Mapping the road to quantum gravity

Apr 23, 2014
Mapping the road to quantum gravity
Perimeter Associate Faculty member Sung-Sik Lee

The road uniting quantum field theory and general relativity – the two great theories of modern physics – has been impassable for 80 years. Could a tool from condensed matter physics finally help map the way?

Perimeter Associate Faculty member Sung-Sik Lee is a condensed matter physicist – but he has his eye on quantum .

Lee lays out the problem: "Physics has one theory to describe how planets orbit the sun and another to describe how electrons 'orbit' an atomic nucleus. Both theories – gravity as described by Einstein's general relativity and quantum – are great triumphs. Both are well-tested and powerful. The trouble is, we can't use both at once."

Relativity says that spacetime is smooth, and only big things can warp it, in ways that are exactly known. Quantum theory says that the smallest parts of the universe are constantly fluctuating and dramatically uncertain. How can something be both smooth and fluctuating, both exact and uncertain? How, in other words, can we make a of gravity?

Physicists simply don't know. Researchers in both string theory and loop have made progress, but a fully functional unified theory has remained out of reach for more than 80 years.

Enter – of all things – condensed matter physics.

Introducing the renormalization group

As far as the condensed matter physicists are concerned, it's all about scale.

In all of physics, but particularly in , our descriptions of physical systems depend on the scale at which we look at them. For instance, if you wanted to know how your tea would spread across the table if you spilled it, you would describe the puddle with hydrodynamics, and completely ignore the fact that the tea actually consists of single molecules and has a complex microscopic structure. But if you wanted to know details about how a very small drop behaved, you would have to change the description to one that takes the microscopic structure into account.

Condensed matter physicists have developed a powerful suite of mathematical tools for "flowing" a theory at one scale into a theory at a different scale. These tools are collectively known as the renormalization group, or RG.

RG tools allow physicists to take what they know about tea molecules and move seamlessly to a description of a spreading puddle. Like the zoom on a camera, the RG changes the distance scale. It's perhaps simplistic, but nonetheless true, that distance scales are exactly what separates quantum theory from gravitational theory – one is the physics of the small and one is the physics of the large. Could the renormalization group be the tool that finally unites them?

Maybe. A growing body of researchers, from around the world, is trying to find out. Lee wants to use the RG to better understand the relationship between quantum theory and gravity. Specifically, he wants to make a constructive proof of the AdS/CFT correspondence.

Introducing the AdS/CFT conjecture

At Perimeter and places like it, the phrase "AdS/CFT correspondence" comes up a lot. If it's always sounded like Greek to you, here's some background.

AdS is short for anti-de Sitter space. When we say "space" in this case, we mean not the cosmic emptiness of outer space, but space in the mathematical sense – space as geometry. If you imagine drawing a triangle on a piece of paper and another on the surface of a sphere, you might intuit that the rules of geometry depend on the space you're dealing with. Space as a piece of paper is technically called Euclidean space. Space as the surface of a sphere is technically called elliptical space.

Anti-de Sitter space is elliptical space that obeys the tenets of special relativity – elliptical space that can stretch or contract in extreme circumstances. When physicists say that gravity bends space like a bowling ball on a rubber sheet, anti-de Sitter space is probably the space they have in mind. Thus, the "AdS" part of AdS/CFT refers to a particular description of gravity.

CFT, meanwhile, is short for conformal field theory. Field theories are the language of quantum mechanics. They describe how a field – an electrical field, for example – might change over space and time. Conformal field theories are a subclass of field theories where certain properties of the theory don't change when scale is changed.

The AdS/CFT correspondence states that for every conformal field theory, there is a corresponding theory of gravity with one more dimension. A two-dimensional CFT would correspond to a three-dimensional theory of gravity, for instance. The two theories look very different, but the AdS/CFT correspondence says that, mathematically, they are identical.

Using the renormalization group to prove the AdS/CFT conjecture

Proposed by Juan Maldecena in 1997, the AdS/CFT correspondence – which is also known as the Maldecena duality or the gauge/gravity duality – has been hugely fruitful. There were intractable problems in field theory that could suddenly be solved in AdS, and deep questions about gravity that could suddenly be addressed via well-explored field theories. But despite its success, AdS/CFT remains a conjecture: it's never been proved.

"There is a lot of evidence for the conjecture, but there's no proof," says Lee, who is jointly appointed to Perimeter and to McMaster University. "We know for sure that it works in some special cases. We believe that it applies more generally in other cases, but we don't know how to make the connection."

What's needed, Lee says, is constructive proof. That is, he's not satisfied with knowing that A equals B – he wants to map the path between A and B. That path could then be followed from A' to B', from A* to B* – from field theory to gravity. Lee hopes the renormalization group can be that path.

The idea that RG is behind the AdS/CFT correspondence is not new. The AdS/CFT conjecture maps an N dimensional field theory into a N+1 dimensional theory of gravity. The extra dimension is widely interpreted as a length scale (for reasons not discussed here). Since moving theories from one length scale to another is exactly what the renormalization group is for, many experts believe that RG will be key to any proof of the AdS/CFT conjecture.

But there's still a problem.

Toward a quantum renormalization group

"The problem with the renormalization group is that it predicts things in a way that is deterministic and classical," Lee says. For example, consider one of basic things physicists need to compute: the coupling constant, which predicts the strength of the force between two objects. "Say I have a coupling constant and it has value X at one scale. If I double the length scale, the renormalization group will tell me exactly what the new coupling constant will be."

That sounds like the good news, but it's actually the bad news. "We are talking about quantum gravity," says Lee. "Coupling constants will not be exactly known. They will be quantum and dynamical."

To address this, Lee is working on an extension of the renormalization group which he calls the quantum renormalization group. Whereas traditional RG makes the coupling constants "flow" along a smooth and deterministic path from one exact value to another, Lee's quantum RG will have built in uncertainty about the start and end points of that path, and some wobble along the way.

"Quantum systems can do strange things," Lee says. "If we are to truly understand them, we need to make our theory stranger, too."

The road from quantum mechanics to gravity has long been unpassable. Lee hopes his strange and wobbly quantum map will help physicists at last find their way.

Explore further: Expanding universe can emerge in remarkably simple way, scientists say

add to favorites email to friend print save as pdf

Related Stories

Quantum steps towards the Big Bang

Sep 03, 2013

(Phys.org) —Present-day physics cannot describe what happened in the Big Bang. Quantum theory and the theory of relativity fail in this almost infinitely dense and hot primal state of the universe. Only ...

New work gives credence to theory of universe as a hologram

Dec 13, 2013

(Phys.org) —In publishing a story regarding work reported by Japanese physicists last month, Nature News has set off a bit of a tabloid firestorm by describing an obscure bit of physics theory as "the clearest evide ...

Spacetime May Have Fractal Properties on a Quantum Scale

Mar 25, 2009

(PhysOrg.com) -- Usually, we think of spacetime as being four-dimensional, with three dimensions of space and one dimension of time. However, this Euclidean perspective is just one of many possible multi-dimensional ...

Recommended for you

Particles, waves and ants

Nov 26, 2014

Animals looking for food or light waves moving through turbid media – astonishing similarities have now been found between completely different phenomena.

User comments : 11

Adjust slider to filter visible comments by rank

Display comments: newest first

Benni
1 / 5 (2) Apr 23, 2014
"Space as the surface of a sphere is technically called elliptical space.
Anti-de Sitter space is elliptical space that obeys the tenets of special relativity – elliptical space that can stretch or contract in extreme circumstances. When physicists say that gravity bends space like a bowling ball on a rubber sheet, anti-de Sitter space is probably the space they have in mind. Thus, the "AdS" part of AdS/CFT refers to a particular description of gravity."

Above quoted directly from the article: this being the reason why Einstein declared in his General Relativity that the entire Universe is "spherical or quasi-spherical, not flat.

aaron35
Apr 23, 2014
This comment has been removed by a moderator.
Uncle Ira
2.6 / 5 (5) Apr 23, 2014

Above quoted directly from the article: this being the reason why Einstein declared in his General Relativity that the entire Universe is "spherical or quasi-spherical, not flat.



@ Benni-Skippy, the Einstein-Skippy declared a lot of stuffs that turned out to not work out so good. You Cher seem to be obsessed with this "spherical or quasi-spherical, not flat" busyness. Maybe you should let some of the smart peoples try to tell you about all the new stuffs that has been found out since Einstein-Skippy got to be dead and dust sixty or fifty years ago.

What Neg, they don't got none of the books at your library that are newer then when Einstein-Skippy wrote that one you are so much the fond of?
Bob Osaka
2.5 / 5 (2) Apr 23, 2014
"Quantum systems can do strange things.... If we are to truly understand them, we need to make our theory"...simpler.
Mimath224
3 / 5 (2) Apr 23, 2014
Of course I'm no expert here but I wonder if Mr. Lee is formulating a 3rd Rn scheme (I am only aware of 2). In such I expect it would be more 'general' thus being able to cope with infinities both large and small. But something has always made me wonder about 'Nature' itself. I am being very simplistic here but just looking at some real numbers, 137 for example and using 360 deg circle 360/137 is approaching the to square of the so called 'Golden ratio' (1.6210....[16.18033989...]. What I am suggesting is that perhaps some macro 'natural forms' mirror some micro forms...on the other hand, probably a layman's 'whimsical nonsense'.
arom
1 / 5 (2) Apr 24, 2014
The road uniting quantum field theory and general relativity – the two great theories of modern physics – has been impassable for 80 years. Could a tool from condensed matter physics finally help map the way?
Physicists simply don't know. Researchers in both string theory and loop quantum gravity have made progress, but a fully functional unified theory has remained out of reach for more than 80 years.

Maybe the problem is because we do not know both the mechanism of gravity and quantum mechanics, understand them could guide the way to a simple unified theory …
http://www.vacuum...=9〈=en
tadchem
5 / 5 (1) Apr 24, 2014
... using 360 deg circle 360/137 is approaching the to square of the so called 'Golden ratio' (1.6210....[16.18033989...]. What I am suggesting is that perhaps some macro 'natural forms' mirror some micro forms...on the other hand, probably a layman's 'whimsical nonsense'.

I suggest that the latter is true - the 'whimsical nonsense.'
Dividing 360 (an arbitrary number used in describing angles) by 137 (an *approximation* to the fine structure constant) has no a priori justification. Rather than 360 you could have chosen 400 (the number of gradians in a circle), 4 (the number of quandrants), 6 (the number of time a radius will subdivide a circumference), 8 (the number of cardinal directions in feng shui), or pretty much anything else you desire. There are enough real-world numbers out there that one can find 2 whose ratio will approximate nearly any quantity to any desired degree of accuracy.
qquax
not rated yet Apr 27, 2014
"... Juan Maldacen, who in 1997, came up with what is now known as string theory ..."

Who knew? And here I always thought work on string theory has been going on for several decades. http://en.wikiped...g_theory

Mimath224
not rated yet Apr 27, 2014
@tadchem, sorry about the delay. Yes, that's my point.'Nature' seems to have solved many problems and I wonder if the answer/route to a 'unification' is 'out there' and I was just using √ +1]/2 as an example
Mimath224
not rated yet Apr 27, 2014
@tadchem sorry for the delay. Yes that's my point. Maybe 'nature' out there has an answer/route to a 'unification' 'out there'. I used √ 5 +1/2 as an example.
Pejico
Apr 27, 2014
This comment has been removed by a moderator.
Mimath224
not rated yet Apr 27, 2014
I used √ 5 +1/2 as an example should read [( √ 5 ) +1]/2
Brad Watson_ Miami
not rated yet May 03, 2014
M-theory/supergravity theory: 7D hyperspace + 4 common dimensions = 11D spacetime

------------------------------------------------

Unified Strings (U21 S19) Theory (M-theory/supergravity theory + time analysis thus providing symmetry)...

3D regular space + 7D hyperspace + 7 aspects regular time + 4 aspects hypertime = 21D/a spacetime

This 'theory of everything' actually falls under the umbrella of Plan-it Theory: GOD=7_4 algorithm or FOD=6_4 (on Planet Nestor). I've collected a great deal of indirect proof of Unified Strings (U21 S19) Theory and it makes the BIGGEST prediction! "Identifying 'True Earth-like Planets' - All New Worlds Are Built On 7_4 (like Earth) Or 6_4".

I presented this at the NASA Conference 'Missions for Exoplanets: 2010-2020' held at the Pasadena Hilton April 21-23, 2009. I've tweaked it since and it can be found at http://PlanetNest...spot.com .
Pejico
May 03, 2014
This comment has been removed by a moderator.

Please sign in to add a comment. Registration is free, and takes less than a minute. Read more

Click here to reset your password.
Sign in to get notified via email when new comments are made.