A jewel at the heart of Quantum Physics ~ The Amplituhedron ~ Arkani-Hamed and Trnka

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SUSANakaTHE13THBRIDGE - Posted Dec 12th

Theories of wormhole metrics describe the spacetime geometry of a wormhole and serve as theoretical models for time travel.
An example of a (traversable) wormhole metric is the following:

One type of non-traversable wormhole metric is the Schwarzschild solution (see the diagram below):


so, how many different aspects are there to this drawings
- i am esp; interested in the triangular pie shapes to it !!!
thank you

Post last edited Dec 12th


A Jewel at the Heart of Quantum Physics


how many different aspects are in this figure ?

SUSAN LYNNE SCHWENGER aka THE exchanger aa THE 13TH BRIDGE




A Jewel at the Heart of Quantum Physics



how many different aspects are in this figure ?

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The amplituhedron is like a hologram of nature in geometry. The following excerpt describes this 'multifacetness' as intrinsically infinite, just as a hologram of a 3D object in holography recreates the original object in all detail, albeit in a diminished intensity of the energy.
The 8-gluon permutation of Unitary Symmetry {SU(3)} as a corner stone of Quantum Theory in the application of Quantum-Chromo-Dynamis or QCD, is used to model the Strong Nuclear Interaction within the atomic nucleus to exemplify the permuatation pattern of the amplituhedron.

The 8 ways to arrange two energy states say as given by Einstein's Mass-Energy equivalence E=mc² and describing the 'Black' matter based energy selfstate and the Planckian Law of Quantum Mechanics in E=hf, describing the Radiation 'White' energy state, can then be modeled in WWW as a 'pure' radiation state and a 'pure' matter state BBB with 6 hybrid energy states of WWB and WBW and BWW and BBW and BWB and WBB in between.
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.


Nima Arkani-Hamed


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

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.”


Shawnee 75


transferred from: http://www.thuban.spruz.com/forums/...007F&fid=F24860EF-C75A-4FF1-BEAF-C2046C77F702

 

Posted Oct 11th 2013

A Jewel at the Heart of Quantum Physics



Illustration by Andy Gilmore
Artist’s rendering of the amplituhedron, a newly discovered mathematical object resembling a multifaceted jewel in higher dimensions.
Encoded in its volume are the most basic features of reality that can be calculated
— the probabilities of outcomes of particle interactions.
By: Natalie Wolchover
September 17, 2013

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
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.

United States Postal Service
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 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 Tommy 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
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.”

Arkani-Hamed et al.
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.
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.
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.

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

Courtesy of Jaroslav Trnka
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.
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.”
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.”


https://www.simonsfoundation.org/quanta/20130917-a-jewel-at-the-heart-of-quantum-physics/

 

https://www.simonsfoundation.org/quanta/20130917-a-jewel-at-the-heart-of-quantum-physics/

Comments for this entry
m says:
September 17, 2013 at 8:34 pm
trying to comprehend this hypothesis this is like a blind man trying to grab smoke with a mall in each hand…for us laymen that is..
Jose says:
September 17, 2013 at 9:50 pm
Buky Fuller’s Synergetic’s might prove useful after 6 decades of playing second fiddle to mainstream science.
Krib Veiqb says:
September 18, 2013 at 3:54 am
This is exceptionally well written and very interesting. Thank you!
David B. says:
September 18, 2013 at 9:47 am
Good job Natalie Wolchover! Your article is a lucid explanation of an arcane topic.
It is clear and interesting to read, and it gives relevant perspective from the history of modern physics. Thank you!

Wizard Garber says:
September 18, 2013 at 10:57 am
Using geometry to predict the behavior of particles is nothing new.
The standard model is geometric. Dr. Garrett Lisi has been positing the use of the E8 Lie Group geometry to predict particle behavior since 2007.
Michael H says:
September 18, 2013 at 11:25 am
Beautifully written. Thank you.
Ignacio Mosqueira says:
September 18, 2013 at 11:34 am
It is a far cry to say that a theory doesn’t explicitly rely on unitarity or space-time than saying that we need to give up on these concepts.
I don’t read anything in this article that captures the essence of that statement.
Both of those issues seem to be stumbling blocks in quantum gravity
but I don’t see how it helps to say that “unitarity is not fundamental”
without giving an alternative interpretation of the sum over histories approach to QM.
I would frankly prefer that the authors do not make such statements until they do have a consistent framework
that gives up on unitarity in particular.
There was a lot of similar talk at the fuzz or fire conference in Santa Barbara and it was equally unsatisfying.
Luke Lea says:
September 18, 2013 at 11:38 am
A “geometrical object” without “space” ?
D P says:
September 18, 2013 at 11:56 am
These are exciting times. Great article; it managed to strike a good balance for those of us familiar with physics but not deeply well-educated about it.

John says:
September 18, 2013 at 12:34 pm
Normally in write-ups of new physics results, there’s always some physicist quoted who points out some issues with the approach
or that it’s too early to make any firm conclusions. This article doesn’t really have that.
gregor says:
September 18, 2013 at 12:47 pm
Haha! But does it explain the explosive omnipresence of the Kardashians in the American cultural landscape?
Ryan S says:
September 18, 2013 at 12:56 pm
I suppose they mean conceptually geometric rather than physically geometric.
This reminds me of a proposition that reality is a holographic projection on the surface of a hypersphere.
The article even mentions, “a master amplituhedron with an infinite number of facets,
analogous to a circle in 2-D, which has an infinite number of sides.” Sounds like a hypersphere to me.
Also, regarding gravity, if they’re willing to throw out unitarity and locality, why not gravity?
It could equally be a “property that merely arises as consequences of the jewel’s geometry.
Tony says:
September 18, 2013 at 1:25 pm
Jose, that was my thought too. Fuller’s geometric approach was quite elegant, and this article kept reminding me of it.
Adubs says:
September 18, 2013 at 1:34 pm
“But the new amplituhedron research suggests space-time, and therefore dimensions, may be illusory anyway.”
Yeah I read Michael Talbot’s The Holographic Universe. So not surprised.

john werneken says:
September 18, 2013 at 1:47 pm
Wow. Theory of Everything, maybe. A fundamental reality, maybe. Wow!
Logan Linthicum says:
September 18, 2013 at 2:47 pm
Thank you very much for this deeply satisfying article. It is rare to find an example of scientific journalism that is both comprehensible
to one not in the field and not simplified to the point of uselessness.
Greatly simplifying the calculation of particle interactions makes the simulation of our universe more feasible, right?
To my mind, any discoveries in this direction increase the likelihood that that the universe we inhabit is itself a simulation.
Ruth E. Kastner (@rekastner) says:
September 18, 2013 at 2:56 pm
This is exciting indeed. I’ve recently proposed that quantum mechanics is telling us about a domain that is not contained in spacetime
— a domain from which space and time are emergent and approximate notions.
This work lends further support to the idea that we must let go of spacetime as a fundamental substance. Rather, it is a construct based on our everyday experience.
Richard W. Fitch says:
September 18, 2013 at 3:04 pm
Clifford Pickover ~~ “Mathematics is the Loom upon which God weaves the Fabric of the Universe.”
Mike says:
September 18, 2013 at 3:12 pm
Great article Natalie. Very interesting stuff. I can’t wait to see how Sheldon and Leonard deal with this new revelation.
Jake says:
September 18, 2013 at 3:30 pm
If I’m understanding this correctly, they’re saying they may have found an object that contains and dictates our entire universe.
So if this theory proves reliable, and if their search for a gravityhedron works out, we would be able literally to see the shape of our universe.
This is so cool.
Ron says:
September 18, 2013 at 3:34 pm
Does this complement string theory, or negate it? There’s a paragraph that mentions ST, but is confusing to my layman’s brain.
Crowe says:
September 18, 2013 at 3:38 pm
I was struck by the analog that to calculate the area under a curve, you can add up a large sum of rectangles (Feyman),
but in the limit you can get a closed form solution (jewel thing).
BubbhaD says:
September 18, 2013 at 3:46 pm
Shaving with Occam’s Razor again….
Dave says:
September 18, 2013 at 4:28 pm
Suggests that a multidimensional fractal formulation may also be profitable, where
the geometric object representing the scattering amplitudes is the surface calculated in n-space.
It always seemed like feynman diagrams had a recursive fractal aspect…..
FredInIT says:
September 18, 2013 at 4:34 pm
While this may end up being smoke and mirrors, a hand-waiving exercise, or my favorite ‘I think you should be more explicit here in Step 2.’
Then again, it may not be.
Just as Algebra is an abstraction of arithmetic. And calculus is an extension of Algebra using infinities.
Geometry is a method of representing Algebra, arithmetic and calculus graphically – I view this as just a new method of representing something else.
It’s a tool that can be used to discern the tautology of possible outcomes.
Rather than just throwing numbers at formula via brute force and trying to sift the wheat from the chaff
you can narrow the range down to those that have a good chance of working (lie within the outcome set) and those that do not.
If it helps to develop GUT – great. If it helps to reduce the amount of computing power needed at the LHC,
among other facilities, by identifying calculating short cuts. Even better. If it doesn’t seem to be able to do any of these
– it’s still a pretty cool picture. One that easily could be framed and hung on the wall of the Guggenheim or used in some display at MSI in Chicago.
That alone makes it a work of art. If it does what the authors claim – all the better.
Especially if it can, as this wonderful article did, help bring an immensely complex subject such as this to the unwashed masses. Such as myself.
FredInIT.
John Willis says:
September 18, 2013 at 4:58 pm
So maybe I misunderstand. But it seems they are taking the structure of a Mathematical Geometric Proof
or the rules for creating one and applying those to construct simpler rules for estimating Scattering Amplitudes..
based on the evidence, or supported by the outcomes.
.
The “help” the new model seems to provide are the “Intuitive” leaps followed by the confirmation of those intuitive leaps in making calculations.
.
Building up a framework of “Intuitive” axioms or rules “like those used in Geometry..” extended to a space not limited
by previous assumptions about how geometry corresponds to familiar space and time so far is proving more efficient
at making more correct rules which can be proved correct through experimentation.
.
Intuiting that a useful theorem for Quantum Gravity is very interesting.. but either its too difficult to explain to the lay person in this article..
or so far has actually proved elusive.. kind of reminds me of Fermat’s Last Theorem.
We could could intuit its True and that someday we would have a Proof.. but for over 300 yrs it was still an elusive goal.
.
I very much liked the article. And the history behind the underpinnings driven by the SuperCollider.. the perspective was great.
DZVROD says:
September 18, 2013 at 5:41 pm
This Could Be The DNA Of The Universe
B Miller says:
September 18, 2013 at 5:59 pm
It’s stunning to contemplate that we – us right now reading this – live in this split second of human history when mankind
is capable of even attempting to calculate and discover the very fabric of our universe and reality.
Our ancestors for thousands, millions, and even billions of years back did little more than muck around looking for enough food and shelter
to stay alive one more day.
Calvin says:
September 18, 2013 at 6:15 pm
My question is this… can an amplituhedron be used to build an infinite improbability drive?
Jaap Winius says:
September 18, 2013 at 6:39 pm
This is reminiscent of Lisi’s proposed unified field theory based on the E8 Lie group. However, although both approaches are inventive and suggestive,
neither make (falsifiable) predictions regarding new physics. It seems an intriguing, fortuitous and very useful discovery, but so far nothing more.
Here’s hoping that will change.
Uranium Willy says:
September 18, 2013 at 7:13 pm
I have often wonder if space time is an emergent property, quantum physics only seems odd if you try to imagine particles all getting there spacial properties
by being defined relative to a single unifying space time. But quantum physics seems saying that spatial properties are relative,
for an entwined pair the spin of one particle is defined relative to the other, but it isn’t defined to anything out side the system,
until it interacts with something outside the system, this not a problem if you forget about space time,
and just treat them as individual relationships between particles.
This also solves the cat in the box paradox, if spacial properties can be relative, then whether the cat is dead or alive is determined
by the relationship between mater in the box, and when we look in the box we only resolve relationships between the inside of the box and the outside,
just as the spin between the two particles is already defined so is the relationship between matter in the box and therefore the state of the cat.
You can also be in the box with the cat and then the universe out side the box becomes the cat in the box experiment,
so the whole specialness of the observer is removed.
William says:
September 18, 2013 at 9:40 pm
Space time as you all put it is just an illusion. A construct of our world. Space time is the exception in the universe. In the rest of the universe
and higher densities space time has no real meaning. Everything exists simultaneously. It still does here but we have a very limited perception of reality.

Harrison Rose says:
September 18, 2013 at 9:43 pm
A wonderfully written piece. I hope it wins an award for science journalism.
My math is 30 years out of date, but I’ve been wondering about a potential relationship between the necessary existence of dark matter
and dark energy based upon the apparent total mass of the Universe and the possibility of parallel realities and a multiverse.
Now, if we add the amplituhedron as a simplifying structure, I wonder if it can turn out that taking several (I believe it may be six or eight)
symmetric universes as a whole in this geometry where each of the symmetries could be a universe, could we account for the mass
and remove the need for dark matter? I wish I had the capabilities to answer this.
I would love to hear from real physicists if my concept makes any sense. If it does, it has enormous ramifications.
Jeff Kilgore says:
September 18, 2013 at 10:17 pm
Gilmore’s illustration is something one can enjoy without understanding those things that laymen like myself will never understand. Beautiful.
Hunter Gillespie says:
September 19, 2013 at 12:01 am
A very well written article. After reading this I was left wondering if the properties of M theory’s Branes could potentially be analogous to this amplituhedron
if completed in its final form. Perhaps with the amplituhedron we are complimenting M theory by describing the geometry of our universes P-Brane.
Having said that, this leaves me with the feeling of the holographic principle (us being 3d representations of 2d information on the walls of our hypersphere,
or more disconcerting, that we are starting to describe the programming of the simulation.
JJ says:
September 19, 2013 at 1:03 am
“You can easily do, on paper, computations that were infeasible even with a computer before.”
Ha! Yeah right, Jake. YOU can easily do it. I’m going to go get a sandwich and try to forget that my experience of reality is illusory.
rob says:
September 19, 2013 at 1:12 am
I dropped out of a class in grad school because of a homework assignment that required me to compute some 50 Feynman diagrams.
This article makes me feel vindicated yet nostalgic for the days when I could actually study things like this.
Tug Brice says:
September 19, 2013 at 1:48 am
To me, this is beauty. The fact that the behavior of the world can be described with some fair degree of accuracy with a simple,
elegant solution is truly awe inspiring.
Every major step forward has been simple and beautiful in their time. Newton’s original equation for gravity and his laws of motion.
Einstein’s relativity. Even Feynman’s diagrams that were the center of his QED had a simplicity that won him the Nobel.
As we learned more, these theories grew more complex until there came another return to simplicity and beauty. Quantum Field theory is pretty complex,
and String theory even more so. Maybe this is the next leap forward, the next simple, beautiful idea.
Daniel says:
September 19, 2013 at 2:03 am
Fascinating stuff!
Also, I love that the comments on articles such as this, are so rife with positivity and humor! I wonder if there’s a connection between education and curiosity,
and happy comments? ;P
analogs in a digital world says:
September 19, 2013 at 3:19 am
Linearized physics of discrete space geometry is not the same as discrete physics of discrete space geometry.
Linearization error makes all the difference in the world. Linearized physics breaks down at discrete scales. Discrete physics doesn’t.
http://www.stat.colostate.edu/~estep/research/projects/linearization.html
The greatest advantage of quantum gravity over other theories is that it tries to build the model of the world from ground up.
That is the only proper way to build a model of a discrete world.
Hardik Panjwani says:
September 19, 2013 at 3:37 am
What I got from the article was that they have a new method of computing scattering amplitudes that is insanely efficient.
Good news for grad students who forget to add a one diagram in a calculation of 120 diagrams and then curse the day they got into theoretical physics.
What makes their method special is that the formulation seems to indicate that there is merit in thinking of spacetime as an emergent phenomenon
rather than as a background. This is very good as talking about gravity as an emergent phenomenon by itself is tricky
but if spacetime is emergent along with gravity it solves some of the issues involved in formulating quantum gravity along this track.
To make an analogy, Feynman figured out a calculation method with diagrams but Wilson gave us a conceptual shift
with the idea of renormalization group and the resulting EFT’s.
These guys might be on track to give us a calculation method AND a conceptual shift in one package. Thats big.
Also, I have a name suggestion for the ‘master amplituhedron’: the one ring to rule them all.
Dan Bernitt says:
September 19, 2013 at 4:52 am
I once heard a lecture / talk by Feynman . It still is the most impressive and interesting talk I ever heard.
He could grasp technical subjects and explain them in a powerful way.
Zwi Curio says:
September 19, 2013 at 5:30 am
This has nothing to do with Garrett Lisi’s E8 stuff.
Bjornar Simonsen says:
September 19, 2013 at 6:49 am
I can dishonestly say that I understood everything in this article.
Brett Bourne says:
September 19, 2013 at 7:10 am
Tony & Jose – thanks for bringing Buckminster Fuller into this – his search was for Nature’s geometry which he called the geometry of thinking,
a geometry which works equally well in describing the initial structures and movement in Universe, and everything else.
He closed the gap between his large and small-scale pictures 50 years ago and predicted how long it would take more conventional science to catch up – bravo.
Devin Harper says:
September 19, 2013 at 7:41 am
I think the missing link that this amplituhedron needs is Erik Verlinde’s entropic gravity, not Garrett Lisi’s work.
Alex Wissner-Gross has also shown that entropy is how (artificial) intelligence works, consolidating (perhaps) thousands of lines of code
from several different fields of AI into a single fuction based on thermodynamics just like how amplituhedron consolidates hundreds of Feynman diagrams
(and thousands of mathematical terms) into a single function as well.
ben says:
September 19, 2013 at 8:15 am
Extremely minor, but the video from the conference in 16:9 (instead of 4:3): http://susy2013.ictp.it/video/05_Friday/2013_08_30_Arkani-Hamed_16-9.html (16:9)
Ian Cumming says:
September 19, 2013 at 8:18 am
I am very surprised that no one mentioned it.
This is a result for Steven Wolframs ‘A New Kind Of Science’
Premise: Simple laws produce profoundly complex results.
Simple law: Simplifying the calculations of particle interactions, produces the results of amplitude calculations.
A unit circle is a geometric solution to many trigonometry problems. Same principal, much more complex solution to a very very complex problem.
Mark these words: There will be rooms full of 5th graders able to use this, in the next generation.
David says:
September 19, 2013 at 8:20 am
First, this is a phenomenally well-written science article, kudos to the author!
I also saw a couple comments here that I, as a moderately-informed layperson, may be able to clarify, mostly stemming from confusion
about what this object actually means; contrasting it with string theory may help.
String theory proposes that the universe is made of strings, and calculates what that would look like.
There are other “theories of everything” (which is a terrible name) that make different assumptions, and then make predictions.
This object is not that; as far as I understand, it is a mathematical tool designed for a specific purpose, not a predictive theory.
Wizard Garber mentioned, “Using geometry to predict the behavior of particles is nothing new…
Dr. Garrett Lisi has been positing the use of the E8 Lie Group geometry to predict particle behavior since 2007.”
This is true, but the E8 geometry is used to predict individual particle properties (some of which are interaction particles),
while this object is used to predict scattering probabilities.
Both are incomplete, both have problems with gravity (amongst other things), and both are just tools to help learn more, rather than fundamental descriptions of reality.
Ignacio Mosqueira says, “It is a far cry to say that a theory doesn’t explicitly rely on unitarity or space-time than saying that we need to give up on these concepts.”
This is not what the authors are saying. They have dropped the assumptions of unitarity and locality in their math, and produced an abstract object.
This object just so happens to give the same answers as the equivalent Feynmann sum.
The insight is simply that, if getting the right answer doesn’t depend on those two properties, maybe reality also doesn’t?
Jake says, “If I’m understanding this correctly, they’re saying they may have found an object that contains and dictates our entire universe,”
which is unfortunately not correct. They have found a neat mathematical object, no more descriptive of our actual physical universe than,
say, a slice of angel food cake – it just has slightly more predictive power.
And finally, if I’m wrong about any of this, for the love of the FSM tell me! Being wrong when you think you’re right is just the worst…
Mark Fergerson says:
September 19, 2013 at 8:25 am
Very well-written, clear article on some difficult topics. A couple of points seem to me to indicate that the unitarity and locality issues
may not be completely intractable. Unitarity shouldn’t necessarily require an infinite number of observations of a particular particle interaction
because there are only a finite number of ways such interactions can go, determined by the selection rules appropriate for given quantum numbers
for the particles involved, considering CPT conservation etc. (hence the “master amplituhedron” may not have exactly an infinite number of facets
due to similar conservation rules for baryons and so on). Locality seems completely different
but if the Heisenberg Uncertainty principle doesn’t eventually fall, the complementarity of momentum and position
should mean that two of mass, time, and space are quantizable, but all three need not be.
Since mass empirically doesn’t seem to be quantized, that may indicate that time and space are, so that the infinities in measuring space and time separations
below the Planck limits become “merely” Very Large. That in turn might resolve the dimensional difference disconnect between string theory and QFT.
Michael says:
September 19, 2013 at 8:27 am
amplituhedron ! So beautiful even though I’m so far from the understanding.
and Natalie Wolchover! Thanks!
P Slatter says:
September 19, 2013 at 8:55 am
An amazing piece of science. What does this mean to humans? Of course it has so many applications – the mind boggles.
As the article states 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.”
Grammatically this is akin to using a word to define itself. Geometrically speaking , space and time are not to be considered essential for geometry
but merely something that dimensionionally emergesas the shape takes form.
Breathtaking in its beauty, scattering in its complexity, and counter logical in its form.
evanh says:
September 19, 2013 at 9:02 am
Harrison, I don’t think that would remove dark anything, but rather confirm it as extremely exotic.
As opposed to something, at least a little more mundane, like finding ten time more black holes than expected.

srhie says:
September 19, 2013 at 10:24 am
luke lea, I gather that the stuff is grassmannian+. you put it in a big enough euclidean space and space time
MIGHT show up as some sort of a solution(s) of einstein equation (at lower energy limit)?
I am wondering what the vacuum looks like. no particles. so no legs. at least we should be able to describe vacuum
to be able to say quantum gravity or whatever may have been found?
Bill Lasley says:
September 19, 2013 at 10:41 am
Awesome Article. Totally excited about the advances that may come from this line of research. Must read more of her articles.
Matt Severson says:
September 19, 2013 at 11:47 am
@ Ignacio, from what I vaguely understand, locality and unitarity are emergent properties of this object.
Francis Ferry says:
September 19, 2013 at 12:13 pm
Thank you, Natalie, for this well-written and (for the most part) general-audience-friendly article on what is a rather arcane topic,
and a mind-bending way of perceiving reality.
Your work here (and as I read further, throughout Quanta) reminds me of the stellar book by Isaac Asimov, “Atom: Journey Across the Subatomic Cosmos”.
Please, if you are so inclined, the world desperately needs a similar tome on the latest advances in subatomic physics.
I would love to see such a book by you on my shelf.
Greg says:
September 19, 2013 at 12:46 pm
Time does not exist. It is not an object that can interact with other objects. It is just a human construct. I’m glad to see Big Physics coming around to this idea.
Additionally, there is only one dimension, that of volume. Length (1D) is not independent of width (2D), nor width to depth (3D),
therefore we do not live in three dimensions, only one. We use the Euclidean concept of dimensions, and they work well enough at the crude macroscopic level.
However, the concept of one “place,” i.e. a fixed location based on coordinates, at the quantum level has repeatedly shown that multiple dimensions
and therefore “place” is just another human construct that does not stand up to scrutiny.
It appears that after decasdes of hitting one’s head against the wall Physics has decided that they are getting no where
and it is time to look and the very basic foundations of our understanding of Physical “Laws.”

Garth says:
September 19, 2013 at 1:26 pm
This is an amazing development. Having had to learn Feynman diagrams and the accursed renormalization in grad school,
I just knew there had to be something better! I really hope this is it.
But I think it’s philosophically incorrect to call spacetime ‘illusory’, no matter what comes of this.
That’s indisputably how the universe presents itself from a particular point of view; the amplituhedron (among other things)
shows us that other points of view are possible. But I don’t see any reason to label one point of view as more ‘real’ than another.
The amplituhedron is a model, like other models; a very beautiful one, perhaps a very useful one. But it isn’t and can’t be the universe, full stop.
As C. S. Lewis said (don’t have the exact quote handy, but this is close),
“The hill that looks green when you are standing on it looks blue from ten miles away.
Both are equally good facts.” What’s the ‘real’ color of the hill?
To answer that question, I first ask, “Where are you standing?”
Garth says:
September 19, 2013 at 1:50 pm
Oh, and Greg: While you are correct to say that time is not an object that can interact with other objects,
I would argue that is not at all the same as the statement, ‘Time does not exist.’
In much the same way, I think Eddington was dead wrong to move from the statement,
“The atom is mostly empty space,” (though one can quibble whether electric fields are really ‘empty space’)
to “Solidity is an illusion.” Of course it isn’t. At the human scale it is very much a reality.
We can to some degree explain the experience of solidity from what we know of atoms, true.
But it’s only by using solid instruments with our solid bodies that we ever came to know of atoms in the first place.
‘Emergent’ does not mean ‘illusion’ – the emergence is an ‘equally good fact’ as the level it emerges from.
Greg says:
September 19, 2013 at 2:25 pm
What a fascinating discussion. I do firmly beleive that Time is a human construct, like numbers.
We NEED numbers and time to make sense of our surroundings but they do not exist separate from our own minds.
Time is not a force. Time does not have energy. Time does not have volume.
The universe is an infinite series of waves at infinite frequencies that coalese into energy, matter, and objects
and is constantly changing to different frequencies, matter and objects. The universe is an uncaring thing and it certainly doesn’t care what we tink of it.

Alejandro Rivero says:
September 19, 2013 at 3:02 pm
I wonder if the finding is relate to this history from Predrag Cvitanovic: http://www.cns.gatech.edu/~predrag/papers/finitness.html
DavidJ says:
September 19, 2013 at 3:19 pm
Ah-oh, theoretical physicists are discovering that everything is exponentially simpler than theoretical physicists thought it was…
MartyG says:
September 19, 2013 at 4:54 pm
Thanks for once again providing yet another resource for my introductory physics course.
“Time,” after all, really is only a four-letter word representing an “idea” which is also a four-letter word which is …
aw shucks, four-letter words fail me. To quote Robin Williams “Reality–Man what a concept!”
BK Tukeli says:
September 19, 2013 at 5:49 pm
Some of the best science writing I’ve read in a while. Thank you.
My interpretation of unitarity: asserting that probability always sums to one is similar to stating an outcome always occurs.
Self-evident and superfluous, perhaps?
Peter Key says:
September 19, 2013 at 6:24 pm
I think I’m going to dress as an amplituhedron for Halloween.
Lauging Skeptic says:
September 19, 2013 at 6:39 pm
What about N=2? Or is there no such thing as an unmediated dual particle interaction in their model?
Ben says:
September 19, 2013 at 6:44 pm
This is really, really well written. Thank you.
Marc says:
September 19, 2013 at 7:36 pm
Thank you, very concisely written and utterly fascinating.
Jordon Flato says:
September 19, 2013 at 8:20 pm
Seems to me we Flatlanders are starting to see the beginnings of a sphere enter our field of view….
Tom Knepher says:
September 19, 2013 at 11:53 pm
Brilliantly written. My 72-year-old brain actually understood (most of) it.
George E says:
September 20, 2013 at 1:37 am
What does this mean exactly?
“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.”
The object just exists and as a result of its structure time arises from its shape?
Oscar says:
September 20, 2013 at 1:50 am
This is so well written and so interesting, that I actually stop texting a pretty girl who likes me, just to read it hahaha
Justin Plunkett says:
September 20, 2013 at 2:25 am
This may be the most beautiful object I’ve ever seen.
This immaculate rainbow of fractal facets may be the first visually comprehensible representation of god.
Well, at least to me. This is looking behind the curtain.
A freshly discovered geometric form in which is encoded the basic features of reality. My mind is blown.
Congratulations to the scientists, as well as the author of the article.
neal zarka says:
September 20, 2013 at 5:16 am
all of this looks incredibly interesting but i don’t understand the relationship between a polygon and the understanding of our universe.
Seriously I’d like to have this enthusiasm but I’m so lost ! Anyway I’m happy to see that humanity have a new tool to work with !

Jim says:
September 20, 2013 at 6:16 am
I think my brain needs a Cigarette, a Shower and a cold bucket of ice after reading that. Gorgeously written,
and the information was quite easy to understand, and I am not a huge math person.
Finding that it may actually be all geometrically based may give credence to all those experiments into symbolism in the 15th century.
Were they on the right track back then?
Michael says:
September 20, 2013 at 9:52 am
Very well written article. Admittedly, the theories are beyond my level. As a layman, and one in the business world,
the words that jumped out at me were ones like “efficient”, “accurate” and “simple”. (not necessarily exact quotes).
If we can get 20% more efficiency out of all of our theoretical physics grad students, post docs and full researchers,
we will likely be able to advance more discoveries faster. Whether or not time is “real”, that efficiency will be of great benefit.
David Challener says:
September 20, 2013 at 10:02 am
1) The sketch says it is for 8 gluons, but only has 7 points, and the title says “7 point”, though the numbers below go from 1 to 8.
2) Any chance you could actually show us the “one-term, beautiful little function” rather than just refer to it? We are not all mathematically challenged.
Peter says:
September 20, 2013 at 11:07 am
Here in Beijing I recently showed my students a 1995 (?) video on the Mandelbrot Set, no, not for mathematical purposes,
but to try to help illustrate the idea of “figure,” and how it relates to understanding virtue in Plato’s “Meno.”
Socrates seems intent on finding a simple, fundamental virtue from which other virtues are “emergent,” to use the language used in Arkani-Hamed’s lecture video.
I will leave it at this. I am no mathematician. Is this amplituhedron, like the Mandelbrot set, a fractal of some sort?
Both seem to be trying mathematically to convey the idea that something of infinite complexity, such as particle interactions, can be understood very simply.
I would like to join my voice with others in complementing Ms. Wolchover on the clarity and comprehensibility — to a certain extent — of this article.

Purushottam Dixit says:
September 20, 2013 at 12:38 pm
Quote: “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”
I am not sure if stating probabilities as property of nature is a correct statement. Probabilities quantify state of knowledge about nature and not nature itself.
Darrel Jarmusch says:
September 20, 2013 at 1:06 pm
David said “They have found a neat mathematical object, no more descriptive of our actual physical universe than, say, a slice of angel food cake
– it just has slightly more predictive power.” The same could be said for quantum mechanics, that was the point of Schrödinger’s cat,
and a fundamental aspect of Einstein’s criticisms of quantum mechanics, that quantum mechanics is not descriptive, merely predictive.
For many physicists, even for most, the predictive value of a theory is good enough regardless of it’s ability to actually describe reality.
Some people, many of them not physicists, interpret a theory as descriptive of reality merely because it is predictive thus leading to belief in absurdities and logical contradictions such as the possibility of a Schrödinger’s cat being real, or the idea that unitarity could be violated.

Jonathon says:
September 20, 2013 at 2:23 pm
This may be a naive question, but if “the new amplituhedron research suggests space-time, and therefore dimensions, may be illusory anyway,”
then shouldn’t gravity also be “illusory?” If space and time are illusions, then shouldn’t adhering to the surface of an illusion
(as gravity keeps me pinned to the Earth) must therefore also be an illusion? If true, maybe there IS no other shape that describes it.
William F. Maddock says:
September 20, 2013 at 4:59 pm
Sorry to throw water on the party, here (I’m as excited as anyone here, by the way), but we do need to keep in mind that this is,
after all, only a mathematical construct, until it is proven otherwise.
Frederick Caplan says:
September 20, 2013 at 9:46 pm
The use of a physical construct to re formulate exceedingly complex equations and simplify them to the point where infinities
are eliminated and solution appears possibly is amazingly similar to the relationship between M Theory and String Theory.
Could one observe that it is possible that the relationship suggests a relationship to a larger unitary theory with a geometric solution that may apply to both theories .

EarthSigh says:
September 21, 2013 at 1:28 am
Coincident with this article’s release is my reading of Mario Livio’s “Is God a Mathematician?” In this book Livio lucidly develops the amazing correspondence
between mathematical abstractions and perceived reality. As I read this article I was particularly struck by the Greek’s fascination with geometry.
In asserting that “all is number” might the Pythagoreans have intuited something very close to the truth?
Here’s hoping this exciting new model is as fruitful as anticipated!
John Vermeer says:
September 21, 2013 at 4:47 am
What a beautiful jewel with 2 missing pieces. I predict that when connect gravity to the equation then the jewel will be complete
Ken says:
September 21, 2013 at 10:28 am
“…time and space are only sensible forms of our intuition, but not determinations given for themselves or conditions of objects as things in themselves.”
- Immanuel Kant
Leo Weitzman says:
September 21, 2013 at 11:26 am
Brilliant article on all counts. The concept reminds me of a historical observation that we only understood the mechanics of the planets
when Copernicus changed the center of our calculations from the earth to the sun.
This concept appears breaks our coordinate system from our space-time to a broader “whatever”.
Circle or Square? says:
September 21, 2013 at 12:11 pm
When all is said and done, the physicists will find that we are geometric figures in Flatland.
George says:
September 21, 2013 at 12:39 pm
All,
To me, an electrical engineer, this looks like the physics world has been stuck in discrete mathematics, digital mathematics since Feyman.
If you digitized a sine wave (what happens when you create a CD or MP3 file from an analog LP record) , you would
(1) have an approximation of the sine wave,
(2) a Taylor Series of infinite products,
and (3) be left with an inability to use calculus for problem solving and instead would have to use arithmetic, matrix mathematics and other discrete methods.
You would have to do all analysis using computers (as in digital processing) and would not be able to use ‘analog’ mathematics: calculus & geometry.
You would be pursuing greater and greater computing speed, parallelism and memory because you are stuck in the digital, discrete world.
It looks like physics love affair with discrete mathematics may be coming to a close with a focus on geometry leading back to analog formulas,
leading to calculus and the ability to perform analysis on paper.
Unless with think the universe is a big discrete processing machine. Nothing in the universe seems discrete.
It seems to crave exponential and trigonometric terms.
George
Rick says:
September 21, 2013 at 1:45 pm
This is some of the best science writing I’ve ever seen. As a layman (elementary spcecial education teacher)
I still enjoy keeping up on the newest ideas and research.
Natalie’s level of skill in helping a novice like me to begin to grasp the basic concepts of the article is laudatory. Thank you so much!
SaNa says:
September 21, 2013 at 2:41 pm
As a non-physicist, I found this article interesting and exciting. I love profound learning. Looking forward to the implications in future practice and research`
Paige says:
September 21, 2013 at 8:46 pm
Cool! Definitely reinforces my desire to major in math and/or physics. Can’t wait to actually fully understand this.
Carole says:
September 22, 2013 at 1:54 am
I’m a lay person when it comes to physics and mathematics so please forgive me if these three questions are very stupid.
I’m just trying to wrap my head around things. Perhaps someone has some insight:
1. Why is N-dimensions described where N= the number of particles involved in the scattering process?
Does this mean that each particle is a separate dimension?
How is the number of particles involved in scattering equal to the number of dimensions?
2. What are the implications for the different theories about how the universe started?
Does this mean that if you say two branes collided to form the universe you’re really describing a mathematical formulation of equivalency
wherein the actual, and equivalent, means of creation was a facet of this geometrical jewel form?
3. So reality is described by a geometrical shape. Can that tie into the theory that reality as we understand and see it is simply a projection
of other underlying mathematical processes? Are we a projection of the mathematical expression of simplified amplituhedrons on the master amplituhedron?
Again, sorry if these are ridiculous questions.
Bo Martins says:
September 22, 2013 at 4:02 am
Thank you for the historic perspective – how the thirty-year old discovery graduately lead to this beautiful result.
It will be exiting to see the predictive value of the discovery. The LHC must be perfect for that purpose.
Miguel says:
September 22, 2013 at 6:27 am
The amplituhedron, or how to say “twistor diagram” 7 times without mentioning Roger Penrose even once.
George Handlon says:
September 22, 2013 at 3:39 pm
Beautifully written… and something you save to read again… taking the time to muse on the progress of the thoughts here.
It certainly brought the work of Buckminster Fuller to my mind… and a particular comment he made (best I can remember it here on the spot):
“When I develop an idea – if it is not simple, or beautiful… then I know that it is wrong.” Michio Kaku is quite public with his quest for a “theory of everything”…
perhaps this is part and particle of that. This is simple and beautiful in it’s presentation and understanding
– I do like the thought of the Mandelbrot potential in this exploration of the “Amplituhedron”. A device with a strange banner…. Excelsior!
M. Report says:
September 22, 2013 at 4:20 pm
Second the emotion that Stephen Wolfram’s Mathematica
may be the language used to describe the jewel in the lotus;
The amplituhedron is even more beautiful than the seashell
on the cover of ‘A New Kind of Science’.
Casey SLedge says:
September 22, 2013 at 6:13 pm
I certainly hope none of my tax dollars was spent on wasting time on this nonsense.
When are scientists going to concentrate on real problems like feeding everybody and quit worrying about what causes gravity and other ridiculous studies? Let these “mathematicians” get real jobs that actually benefit real people.
Robert L says:
September 22, 2013 at 6:42 pm
This is a fascinating development, but I am posting mainly to commend the author of this article explaining it…
Usually science reporting leaves me disappointed or disgusted in how incomplete or just plain wrong it is
- the author of this article did an astoundingly good job explaining this extremely complicated subject- without dumbing it down.
Actually, “astoundingly good” is an understatement- I feel comfortable in saying this is quite likely the BEST example of science reporting I have ever seen
– and as a scientist I have read (and usually winced while reading) many examples of science journalism…
I was impressed- Natalie Wolchover is the epitome of what science journalism SHOULD be. I plan to look up whatever else she has written today…
Thank you for the work you put into this Natalie- I hope to read a LOT more from you!
BRILLIANT work!
DonnaE says:
September 22, 2013 at 6:54 pm
Oh Lord – now I know how Penny from “The Big Bang Theory” feels…
Larry Benjamin says:
September 22, 2013 at 8:34 pm
Interesting that this construct appears to be derived from the tetrahedron. R. Buckminster Fuller proposed this in “Synergetics,”
that the entire structure of the universe is explained by the fact that the tetrahedron is the simplest possible structure,
and that there is no other way to arrange four points in a structure, other than as a tetrahedron.
(A square is unstable unless it is triangulated, in which case it becomes a flat tetrahedron.)
Bill says:
September 22, 2013 at 9:43 pm
The conclusions do not bare out to the hypothesis. Imagine you did not know about, circles, sin, cos, tan, radius, …
All you knew was the a function that was an infinite summation. Then suddenly someone discovers the circle, and that your summation
was nothing but a taylor expansion of the sin function. Suddenly your math becomes much easier with this new understanding.
That does not mean everything you previously understood was wrong. It just means you have a much better tool to think about problems.
It is reasonable to expect and summation formula, including feynman diagrams represent some sort of geometry.
Finding that geometry gives a new and powerful tool. But it does not mean what you know about feynman diagrams is wrong.
In fact just like a small angle approximation, the first order and usually second order diagrams can still be increadably useful
for understanding and solving a certain class of problems.
Nicholas says:
September 23, 2013 at 2:20 am
They say that the better one understands a subject, the better they can explain it in simple terms. Thank you Natalie for having such a keen grasp of your field!
Nilbud says:
September 23, 2013 at 3:06 am
Twistors and all that is tricky but how Roger Penrose doesn’t get a mention is hard to grasp.
tetrahedronism says:
September 23, 2013 at 5:58 am
Someone once metioned that, one should think in form instead of formulae ..
(great article)
Doug B says:
September 23, 2013 at 9:37 pm
Very interesting article. From what I understand, a little Aristotelian philosophy could have debunked the concepts of “locality” and “unitarity”
(the “central pillars of quantum field theory”) from the very beginning. Both concepts violate the Law of Identity (that an existent is what it is).
“Locality” suffers from the same fallacy as Zeno’s Paradox (e.g. that space can be infinitely divided thus we can never travel from point A to point B).
Namely, an existent has identity, i.e., is something with defined limits (however construed).
Thus, “infinity” as such does not have (metaphysical) existence, so there is no problem of traversing from A to B
(the distance is what it is, whether one inch or a Planck length). “Unitarity” also violates the Law of Identity because it seems to assume (?)
an infinite number of possible outcomes. However, A is A, so a particle only can act in ways limited by its nature (the Law of Causality). . . .
Gee, it’s too bad these poor quantum physicists had to go through all that tortuous mathematics and mind experimentation
before realizing that the foundations of their field may be made of sand. But maybe I should study physics before casting any quantum stones.
zeromus3 says:
September 24, 2013 at 6:41 am
The basic idea is that we still aren’t sure what the fundamentals of our universe are.
We understand the over arching workings at certain levels but lack the basic building blocks.
I think of it like seeing the building instead of the structure of the building.
The more complete our knowledge of the fundaments, the simpler the outer workings appear to be when looked at this way.
I think of this as a wonderful leap forward and that we may soon integrate the large and small scales…
we seem to know the fields of mathematics and physics required to do so, and that lends to focused study that will draw brilliant minds. We have a path!
Nick Gotts says:
September 24, 2013 at 9:30 am
I’m amused by how many people are jumping on this to claim that it somehow vindicates their particular intellectual hero
(Garrett Lisi, Buckminster Fuller, Stephen Wolfram, Benoit Mandelbrot, Immanuel Kant*…).
Nope: whether or not it turns out to be as significant as the article suggests, this is new stuff, and the credit for it goes to Nima Arkani-Hamed and his colleagues.
*Roger Penrose is named with rather more justification, as the originator of twistor theory, but the amplihedron work appears to go well beyond that.

Z.R. Wilson says:
September 24, 2013 at 12:12 pm
Ryan S, I had the same exact thought. I’ve pondered, almost ceaselessly, over the nature of gravity;
especially considering that it appears to become loosened or to disappear, altogether, at the subatomic level.
One hypothesis I’ve formulated on the subject is that gravity does not necessarily exist independent of matter,
but may be a reaction thereof. As particles collide, the energy they produce may be tantamount to the fusion of weak and strong forces,
giving rise to electromagnetism.
The energy bonds that then form may be what constitutes gravity, the result of nuclear energy producing electromagnetic energy.
This would explain why, generally speaking, the more mass a body contains, the stronger its gravitational force;
along with the fact that most matter doesn’t simply scatter away once, strong enough, bonds have been formed.
This may actually also explain the nature of black holes. Upon exceeding the Schwarzschild Radius,
it is possible that the amount of energy produced at the core of said structure produces,
hypothetically speaking, a planck temperature that results in infinite energy and, as a result, infinite gravity.
Of course, I’m open to discussing and or being refuted on the subject. I’m here to learn, after all.
Pete Stiles says:
September 24, 2013 at 12:53 pm
A wonderful article I just wish “they” had called it “amplihedron” and not “amplitehedron” the latter being almost impossible for me to get my tongue around.
B. Rodriguez says:
September 24, 2013 at 5:11 pm
@Casey SLedge
“I certainly hope none of my tax dollars was spent on wasting time on this nonsense.
When are scientists going to concentrate on real problems like feeding everybody and quit worrying about what causes gravity and other ridiculous studies?”
Are you speaking of scientists in general? …because it would be horribly ignorant to think that they don’t play an important role in helping the real world.
As for *theoretical physicists* in particular, then I can understand where you’re coming from.
It’s important to realize though that theoretical science comprises only a fraction of the scientific community as a whole, in research or in practice.
All in all, the ‘useless crap’ that theoretical scientists do today is no different in essence than what the innovative thinkers of the past have done.
Who knew that a bunch of freaks studying ‘little animals’ under a microscope would give us modern medicine and disease prevention?
Who knew that Einstein’s Theory of Relativity is the reason why our GPS systems work and modern transportation is even feasible?
Theoretical science mostly serves its purpose in the ‘long long-term’, but it does have its quick benefits.
Not all scientists are theorists, far from it. Indeed, many devote themselves to solving real-world problems.
Even pure physics plays a part if you try to understand it. Each scientist does his/her thing and serves a purpose.

Hatchemoto Mishimuri says:
September 24, 2013 at 5:28 pm
This article is beautifully written. It takes obscure concepts and put them in terms that the rest of us can *almost* comprehend. Well done Natalie!
Hatchemoto Mishimuri says:
September 24, 2013 at 5:30 pm
@Peter Stiles: “amp li TU hee dron”
Bill F says:
September 24, 2013 at 10:36 pm
I agree with those above commenting on the lack of attribution of the “twistor” concept to Roger Penrose.
I await with interest his comments on the amplituhedron and its implications.
Ion S. says:
September 25, 2013 at 6:08 pm
Natalie’s writing is spell binding, judging by the laudatory comments here;
too good, in fact, as it gives us the illusion of grasping the arcane problems
tackled by the experts working in this field. Clearly, Natalie’s writing alone
has sufficient power of attraction, and I wish her article was devoid of pictures
and images of any kind; the artist’s colorful depiction of the amplituhedron,
and even the slides from Arkani-Hamed’s lecture, tickle our minds into believing
that we can attain some easy, intuitive understanding of the nasty math underneath.
As a physicist, I can honestly say that this is so far down the rabbit hole,
that it should come with a warning, when popularized in blogs and magazines.
ktttn says:
September 25, 2013 at 6:34 pm
I’m sure I’m not the only one to grab a piece of paper and papercraft the 8 gluon model.
Dave M says:
September 25, 2013 at 10:57 pm
OK – very well written article on a very complex and very cool theory. Also, very interesting comments from just about everyone!
The use of geometry to describe interaction models s not surprising. But the lack of space/time or unity principles as basic tenets
– in effect moving them to outcomes of the model rather than basic principals – is awesome.
The ability to finally include gravity in a coherent model along with other observed implications of the model is truly amazing.
This is certainly the start of the perception change necessary to move our understanding forward. But I suspect it isn’t the last. Still – very cool!
Randall says:
September 26, 2013 at 12:53 pm
I rarely comment on articles, but would like to add my own thanks to the many others for Natalie Wolchover’s incredibly well written article. Thank you.
Rudie says:
September 27, 2013 at 6:07 am

How is this meant? Because scientists have made virtual photons real by giving them extra energy with magnetic fields.
http://www.chalmers.se/en/news/pages/chalmers-scientists-create-light-from-vacuum.aspx
http://www.nature.com/news/2011/110603/full/news.2011.346.html
http://www.popsci.com/science/article/2011-06/quantum-first-light-created-vacuum
And also the Casimir effect is explained with virtual particles.
Mark B. says:
September 27, 2013 at 2:22 pm
On my third read-through of this interesting article. Thanks to the author!
A question / comment regarding this minor point in the article: “…
Virtual particles are never observed in nature, but they were considered mathematically necessary for unitarity…”
My understanding is that the existence of virtual particles is extremely fleeting, but the reality of their existence has been confirmed:
1. by their effect on the fine structure of lines found in the optical spectra of the hydrogen atom
2. as reported here:
http://phys.org/news/2011-11-scientists-vacuum.html
“Chalmers scientist, Christopher Wilson and his co-workers have succeeded in getting photons
to leave their virtual state and become real photons, i.e. measurable light.”
Deepak Singhal says:
September 29, 2013 at 12:35 am
How would one validate the accuracy of this model, if current model requires calculations “that even a computer cant do”?
Ron Blouch says:
September 30, 2013 at 9:46 am
One more “beautifully written” to add to the prior ones. You made an extremely complex story as simple
as it could be made yet not simpler than it needed to be. A work of art.
Paul says:
September 30, 2013 at 4:44 pm
Space and time are the product of geometry? Not the field in which it can play?
Theodore Pterosaur says:
October 1, 2013 at 4:03 am
It is not clear that this geometric object is anything other than the expression of a class of complementarities.
It happens to facilitate mathematical calculation but should not be considered any more “real” than the visualization of backwards time-travel
in Feynman diagrams. To call it “jewel-like” may therefore be misleading, as it invites the reader to consider physicality.
The headline, juxtaposing “jewel” with “heart”, is an example of how this misleading may be subtle, suggesting,
however unintentionally and metaphorically, some sort of tangibility. The poetic bow to the Eightfold Way may be lost on many readers.
J L Douglas says:
October 1, 2013 at 1:19 pm
Elegance and simplicity. It must be very close the truth.
B Mitchell says:
October 9, 2013 at 5:08 pm
Does the thought experiment on locality imply that space-time doesn’t exist in environments smaller than the Planck length?
Mark Jamison says:
October 10, 2013 at 2:12 pm
Great Article. I have been following the work of Richard Feynman, Leonard Susskind, and Edward Witten for many years.
It is interesting to see how string theory has developed into the Holographic projection theory of matter being projeted on to a two dimensional hypersphere.
it is also interesting to note that the data is based on how a Black hole works based not on volume,
but on the information being preserved on the the surface structure.
What comes to my mind is that geometry is the key player both in the micro and macro realms of the universe.
And that our thinking has to change with regards to space-time and gravity being fundamental. They all may well be emergent properties of the amplituhedron.
https://www.simonsfoundation.org/quanta/20130917-a-jewel-at-the-heart-of-quantum-physics/