By studying the mysterious characteristics of black holes, physicists have deduced the absolute limit of the amount of information that a certain part of space or a certain amount of matter and energy can contain. Relevant research results show that our universe may not be the three-dimensional space we imagined, but it may be some kind of holographic figure written on a two-dimensional surface. Our three-dimensional cognition of the daily world is either a metaphysical illusion or one of two ways to observe reality. A grain of sand may not contain the whole universe, but flat panel displays may.
The founder of orthodox information theory is Shannon, an American applied mathematician. He published a series of groundbreaking papers in 1948, and the concept of entropy introduced is now widely used in the measurement of information. Entropy has always been the core concept of thermodynamics (a branch of physics that studies heat). Entropy in thermodynamics is usually used to characterize the disorder degree of physical systems. 1877, the Austrian physicist Boltzmann put forward a more accurate description: under the condition of keeping the macroscopic characteristics unchanged, all possible different microscopic states of particles contained in a mass of matter are entropy. For example, the indoor air around you, you can calculate all possible distribution patterns and all possible motion patterns of a single air molecule.
When Shannon tried to quantify the information in the information, he naturally proposed the same formula as Boltzmann. Shannon entropy of a message is the number of bits required to encode the message. Shannon entropy can't tell us the value of a message, because the latter mainly depends on the context. However, as an objective information measure, Shannon entropy has been widely used in science and technology. For example, the design of any modern communication facilities-mobile phones, modems, CD players, etc. -inseparable from Shannon entropy.
Conceptually, thermodynamic entropy and Shannon entropy are equivalent: the number of different composition modes represented by Boltzmann entropy reflects Shannon information that must be known in order to realize a certain composition mode. But there are still some subtle differences between these two entropies. First of all, the unit of thermodynamic entropy used by chemists or refrigeration engineers is energy divided by temperature, while Shannon entropy used by communication engineers is expressed in bits, which is essentially unitless. This difference is entirely a matter of habit.
Even if the same unit is used, there is still a huge difference between the two entropy values. For example, the Shannon entropy of a silicon wafer with 1G data is about 10* 10 bits (1 byte equals 8 bits), which is much smaller than the thermodynamic entropy of the chip at room temperature, which is about 10*23 bits. This difference comes from the different degrees of freedom considered when calculating two entropies. A degree of freedom refers to a variable, such as a coordinate representing the position or velocity component of a particle. The Shannon entropy of the above chip only cares about the state of all transistors etched on the silicon crystal, regardless of whether the transistors are on or off; It is either 0 or 1, which is a single binary degree of freedom. On the other hand, thermodynamic entropy depends on the state of billions of atoms (and their surrounding electrons) contained in each transistor. With the development of miniaturization technology, one atom can store one bit of information in the near future. By then, the Shannon entropy of microchip will be close to the thermodynamic entropy of its material in order of magnitude. When these two kinds of entropy are calculated with the same degree of freedom, they will be exactly the same.
So is there a limit to the degree of freedom? Atoms are composed of nuclei and electrons, nuclei are composed of protons and neutrons, and protons and neutrons are composed of quarks. Today, many physicists think that electrons and quarks are only excited States of superstrings, and they think superstrings are the most basic entities. However, the rise and fall of physics in the past century tells us that we can't be so arbitrary. The structural levels of the universe may be much more than today's physics dreams.
Without knowing the final composition of a mass or its deepest structure, we can't calculate its final information capacity or its thermodynamic entropy. This deepest structural level can be called X-layer. (This uncertain description has no problem in actual thermodynamic analysis. For example, when analyzing an automobile engine, quarks in atoms can be ignored, because they will not change state in a relatively mild environment like the engine. According to the rapid development of miniaturization technology, it is conceivable that quarks can be used to store information in the future, perhaps one quark and one bit. How much information can a cubic centimeter store by then? What if superstrings or deeper structures can be further used to store information? Surprisingly, in the past 30 years, the achievements in the field of gravitational physics have provided some clear answers to these seemingly abstruse questions. The central role of these achievements is the black hole. Black holes are the product of general relativity (the theory of gravitational geometry put forward by Einstein in 19 15). According to this theory, gravity comes from the distortion of time and space, which makes objects move like a force pushing them. On the contrary, the existence of matter and energy leads to the distortion of time and space. According to Einstein's equation, a mass of matter or energy dense enough can bend space-time to the extreme degree of tearing, and then a black hole is formed. At least in the field of classical (non-quantum) physics, relativity determines that any matter that enters a black hole can no longer escape from it. This point with no turning back is called the horizon of a black hole. In the simplest case, the horizon is a sphere, and the larger the black hole, the larger the surface area of the sphere.
It is impossible to explore the inside of a black hole. No specific information can escape to the outside world through the horizon. However, before entering the black hole and disappearing forever, a mass of matter can still leave some clues. Its energy (according to Einstein's equation E = MC 2, any mass can be converted into energy) will be reflected as the increment of black hole mass without exception. If it rotates around a black hole before being captured by it, its angular momentum will be added to the angular momentum of the black hole. The mass and angular momentum of a black hole can be measured by the influence of the black hole on the surrounding space-time. In this way, black holes also obey the conservation criteria of energy and angular momentum. But another basic law, the second law of thermodynamics, seems to be broken.
The second law of thermodynamics is a summary of the commonly observed phenomenon: most processes in nature are irreversible. After the cup was broken from the table, no one saw the fragments bounce back to form a complete cup. The second law of thermodynamics forbids the occurrence of these inverse processes. It points out that the entropy of isolated systems will never decrease; Entropy remains unchanged at most, and in most cases the entropy value increases. This law is the core of physical chemistry and engineering, and it is considered to have the greatest influence on other fields except physics.
As Wheeler first pointed out, when a substance disappears in a black hole, its entropy seems to disappear forever, and the second law of thermodynamics seems to be invalid at this time. The clue to solve this puzzle first appeared in 1970. Christodoulou (who was Wheeler's graduate student at Princeton University at that time) and Stephen W. Hawking of Cambridge University in England independently proved that the final total surface area of the horizon will not decrease in many different processes (such as the merger of black holes). Hawking put forward the theory that the entropy of a black hole is proportional to the surface area of its event horizon in 1972 by comparing this property with the characteristic that entropy tends to increase. According to his speculation, after the matter falls into a black hole, the increase of the entropy value of the black hole can always compensate or overcompensate the entropy of the "loss" of the matter. More broadly, the sum of the entropy value of a black hole and its ordinary entropy value will never get smaller. This is the generalized second law (GSL for short).