Gravity is mathematically relatable to dynamics of subatomic particles

Gravity is mathematically relatable to dynamics of subatomic particles
Gravity, the force that brings baseballs back to Earth and governs the growth of black holes, is mathematically relatable to the peculiar antics of the subatomic particles that make up all the matter around us. Credit: J.F. Podevin

Albert Einstein's desk can still be found on the second floor of Princeton's physics department. Positioned in front of a floor-to-ceiling blackboard covered with equations, the desk seems to embody the spirit of the frizzy-haired genius as he asks the department's current occupants, "So, have you solved it yet?"

Einstein never achieved his goal of a unified theory to explain the natural world in a single, coherent framework. Over the last century, researchers have pieced together links between three of the four known physical forces in a "," but the fourth force, gravity, has always stood alone.

No longer. Thanks to insights made by Princeton faculty members and others who trained here, gravity is being brought in from the cold—although in a manner not remotely close to how Einstein had imagined it.

Though not yet a "theory of everything," this framework, laid down over 20 years ago and still being filled in, reveals surprising ways in which Einstein's theory of gravity relates to other areas of physics, giving researchers new tools with which to tackle elusive questions.

The key insight is that gravity, the force that brings baseballs back to Earth and governs the growth of , is mathematically relatable to the peculiar antics of the that make up all the matter around us.

This revelation allows scientists to use one branch of physics to understand other seemingly unrelated areas of physics. So far, this concept has been applied to topics ranging from why black holes run a temperature to how a butterfly's beating wings can cause a storm on the other side of the world.

This relatability between gravity and subatomic provides a sort of Rosetta stone for physics. Ask a question about gravity, and you'll get an explanation couched in the terms of subatomic particles. And vice versa.

"This has turned out to be an incredibly rich area," said Igor Klebanov, Princeton's Eugene Higgins Professor of Physics, who generated some of the initial inklings in this field in the 1990s. "It lies at the intersection of many fields of physics."

From tiny bits of string

The seeds of this correspondence were sprinkled in the 1970s, when researchers were exploring tiny subatomic particles called quarks. These entities nest like Russian dolls inside protons, which in turn occupy the atoms that make up all matter. At the time, physicists found it odd that no matter how hard you smash two protons together, you cannot release the quarks—they stay confined inside the protons.

One person working on quark confinement was Alexander Polyakov, Princeton's Joseph Henry Professor of Physics. It turns out that quarks are "glued together" by other particles, called gluons. For a while, researchers thought gluons could assemble into strings that tie quarks to each other. Polyakov glimpsed a link between the theory of particles and the theory of strings, but the work was, in Polyakov's words, "hand-wavy" and he didn't have precise examples.

Meanwhile, the idea that fundamental particles are actually tiny bits of vibrating string was taking off, and by the mid-1980s, "string theory" had lassoed the imaginations of many leading physicists. The idea is simple: just as a vibrating violin string gives rise to different notes, each string's vibration foretells a particle's mass and behavior. The mathematical beauty was irresistible and led to a swell of enthusiasm for string theory as a way to explain not only particles but the universe itself.

Gravity is mathematically relatable to dynamics of subatomic particles
Credit: J.F. Podevin

One of Polyakov's colleagues was Klebanov, who in 1996 was an associate professor at Princeton, having earned his Ph.D. at Princeton a decade earlier. That year, Klebanov, with graduate student Steven Gubser and postdoctoral research associate Amanda Peet, used string theory to make calculations about gluons, and then compared their findings to a string-theory approach to understanding a black hole. They were surprised to find that both approaches yielded a very similar answer. A year later, Klebanov studied absorption rates by black holes and found that this time they agreed exactly.

That work was limited to the example of gluons and black holes. It took an insight by Juan Maldacena in 1997 to pull the pieces into a more general relationship. At that time, Maldacena, who had earned his Ph.D. at Princeton one year earlier, was an assistant professor at Harvard. He detected a correspondence between a special form of gravity and the theory that describes particles. Seeing the importance of Maldacena's conjecture, a Princeton team consisting of Gubser, Klebanov and Polyakov followed up with a related paper formulating the idea in more precise terms.

Another physicist who was immediately taken with the idea was Edward Witten of the Institute for Advanced Study (IAS), an independent research center located about a mile from the University campus. He wrote a paper that further formulated the idea, and the combination of the three papers in late 1997 and early 1998 opened the floodgates.

"It was a fundamentally new kind of connection," said Witten, a leader in the field of string theory who had earned his Ph.D. at Princeton in 1976 and is a visiting lecturer with the rank of professor in physics at Princeton. "Twenty years later, we haven't fully come to grips with it."

Two sides of the same coin

This relationship means that gravity and subatomic particle interactions are like two sides of the same coin. On one side is an extended version of gravity derived from Einstein's 1915 theory of general relativity. On the other side is the theory that roughly describes the behavior of subatomic particles and their interactions.

The latter theory includes the catalogue of particles and forces in the "standard model" (see sidebar), a framework to explain matter and its interactions that has survived rigorous testing in numerous experiments, including at the Large Hadron Collider.

In the standard model, quantum behaviors are baked in. Our world, when we get down to the level of particles, is a quantum world.

Notably absent from the standard model is gravity. Yet quantum behavior is at the basis of the other three forces, so why should gravity be immune?

The new framework brings gravity into the discussion. It is not exactly the gravity we know, but a slightly warped version that includes an extra dimension. The universe we know has four dimensions, the three that pinpoint an object in space—the height, width and depth of Einstein's desk, for example—plus the fourth dimension of time. The gravitational description adds a fifth dimension that causes spacetime to curve into a universe that includes copies of familiar four-dimensional flat space rescaled according to where they are found in the fifth dimension. This strange, curved spacetime is called anti-de Sitter (AdS) space after Einstein's collaborator, Dutch
astronomer Willem de Sitter.

The breakthrough in the late 1990s was that mathematical calculations of the edge, or boundary, of this anti-de Sitter space can be applied to problems involving quantum behaviors of subatomic particles described by a mathematical relationship called conformal field theory (CFT). This relationship provides the link, which Polyakov had glimpsed earlier, between the theory of particles in four space-time dimensions and string theory in five dimensions. The relationship now goes by several names that relate gravity to particles, but most researchers call it the AdS/CFT (pronounced A-D-S-C-F-T) correspondence.

Gravity is mathematically relatable to dynamics of subatomic particles
Credit: J.F. Podevin
Tackling the big questions

This correspondence, it turns out, has many practical uses. Take black holes, for example. The late physicist Stephen Hawking startled the physics community by discovering that black holes have a temperature that arises because each particle that falls into a black hole has an entangled particle that can escape as heat.

Using AdS/CFT, Tadashi Takayanagi and Shinsei Ryu, then at the University of California-Santa Barbara, discovered a new way to study

entanglement in terms of geometry, extending Hawking's insights in a fashion that experts consider quite remarkable.

In another example, researchers are using AdS/CFT to pin down chaos theory, which says that a random and insignificant event such as the flapping of a butterfly's wings could result in massive changes to a large-scale system such as a faraway hurricane. It is difficult to calculate chaos, but black holes—which are some of the most chaotic quantum systems possible—could help. Work by Stephen Shenker and Douglas Stanford at Stanford University, along with Maldacena, demonstrates how, through AdS/CFT, black holes can model quantum chaos.

One open question Maldacena hopes the AdS/CFT correspondence will answer is the question of what it is like inside a black hole, where an infinitely dense region called a singularity resides. So far, the relationship gives us a picture of the black hole as seen from the outside, said Maldacena, who is now the Carl P. Feinberg Professor at IAS.

"We hope to understand the singularity inside the black hole," Maldacena said. "Understanding this would probably lead to interesting lessons for the Big Bang."

The relationship between gravity and strings has also shed new light on quark confinement, initially through work by Polyakov and Witten, and later by Klebanov and Matt Strassler, who was then at IAS.

Those are just a few examples of how the relationship can be used. "It is a tremendously successful idea," said Gubser, who today is a professor of physics at Princeton. "It compels one's attention. It ropes you in, it ropes in other fields, and it gives you a vantage point on theoretical physics that is very compelling."

The relationship may even unlock the quantum nature of gravity. "It is among our best clues to understand gravity from a quantum perspective," said Witten. "Since we don't know what is still missing, I cannot tell you how big a piece of the picture it ultimately will be."

Still, the AdS/CFT correspondence, while powerful, relies on a simplified version of spacetime that is not exactly like the real universe. Researchers are working to find ways to make the theory more broadly applicable to the everyday world, including Gubser's research on modeling the collisions of heavy ions, as well as high-temperature superconductors.

Also on the to-do list is developing a proof of this correspondence that draws on underlying physical principles. It is unlikely that Einstein would be satisfied without a proof, said Herman Verlinde, Princeton's Class of 1909 Professor of Physics, the chair of the Department of Physics and an expert in string , who shares office space with Einstein's desk.

"Sometimes I imagine he is still sitting there," Verlinde said, "and I wonder what he would think of our progress."


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Dec 18, 2018
Like that recent 'higher dimensions' notion with the scary-large 'Set', this bears further explanation...
Sadly, I lack the math to tackle the math to tackle the math to even begin to visualise the work...
;-((

Dec 18, 2018
Sadly, I lack the math to tackle the math to tackle the math to even begin to visualise the work...
Same here, like it's obvious there's math for the physics, but at some point it's necessary to know the deeply connected physics of the maths :)

Dec 18, 2018
AdS/CFT correspondence seems to be the most promising direction currently available to pursue quantum gravity. In other words, string physics.

Seems like nothing else is making any progress. I don't see any bold predictions coming from Loop Quantum Gravity, for example. And there are predictions coming from AdS/CFT correspondence.

Looks like string physics is the only game in town.

Dec 18, 2018
So where is the "one Inch equation" that explains everything and is simple enough that even ordinary Ordinary people can understand it ? (Like the famous E=mc2)

Dec 18, 2018
#S-age, hindsight is 20/20.
IIRC, E=Mc^2 fell out of many horribly complex equations after many years work to find a way through the half-seen maze...
Just like Euler's Identity so-elegantly linked e, i & Pi...

Maldacena, Polyakov & Co may have found a new entrance to this maze of math. It may be a dead end, or the wrong maze entirely.

We may have to wait for another 'Ramanujan' to attack the arcane complexity from an unexpected direction-- Perhaps with a 'chain saw'...

Dec 18, 2018
Where you cannot hear the shapeness of a drum, the scar has auxiliaries in overtone. Yet for all the truncated, there is no generalization of fractons.

There is no means of seeing a monopole seeding, but there is a means of observing symmetry-breaking-induced non-linearity. Is there something to the classical theories gauging, to no longer require effective theories? How is it the self-similarity of Hall effects is left for non-exact codings, rarely self similar, in a feedback loop with the environment?

How odd life to leave self interaction, not capable of distinguishing, only to face Kolmogorov counts that rely on dynamism in forces non-equilibrium.

Dec 18, 2018
Loop quantum gravity makes a local faith, where strings take us to the edges of the island of knowledge for relational visualization.

Dec 18, 2018
Ironic that almost at the same time Maldacena, Witten, et al were formalizing AdS/CFT, Perlmutter, Schmidt, and Suntzeff were revealing that we actually live in a deSitter rather than an anti-deSitter universe. So when the author of this article states that "AdS/CFT correspondence...relies on a simplified version of spacetime that is not exactly like the real universe," well, lets just call that a major understatement :)

I understand that progress is nonetheless being made to apply their solution to a deSitter case, however.

Dec 18, 2018
The idea isn't to make a toy universe. Instead, what has turned out to be true is that some problems are easier to solve in AdS space and some in CFT. Because they are equivalent, we can choose the easier way.

Dec 18, 2018
Interestingly, if one models a gravity field as an intrinsic spacetime curvature, one gets an AdS space. In de Sitter space, everything moves apart; in Anti de Sitter space, everything moves together. This is why AdS is seen as a gravity theory.

Dec 18, 2018
Standard version of string pseudoscience which will never yield any confirmable predictions.

Dec 18, 2018
so basically Nikola Tesla was right again and others take credit

Dec 18, 2018
String theory is a useful physics tool, but a review that starts out with that gravity is not linked to other forces is overblown and unconvincing. While we have not detected gravitons yet, we have detected their classical counterparts and we know that weak gravity against an average flat cosmological background can be approximated by a quantum field theory same as other interactions. It is when we demand that not only special relativity of particles systems but all laws are preserved that we have to add general relativity effects.

In a sense, if AdS is a simplified toy system, already mundane quantum field gravity is.

Loop Quantum Gravity


That seems to be a dead end, it has no dynamics (cannot give simple harmonic oscillators).

-tbctd-

Dec 18, 2018
-ctd-

where is the "one Inch equation" that explains everything


That would be "The Core Theory" of all particles and interactions [ where is the "one Inch equation" that explains everything [ http://www.prepos...-shirts/ , https://www.youtu...QfWC_evg "The theory of everything (so far)" @ 40:50 ].

we actually live in a deSitter rather than an anti-deSitter universe


No, we don't. It just so happens that the FLRW universe can be approximated by a simple dS geometry in the current dark energy era (and during inflation). The cosmnological (average) curvature is for example always better approximated by Minkowski space.

In de Sitter space, everything moves apart; in Anti de Sitter space, everything moves together.


? Counterexamples would be the FLRW/approximative dS solution of a collapsing "negative dark energy" universe; and a white hole/approximative AdS solution for a local singularity.

Dec 18, 2018
And the trivial comments:

I have a theory


If you have it, you have not shown us that, but word soup with no quantitative results. Even better, do a theory in peer review publication, then come back and say something worthwhile.

string pseudoscience


No. It is at least a useful tool with real physics chops, remember? If it is anything more, substantiated physics, is still an open question.

Tesla


? Lived before string theory was invented.

Dec 19, 2018
... if Atiyah's prediction for future measurements of the fine structure constant (and G) holds up, not sure I could refrain from mathematical dogmatism quite as well as I do now, apologies to the forum in advance

Dec 19, 2018
so basically Nikola Tesla was right again and others take credit

Everyday they are getting closer to realizing the ether exists.

Dec 20, 2018
There may well be a one inch equation but it is likely to have Ψ and γ in it so it will not be as T shirt wearable as E=MC². Nor as easily applicable to blowing stuff up.

We are waiting for another Paul Dirac to do for QED/QFT and GR what Dirac did for QM and SR.

But unless it can be reduced to a toy model; like GR can reduce to a 2D Penrose diagram; we may need a 10 dimensional computer assisted brain to visualise it and generate useful solutions: Like deriving the 17 lab-measured values hand-stitched into the standard model.

Dec 20, 2018
... if Atiyah's prediction for future measurements of the fine structure constant (and G) holds up, not sure I could refrain from mathematical dogmatism quite as well as I do now, apologies to the forum in advance

I totally screwed up. I was copying a portion of your post and I hit 1 star. Please ignore this and put it as a 5.

If you're curious I was copying to google Atiyah because I didn't remember about the Riemann hypothesis.

Dec 20, 2018
And BTW Atiyah is a true mathematical genius. You absolutely have to read his Wikipedia page. A real wild talent. He deserves every award he's won.

Dec 20, 2018
You absolutely have to read his Wikipedia page
I did just that. Now I need a good stiff drink.

I wonder whether his proof of the RH turns out to be more than just conjecture.

Dec 20, 2018
I'd say we build a black hole computer to study that quantum chaos thing. Who offers a building site?

Dec 20, 2018
Who offers a building site
Dark side of the moon, obviously...

Dec 20, 2018
Gah, I wish i could truly understand this stuff.

Dec 20, 2018
we actually live in a deSitter rather than an anti-deSitter universe


No, we don't. It just so happens that the FLRW universe can be approximated by a simple dS geometry in the current dark energy era (and during inflation). The cosmnological (average) curvature is for example always better approximated by Minkowski space.


Hey, don't get me wrong, I LOVE Minkowski space (it doesn't overtax my poor old tired brain), but I'm wondering how you can be so categorical given our positive CC and the fact all evidence points to our universe being open (and parallel timelike geodesics eventually wildly diverging). Throw in a little matter (like just 5% of the total content), add a little energy to get things moving and poof, voila! A de Sitter space you can go fishing in!

Dec 20, 2018
Hopefully the ToE solution will turn out to be related to the Gravity (4D), surface (2D) or string (n-Dimensional ) TENSIONs in spacetime geometry. As Energy and therefore Mass is Tension times distance. As this would enable forces and particle masses to emerge out of nothing but space and time and energy; as they do daily at the LHC. Without giving physicists an impossible headache nor giving up the quantum fields emergent from space-time.

A single equation to describe how single charges (mass), dual charges(+ and -) and triple charges (RGB of quarks) arise and create tension toward each other out of n-Dimensional spacial geometry: Would be worthy of an extra wide T-shirt.

(The weak 'force' should emerge along side the other three forces: As it picks up gravitational Mass, creates Electro-Weak interactions, and changes flavours in QED by interacting with the other three charge/tension types i.e. 'forces of nature')

Dec 20, 2018
...nor giving up the quantum fields emergent from space-time.


Hum...it seems more likely (to me at any rate) that it's space and time that emerge from the interactions of the excitations of the quantum field and that the quantum field is what is actually fundamental.

Dec 20, 2018
There are certainly indications that Minkowski space-time (3D - Time) is emergent. But I was thinking of some hypothetical n-Dimensional 'space-time' which is deformable to produce all the 'fields' of QFT and which our universe, and all its physical laws, presumably 'banged' out of.

String theorists spotted the string tension > energy relations I mentioned. I just reflected it back to space-time geometry-warping Tension=Gravity to show GR as conceptually similar to QFT and Strings. I just hope the next 'Dirac' has got a similar three years spare to do the maths.

Dec 20, 2018
You guys can argue whether field is fundamental or dimension is fundamental for days, but the evidence says field is a distortion or warping of dimension. I'll let you work that out.

Dec 20, 2018
Who offers a building site
Dark side of the moon, obviously...

Aren't the Chinese planning a probe to go there? Could ask them to help eh?

Dec 20, 2018
You guys can argue whether field is fundamental or dimension is fundamental for days, but the evidence says field is a distortion or warping of dimension. I'll let you work that out.

@Da Schneib, Ha, that's a bit unfair on laymen like me. I need details. Seriously though, I find this stuff fascinating though I don't pretend grasp the advanced arguments...well advanced by my standards not yours. That's why I like to follow you guys. Presumably, similar to QFT one might try to visualize an SSTFT where this would depend on/or initiate more dimensions than QFT...or is that nonsense? Advice please.

Dec 20, 2018
QFT represents everything as dimension, but it still cannot answer the question of whether field or dimension is the fundamental entity since even there field is a distortion or warping of dimension.

Dec 21, 2018
Yes, we could argue over this one till Christmas...

Dec 21, 2018
Da Schneib, if you want to chime in about this some more your thoughts are always welcome. I wouldn't even want to hint that it's anything settled and what you write is definately food for thought. That'll be something to read more about during any downtime over Christmas.

Dec 21, 2018
There are certainly indications that Minkowski space-time (3D - Time) is emergent. But I was thinking of some hypothetical n-Dimensional 'space-time' which is deformable to produce all the 'fields' of QFT and which our universe, and all its physical laws, presumably 'banged' out of.


O.K., I can certainly buy that, and that brings up an interesting nuance: what is one refering to when they use the term "Space-time"? I admit that whenever I see the term I instinctively think of Minkowski space-time, so if the reference is actually to higher a dimentional space-time model (with the rest of what that implies) I end up "not getting it" unless it's explicitly pointed out for that instance of the term!

Dec 21, 2018
A problem at this point: although we have the Higgs mechanism to account for particle masses, neutrinos acquire their tiny mass by some other mechanism and nobody has any idea what that mechanism might be. Considering the abundance of neutrinos, that is not a trivial gap in our knowledge. As a side note, I wonder about the the status of "worldlines" in spacetime when you consider quantum weirdness. Does anyone have any idea what the spacetime trajectory of a superposition of states would look like? What a worldline would mean for electrons in a double slit experiment? I haven't seen anyone tackling such questions, although answers might be implicit in various theories. Maybe considerations like these are not even germane.

Dec 21, 2018
@Gawad I included time in the n-dimensional structure for completeness: Though there is even more evidence that time is emergent, as only particles with mass experience time at all.

The fact that two entangled particles can, and do, change each other across 'space' and without any 'time' delay; does make you wonder what space and time actually are; since this conflicts with relativity (our best theory of space and time).

It does seem that something pretty weird happened in the inflationary epoch to give us the Minkowski space we 'massive objects' experience today. Where x²+y²+z²- c² t² gives a true 'invariant' distance².

Dec 21, 2018
@EyeNStein Indeed, and the implications are even stranger when we try to consider how our universe might have looked without a (seed) mass generating mechanism like the Higgs. With all particles being massless and moving at C "spacewise", in this timeless universe all possible interactions (with no particles ever binding) would have occured instantaneously. Which is why they should have call the Higgs the "Thank (God)" particle instead. To top up what you point out about the issue of "spooky interaction", I'd also point out that just the fact that outside an interaction a particle's position is simply undetermined, and the possiblity of it being anywhere is never actually zero (except, e.g., at very specific nodes, where it is explicitly forbidden). hints at the indeterminacy of space, at least for our low energy effective Minkowski S-T. After all, in Relativity space and time really are intrinsically intertwined. I don't see how one could be emergent without the other as well.

Dec 21, 2018
All that to say that (AFAIC) everything actually begins to make more sense when you understand properties such as position (in both space and time), momentum, energy and mass, and even charge (electric, colour, etc), spin etc. as being constrained but undetermined outside of actual interactions. The instinctive impression, that we live in a Newtonian universe ruled by hidden variables, is extremely difficult to let go of (even for those who should know better most of the time :-), and it is extremely misleading.

Dec 22, 2018
Does anyone have any idea what the spacetime trajectory of a superposition of states would look like? What a worldline would mean for electrons in a double slit experiment? I haven't seen anyone tackling such questions, although answers might be implicit in various theories. Maybe considerations like these are not even germane.
I kinda think they're key. If you looked at a Penrose diagram under a microscope, wouldn't you see Feynman diagrams? Some things are scale invariant and some things aren't, and the notion of a minimum interval between any two points is certainly implicit at all scales, dunno if that's helpful...
- - -
@DS, no worries, thanks for checking

Dec 22, 2018
Thanks, @Proto, goodwill is good will. I always figure it's better to admit one's mistakes and apologize than hope no one noticed.

Dec 22, 2018
A problem at this point: although we have the Higgs mechanism to account for particle masses, neutrinos acquire their tiny mass by some other mechanism and nobody has any idea what that mechanism might be.
Let me stop you right there. No one is suggesting the heavy left-handed neutrinos don't get mass by the Higgs mechanism. What's being suggested is that because neutrinos can oscillate between different states their occasional oscillation into the left-handed varieties gives them non-zero mass. It's quite important since there is a significant chance that the left-handed neutrinos may turn out to be DM.

Dec 22, 2018
Meanwhile we seem to have an actual rational conversation here. There should be more of these.

Dec 24, 2018
@ g

All that to say that (AFAIC) everything actually begins to make more sense when you understand properties such as position (in both space and time), momentum, energy and mass, and even charge (electric, colour, etc), spin etc. as being constrained but undetermined outside of actual interactions. The instinctive impression, that we live in a Newtonian universe ruled by hidden variables, is extremely difficult to let go of (even for those who should know better most of the time :-), and it is extremely misleading.

Newtonian universe still holds true since GR is bollocks

Dec 26, 2018
'"One person working on quark confinement was Alexander Polyakov, Princeton's Joseph Henry Professor of Physics. It turns out that quarks are "glued together" by other particles, called gluons. For a while, researchers thought gluons could assemble into strings that tie quarks to each other.....'

Quark confinement is the biggest can of worms in this article. I don't accept infinite density. At some point a black hole has to become massive enough and dense enough to slow quark motion down. Since quark movement accounts for creating the mass of an atom through relativistic motion that reduction has to be released as energy escaping from the black hole. Perhaps we have just not been able to observe it happening in the universe yet. When it does it might make it look like a big bang has occurred.

Why don't quarks tunnel?

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