The discrete-time physics hiding inside our continuous-time world
Apr. 18, 2019
Scientists believe that time is continuous, not discrete - roughly speaking, they believe that it does not progress in "chunks," but rather "flows," smoothly and continuously. So they often model the dynamics of physical systems as continuous-time "Markov processes," named after mathematician Andrey Markov. Indeed, scientists have used these processes to investigate a range of real-world processes from folding proteins, to evolving ecosystems, to shifting financial markets, with astonishing success. However, invariably a scientist can only observe the state of a system at discrete times, separated by some gap, rather than continually. For example, a stock market analyst might repeatedly observe how the state of the market at the beginning of one day is related to the state of the market at the beginning of the next day, building up a conditional probability distribution of what the state of the second day is given the state at the first day. In a pair of papers, one appearing in this week's Nature Communications and one appearing recently in the New Journal of Physics, physicists at the Santa Fe Institute and MIT have shown that in order for such two-time dynamics over a set of "visible states" to arise from a continuous-time Markov process, that Markov process must actually unfold over a larger space, one that includes hidden states in addition to the visible ones. They further prove that the evolution between such a pair of times must proceed in a finite number of "hidden timesteps", subdividing the interval between those two times. (Strictly speaking, this proof holds whenever that evolution from the earlier time to the later time is noise-free - see paper for technical details.) "We're saying there are hidden variables in dynamic systems, implicit in the tools scientists are using to study such systems," says co-author David Wolpert (Santa Fe Institute). "In addition, in a certain very limited sense, we're saying that time proceeds in discrete timesteps, even if the scientist models time as though it proceeds continually. The scientists may not have been paying attention to those hidden variables and those hidden timesteps, but they are there, playing a key, behind-the-scenes role in many of the papers those scientists have read, and almost surely also in many of the papers those scientists have written." In addition to discovering hidden states and time steps, the scientists also discovered a tradeoff between the two; the more hidden states there are, the smaller the minimal number of hidden timesteps that are required. According to co-author Artemy Kolchinsky (Santa Fe Institute), "these results surprisingly demonstrate that Markov processes exhibit a kind of tradeoff between time versus memory, which is often encountered in the separate mathematical field of analyzing computer algorithms. To illustrate the role of these hidden states, co-author Jeremy A. Owen (MIT) gives the example of a biomolecular process, observed at hour-long intervals: If you start with a protein in state 'a,' and over an hour it usually turns to state 'b,' and then after another hour it usually turns back to 'a,' there must be at least one other state 'c' - a hidden state - that is influencing the protein's dynamics. "It's there in your biomolecular process," he says. "If you haven't seen it yet, you can go look for it." The authors stumbled on the necessity of hidden states and hidden timesteps while searching for the most energy-efficient way to flip a bit of information in a computer. In that investigation, part of a larger effort to understand the thermodynamics of computation, they discovered that there is no direct way to implement a map that both sends 1 to 0 and also sends 0 to 1. Rather, in order to flip a bit of information, the bit must proceed through at least one hidden state, and involve at least three hidden time steps. (See attached multimedia for diagram) It turns out any biological or physical system that "computes" outputs from inputs, like a cell processing energy, or an ecosystem evolving, would conceal the same hidden variables as in the bit flip example. "These kinds of models really do come up in a natural way," Owen adds, "based on the assumptions that time is continuous, and that the state you're in determines where you're going to go next." "One thing that was surprising, that makes this more general and more surprising to us, was that all of these results hold even without thermodynamic considerations," Wolpert recalls. "It's a very pure example of Phil Anderson's mantra 'more is different,' because all of these low-level details [hidden states and hidden timesteps] are invisible to the higher-level details [map from visible input state to visible output state]." "In a very minor way, it's like the limit of the speed of light," Wolpert muses, "The fact that systems cannot exceed the speed of light is not immediately consequential to the vast majority of scientists. But it is a restriction on allowed processes that applies everywhere and is something to always have in the back of your mind." Research paper
NASA's Newest Planet-Hunting Telescope Has Already Found an Earth-like World
Apr. 17, 2019
Over the last few years, we’ve discovered so many planets around other stars that we now know that nearly every star has a few. These exoplanets come in all kinds of different types, but the most interesting are the Earth-like ones. A new announcement from NASA’s newest planet-hunting telescope suggests it has found its first one. The most successful tool we’ve ever built to find exoplanets was the Kepler Space Telescope, which operated during the first half of this decade. Kepler managed to discover thousands of planets before shutting down for good last year. At the same time, NASA’s successor to Kepler, the TESS telescope, was launched into orbit. TESS stands for Transiting Exoplanets Survey Satellite, and features a collection of upgrades that make it even better at finding hidden planets. TESS is capable of spotting very small and faint planets, making it ideal for searching for tiny earth-like worlds. In a recent update, a group of researchers announced that TESS had found its first one. The world in question is called HD 21749c, and is one of two new planets discovered in a star system 53 light-years away. While it may be nearly the same size as Earth, there’s little chance it could ever support life, only orbiting a few million miles from its host star. That’s much closer than Mercury is to our own star, meaning that this world is likely extremely hot. Still, if we can discover this one world it means we can discover other earth-like worlds elsewhere in our galaxy. Perhaps one of those might be earth-like enough to potentially support life.
We Could Soon Watch a Black Hole in Action, Gobbling Up Matter in Real Time
Apr. 17, 2019
DENVER — Last week, the Event Horizon Telescope (EHT) released the first-ever image of a black hole's shadow cast against the hot gas of its accretion disk. That image, of the black hole at the center of galaxy Messier 87 (M87), was front page news all over the world. Soon, the EHT will produce the first movie of that hot gas whirling chaotically around the shadow, said project leaders who spoke Sunday (April 14) here at the April meeting of the American Physical Society. The EHT isn't a single telescope. Rather, it's a network of radio telescopes all over the world making precisely timed recordings of radio waves all together, and these recordings can be combined such that the different telescope all act as one. As more individual radio telescopes join the EHT and the team updates the project's recording technology, the detail of the images should increase dramatically, Shep Doeleman, the Harvard University astronomer who lead the EHT project said in his talk. And then, the team should be able to produce movies of black holes in action, he said. "It turns out that even now, with what we have, we may be able, with certain prior assumptions, to look at rotational signatures [evidence of the accretion disk swirling around the event horizon]," Doeleman said. "And then, if we had many more stations, then we could really start to see in real time movies of the black hole accretion and rotation." [9 Ideas About Black Holes That Will Blow Your Mind] Advertisement In the case of the black hole in M87, Doeleman told Live Science after his talk, making a movie will be pretty straightforward. The black hole is enormous, even for a supermassive black hole at the center of a galaxy: It's 6.5 billion times the mass of Earth's sun, with its event horizon — the point beyond which not even light can return — enclosing a sphere as wide as our entire solar system. So, the hot matter of this black hole's accretion disk takes a long time to make a single trek around the object. "The time scale over which [M87] changes appreciably is greater than a day. That's great," Doeleman said, because it means the EHT to shoot a movie of the object one frame at a time. "We can … make our image. Then, if we want to make another one, or a time-lapse movie, then we just go out the next day or the next week. And we might do it seven weeks in a row and get seven frames of a movie and then kind of see something move around in that way," he said But the M87 black hole isn't the only supermassive black hole that the EHT is observing. The team is also looking at Sagittarius A*, the supermassive black hole at the center of our own galaxy, and plans to release the first image of that object soon. And the EHT researchers also aim to make movies of that much nearer and better-studied black hole, but that project will be more complicated, Doeleman said. [11 Fascinating Facts About Our Milky Way Galaxy] SagA* is about 1,000 times less massive than the M87 black hole, Doeleman said, so the image changes 1,000 times more quickly. "So, what that means is it will change in minutes or hours," Doeleman said. "You have to develop a fundamentally different algorithm, because it's as if you have the lens cap off on your camera and something's moving while you're taking an exposure." To make a movie, he said, the EHT would not only have to collect all the data necessary to produce an image of the black hole, but also break up that data up into different chunks by time. Next, the team would compare those chunks to one another using sophisticated algorithms to figure out how the image changed even as it was being captured. "We have to figure out a way to look at the first little bit of data, and then the second little bit of data, and then to make a movie," he said. "So members of our team are working on what we call dynamical imaging." This approach uses models of how the image would be expected to move, comparing those models to the actual data to see if it fits. "You've got to be smart and figure out how data from this time slice is related to that time slice right after," Doeleman said. "So, for example, you could say, 'OK, you can move but you can't move that far.'" Using those sorts of constraints, he said, the team can convert even very limited amounts of data from any given minute into complete pictures of SagA* in motion. As a result, the team expects to make movies of the smaller black hole in a single night. Those movies, said Avery Broderick, an astrophysicist at the University of Waterloo in Canada who works on interpreting the EHT's images, should reveal new details about the behavior of accretion disks around black holes, including how they gobble up matter. "We'll be able to map space-times by looking at black hole cinema, not portraiture," Broderick said. Spaced Out! 101 Astronomy Images That Will Blow Your Mind The 11 Biggest Unanswered Questions About Dark Matter Stephen Hawking's Most Far-Out Ideas About Black Holes Originally published on Live Science.
Dr. Howard Lee received the NSF MRI award to acquire an Ebeam lithography system
Mar. 6, 2019
Dr. Howard Lee received the NSF MRI award to acquire an Ebeam lithography system. Congratulations!
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