bread and circus” mentality of the befuddled masses is the result of the Freemasonization of America.

**National Football League** – Wikipedia, the free encyclopedia

The National Football League (NFL) is a professional American football league consisting of **32 teams**,

https://en.wikipedia.org/wiki/National_Football_League

**32-Mile-Wide ‘No Drone Zone’ Surrounds Super Bowl 50 Site on Sunday** | KTLA

http://ktla.com/2016/02/03/32-mile-wide-no-drone-zone-surrounds-super-bowl-50-site-on-sunday/

SAT FEB. 6, 2016

**Monday Morning Headline: ‘Panthers, Newton Secure Place in History with Dominant Win over Denver’**

**You want a Super Bowl 50 prediction? Here’s the entire game story from Sunday—filed just a little bit early**

Yards weren’t coming any easier for the Broncos. After a quick **three and out to open the game and another drive of just 18 yards, Denver took over at its own 32**-yard line following Carolina’s second punt of the day. On first and 10, Manning lined up in the Pistol formation and faked a quick handoff to C.J. Anderson before turning his head back upfield.

http://mmqb.si.com/mmqb/2016/02/06/nfl-super-bowl-50-prediction-panthers-win

If you hadn’t noticed.

18 and 32 have been reoccurring in this post.

18 being 6+6+6.

PEYTON MANNING TO RETIRE AFTER 18 NFL SEASONS…

8 / 18 = 0.444444444

Or 9 x 4 = 36

Or 18 + 18

6+6+6 + 6+6+6

What are the odds?

Americans will bet billions illegally during NFL season, group says – Yahoo Sports

http://sports.yahoo.com/news/americans-bet-billions-illegally-during-nfl-season-group-000816050–nfl.html

THE NFL’S DIRTY SECRET | SAN DIEGO READER By Don Bauder, July 4, 2012

Picture a couple cozily cohabitating for more than 90 years but publicly pretending they aren’t conjoined. That’s the National Football League and the gambling industry (both legal and illegal).

This faux separation is in the news again. Today, Nevada is the only state in which sports gambling is legal, regulated, policed, and taxed, but it only accounts for about 1 percent of sports wagering, according to the American Gaming Association. New Jersey wants sports gambling permitted at its racetracks and in Atlantic City; other revenue-hungry states want in on the action, too.

The National Football League, which earlier beat back Delaware when it wanted to have Nevada-like privileges, might sue New Jersey. Well, sue with a wink. Commented one wag on the ProFootballTalk website, “NFL has its headquarters in New York, but ‘dey keep de books in Joisey.’” In reality, Joisey’s all-powerful mob will probably decide whether the state goes for legalized sports gambling. Dem kneecappers may prefer to keep it in their own hands, although if they surreptitiously control the Atlantic City casinos and state racetracks (quite possible), they might want sports gambling legalized. In either case, the league will quietly rejoice.

The National Football League’s feigned indignation about gambling is a joke. A conservative estimate is that $80 billion to $100 billion is wagered on NFL games each year, only a fraction legally. People place their bets through bookies, office pools, fantasy football, and the like. This gambling clearly boosts attendance and TV revenue, the mother’s milk of the sport. When you have money in a game, your interest is intensified. (Would you even bother to watch a horse race if you had no cash on a nag?)

The National Football League’s actions belie its supposed contempt for gambling. For example, the league requires teams to state before games what players may have to sit out because of injury and what players are questionable. That information only benefits gamblers. And does the league complain that newspapers run the point spreads on the games? Of course not.

The long-running but secret alliance of pro football and gambling has been chronicled thoroughly in the book Interference: How Organized Crime Influences Professional Football, by Dan E. Moldea (Morrow). In the early 1920s, one George Halas turned to Charles Bidwill, a bootlegger, gambler, racetrack owner, and associate of Chicago’s Al (Scarface) Capone’s mob, to finance the Chicago Bears. Later, Bidwill bought the Chicago Cardinals. The Bidwill family now owns the Arizona Cardinals.

In 1925, bookie Tim Mara bought the New York Giants. His heirs still have half the team. Notorious gambler Art Rooney took over the Pittsburgh Steelers. His family still controls the team; the Rooney empire is purportedly breaking up so that the racetracks and casinos won’t be mixed with the football team.

In the sport’s first half-century, one team after another was owned by high rollers, often with sordid connections. The Cleveland Browns were owned by crime syndicate bookmaker Arthur (Mickey) McBride, head of the Continental Racing Wire, the mob’s gambling news service. The U.S. Senate’s Kefauver Committee called that news service “Public Enemy Number One.”

In 1961, the team was sold to Art Modell, who, among many things, was a partner in a horse-racing stable with one Morris (Mushy) Wexler, whom the Kefauver Committee named one of the “leading hoodlums” in McBride’s wire service. In 1969, Modell got married in the Las Vegas digs of William (Billy) Weinberger, president of Caesars Palace, whose hidden owners included such dignitaries as Tony (Big Tuna) Accardo, Sam (Momo) Giancana, and Vincent (Jimmy Blue Eyes) Alo. When he died in 1996, the Las Vegas Sun called Weinberger “the dean of casino gaming.”

A 1969 happening spotlights the National Football League’s blatant hypocrisy. New York Jets quarterback Joe Namath invested in a Manhattan bar. The National Football League told him to sell his shares because the joint had ties to big-time gamblers and unsavory individuals. The league said nothing about Modell’s ties — or the unsavory ties of numerous other team owners. (The late Carroll Rosenbloom, a high roller with a major interest in a mobbed-up Bahamian casino, owned the Baltimore Colts and Los Angeles Rams at different times. His second wife and widow, entertainer Georgia Frontiere — who had been married five times before latching on to Rosenbloom — inherited control of the Rams and moved them to St. Louis when she got a stadium 96 percent funded by taxpayers.)

There have been too many incidents to recount here. The Youngstown DeBartolo family, long involved in casinos and racetracks, owns the San Francisco 49ers. In the late 1990s, Edward DeBartolo Jr., then head of the 49ers, paid a Louisiana governor $400,000 to get a riverboat casino license. The governor went to the slammer; DeBartolo got a wrist slap but had to leave the 49ers. The family still runs the team, while DeBartolo Jr. runs the company that is based back in Youngstown.

Not surprisingly, San Diego has been in the middle of the NFL/gambling love affair. The late Pete Rozelle, Rancho Santa Fe resident and onetime head of the NFL, deftly tiptoed around team owners’ mob/gambling ties, Moldea shows in his book. Rozelle stepped on players suspected of consorting with gamblers (but never told them not to associate with their mobbed-up team owners).

The Chargers were founded by longtime gambler Barron Hilton, who had both a business and personal relationship with Los Angeles attorney Sidney Korshak, who was described by law enforcement officials as “the link between the legitimate business world and organized crime.” A later owner was Eugene Klein, another Korshak friend with mob and gambling associations. The late Al Davis, a former Chargers coach who wound up owning the Oakland Raiders, was a business associate of San Diego casino owner Allen Glick. Davis’s survivors still control the Raiders. Several Chargers players got into deals with Glick.

Eventually, American states — if not New Jersey — will get their way. You can bet on it. ■

http://sandiegoreader.com/news/2012/jul/04/citylights1-nfl-dirty-secret/

Are Professional Sports Fixed?

**Would you leave a multi-billion dollar business up to chance?**

http://thefixisin.net/

Related:

http://forthtell.blogspot.com/2012/06/11-observations-on-letter-k-in-progress.html

https://forthtell.wordpress.com/2015/04/18/ominous-number-19-2/

https://forthtell.wordpress.com/2015/06/22/1957/

https://forthtell.wordpress.com/2015/07/01/19-11-32-18-666-occult-numeric-signals-in-the-news/

American football could fall like the gladiators of ancient Rome | New York Post

http://nypost.com/2016/12/03/american-football-could-fall-like-the-gladiators-of-ancient-rome/

NFL Ratings Rebound in Most Competitive Season Since 1932 « CBS DC

http://washington.cbslocal.com/2016/12/16/nfl-ratings-rebound-in-most-competitive-season-since-1932/

M=V+P | The Sacred Geometry Of The Game | All Games Have A Freemason Foundation | Challenge You To See It | Click for image: …

Pro Bowl – Wikipedia

https://en.m.wikipedia.org/wiki/Pro_Bowl

Physicists Discover Geometry Underlying Particle Physics | Quanta Magazine

https://www.quantamagazine.org/physicists-discover-geometry-underlying-particle-physics-20130917

Physicists Discover Geometry Underlying Particle Physics

Physicists have discovered a jewel-like geometric object that dramatically simplifies calculations of particle interactions and challenges the notion that space and time are fundamental components of reality.

“This is completely new and very much simpler than anything that has been done before,” said Andrew Hodges, a mathematical physicist at Oxford University who has been following the work.

The revelation that particle interactions, the most basic events in nature, may be consequences of geometry significantly advances a decades-long effort to reformulate quantum field theory, the body of laws describing elementary particles and their interactions. Interactions that were previously calculated with mathematical formulas thousands of terms long can now be described by computing the volume of the corresponding jewel-like “amplituhedron,” which yields an equivalent one-term expression.

“The degree of efficiency is mind-boggling,” said Jacob Bourjaily, a theoretical physicist at Harvard University and one of the researchers who developed the new idea. “You can easily do, on paper, computations that were infeasible even with a computer before.”

The new geometric version of quantum field theory could also facilitate the search for a theory of quantum gravity that would seamlessly connect the large- and small-scale pictures of the universe. Attempts thus far to incorporate gravity into the laws of physics at the quantum scale have run up against nonsensical infinities and deep paradoxes. The amplituhedron, or a similar geometric object, could help by removing two deeply rooted principles of physics: locality and unitarity.

“Both are hard-wired in the usual way we think about things,” said Nima Arkani-Hamed, a professor of physics at the Institute for Advanced Study in Princeton, N.J., and the lead author of the new work, which he is presenting in talks and in a forthcoming paper. “Both are suspect.”

Locality is the notion that particles can interact only from adjoining positions in space and time. And unitarity holds that the probabilities of all possible outcomes of a quantum mechanical interaction must add up to one. The concepts are the central pillars of quantum field theory in its original form, but in certain situations involving gravity, both break down, suggesting neither is a fundamental aspect of nature.

In keeping with this idea, the new geometric approach to particle interactions removes locality and unitarity from its starting assumptions. The amplituhedron is not built out of space-time and probabilities; these properties merely arise as consequences of the jewel’s geometry. The usual picture of space and time, and particles moving around in them, is a construct.

“It’s a better formulation that makes you think about everything in a completely different way,” said David Skinner, a theoretical physicist at Cambridge University.

The amplituhedron itself does not describe gravity. But Arkani-Hamed and his collaborators think there might be a related geometric object that does. Its properties would make it clear why particles appear to exist, and why they appear to move in three dimensions of space and to change over time.

Because “we know that ultimately, we need to find a theory that doesn’t have” unitarity and locality, Bourjaily said, “it’s a starting point to ultimately describing a quantum theory of gravity.”

Clunky Machinery

The amplituhedron looks like an intricate, multifaceted jewel in higher dimensions. Encoded in its volume are the most basic features of reality that can be calculated, “scattering amplitudes,” which represent the likelihood that a certain set of particles will turn into certain other particles upon colliding. These numbers are what particle physicists calculate and test to high precision at particle accelerators like the Large Hadron Collider in Switzerland.

The iconic 20th century physicist Richard Feynman invented a method for calculating probabilities of particle interactions using depictions of all the different ways an interaction could occur. Examples of “Feynman diagrams” were included on a 2005 postage stamp honoring Feynman.

The iconic 20th century physicist Richard Feynman invented a method for calculating probabilities of particle interactions using depictions of all the different ways an interaction could occur. Examples of “Feynman diagrams” were included on a 2005 postage stamp honoring Feynman.

United States Postal Service

The 60-year-old method for calculating scattering amplitudes — a major innovation at the time — was pioneered by the Nobel Prize-winning physicist Richard Feynman. He sketched line drawings of all the ways a scattering process could occur and then summed the likelihoods of the different drawings. The simplest Feynman diagrams look like trees: The particles involved in a collision come together like roots, and the particles that result shoot out like branches. More complicated diagrams have loops, where colliding particles turn into unobservable “virtual particles” that interact with each other before branching out as real final products. There are diagrams with one loop, two loops, three loops and so on — increasingly baroque iterations of the scattering process that contribute progressively less to its total amplitude. Virtual particles are never observed in nature, but they were considered mathematically necessary for unitarity — the requirement that probabilities sum to one.

“The number of Feynman diagrams is so explosively large that even computations of really simple processes weren’t done until the age of computers,” Bourjaily said. A seemingly simple event, such as two subatomic particles called gluons colliding to produce four less energetic gluons (which happens billions of times a second during collisions at the Large Hadron Collider), involves 220 diagrams, which collectively contribute thousands of terms to the calculation of the scattering amplitude.

In 1986, it became apparent that Feynman’s apparatus was a Rube Goldberg machine.

To prepare for the construction of the Superconducting Super Collider in Texas (a project that was later canceled), theorists wanted to calculate the scattering amplitudes of known particle interactions to establish a background against which interesting or exotic signals would stand out. But even 2-gluon to 4-gluon processes were so complex, a group of physicists had written two years earlier, “that they may not be evaluated in the foreseeable future.”

Stephen Parke and Tomasz Taylor, theorists at Fermi National Accelerator Laboratory in Illinois, took that statement as a challenge. Using a few mathematical tricks, they managed to simplify the 2-gluon to 4-gluon amplitude calculation from several billion terms to a 9-page-long formula, which a 1980s supercomputer could handle. Then, based on a pattern they observed in the scattering amplitudes of other gluon interactions, Parke and Taylor guessed a simple one-term expression for the amplitude. It was, the computer verified, equivalent to the 9-page formula. In other words, the traditional machinery of quantum field theory, involving hundreds of Feynman diagrams worth thousands of mathematical terms, was obfuscating something much simpler. As Bourjaily put it: “Why are you summing up millions of things when the answer is just one function?”

“We knew at the time that we had an important result,” Parke said. “We knew it instantly. But what to do with it?”

The Amplituhedron

Twistor diagrams depicting an interaction between six gluons, in the cases where two (left) and four (right) of the particles have negative helicity, a property similar to spin. The diagrams can be used to derive a simple formula for the 6-gluon scattering amplitude.

Twistor diagrams depicting an interaction between six gluons, in the cases where two (left) and four (right) of the particles have negative helicity, a property similar to spin. The diagrams can be used to derive a simple formula for the 6-gluon scattering amplitude.

The message of Parke and Taylor’s single-term result took decades to interpret. “That one-term, beautiful little function was like a beacon for the next 30 years,” Bourjaily said. It “really started this revolution.”

In the mid-2000s, more patterns emerged in the scattering amplitudes of particle interactions, repeatedly hinting at an underlying, coherent mathematical structure behind quantum field theory. Most important was a set of formulas called the BCFW recursion relations, named for Ruth Britto, Freddy Cachazo, Bo Feng and Edward Witten. Instead of describing scattering processes in terms of familiar variables like position and time and depicting them in thousands of Feynman diagrams, the BCFW relations are best couched in terms of strange variables called “twistors,” and particle interactions can be captured in a handful of associated twistor diagrams. The relations gained rapid adoption as tools for computing scattering amplitudes relevant to experiments, such as collisions at the Large Hadron Collider. But their simplicity was mysterious.

“The terms in these BCFW relations were coming from a different world, and we wanted to understand what that world was,” Arkani-Hamed said. “That’s what drew me into the subject five years ago.”

With the help of leading mathematicians such as Pierre Deligne, Arkani-Hamed and his collaborators discovered that the recursion relations and associated twistor diagrams corresponded to a well-known geometric object. In fact, as detailed in a paper posted to arXiv.org in December by Arkani-Hamed, Bourjaily, Cachazo, Alexander Goncharov, Alexander Postnikov and Jaroslav Trnka, the twistor diagrams gave instructions for calculating the volume of pieces of this object, called the positive Grassmannian.

A sketch of the amplituhedron representing an 8-gluon particle interaction. Using Feynman diagrams, the same calculation would take roughly 500 pages of algebra.

A sketch of the amplituhedron representing an 8-gluon particle interaction. Using Feynman diagrams, the same calculation would take roughly 500 pages of algebra.

Named for Hermann Grassmann, a 19th-century German linguist and mathematician who studied its properties, “the positive Grassmannian is the slightly more grown-up cousin of the inside of a triangle,” Arkani-Hamed explained. Just as the inside of a triangle is a region in a two-dimensional space bounded by intersecting lines, the simplest case of the positive Grassmannian is a region in an N-dimensional space bounded by intersecting planes. (N is the number of particles involved in a scattering process.)

It was a geometric representation of real particle data, such as the likelihood that two colliding gluons will turn into four gluons. But something was still missing.

The physicists hoped that the amplitude of a scattering process would emerge purely and inevitably from geometry, but locality and unitarity were dictating which pieces of the positive Grassmannian to add together to get it. They wondered whether the amplitude was “the answer to some particular mathematical question,” said Trnka, a post-doctoral researcher at the California Institute of Technology. “And it is,” he said.

Arkani-Hamed and Trnka discovered that the scattering amplitude equals the volume of a brand-new mathematical object — the amplituhedron. The details of a particular scattering process dictate the dimensionality and facets of the corresponding amplituhedron. The pieces of the positive Grassmannian that were being calculated with twistor diagrams and then added together by hand were building blocks that fit together inside this jewel, just as triangles fit together to form a polygon.

Like the twistor diagrams, the Feynman diagrams are another way of computing the volume of the amplituhedron piece by piece, but they are much less efficient. “They are local and unitary in space-time, but they are not necessarily very convenient or well-adapted to the shape of this jewel itself,” Skinner said. “Using Feynman diagrams is like taking a Ming vase and smashing it on the floor.”

Puzzling Thoughts

Locality and unitarity are the central pillars of quantum field theory, but as the following thought experiments show, both break down in certain situations involving gravity. This suggests physics should be formulated without either principle.

Locality says that particles interact at points in space-time. But suppose you want to inspect space-time very closely. Probing smaller and smaller distance scales requires ever higher energies, but at a certain scale, called the Planck length, the picture gets blurry: So much energy must be concentrated into such a small region that the energy collapses the region into a black hole, making it impossible to inspect. “There’s no way of measuring space and time separations once they are smaller than the Planck length,” said Arkani-Hamed. “So we imagine space-time is a continuous thing, but because it’s impossible to talk sharply about that thing, then that suggests it must not be fundamental — it must be emergent.”

Unitarity says the quantum mechanical probabilities of all possible outcomes of a particle interaction must sum to one. To prove it, one would have to observe the same interaction over and over and count the frequencies of the different outcomes. Doing this to perfect accuracy would require an infinite number of observations using an infinitely large measuring apparatus, but the latter would again cause gravitational collapse into a black hole. In finite regions of the universe, unitarity can therefore only be approximately known.

Arkani-Hamed and Trnka have been able to calculate the volume of the amplituhedron directly in some cases, without using twistor diagrams to compute the volumes of its pieces. They have also found a “master amplituhedron” with an infinite number of facets, analogous to a circle in 2-D, which has an infinite number of sides. Its volume represents, in theory, the total amplitude of all physical processes. Lower-dimensional amplituhedra, which correspond to interactions between finite numbers of particles, live on the faces of this master structure.

“They are very powerful calculational techniques, but they are also incredibly suggestive,” Skinner said. “They suggest that thinking in terms of space-time was not the right way of going about this.”

Quest for Quantum Gravity

The seemingly irreconcilable conflict between gravity and quantum field theory enters crisis mode in black holes. Black holes pack a huge amount of mass into an extremely small space, making gravity a major player at the quantum scale, where it can usually be ignored. Inevitably, either locality or unitarity is the source of the conflict.

“We have indications that both ideas have got to go,” Arkani-Hamed said. “They can’t be fundamental features of the next description,” such as a theory of quantum gravity.

String theory, a framework that treats particles as invisibly small, vibrating strings, is one candidate for a theory of quantum gravity that seems to hold up in black hole situations, but its relationship to reality is unproven — or at least confusing. Recently, a strange duality has been found between string theory and quantum field theory, indicating that the former (which includes gravity) is mathematically equivalent to the latter (which does not) when the two theories describe the same event as if it is taking place in different numbers of dimensions. No one knows quite what to make of this discovery. But the new amplituhedron research suggests space-time, and therefore dimensions, may be illusory anyway.

“We can’t rely on the usual familiar quantum mechanical space-time pictures of describing physics,” Arkani-Hamed said. “We have to learn new ways of talking about it. This work is a baby step in that direction.”

Even without unitarity and locality, the amplituhedron formulation of quantum field theory does not yet incorporate gravity. But researchers are working on it. They say scattering processes that include gravity particles may be possible to describe with the amplituhedron, or with a similar geometric object. “It might be closely related but slightly different and harder to find,” Skinner said.

Physicists must also prove that the new geometric formulation applies to the exact particles that are known to exist in the universe, rather than to the idealized quantum field theory they used to develop it, called maximally supersymmetric Yang-Mills theory. This model, which includes a “superpartner” particle for every known particle and treats space-time as flat, “just happens to be the simplest test case for these new tools,” Bourjaily said. “The way to generalize these new tools to [other] theories is understood.”

Nima Arkani-Hamed, a professor at the Institute for Advanced Study, and his former student and co-author Jaroslav Trnka, who finished his Ph.D. at Princeton University in July and is now a post-doctoral researcher at the California Institute of Technology.

Nima Arkani-Hamed, a professor at the Institute for Advanced Study, and his former student and co-author Jaroslav Trnka, who finished his Ph.D. at Princeton University in July and is now a post-doctoral researcher at the California Institute of Technology.

Courtesy of Jaroslav Trnka

Beyond making calculations easier or possibly leading the way to quantum gravity, the discovery of the amplituhedron could cause an even more profound shift, Arkani-Hamed said. That is, giving up space and time as fundamental constituents of nature and figuring out how the Big Bang and cosmological evolution of the universe arose out of pure geometry.

“In a sense, we would see that change arises from the structure of the object,” he said. “But it’s not from the object changing. The object is basically timeless.”

While more work is needed, many theoretical physicists are paying close attention to the new ideas.

The work is “very unexpected from several points of view,” said Witten, a theoretical physicist at the Institute for Advanced Study. “The field is still developing very fast, and it is difficult to guess what will happen or what the lessons will turn out to be.”

Note: This article was updated on December 10, 2013, to include a link to the first in a series of papers on the amplituhedron.

This article was reprinted on Wired.com.