Tag Archives: quantum information theory

Spacetime Without the Time

anti-de-sitter-spaceSince they were first dreamed up explanations of the very small (quantum mechanics) and the very large (general relativity) have both been highly successful at describing their respective spheres of influence. Yet, these two descriptions of our physical universe are not compatible, particularly when it comes to describing gravity. Indeed, physicists and theorists have struggled for decades to unite these two frameworks. Many agree that we need a new theory (of everything).

One new idea, from theorist Erik Verlinde of the University of Amsterdam, proposes that time is an emergent construct (it’s not a fundamental building block) and that dark matter is an illusion.

From Quanta:

Theoretical physicists striving to unify quantum mechanics and general relativity into an all-encompassing theory of quantum gravity face what’s called the “problem of time.”

In quantum mechanics, time is universal and absolute; its steady ticks dictate the evolving entanglements between particles. But in general relativity (Albert Einstein’s theory of gravity), time is relative and dynamical, a dimension that’s inextricably interwoven with directions x, y and z into a four-dimensional “space-time” fabric. The fabric warps under the weight of matter, causing nearby stuff to fall toward it (this is gravity), and slowing the passage of time relative to clocks far away. Or hop in a rocket and use fuel rather than gravity to accelerate through space, and time dilates; you age less than someone who stayed at home.

Unifying quantum mechanics and general relativity requires reconciling their absolute and relative notions of time. Recently, a promising burst of research on quantum gravity has provided an outline of what the reconciliation might look like — as well as insights on the true nature of time.

As I described in an article this week on a new theoretical attempt to explain away dark matter, many leading physicists now consider space-time and gravity to be “emergent” phenomena: Bendy, curvy space-time and the matter within it are a hologram that arises out of a network of entangled qubits (quantum bits of information), much as the three-dimensional environment of a computer game is encoded in the classical bits on a silicon chip. “I think we now understand that space-time really is just a geometrical representation of the entanglement structure of these underlying quantum systems,” said Mark Van Raamsdonk, a theoretical physicist at the University of British Columbia.

Researchers have worked out the math showing how the hologram arises in toy universes that possess a fisheye space-time geometry known as “anti-de Sitter” (AdS) space. In these warped worlds, spatial increments get shorter and shorter as you move out from the center. Eventually, the spatial dimension extending from the center shrinks to nothing, hitting a boundary. The existence of this boundary — which has one fewer spatial dimension than the interior space-time, or “bulk” — aids calculations by providing a rigid stage on which to model the entangled qubits that project the hologram within. “Inside the bulk, time starts bending and curving with the space in dramatic ways,” said Brian Swingle of Harvard and Brandeis universities. “We have an understanding of how to describe that in terms of the ‘sludge’ on the boundary,” he added, referring to the entangled qubits.

The states of the qubits evolve according to universal time as if executing steps in a computer code, giving rise to warped, relativistic time in the bulk of the AdS space. The only thing is, that’s not quite how it works in our universe.

Here, the space-time fabric has a “de Sitter” geometry, stretching as you look into the distance. The fabric stretches until the universe hits a very different sort of boundary from the one in AdS space: the end of time. At that point, in an event known as “heat death,” space-time will have stretched so much that everything in it will become causally disconnected from everything else, such that no signals can ever again travel between them. The familiar notion of time breaks down. From then on, nothing happens.

On the timeless boundary of our space-time bubble, the entanglements linking together qubits (and encoding the universe’s dynamical interior) would presumably remain intact, since these quantum correlations do not require that signals be sent back and forth. But the state of the qubits must be static and timeless. This line of reasoning suggests that somehow, just as the qubits on the boundary of AdS space give rise to an interior with one extra spatial dimension, qubits on the timeless boundary of de Sitter space must give rise to a universe with time — dynamical time, in particular. Researchers haven’t yet figured out how to do these calculations. “In de Sitter space,” Swingle said, “we don’t have a good idea for how to understand the emergence of time.”

Read the entire article here.

Image: Image of (1 + 1)-dimensional anti-de Sitter space embedded in flat (1 + 2)-dimensional space. The t1- and t2-axes lie in the plane of rotational symmetry, and the x1-axis is normal to that plane. The embedded surface contains closed timelike curves circling the x1 axis, though these can be eliminated by “unrolling” the embedding (more precisely, by taking the universal cover). Courtesy: Krishnavedala. Wikipedia. Creative Commons Attribution-Share Alike 3.0.

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The Arrow of Time

Arthur_Stanley_EddingtonEinstein’s “spooky action at a distance” and quantum information theory (QIT) may help explain the so-called arrow of time — specifically, why it seems to flow in only one direction. Astronomer Arthur Eddington first described this asymmetry in 1927, and it has stumped theoreticians ever since.

At a macro-level the classic and simple example is that of an egg breaking when it hits your kitchen floor: repeat this over and over, and it’s likely that the egg will always make for a scrambled mess on your clean tiles, but it will never rise up from the floor and spontaneously re-assemble in your slippery hand. Yet at the micro-level, physicists know their underlying laws apply equally in both directions. Enter two new tenets of the quantum world that may help us better understand this perplexing forward flow of time: entanglement and QIT.

From Wired:

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.”

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.

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.

“What’s really going on is things are becoming more correlated with each other,” Lloyd recalls realizing. “The arrow of time is an arrow of increasing correlations.”

The idea, presented in his 1988 doctoral thesis, fell on deaf ears. When he submitted it to a journal, he was told that there was “no physics in this paper.” Quantum information theory “was profoundly unpopular” at the time, Lloyd said, and questions about time’s arrow “were for crackpots and Nobel laureates who have gone soft in the head.” he remembers one physicist telling him.

“I was darn close to driving a taxicab,” Lloyd said.

Advances in quantum computing have since turned quantum information theory into one of the most active branches of physics. Lloyd is now a professor at the Massachusetts Institute of Technology, recognized as one of the founders of the discipline, and his overlooked idea has resurfaced in a stronger form in the hands of the Bristol physicists. The newer proofs are more general, researchers say, and hold for virtually any quantum system.

“When Lloyd proposed the idea in his thesis, the world was not ready,” said Renato Renner, head of the Institute for Theoretical Physics at ETH Zurich. “No one understood it. Sometimes you have to have the idea at the right time.”

Read the entire article here.

Image: English astrophysicist Sir Arthur Stanley Eddington (1882–1944). Courtesy: George Grantham Bain Collection (Library of Congress).

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