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Quantum Gravity and Quantum Information F EATURE Kavli IPMU Principal Investigator Yasunori Nomura Research Area： Theoretical Physics Quantum Gravity and Quantum Information Understanding the nature of space and time has the Sun because of this bending of spacetime. brought many revolutions to physics. In old days, This revolutionary theory of spacetime makes the introduction of a coordinate system̶which is an important prediction: because spacetime often attributed to Descartes̶led to Newtonian is dynamical, its distortions can propagate mechanics through contributions by many scientists, independently of the existence of matter. For including Galileo. At the beginning of the 20th example, when heavy bodies such as black holes century, Albert Einstein proposed special relativity, move violently, they disturb spacetime greatly. which, in a sense, unies space and time. According This effect can then propagate to places far to this theory, space and time are closely related, away from the location of the original bodies as causing phenomena such as a contraction of wave of spacetime distortions. This wave is called length and a delay of time when an object moves gravitational wave, and it was rst detected directly at a speed close to that of light. These effects are in 2016, almost 100 years after the formulation of precisely measured in present-day experiments, general relativity. This was an extremely important leaving no room to doubt the theory. The resulting experimental discovery, and for this achievement the concept of spacetime, which treats space and time 2017 Nobel Prize in Physics was awarded. in a unied manner, has been playing a fundamental role in contemporary physics until today. Theory of Quantum Gravity One of the most important properties of spacetime was revealed by Einstein himself about 10 As we have seen, our understanding of spacetime years after the announcement of special relativity. has dramatically evolved over the last few hundred According to this new theory called general years. However, we know that this is not the end. relativity, spacetime is not a xed entity, as one The reason is that our world obeys quantum might imagine from the term“ coordinate system”; mechanics. rather, it is a dynamical object that can be bent Quantum mechanics was discovered at the or distorted. General relativity says that it is these beginning of the 20th century in the process of bending and distortion of spacetime that we call studying microscopic objects such as atoms, but gravity. For example, gravity between the Sun and later it was found to be a more fundamental the Earth arises because the existence of the Sun principle governing the world. Quantum mechanics bends spacetime around it. The Earth moves around makes a number of strange predictions. For 4 Kavli IPMU News No. 43 September 2018 example, an object such as an electron cannot length̶where quantum effects on spacetime and exist in one place; rather, its location spreads gravity become important̶leads to an innumerable probabilistically. (Since this spread is usually so small amount of innities, destroying the predictivity that we cannot perceive it directly in our daily life.) of the theory. This means that in order to obtain It is also possible that two worlds exist parallelly in a complete theory including quantum effects on probability space, the state we call a superposition. spacetime and gravity, it is not enough to simply While these phenomena sound extremely strange consider general relativity and quantum mechanics from the sense of everyday life, the correctness together. The currently most promising theory to of the theory has been repeatedly demonstrated solve this problem is string theory, whose structure experimentally. In fact, the accuracy of these and consequences are vigorously studied by many experiments has dramatically improved in recent researchers. years, so that predictions of quantum mechanics Another reason to study quantum mechanical have now been conrmed precisely at a detailed theory of spacetime and gravity̶commonly level. Furthermore, scientists are advancing the referred to as quantum gravity̶is that it brings development of a computer̶quantum computer̶ about a revolutionary picture of spacetime. As we which has capability completely different from the will see in this article, it is not true that the effect conventional one and which positively utilizes the of quantum gravity becomes important only at the principle of quantum mechanics. Planck length; on the contrary, it has increasingly Let us return the story to spacetime. General become clear that it also plays a decisive role in relativity explains all gravitational phenomena physics at long distances such as the physics of that have been observed until now. This includes black holes and multiverse cosmology. Moreover, minuscule deviations from the predictions of this relatively recent progress is creating a new Newtonian gravity, the existence of gravitational research area that unies two elds of quantum wave, and the expansion of the universe. There gravity and quantum information sciences, which is almost no doubt about the correctness of the have been developed separately so far. Below I will theory at scales we can currently observe. General give a brief overview of this new development. relativity, however, does not contain the effect of quantum mechanics, which is a basic principle of Quantum Mechanics of Spacetime and the world we live in. This is not an experimentally the Holographic Principle urgent problem. The scale at which the quantum The beginning was the physics of black holes. In effect of spacetime becomes important directly can a theory with gravity, when the density of matter be estimated theoretically, which is about 10-33 cm, becomes larger than a certain limit, it produces a the distance called the Planck length. This is about region around it from which nothing can escape 16 orders of magnitude smaller than the smallest due to its strong gravity. The boundary of this Feature length probed so far by the world’s most powerful region is called a horizon, and the inside is a black accelerator. Does this mean that it is meaningless to hole. investigate the quantum effect on spacetime? Black holes had been known to have the There are a number of reasons, at least following intriguing property: in general relativity, theoretically, why this is not the case. One is the the total area of horizons does not decrease. For problem of innity. Quantum mechanics and general example, when a black hole swallows an object, its relativity do not get along very well. Assuming area increases. (Here and below, when we refer to that the theory of gravity at our scales is general the area of a black hole, it means the area of the relativity, its simple extrapolation below the Planck horizon of the black hole.) Also, when two black 5 A2 A3 A1 A3 ≥ A1 + A2 Figure 1: The area, A3, of the black hole formed after the merging of two black holes is equal to or larger than the sum of the areas, A1 and A2, of the original black holes. holes merge into one̶ this phenomenon was absorbed is always equal to or larger than the sum actually observed by the detection of gravity wave of the entropies of the initial black hole and the in 2016!̶the area of the produced black hole is thrown object. equal to or larger than the sum of the areas of the The idea that a black hole has entropy was initial two black holes; see Figure 1. initially received with skepticism. If a black hole The fundamental importance of this fact was has entropy, the rst law of thermodynamics realized by Jacob Bekenstein in his revolutionary requires it to also have temperature. However, paper in 1973. Bekenstein asked what happens to if it has temperature, then it must be radiating. physical quantities when an object is thrown into Isn’t it the case that nothing can come out of a a black hole. The answer is clear for energy. The black hole? This apparent contradiction, however, energy of the thrown object becomes (a part of) was resolved in 1974 when Stephen Hawking the mass of the black hole, so that the total energy performed a calculation which included the effect is conserved. But what about entropy? According of quantum mechanics into general relativity. While to the second law of thermodynamics, entropy his calculation was not based on a complete theory should not decrease. However, the entropy of the of quantum gravity, he could still show that a black thrown object seems to simply disappear when it is hole indeed emits radiation because of quantum absorbed into the black hole. Does this mean that effects. This established the thermodynamics of the second law of thermodynamics is violated? black holes. What Bekenstein suggested in his 1973 paper is A strange thing here is that the entropy of a black that the entropy of the thrown object is converted hole is given by its area. Since a black hole is the into the entropy of the black hole. What is the nal state of the evolution of any initial state, the entropy of the black hole? He proposed that the entropy of the black hole must be indicating“ the area of the horizon is the one. Recall that the largest possible entropy that the region can have.” In total sum of horizon areas does not decrease in modern days, we know that entropy is given by the general relativity. This is exactly the property that logarithm of the number of possible quantum states entropy must have. Indeed, by dening the entropy that the system can take. If space is composed of of a black hole in this way, it can be shown that some simple constituents as in ordinary materials the entropy of the black hole after the object is (e.g., if space can be approximated by a lattice with 6 Kavli IPMU News No.
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