Time’s Arrow Traced to Quantum Source

The arrow of time.


Cups of coffee cool, buildings crumble and stars fizzle out, physicists say, because of a strange quantum effect called “entanglement.”

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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.”

Bristol group.

Courtesy of Tony Short

A watershed paper by Noah Linden, left, Sandu Popescu, Tony Short and Andreas Winter (not pictured) 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 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

Courtesy of Seth Lloyd

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.

“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.”

Coffee entanglement.

Lidia del Rio

As a hot cup of coffee equilibrates with the surrounding air, coffee particles (white) and air particles (brown) interact and become entangled mixtures of brown and white states. After some time, most of the particles in the coffee are correlated with air particles; the coffee has reached thermal equilibrium.

In 2009, the Bristol group’s proof resonated with quantum information theorists, opening up new uses for their techniques. It showed that as objects interact with their surroundings — as the particles in a cup of coffee collide with the air, for example — information about their properties “leaks out and becomes smeared over the entire environment,” Popescu explained. This local information loss causes the state of the coffee to stagnate even as the pure state of the entire room continues to evolve. Except for rare, random fluctuations, he said, “its state stops changing in time.”

Consequently, a tepid cup of coffee does not spontaneously warm up. In principle, as the pure state of the room evolves, the coffee could suddenly become unmixed from the air and enter a pure state of its own. But there are so many more mixed states than pure states available to the coffee that this practically never happens — one would have to outlive the universe to witness it. This statistical unlikelihood gives time’s arrow the appearance of irreversibility. “Essentially entanglement opens a very large space for you,” Popescu said. “It’s like you are at the park and you start next to the gate, far from equilibrium. Then you enter and you have this enormous place and you get lost in it. And you never come back to the gate.”

In the new story of the arrow of time, it is the loss of information through quantum entanglement, rather than a subjective lack of human knowledge, that drives a cup of coffee into equilibrium with the surrounding room. The room eventually equilibrates with the outside environment, and the environment drifts even more slowly toward equilibrium with the rest of the universe. The giants of 19th century thermodynamics viewed this process as a gradual dispersal of energy that increases the overall entropy, or disorder, of the universe. Today, Lloyd, Popescu and others in their field see the arrow of time differently. In their view, information becomes increasingly diffuse, but it never disappears completely. So, they assert, although entropy increases locally, the overall entropy of the universe stays constant at zero.

“The universe as a whole is in a pure state,” Lloyd said. “But individual pieces of it, because they are entangled with the rest of the universe, are in mixtures.”

One aspect of time’s arrow remains unsolved. “There is nothing in these works to say why you started at the gate,” Popescu said, referring to the park analogy. “In other words, they don’t explain why the initial state of the universe was far from equilibrium.” He said this is a question about the nature of the Big Bang.

Despite the recent progress in calculating equilibration time scales, the new approach has yet to make headway as a tool for parsing the thermodynamic properties of specific things, like coffee, glass or exotic states of matter. (Several traditional thermodynamicists reported being only vaguely aware of the new approach.) “The thing is to find the criteria for which things behave like window glass and which things behave like a cup of tea,” Renner said. “I would see the new papers as a step in this direction, but much more needs to be done.”

Some researchers expressed doubt that this abstract approach to thermodynamics will ever be up to the task of addressing the “hard nitty-gritty of how specific observables behave,” as Lloyd put it. But the conceptual advance and new mathematical formalism is already helping researchers address theoretical questions about thermodynamics, such as the fundamental limits of quantum computers and even the ultimate fate of the universe.

“We’ve been thinking more and more about what we can do with quantum machines,” said Paul Skrzypczyk of the Institute of Photonic Sciences in Barcelona. “Given that a system is not yet at equilibrium, we want to get work out of it. How much useful work can we extract? How can I intervene to do something interesting?”

Sean Carroll, a theoretical cosmologist at the California Institute of Technology, is employing the new formalism in his latest work on time’s arrow in cosmology. “I’m interested in the ultra-long-term fate of cosmological space-times,” said Carroll, author of “From Eternity to Here: The Quest for the Ultimate Theory of Time.” “That’s a situation where we don’t really know all of the relevant laws of physics, so it makes sense to think on a very abstract level, which is why I found this basic quantum-mechanical treatment useful.”

Twenty-six years after Lloyd’s big idea about time’s arrow fell flat, he is pleased to be witnessing its rise and has been applying the ideas in recent work on the black hole information paradox. “I think now the consensus would be that there is physics in this,” he said.

Not to mention a bit of philosophy.

According to the scientists, our ability to remember the past but not the future, another historically confounding manifestation of time’s arrow, can also be understood as a buildup of correlations between interacting particles. When you read a message on a piece of paper, your brain becomes correlated with it through the photons that reach your eyes. Only from that moment on will you be capable of remembering what the message says. As Lloyd put it: “The present can be defined by the process of becoming correlated with our surroundings.”

The backdrop for the steady growth of entanglement throughout the universe is, of course, time itself. The physicists stress that despite great advances in understanding how changes in time occur, they have made no progress in uncovering the nature of time itself or why it seems different (both perceptually and in the equations of quantum mechanics) than the three dimensions of space. Popescu calls this “one of the greatest unknowns in physics.”

“We can discuss the fact that an hour ago, our brains were in a state that was correlated with fewer things,” he said. “But our perception that time is flowing — that is a different matter altogether. Most probably, we will need a further revolution in physics that will tell us about that.”

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  • This sounds suspiciously like Boltzmann’s derivation of the thermodynamic arrow of time, in which he effectively smuggled the arrow into the system under consideration without realising he’d done so. It is notoriously easy to assume what one wishes to prove when it comes to time, we are entropy-bound creatures with a strong intuitive notion of how time should operate. But why should entanglement and the spreading of quantum uncertainty operate in one preferred time direction, and not the other? Why should systems “become entangled” along the time axis rather than “unbecoming untangled” ? It still looks a bit like assuming the desired consequence, imho!

    Of course the statement that the entropy of the universe remains constant is correct – entropy is an emergent concept, and only exists because of coarse-graining – and the statement that the laws of physics are time symmetric is correct (apart from kaon decay, if I remember correctly? – and perhaps gravitational collapse). So how does one derive an ongoing increase in entanglement in the preferred time direction from a system that is already as much in equilibrium as it ever will be, and in which physics is (assumed to be) time-symmetric?

    Personally I think this comes down to boundary conditions on the universe. The existence of the Big Bang at one time extremity, but no Big Crunch at the other, introduces an arrow of time as a way of linking the BB singularity to the timelike infinity at the “opposite end” of the universe, and everything else follows from this basic asymmetry of space-time – including the entropy gradient, increasing entanglement, and (perhaps) the differentiation of Everett worlds as one proceeds towards the future.

  • I think that the times arrow that was traced to quantum source is one way closer to explaining how the black holes actually work, and what’s behind their “mechanism”
    Great story to know to be honest, one step closer year by year.

  • wrt space time symmetry, if the arrow of time is a vector, and the “time” we refer to is in fact its norm (because it’s always positive) the equivalent of “negative time” in XYZ space would be a “negative distance” (i.e. the negative norm of a XYZ vector), both of which are impossible, or at least point beyond our traditional time/space universe. Is there is “some” symmetry there?

  • Time and multiverse are the same. Each multiverse spawns through matrix multiplication. As each multiverse diverges times arrow is defined by matrix noncommutative behavior. Time is a side effect of the coherence in each multiverse and the lack of coherence between mutliverses.
    Time cannot be reversed as matrix multiplication cannot.

  • My biggest conundrum about time is simply what do we mean by “the present?” We all feel like we are constantly in the present but yet it seems like the past transitions seamlessly to the future without any present. In the time it takes to think you are in the present the thought is now in the past. As to this “entanglement,” is this responsible for what we call consciousness? When we view a red apple is the conscious feeling or qualia of seeing the apple in some sense due to the entanglement of the apple, the photons bouncing off it, and a pattern of neuronal firing in the brain? As to the “Big Bang,” this is still a theory, and there is no guarantee it will not be replaced by a deeper understanding of the universe.

  • I thought I had a layman’s understanding of what quantum entanglement meant, and how pairs of entangled particles are generated, but here, the author just seems to be waving his hands, using the terms without really describing what they mean.

  • “Our perception that time is flowing”? I don’t have that perception. I don’t even know what it means.

  • The nature of time is movement. Without movement, there can be no time. Time IS movement.

  • “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.”
    Well, no that is NOT the explanation…the explanation for the how things evolve in time is that given the probability of events being overwhelmingly for more disordered* states (there are many more of those than ordered* states), then whether your run the underlying processes forwards or in reverse (in time), the most likely outcome is a disordered state.

    That the direction of time is somehow determined by this idea I find incredibly unappealing. How can you “run things backwards in time” yet imagine that process as moving through time in the “forwards” direction – a little hard to explain what I mean I’m afraid???

    *disordered or ordered are in the mind of the observer – it is just a possible arrangement of things that we call ordered or not.

  • Most mathematical constructions are lovely and very entertaining, but are essentially non-real. It is vitally important to professional calculators, however, to keep their theoretical balls in the air. The arrow of time is an illusion, and the the plethora of ‘calculable’ fantasies, such as black holes, dark energy, ‘neutron stars’, and yes, the BB itself, continues to grow. A clear violation of the law of entropy.

  • If we combine Special Relativity and this article, does that mean that speed slows this entanglement/equilibration psocess, i.e. at the speed of light, this equilibration process completely stops, thus time freezes?

  • What if one of a pair of entangled particles gets drawn into a black hole and the other escapes ? Will information be saved and thus retrieved by virtue of the escaped entangles particle ?

  • “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.”
    –This is wrong. Bell only proved that if the states of the particles are predetermined, then there must be instantaneous communication between them (when a measurement is made on one) in order to produce quantum correlations. Bell favored Bohm’s theory of particles with “true states” over Bohr’s (in which true states only appear as a result of measurements), because he understood that BOTH interpretations require instantaneous communication between entangled particles even at space-like separation; Bohm just makes this more explicit.
    But Bell also favored the GRW interpretation, which tries to specify “collapses” of waves into pure states at the micro-level. This was because it seems impossible to reconcile Bohm’s instantaneous communication with relativity, unlike GRW.

  • I’ve read a few other articles on this , and it seems that the scientists are saying , as has one of the posters here , that if the Universe equilibrates and particles reach their pure state , all particles in correlation sharing the same information , Time will freeze . But what about gravity ? Or Dark Matter ? one pulls and the other pushes , would both be negated , gone ? From what I can understand , time and gravity are integral parts of each other [ that's a layman's guess ] . It would seem to me that discovering or reaching a better understanding of the nature of Dark Matter would illuminate even more on the nature of Time .

  • “In their view, information becomes increasingly diffuse, but it never disappears completely. So, they assert, although entropy increases locally, the overall entropy of the universe stays constant at zero.”

    I don’t understand. Are they implying that there is no final Heat Death of the Universe?

  • ” One aspect of time’s arrow remains unsolved. “There is nothing in these works to say why you started at the gate,” Popescu said, referring to the park analogy. “In other words, they don’t explain why the initial state of the universe was far from equilibrium.” He said this is a question about the nature of the Big Bang.”

    Indeed . The nature of time remains totally unknown . The analogy of approaching a park and going through the gate , then entering and getting lost , thereby never being able to find the gate , is incomplete . I believe once you have gone through the gate , it is impossible to find it again because it no longer exists , no more than yesterday exists aside from your memory of it .This is why I believe Physics will not be able to answer what happened beyond 10 -42 seconds after the Big bang , nor will physics be able to determine any other aspect of the Singularity that exploded bringing about the Big bang . There are no physics for a time when no known physical laws apply

  • Off-topic, but is the picture of the castle ruin a distant reference to the battle between MI6 and Quantum in the newest James Bond trilogy, where the big fight scene in Skyfall was in Scotland?

  • I have long thought that to say space-time is redundant, because time & shifting-space are the same thing.

  • I feel this theory is correct and the reason for that feeling is because it is perfectly reasonable. All they are describing is diffusion at quantum level…mix a drop of purple coloured water into the ocean and eventually the entire ocean will be that drop. As far as the arrow of time is concerned I also feel that is relatively easy to understand. Imagine the big bang being the end of a past quantum diffusion; everything is at the same state therefore it’s a singularity. It comes into contact with the opposite thing….an area with no diffusion. The singularity is compelled to diffuse into the void. It does so violently due to the size of the void. During the process of diffusion from singularity into the void complexity is created. It does this to process material into those required (hydrogen) to eventually enter into its final state of equilibrium…a singularity. Of course time is a measurement of decay for us but is in fact this diffusion process form singularity =fill-void=singularity. Sounds credible to me :)

  • Pardon my intrusion into a place I’m ill prepared to enter, but someone above suggested time is a function of movement, I think it’s a function of change. Whatever the Big Bang was, it doesn’t seem a change in time caused a change in the status quo that existed before time. A physical change occurred as the result of some process, and to travel to the result of that change required a factor of time to take place, call it ’1′. Even if the change undid itself and returned to status quo condition, another unit of time was generated equal to ’1′, so time becomes 1 + 1 = 2. So even if the results suggest time moved backward to the original condition time accumulated. The probability of change occurring so that the status quo was re-attained would have been so small that it wouldn’t take place, and if it did time was still equal to 2. The argument for entanglement describes how change occurs, the complexity of change, and the logical end of change, so that when equilibrium is achieved time will cease.

  • Space-Time.: More time more space. Dark Energy is the expansion force. Ergo: Dark energy equates with time.

  • My feeling is that they have this the wrong way around.

    I suspect that it is the lack of a (thermodynamic) arrow of time that makes the quantum world what it is.

    In the macro world, with a strong arrow of time, we are used to the idea of an object staying at the same spatial location at many different times. At the quantum scale, without an arrow of time at all, an object can exist at many spatial locations at the same time.

    The classical observer of the Copenhagen interpretation of QM then becomes a system with a strong arrow of time and the wave function really does collapse when a quantum system interacts with it.

    Feynman’s path integral formulation would also appear to be consistent with this idea.

  • All colors are derived from white and all sensory input is interconnected and dependent upon mental construction. Dreams are not considered real yet the dreamer can walk or drive through their physical world while experiencing an alternate reality.
    Quantum entanglement suggests that construction of the physical world is a mental process as time only exists in the past.
    “The future has not happened and present is the past by the time it is processed”
    Human consensus of the physical world could be Quantum Entanglement also.

  • When you break down all things in the universe to their most fundamental properties
    (smallest) what do you get?

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