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Theoretical physics: The origins of space and time

Many researchers believe that physics will not be complete until it can explain not just the behaviour of space and time, but where these entities come from.

Zeeya Merali, 08/28/13

“Imagine waking up one day and realizing that you actually live inside a computer game,” says Mark Van Raamsdonk, describing what sounds like a pitch for a science-fiction film. But for Van Raamsdonk, a physicist at the University of British Columbia in Vancouver, Canada, this scenario is a way to think about reality. If it is true, he says, “everything around us -- the whole three-dimensional physical world -- is an illusion born from information encoded elsewhere, on a two-dimensional chip”. That would make our Universe, with its three spatial dimensions, a kind of hologram, projected from a substrate that exists only in lower dimensions.

This 'holographic principle' is strange even by the usual standards of theoretical physics. But Van Raamsdonk is one of a small band of researchers who think that the usual ideas are not yet strange enough. If nothing else, they say, neither of the two great pillars of modern physics -- general relativity, which describes gravity as a curvature of space and time, and quantum mechanics, which governs the atomic realm -- gives any account for the existence of space and time. Neither does string theory, which describes elementary threads of energy.

Van Raamsdonk and his colleagues are convinced that physics will not be complete until it can explain how space and time emerge from something more fundamental -- a project that will require concepts at least as audacious as holography. They argue that such a radical reconceptualization of reality is the only way to explain what happens when the infinitely dense 'singularity' at the core of a black hole distorts the fabric of space-time beyond all recognition, or how researchers can unify atomic-level quantum theory and planet-level general relativity -- a project that has resisted theorists' efforts for generations.

“All our experiences tell us we shouldn't have two dramatically different conceptions of reality -- there must be one huge overarching theory,” says Abhay Ashtekar, a physicist at Pennsylvania State University in University Park.

Finding that one huge theory is a daunting challenge. Here, Nature explores some promising lines of attack -- as well as some of the emerging ideas about how to test these concepts (see 'The fabric of reality'). (請至原網頁瀏覽參考圖片)

Gravity as thermodynamics

One of the most obvious questions to ask is whether this endeavour is a fool's errand. Where is the evidence that there actually is anything more fundamental than space and time?

A provocative hint comes from a series of startling discoveries made in the early 1970s, when it became clear that quantum mechanics and gravity were intimately intertwined with thermodynamics, the science of heat.

In 1974, most famously, Stephen Hawking of the University of Cambridge, UK, showed that quantum effects in the space around a black hole will cause it to spew out radiation as if it was hot. Other physicists quickly determined that this phenomenon was quite general. Even in completely empty space, they found, an astronaut undergoing acceleration would perceive that he or she was surrounded by a heat bath. The effect would be too small to be perceptible for any acceleration achievable by rockets, but it seemed to be fundamental. If quantum theory and general relativity are correct -- and both have been abundantly corroborated by experiment -- then the existence of Hawking radiation seemed inescapable.

A second key discovery was closely related. In standard thermodynamics, an object can radiate heat only by decreasing its entropy, a measure of the number of quantum states inside it. And so it is with black holes: even before Hawking's 1974 paper, Jacob Bekenstein, now at the Hebrew University of Jerusalem, had shown that black holes possess entropy. But there was a difference. In most objects, the entropy is proportional to the number of atoms the object contains, and thus to its volume. But a black hole's entropy turned out to be proportional to the surface area of its event horizon -- the boundary out of which not even light can escape. It was as if that surface somehow encoded information about what was inside, just as a two-dimensional hologram encodes a three-dimensional image.

“This seemed to say something deep about the origins of gravity,” says Jacobson. In particular, the laws of thermodynamics are statistical in nature -- a macroscopic average over the motions of myriad atoms and molecules -- so his result suggested that gravity is also statistical, a macroscopic approximation to the unseen constituents of space and time.

In 2010, this idea was taken a step further by Erik Verlinde, a string theorist at the University of Amsterdam, who showed² that the statistical thermodynamics of the space-time constituents -- whatever they turned out to be -- could automatically generate Newton's law of gravitational attraction.

And in separate work, Thanu Padmanabhan, a cosmologist at the Inter-University Centre for Astronomy and Astrophysics in Pune, India, showed³ that Einstein's equations can be rewritten in a form that makes them identical to the laws of thermodynamics -- as can many alternative theories of gravity. Padmanabhan is currently extending the thermodynamic approach in an effort to explain the origin and magnitude of dark energy: a mysterious cosmic force that is accelerating the Universe's expansion.

Testing such ideas empirically will be extremely difficult. In the same way that water looks perfectly smooth and fluid until it is observed on the scale of its molecules -- a fraction of a nanometre -- estimates suggest that space-time will look continuous all the way down to the Planck scale: roughly 10⁻³⁵ metres, or some 20 orders of magnitude smaller than a proton.

But it may not be impossible. One often-mentioned way to test whether space-time is made of discrete constituents is to look for delays as high-energy photons travel to Earth from distant cosmic events such as supernovae and γ-ray bursts. In effect, the shortest-wavelength photons would sense the discreteness as a subtle bumpiness in the road they had to travel, which would slow them down ever so slightly. Giovanni Amelino-Camelia, a quantum-gravity researcher at the University of Rome, and his colleagues have found⁴ hints of just such delays in the photons from a γ-ray burst recorded in April. The results are not definitive, says Amelino-Camelia, but the group plans to expand its search to look at the travel times of high-energy neutrinos produced by cosmic events. He says that if theories cannot be tested, “then to me, they are not science. They are just religious beliefs, and they hold no interest for me.”

Other physicists are looking at laboratory tests. In 2012, for example, researchers from the University of Vienna and Imperial College London proposed⁵ a tabletop experiment in which a microscopic mirror would be moved around with lasers. They argued that Planck-scale granularities in space-time would produce detectable changes in the light reflected from the mirror (see Nature http://doi.org/njf; 2012).

Loop quantum gravity

Even if it is correct, the thermodynamic approach says nothing about what the fundamental constituents of space and time might be. If space-time is a fabric, so to speak, then what are its threads?

One possible answer is quite literal. The theory of loop quantum gravity, which has been under development since the mid-1980s by Ashtekar and others, describes the fabric of space-time as an evolving spider's web of strands that carry information about the quantized areas and volumes of the regions they pass through⁶. The individual strands of the web must eventually join their ends to form loops -- hence the theory's name -- but have nothing to do with the much better-known strings of string theory. The latter move around in space-time, whereas strands actually are space-time: the information they carry defines the shape of the space-time fabric in their vicinity.

Because the loops are quantum objects, however, they also define a minimum unit of area in much the same way that ordinary quantum mechanics defines a minimum ground-state energy for an electron in a hydrogen atom. This quantum of area is a patch roughly one Planck scale on a side. Try to insert an extra strand that carries less area, and it will simply disconnect from the rest of the web. It will not be able to link to anything else, and will effectively drop out of space-time.

This simulation shows how space evolves in loop quantum gravity. The colours of the faces of the tetrahedra indicate how much area exists at that given point, at a particular moment of time. (請至原網頁瀏覽參考圖片)

One welcome consequence of a minimum area is that loop quantum gravity cannot squeeze an infinite amount of curvature onto an infinitesimal point. This means that it cannot produce the kind of singularities that cause Einstein's equations of general relativity to break down at the instant of the Big Bang and at the centres of black holes.

In 2006, Ashtekar and his colleagues reported⁷ a series of simulations that took advantage of that fact, using the loop quantum gravity version of Einstein's equations to run the clock backwards and visualize what happened before the Big Bang. The reversed cosmos contracted towards the Big Bang, as expected. But as it approached the fundamental size limit dictated by loop quantum gravity, a repulsive force kicked in and kept the singularity open, turning it into a tunnel to a cosmos that preceded our own.

This year, physicists Rodolfo Gambini at the Uruguayan University of the Republic in Montevideo and Jorge Pullin at Louisiana State University in Baton Rouge reported⁸ a similar simulation for a black hole. They found that an observer travelling deep into the heart of a black hole would encounter not a singularity, but a thin space-time tunnel leading to another part of space. “Getting rid of the singularity problem is a significant achievement,” says Ashtekar, who is working with other researchers to identify signatures that would have been left by a bounce, rather than a bang, on the cosmic microwave background -- the radiation left over from the Universe's massive expansion in its infant moments.

Loop quantum gravity is not a complete unified theory, because it does not include any other forces. Furthermore, physicists have yet to show how ordinary space-time would emerge from such a web of information. But Daniele Oriti, a physicist at the Max Planck Institute for Gravitational Physics in Golm, Germany, is hoping to find inspiration in the work of condensed-matter physicists, who have produced exotic phases of matter that undergo transitions described by quantum field theory. Oriti and his colleagues are searching for formulae to describe how the Universe might similarly change phase, transitioning from a set of discrete loops to a smooth and continuous space-time. “It is early days and our job is hard because we are fishes swimming in the fluid at the same time as trying to understand it,” says Oriti.

(待續)

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時間「方向」只會向前的根源 – N. Wolchover
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Time’s Arrow Traced to Quantum Source

Natalie Wolchover, 04/16/14

Coffee cools, buildings crumble, eggs break and stars fizzle out in a universe that seems destined to degrade into a state of uniform drabness known as thermal equilibrium. The astronomer-philosopher Sir Arthur Eddington in 1927 cited the gradual dispersal of energy as evidence of an irreversible “arrow of time.”

But to the bafflement of generations of physicists, the arrow of time does not seem to follow from the underlying laws of physics, which work the same going forward in time as in reverse. By those laws, it seemed that if someone knew the paths of all the particles in the universe and flipped them around, energy would accumulate rather than disperse: Tepid coffee would spontaneously heat up, buildings would rise from their rubble and sunlight would slink back into the sun.

“In classical physics, we were struggling,” said Sandu Popescu, a professor of physics at the University of Bristol in the United Kingdom. “If I knew more, could I reverse the event, put together all the molecules of the egg that broke? Why am I relevant?”

Surely, he said, time’s arrow is not steered by human ignorance. And yet, since the birth of thermodynamics in the 1850s, the only known approach for calculating the spread of energy was to formulate statistical distributions of the unknown trajectories of particles, and show that, over time, the ignorance smeared things out.

Now, physicists are unmasking a more fundamental source for the arrow of time: Energy disperses and objects equilibrate, they say, because of the way elementary particles become intertwined when they interact -- a strange effect called “quantum entanglement.”

“Finally, we can understand why a cup of coffee equilibrates in a room,” said Tony Short, a quantum physicist at Bristol. “Entanglement builds up between the state of the coffee cup and the state of the room.”

A watershed paper by Noah Linden, left, Sandu Popescu, Tony Short and Andreas Winter in 2009 showed that entanglement causes objects to evolve toward equilibrium. The generality of the proof is “extraordinarily surprising,” Popescu says. “The fact that a system reaches equilibrium is universal.” The paper triggered further research on the role of entanglement in directing the arrow of time.

Popescu, Short and their colleagues Noah Linden and Andreas Winter reported the discovery in the journal Physical Review E in 2009, arguing that objects reach equilibrium, or a state of uniform energy distribution, within an infinite amount of time by becoming quantum mechanically entangled with their surroundings. Similar results by Peter Reimann of the University of Bielefeld in Germany appeared several months earlier in Physical Review Letters. Short and a collaborator strengthened the argument in 2012 by showing that entanglement causes equilibration within a finite time. And, in work that was posted on the scientific preprint site arXiv.org in February, two separate groups have taken the next step, calculating that most physical systems equilibrate rapidly, on time scales proportional to their size. “To show that it’s relevant to our actual physical world, the processes have to be happening on reasonable time scales,” Short said.

The tendency of coffee -- and everything else -- to reach equilibrium is “very intuitive,” said Nicolas Brunner, a quantum physicist at the University of Geneva. “But when it comes to explaining why it happens, this is the first time it has been derived on firm grounds by considering a microscopic theory.”

If the new line of research is correct, then the story of time’s arrow begins with the quantum mechanical idea that, deep down, nature is inherently uncertain. An elementary particle lacks definite physical properties and is defined only by probabilities of being in various states. For example, at a particular moment, a particle might have a 50 percent chance of spinning clockwise and a 50 percent chance of spinning counterclockwise. An experimentally tested theorem by the Northern Irish physicist John Bell says there is no “true” state of the particle; the probabilities are the only reality that can be ascribed to it.

Quantum uncertainty then gives rise to entanglement, the putative source of the arrow of time.

When two particles interact, they can no longer even be described by their own, independently evolving probabilities, called “pure states.” Instead, they become entangled components of a more complicated probability distribution that describes both particles together. It might dictate, for example, that the particles spin in opposite directions. The system as a whole is in a pure state, but the state of each individual particle is “mixed” with that of its acquaintance. The two could travel light-years apart, and the spin of each would remain correlated with that of the other, a feature Albert Einstein famously described as “spooky action at a distance.”

“Entanglement is in some sense the essence of quantum mechanics,” or the laws governing interactions on the subatomic scale, Brunner said. The phenomenon underlies quantum computing, quantum cryptography and quantum teleportation.

Seth Lloyd, now an MIT professor, came up with the idea that entanglement might explain the arrow of time while he was in graduate school at Cambridge University in the 1980s.

The idea that entanglement might explain the arrow of time first occurred to Seth Lloyd about 30 years ago, when he was a 23-year-old philosophy graduate student at Cambridge University with a Harvard physics degree. Lloyd realized that quantum uncertainty, and the way it spreads as particles become increasingly entangled, could replace human uncertainty in the old classical proofs as the true source of the arrow of time.

Using an obscure approach to quantum mechanics that treated units of information as its basic building blocks, Lloyd spent several years studying the evolution of particles in terms of shuffling 1s and 0s. He found that as the particles became increasingly entangled with one another, the information that originally described them (a “1” for clockwise spin and a “0” for counterclockwise, for example) would shift to describe the system of entangled particles as a whole. It was as though the particles gradually lost their individual autonomy and became pawns of the collective state. Eventually, the correlations contained all the information, and the individual particles contained none. At that point, Lloyd discovered, particles arrived at a state of equilibrium, and their states stopped changing, like coffee that has cooled to room temperature.

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關於時間的理論 - J. Lloyd
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The incredible truth about time

Theories of science have ignored time... until now. A new idea reveals how it created the Universe - and you, writes Robert Matthews.

James Lloyd, 03/25/14

Time: it rules our lives, and we all wish we had more of it. Businesses make money out of it, and scientists can measure it with astonishing accuracy. Earlier this year, American researchers unveiled an atomic clock accurate to better than one second since the Big Bang 14 billion years ago.

But what, exactly, is time? Despite its familiarity, its ineffability has defied even the greatest thinkers. Over 1,600 years ago the philosopher Augustine of Hippo admitted defeat with words that still resonate:

“If no-one asks me, I know what it is. If I wish to explain it to him who asks, I do not know.”

Yet according to theoretical physicist Lee Smolin, the time has come to grapple with this ancient conundrum: “Understanding the nature of time is the single most important problem facing science,” he says.

As one of the founders of the Perimeter Institute for Theoretical Physics in Ontario, Canada, which specialises in tackling fundamental questions in physics, Professor Smolin has spent more time pondering deep questions than most. So why does he think the nature of time is so important? Because, says Smolin, it is central to the success of attempts to understand reality itself.

To most people, this may sound a bit overblown. Since reality in all its forms, from the Big Bang to the Sunday roast, depends on time, isn’t it obvious that we should take time seriously? And didn’t scientists sort out its mysteries centuries ago?

Timeless physics

Prepare for a shock. Scientists have indeed tackled the mystery of time and reached an astounding conclusion. They insist that the most successful theories in physics prove that time does not exist.

But now Smolin has news for these scientists. He thinks they’ve been led to dismiss the reality of time by a mix of deep-seated beliefs and esoteric mathematics. And in a controversial new book Time Reborn, he sets out the dangers of persisting with this folly, and the promise of accepting time’s fundamental importance. If he’s right, it means far from being irrelevant, time is of crucial importance to explaining how the Universe works and is even responsible for our very existence.

Smolin is under no illusions about what he’s taking on. “The scientific case for time being an illusion is formidable,” he says. “The core of the case against time relies on the way we understand what a law of physics is.” He isn’t saying the laws are wrong, just that scientists don’t understand their true origins. “According to the standard view, everything that happens in the Universe is determined by laws,” he says. “Laws are absolute – they don’t change with time”. It’s this attribute that makes laws so powerful in predicting the future: plug in the Earth’s position today into the law of gravity, and it’ll give a pretty accurate location for its position a million years from now.

The laws also seem to reveal the true nature of time: “They suggest the flow of time is just a convenient illusion that can be replaced by computation,” says Smolin. In other words, time is just a trick that makes the equations spit out the right answers.

Emboldened by the seemingly limitless power of their laws and concept of time, physicists have sought to understand the properties of everything – including the Universe as a whole, in all its infinite majesty. But time and again, when they’ve attempted this, they’ve run into problems.

Over 300 years ago, Sir Isaac Newton tried to apply his law of universal gravity to the whole Universe, only to see it collapse when dealing with the infinite extent of space. A century ago, Albert Einstein applied his far more powerful theory of gravity, General Relativity, to the cosmos, but it broke down at the large scale – when explaining the Big Bang.

Quantum conundrum

In the mid-1960s, the American theorist John Wheeler and his collaborator Bryce DeWitt decided to see what insights might emerge from applying the most successful theory in all science – quantum theory – to the cosmos. Most often applied to the sub-atomic world, quantum theory can – in principle at least – be applied to everything, even the large-scale workings of the Universe.

Wheeler and DeWitt succeed in producing a nightmarishly complex equation that, according to quantum theory, captures the true nature of the Universe. But the equation spawned a shocking insight. Of all the quantities it contained, one that everyone expected it to include had simply vanished: ‘t’ for time. “According to the Wheeler-DeWitt equation, the quantum state of the Universe is just frozen,” says Smolin. “The quantum Universe is a Universe without change. It just simply is.”

The contrast with apparent reality could hardly be more stark. Astronomers insist the Universe began in a Big Bang and is still expanding. Stars are constantly being born and dying – along with ourselves. Clearly, something is wrong.

Many theorists have tried to find ways of getting what we perceive to be time to emerge from the ‘timeless’ Universe described by the Wheeler-DeWitt equation. “I’ve pondered these approaches”, says Smolin, “and I remain convinced none of them work.” He believes only a fundamental re-think about time can solve the crisis.

Not everyone agrees, however. Some insist that the Wheeler-DeWitt equation reveals the truth about time – no matter how unpalatable we find it. Chief among them is the British theoretical physicist Dr. Julian Barbour, Visiting Professor at Oxford University. He has spent decades wrestling with the meaning of the Wheeler-DeWitt equation, and is renowned for his 1999 magnum opus The End Of Time.

Unlike Smolin, Barbour insists the Wheeler-DeWitt equation’s implication for time cannot be dismissed. He argues that the Universe is really a vast, static array of ‘nows’, like frames on some cosmic movie-reel. At any given moment, or ‘now’, time does not need to be factored in to explanations of how the Universe works. The sense of time passing comes from our minds processing each of these frames – or ‘time capsules’, as Barbour calls them. Time itself, however, doesn’t exist.

Smolin greatly admires Barbour’s efforts: “It’s the best thought-through approach to making sense of quantum cosmology,” he says. He has even incorporated some of Barbour’s latest ideas into his own. But he believes it suffers from the same flaws as all ‘timeless’ theories of the Universe: it struggles to make testable predictions, and it can’t explain where the timeless laws of physics come from in the first place.

Radical thinking

Smolin thinks he can do all this, and more. And to do it, he calls on the properties of the most extraordinary objects in the Universe today: black holes.

Formed from the collapse of giant stars, black holes are notorious for having gravitational fields so strong not even light can escape them. Exactly what happens inside them isn’t known for sure, but there are hints from quantum theory that the centre of black holes may be the birth-places of whole new universes, each with different laws of physics.

Smolin points out that if this is correct, then a kind of cosmic version of Darwinian natural selection could apply, in which the most common universes will be those most suitable for producing black holes. And this, he says, can be put to the test in our Universe. After countless aeons of cosmic evolution, our Universe should by now be ruled by laws of physics well-suited to producing black holes. According to Smolin, astrophysicists can check to see if this is actually true – and to date the evidence suggests it is.

The most striking evidence, though, may be our own existence. Black holes are formed from the death of huge stars in supernova explosions. Intriguingly, these are the very same stars that produce the carbon, oxygen and other elements required for life. If there were no giant stars, there would be no universe-spawning black holes and no evolving laws of physics – and no us, either.

Smolin is thus suggesting that our very existence may be evidence for cosmic evolution. And since evolution can only happen over time, that in turn suggests time is real. It’s an astonishing line of argument for the reality of time – and one that doesn’t convince everyone. “I find these ideas very speculative – to say the least,” says theorist Prof Claus Kiefer of the University of Cologne in Germany. He doubts even the starting point for Smolin’s argument for the reality of time: “There is no evidence whatsoever that new universes are born inside black holes.”

A matter of time

What everyone agrees on, however, is that time certainly seems real. And there can be no disputing the boldness of Smolin’s arguments.

If he’s right, our Universe is just the latest in an endless series. Over time, over successive universes, the laws of physics have been evolving to the point where the conditions are just right to form not just black holes – the birthplaces of new universes – but also the building blocks of life, including us. In other words, time explains the apparent fluke that our Universe has just the right combination of conditions to allow our existence.

So is Smolin right about all this – or is time really an illusion, as most theorists insist? Only time will tell.

Robert Matthews is Visiting Reader in Science at Aston University, Birmingham. This article first appeared in the August 2013 issue of Focus.

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Theoretical physics: The origins of space and time

Causal sets

Such frustrations have led some investigators to pursue a minimalist programme known as causal set theory. Pioneered by Rafael Sorkin, a physicist at the Perimeter Institute in Waterloo, Canada, the theory postulates that the building blocks of space-time are simple mathematical points that are connected by links, with each link pointing from past to future. Such a link is a bare-bones representation of causality, meaning that an earlier point can affect a later one, but not vice versa. The resulting network is like a growing tree that gradually builds up into space-time. “You can think of space emerging from points in a similar way to temperature emerging from atoms,” says Sorkin. “It doesn't make sense to ask, 'What's the temperature of a single atom?' You need a collection for the concept to have meaning.”

In the late 1980s, Sorkin used this framework to estimate⁹ the number of points that the observable Universe should contain, and reasoned that they should give rise to a small intrinsic energy that causes the Universe to accelerate its expansion. A few years later, the discovery of dark energy confirmed his guess. “People often think that quantum gravity cannot make testable predictions, but here's a case where it did,” says Joe Henson, a quantum-gravity researcher at Imperial College London. “If the value of dark energy had been larger, or zero, causal set theory would have been ruled out.”

Causal dynamical triangulations

That hardly constituted proof, however, and causal set theory has offered few other predictions that could be tested. Some physicists have found it much more fruitful to use computer simulations. The idea, which dates back to the early 1990s, is to approximate the unknown fundamental constituents with tiny chunks of ordinary space-time caught up in a roiling sea of quantum fluctuations, and to follow how these chunks spontaneously glue themselves together into larger structures.

The earliest efforts were disappointing, says Renate Loll, a physicist now at Radboud University in Nijmegen, the Netherlands. The space-time building blocks were simple hyper-pyramids -- four-dimensional counterparts to three-dimensional tetrahedrons -- and the simulation's gluing rules allowed them to combine freely. The result was a series of bizarre 'universes' that had far too many dimensions (or too few), and that folded back on themselves or broke into pieces. “It was a free-for-all that gave back nothing that resembles what we see around us,” says Loll.

This simplified version of causal dynamical triangulation uses just two dimensions: one of space and one of time. The video shows two-dimensional universes generated by pieces of space assembling themselves according to quantum rules. Each colour represent a slice through the universe at particular time after the Big Bang, which is depicted as a tiny black ball. (請至原網頁瀏覽參考圖片)

But, like Sorkin, Loll and her colleagues found that adding causality changed everything. After all, says Loll, the dimension of time is not quite like the three dimensions of space. “We cannot travel back and forth in time,” she says. So the team changed its simulations to ensure that effects could not come before their cause -- and found that the space-time chunks started consistently assembling themselves into smooth four-dimensional universes with properties similar to our own¹⁰.

Intriguingly, the simulations also hint that soon after the Big Bang, the Universe went through an infant phase with only two dimensions -- one of space and one of time. This prediction has also been made independently by others attempting to derive equations of quantum gravity, and even some who suggest that the appearance of dark energy is a sign that our Universe is now growing a fourth spatial dimension. Others have shown that a two-dimensional phase in the early Universe would create patterns similar to those already seen in the cosmic microwave background.

Holography

Meanwhile, Van Raamsdonk has proposed a very different idea about the emergence of space-time, based on the holographic principle. Inspired by the hologram-like way that black holes store all their entropy at the surface, this principle was first given an explicit mathematical form by Juan Maldacena, a string theorist at the Institute of Advanced Study in Princeton, New Jersey, who published¹¹ his influential model of a holographic universe in 1998. In that model, the three-dimensional interior of the universe contains strings and black holes governed only by gravity, whereas its two-dimensional boundary contains elementary particles and fields that obey ordinary quantum laws without gravity.

Hypothetical residents of the three-dimensional space would never see this boundary, because it would be infinitely far away. But that does not affect the mathematics: anything happening in the three-dimensional universe can be described equally well by equations in the two-dimensional boundary, and vice versa.

In 2010, Van Raamsdonk studied what that means when quantum particles on the boundary are 'entangled' -- meaning that measurements made on one inevitably affect the other¹². He discovered that if every particle entanglement between two separate regions of the boundary is steadily reduced to zero, so that the quantum links between the two disappear, the three-dimensional space responds by gradually dividing itself like a splitting cell, until the last, thin connection between the two halves snaps. Repeating that process will subdivide the three-dimensional space again and again, while the two-dimensional boundary stays connected. So, in effect, Van Raamsdonk concluded, the three-dimensional universe is being held together by quantum entanglement on the boundary -- which means that in some sense, quantum entanglement and space-time are the same thing.

Or, as Maldacena puts it: “This suggests that quantum is the most fundamental, and space-time emerges from it.”

References

1. Jacobson, T. Phys. Rev. Lett. 75, 1260–1263 (1995).

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2. Verlinde, E. J. High Energy Phys. http://dx.doi.org/10.1007/JHEP04( class="year">2011)029 (2011).

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3. Padmanabhan, T. Rep. Prog. Phys. 73, 046901 (2010).

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