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Over the past few decades, as many of us spend a lot of time online, the real world seems to have become broader. In one field of theoretical physics, however, the situation seems to be moving in the opposite direction. For the past two decades (although this article was written in 2009, it is still worth reading), string theorists have been discussing the idea that the time and space we live in, including ourselves, may be an illusion. It's a hologram generated by "some kind of reality". This reality lacks a key feature of the world we perceive: the third dimension. Professor Juan Mardasina (Juan Maldacena) of the Princeton Institute of Advanced Studies played an important role in the development of the idea of holographic principles. In the 1990s, Mardacina proposed the first cosmological model to realize the holographic principle. Recently, he was interviewed by the author during his visit to Cambridge.

The enigmatic holographic principle of the 20th century stems from one of the biggest scientific problems of the 20th century: the incompatibility between the two basic physical theories of general relativity and quantum mechanics.

At the beginning of the 20th century, Einstein found that time and space were inseparable, and he called the structure formed by the two as time and space. His general theory of relativity points out that space-time itself is distorted by massive objects, and gravity is the result of this distortion. It's like placing a billiard ball on a trampoline, which creates a depression that rolls nearby marbles into it; similarly, massive objects, such as planets, bend space-time, causing nearby objects to be attracted by their gravity. According to Einstein, gravity is not something that spreads through space, but is caused by the geometry of space-time itself.

General relativity mainly describes the world of planets and galaxies, while quantum mechanics mainly focuses on the subatomic scale, that is, the field of elementary particles that make up matter. On this scale, the mass is so small that gravity is negligible. Quantum field theory is a quantum mechanical description of particle physics, which holds that elementary particles transmit forces through messenger particles called gauge bosons: one elementary particle transmits forces to another by sending some gauge bosons.

Figure 1. Huge objects distort space-time during the development of the 20th century, the electromagnetic force, weak nuclear force and strong nuclear messenger particles of the four fundamental forces were all observed in the experiment. In order to maintain theoretical consistency, Einstein's theory should be able to be rewritten with similar messenger particles. Physicists call gravitational messenger particles gravitons (graviton), but so far we have not found any trace of them. Even more frustrating is that trying to describe gravitons in quantum field theory leads to meaningless answers. "simply quantizing gravity doesn't work, which leads to mathematical inconsistencies," Mardasina said. "We need something new."

So far, a much-anticipated new theory of quantum gravity has not been discovered. A strong competitor is string theory, or "string theory family"-because string theory is actually a collection of logically self-consistent theories. The core idea of string theory is to treat elementary particles as tiny vibrating strings, which provides a way for us to bypass the mathematical problems of simple quantum gravity. As a mathematical theory which attracts many theorists for its beauty, the disadvantage of string theory is that it does not give a complete description of the world, and many physical quantities cannot be described by it. In addition, string theory has not been verified by experiments, and in fact it can not be verified. However, it is string theory that provides Mardasina with a clue to the mystery of quantum gravity: regarding gravity as an illusion produced by a quantum hologram.

Figure 2. Quantum mechanics well describes the contradiction between general relativity and quantum mechanics in the black hologram of the subatomic world, and will not cause trouble to most practical applications. Physicists usually study the large-scale world, where the quantum effect is not obvious, or the small-scale world, where particles are lighter and gravity has less influence. However, in a special case, the conflict between the two theories becomes particularly obvious: when a large amount of mass is concentrated in a small area of space, a black hole is formed. The gravity produced by black holes is so strong that even light can not escape, so when studying black holes, we can not ignore the influence of gravity. At the same time, the small scale of the black hole also means the existence of quantum effects. Therefore, in order to explain the phenomena in black holes, we do need a unified theory of quantum gravity.

Black hole is the original theoretical source of holographic principle. They have a boundary that cannot be returned, called the event horizon. Once you cross this boundary, you will be sucked into the black hole and can no longer escape. A lot of information will disappear with you when you fall into a black hole. This information includes not only your DNA and one or two of the best ideas, but also the countless combinations of blood cells in your veins and all the confusing thoughts in your head. In the world of black holes, however, things seem much simpler. Classical physics assumes that nothing can escape from a black hole and that a black hole can be fully described by only three pieces of information: its mass, charge, and speed of rotation. So, when you fall into a black hole, all the information you need will be sucked into these three parameters of the black hole-your fall makes the universe a little easier.

Figure 3. The reduced complexity of a simulated black hole set in the Milky way usually worries physicists because it violates one of the most basic laws of physics: the second law of thermodynamics. The second law of thermodynamics states that things never get easier. The total amount of information needed to describe a system is measured by a physical quantity called entropy. In classical physics, entropy is defined for thermodynamic systems, such as ice that melts under the sun. Classical entropy measures the degree to which heat (or energy) is dissipated in a system.

However, energy is related to excited atoms (in ice, water molecules are arranged orderly in a fixed lattice, while in liquid water, they move around), so entropy is also a measure of the degree of disorder in the system. The degree of disorder of the system is related to information: the periodic arrangement of water molecules in ice crystals can be described in one sentence, but for liquid water, you need to provide the exact location of each molecule, which involves a lot of information. Therefore, entropy is related to both thermodynamics and information.

The second law of thermodynamics states that entropy will never decrease. Under the condition of thermodynamics, this means that the system will strive to reach an equilibrium state where the energy is completely dissipated. In the context of information, this means that things don't automatically get easier. From a classical point of view, a black hole is not a hot object and is very simple to describe, so there should be no entropy. When you fall into a black hole, your positive entropy becomes the zero entropy of the black hole, which violates the second law of thermodynamics.

When this potential problem is noticed, some physicists have no choice but to accept the fact that the second law of thermodynamics may not be as basic as we think. However, one physicist, Jacob Beckenstein (Jacob Bekenstein), is reluctant to give up easily. In 1972, Beckenstein discovered the relationship between entropy and the properties of black holes discovered by Stephen Hawking (Stephen Hawking). Hawking has been thinking about the event horizon of a black hole, which is like an eggshell wrapped in a certain volume of space-it is a surface, and you can measure its area. Hawking has proved that the area of the event horizon will never shrink, and that no matter what you do or invest in a black hole, the event horizon will only increase, just like entropy.

Figure 4. The second law of thermodynamics paves the way for holographic principles-an analogy with thermodynamics that was initially thought of as a pure coincidence. But Beckenstein offers a controversial explanation: "Beckenstein thinks you can think of the area of the event horizon as a form of entropy," Maldasina explains. " The idea was not clear at first, but it became clearer when Hawking discovered in 1974 that black holes could radiate energy (now known as Hawking radiation). " In other words, black holes are hot objects, so they must have entropy. "combining Beckenstein's original idea with Hawking radiation, we can calculate that the entropy of a black hole is indeed equal to the area of a black hole measured on a certain scale of length, the Planck unit. Because the Planck unit is very small, the entropy of a black hole is quite large." Although a black hole occupies a three-dimensional volume of space, its information content seems to be a feature of its two-dimensional event horizon.

Holography in real life? You might think that a black hole is a very strange thing, but physicists Gerardus't Hooft and Leonard Leonard Susskind go a step further by considering the amount of information in ordinary space. Whether it is the pages of books, the neurons of the brain, or the photons transmitted through optical fiber on the Internet, the information exists in physical form. This physical form involves energy. Since energy equals mass (recall Einstein's E=mc ²), compressing information into a limited area of space is equivalent to compressing mass into it. If you try to compress too much mass / information into it, you will get a black hole, so the information content of the limited area of non-black hole space is limited. Te Hooft and Saskander calculated this limit and found that it is measured in the same way as black holes, measured by the surface area of the boundary of the region.

"it may sound very simple and childish, but in all our other descriptions of the world, variables increase with volume," Mardasina said. "for example, if we want to describe an electromagnetic field in a space, we will divide the volume into many parts and describe each part of the electromagnetic field." If you double the size of the area, you should also double the number of partitions, so the amount of information needed for your description should also be doubled. According to this intuitive idea, information should increase with the increase of volume, not with the increase of area as described by the holographic principle. If the holographic principle is correct, then our three-dimensional method of physics is wrong. We should be able to use a more streamlined version of physics, one that depends on area rather than volume. This raises the puzzling question of whether the third dimension really exists, or whether it is just an illusion, just like a three-dimensional image created in a hologram.

So far, no one has found an exact formula for the two-dimensional version of physics that describes our three-dimensional world. However, Saskander redefined string theory in 1995, centering on the holographic principle. Then in 1997, only 29-year-old Juan Mardasina came up with a detailed description of the first holographic universe in history.

The negative curve of Maldasina's universe is not entirely in line with the universe in which we actually live: it is a model, a "toy" universe with its own complete set of physical rules. Because all the physical phenomena that occur in it can be described by physical theories defined only on the boundary, the toy universe is a hologram. More importantly, in this universe, the problem between gravity and quantum mechanics has been completely solved: the theory defined on the boundary is pure quantum, it does not include gravity, but the creatures living in it can still feel gravity. In this universe, gravity is only part of the hologram illusion.

In order to understand Maldasina's toy world, we first need to understand the world of map making. In order to show the sphere on a flat piece of paper, we need to cut the sphere and flatten it, which inevitably introduces some distortion. In the traditional Mercator projection of the earth, this distortion is most serious near the poles. When you look at the map, Greenland looks as big as Africa, but in fact it is more than 14 times smaller. In addition, if you project the shortest path from London to Sydney on a map, what you get is not a straight line, but a curve. On such a map, the straight line does not correspond to the shortest path.

Figure 5. The Mercator projection of the earth. Red discs actually have the same area, but their different sizes on the map illustrate the distortion of the map. MC Escher's famous woodcut "Circle Limit III" shows a two-dimensional version of the Maldasina universe. Similar to the Mercator projection, there is some distortion here. In Escher's map, the shortest route between two points is not the straight line that connects them, but an arc that intersects at right angles to the boundary circle of the disk.

Figure 6. MC Escher's "circle limit III". The shortest path is expressed in white. If you use this new metric to measure the size of fish, you will find that, contrary to their appearance, they do not get smaller and smaller as they approach the boundary circle. They are actually equal in size. Just as travelers walking on the surface of the earth will not realize the distortion shown by the Mercator projection, people living in this so-called hyperboloid world will never notice any distortion in the size of the fish. More importantly, in order to reach the boundary circle, the hyperbola must pass through an infinite number of copies of fish of the same size. In other words, it will have to span infinite distances. For a hyperbola, the boundary circle is infinitely far away.

Unlike hyperboloid maps, a "real" hyperboloid is almost impossible to draw because it is seriously distorted. The hyperboloid has what mathematicians call negative curvature. This small area of the "plane" looks like a saddle: in one direction, they look like the summit of a ridge; in the other direction, they look like the bottom of a valley.

For external observers like us, this strange two-dimensional world has an interesting feature: although according to the new metrics, their range is infinite, but we can see their boundaries-- which is exactly what we need to apply the holographic principle, which describes the interior of the space region according to the boundary. In Mardacina's cosmic model, he used a hyperboloid three-dimensional simulation plus as the fourth dimension of time to form a model called Anti de Sitter space, named after the Dutch physicist William de Sitter.

Toy physics anti-de Siddhi space is very different from the world we actually live in, where time and space are distorted in strange ways, but this does not prevent us from creating a set of physical rules for it. What you need are basic concepts, such as elementary particles and forces, and the mathematical laws that describe their interaction. Mardacina uses a version of string theory to describe the physical phenomena in his model universe. As you remember, string theory includes quantum mechanics and gravity, so creatures living in Mardacina's model universe will feel gravity in a way similar to ours.

Figure 7. A key discovery of the holographic universe Mardasina is that the string theory that describes the interior of the universe leaves a "shadow" on the boundary of the universe: you can define a quantum field theory on the boundary. so that every elementary particle in the interior has a corresponding particle on the boundary, and every interaction between the internal elementary particles precisely corresponds to the interaction between the boundary particles. Now you can completely use the boundary theory to describe, for example, the act of throwing an apple inside. This means that you can even completely ignore the inner world without losing any information-the world is a real hologram.

From the point of view of quantum gravity, the key is that the theory on the boundary is a very familiar quantum theory of particle physics, which is very similar to the theory used to describe the process of subatomic particles in nature. They only involve small scales, so they do not include gravity. However, the quantum theory on this boundary can fully describe the mysterious theory of quantum gravity in the inner world. This is the first time that we have been able to describe a quantum spacetime completely.

But what does it mean to us? So far, Mardasina's model is just a model. We don't know whether the universe we live in is a hologram, and we still don't have a consistent quantized description of gravity that applies to our world. The assumption of negative curvature in the Mardasina model is very important, but our universe shows a slight positive curvature in the observations. "We don't know if there is a similar description in the case of positive curvature," says Mr Mardasina. "people are exploring ideas, but we don't have a complete answer yet."

But what does it mean if it turns out that the holographic principle does apply to the world we live in? Does this mean that we and time and space are just an illusion? "Yes, you can say that we are an illusion or an emerging phenomenon," Mardasina said. If we live in such a universe, then in a sense we are actually some kind of approximate description. But this is not a new concept in physics. Take the lake as an example, it looks like a well-defined surface on which insects can walk. But if you look at it with a powerful enough microscope, you will see that there are molecules moving around and there is no clearly defined surface. The situation may be similar for time and space, it is not clearly defined in an absolute sense, but we are too big to be aware of it. Like insects on the lake, our eyes for observing the world are too rough to reveal the true nature of time and space. Ignorance is bliss, and although it is fun to explore the philosophical aspects of things, from a daily practical point of view, it may not matter whether we live in holograms or not. "

However, for Maldasina himself, does he really believe that the holographic principle is true? He responded: "well, I think of this idea as a model, but it is a model that gives a complete mathematical description of quantum space-time. Therefore, we should take it seriously until someone refutes it or comes up with a better idea."

Author: Marianne Freiberger

Translation: K.Collider (

Revision: Xiao Cong

Original link: The illusory Universe

This article comes from the official account of Wechat: Institute of Physics, Chinese Academy of Sciences (ID:cas-iop), author: M. Freiberger

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