Discussion on the inherent law of lottery when we flip a coin, roll a dice and turn a roulette wheel, we can't find the law, so we say it is random, thus establishing the probability theory. Since then, under the cloak of science, human beings have once again demonstrated their arrogance and ignorance!

Fate is predestined.

Author ian stewart [from New Scientist Weekly]

All natural things are unsolved art of human beings.

All accidents have an invisible direction.

All disharmony is an incomprehensible harmony.

All small evils are another manifestation of great goodness.

Alexander pope.

Humans are very good at discovering laws. This ability is one of the cornerstones of science. When we find a law, we will try to formulate it and then apply this formula to help us understand the world around us. If we can't find the law, we will not attribute it to ignorance, but to another concept that we especially like to use. We call it randomness.

Randomness in traditional ideas

When we toss coins, dice and turn roulette, we can't find the rules, so we say they are random. Until recently, we have not found the laws of weather changes, epidemic outbreaks or liquid turbulence, which we also call random. In fact, there is another solution to "randomness": it may have inherent laws, or it may just reflect human ignorance. When we study the activities in the real world, we will unconsciously think that they are either regular or random. Is the weather really random or regular? Is the number of dice rolled random or certain? Physicists regard randomness as the absolute basis of micro-science of quantum mechanics: they think that no one can predict when radioactive atoms will decay. But if this is true, what triggered this incident? How do atoms "know" when they should decay? To answer these questions, we must find out what kind of randomness we are discussing. Is it the real essence of reality, or is it an illusion that reflects how we simulate reality? Let's start with the simplest concept. If what a system does next is not determined by its previous decision, then it can be said that the system is random. For example, there is a completely "symmetrical" coin that has been thrown six times in a row, all heads. The probability of head and back appearing for the seventh time is still 50-50. Conversely, if what a system has done before has a foreseeable impact on the future, then the system is regular. In less than a second, we can predict the sunrise tomorrow morning, and every morning, we are proved right. So, the result of flipping a coin is random, but sunrise is not. The regularity of sunrise comes from the geometric regularity of earth orbit. The statistical law of random coins is much more complicated. Experiments show that if the coin is symmetrical, in the long run, the probability of the front and the back will eventually be equal. In the long run, the probability of the coin appearing on both sides is finally equal, which is a pure statistical phenomenon after a large number of throwing. A deeper question-and the answer is even more confusing-is: How do you "know" that when a coin falls, there should be as many heads as tails? When people study this problem more deeply, they will get the answer: coins are not a random system at all.

Randomness and disorder

We can use a thin disk as a model of a coin. If the wafer is thrown vertically, the speed is known and the rotation speed is known, we can calculate the exact number of revolutions before the wafer stops landing. If the disc is bounced, the calculation may be more difficult, but in theory, we should be able to calculate the result. Coin toss is a classic mechanical system. It also follows the laws of motion and gravity, making the orbits of planets predictable. In that case, why is the movement of coins unpredictable? Obviously, it is possible in theory. But in practice, you can't know the speed at which the coin is thrown or rotated, and both of them have a decisive role in the final result. From the moment the coin was thrown-regardless of the influence of wind speed, travel distance and other external factors-its fate was decided. But because people don't know the speed of throwing or spinning, even if your calculation speed is faster, the inevitable fate of coins is still unknown. So is the dice. It can be simplified as a jumping cube, and its behavior is mechanical and dominated by deterministic factors. However, there is another dimension to this problem. The unpredictability of the rolling process of dice lies not only in the unknown initial situation, but also in the uniqueness of its movement: its movement is disorderly. Disorder is not random, but the limitation of human measurement accuracy, which means it is unpredictable. In stochastic systems, what happened in the past has no influence on the future; In a disordered system, what happened before has an impact on the future, but the results obtained according to various factors will become fallacies because of some minimal observation errors. The first slight error will develop rapidly in the process of movement, which will eventually lead to a far cry from the truth. The coin thrown out is slightly similar to this one: if the error between the initial speed and the rotational speed is large enough, we will not be able to predict the result correctly. But the coin is not really out of order, because the initial error develops slowly when the coin rotates in the air. In a truly disordered system, small errors will develop rapidly in geometric series. When the regular cube bounces off the flat table, the edges and corners of the dice begin to play a role, causing changes that develop in geometric series. So the seemingly random dice are caused by two reasons: like coins, people don't know its initial state; Its disorderly (but definite) movement.

exemplary deportment

So far, everything I have said is based on the selected mathematical model. So, does the model chosen by people determine the randomness of a physical system? To answer this question, let's take a look at the first great achievement of stochastic model in physics: statistical mechanics. This theory supports thermodynamics-gas physics. The demand for making more efficient steam engines has promoted the development of this discipline to some extent. How efficient can a steam engine be? Thermodynamics gives a very clear boundary. In the early development of thermodynamics, people paid attention to several macro variables, such as volume, pressure, temperature and heat. The so-called "gas law" relates these variables. For example, Boyle's law holds that the pressure of a certain mass of gas is inversely proportional to its volume at a certain temperature. This law is completely certain: knowing the volume can calculate the pressure, and vice versa. However, people soon found that the movement of gas at the micro level was accidental: gas molecules collided irregularly with each other. Ludwig boltzmann was the first person to study the relationship between molecular collision and gas law (and many other laws). His theory uses tiny hard spheres as the model of gas molecules, and draws the conclusion that several classical variables-pressure, volume and temperature-are expressed as the statistical average of assumed inherent random motion. But is this assumption reasonable? Just as the movements of coins and dice are basically certain, a system composed of many tiny hard spheres should also be certain, because each sphere obeys the laws of mechanics. If the initial position and velocity of each sphere are known, then the subsequent motion is completely determined. But Boltzmann did not try to explore the exact path of each sphere, but assumed that the position and velocity of all spheres followed a statistical law and would not tend to any trend. For example, under the assumption that all spheres are equally likely to move in any direction, pressure is a measure to mark the average force when these spheres collide with the inner wall of their containers. Statistical mechanics expresses the deterministic motion of a large number of spheres in statistical sense, such as average value. In other words, it uses stochastic model at the micro level to prove the deterministic model at the macro level. Is this reasonable? This is reasonable, although Boltzmann didn't know it at the time. He actually asserted two things: the motion of the sphere is disorderly; This is a special disorder situation, which finally shows a certain average state. The conversion of arguments is very interesting. An initial deterministic model (gas law) is based on a stochastic model (tiny sphere), and randomness is recognized as the logical result of deterministic motion. So, is the gas random? It all depends on your perspective. Some angles are best to use statistical models, and some angles should use deterministic models. There is no answer to this question, it depends on the specific situation. So we have two different models, and there is some mathematical relationship between them. Both models are unrealistic, but they both describe reality properly. It seems meaningless to discuss whether reality is random: randomness is a mathematical feature of people's thinking methods about a system, not the system itself. Fundamentals of quantum mechanics

So, is nothing really random? We can't be sure until we know the nature of the quantum world. In the usual explanation, quantum mechanics thinks that at the subatomic level, the universe is absolute and purely random. The "hidden variable"-whose disorderly but definite behavior dominates the fate of quantum dice-does not exist. Quantum is random, that's all. Is that really the case? Of course, this judgment has a mathematical basis. In 1964, john bell proposed a method to detect whether a quantum is random or dominated by a hidden variable, which is a quantum property that we still don't know how to observe. Bell's work center is to separate two interacting quantum particles, such as electrons, far away. Through a series of special measurements on these two particles which are far apart, people can determine whether their properties are based on randomness or dominated by hidden variables. This answer is very important: it determines whether the two quantum systems that interacted before can affect each other's properties in the future-even if they are at two ends of the universe. Most physicists believe that experiments based on Bell's work prove that randomness-and odd "long-distance interaction"-plays a leading role in quantum systems. However, some scientists believe that Bell involved some vague premises in his proof, that is, something that has not been generally recognized. Therefore, there is still room for clear explanation of quantum randomness. Quantum mechanics will not change much because of deterministic theory, just as hard balls have not changed thermodynamics. But it can give us a new understanding of many puzzling problems. It will also make quantum theory return to the ranks of other statistical sciences: accidental in some ways and certain in some ways. Aside from quantum theory, we can say with certainty that there is no so-called randomness in reality. In fact, all seemingly random phenomena are not due to the unpredictability of nature itself, but to human ignorance or other restrictions on the process of understanding the world. This theory is not new. Alexander pope wrote in his "On Man": "All natural things are human unsolved art/all accidents, with invisible directions/all discordant, incomprehensible harmony/all minor evils, which is another representation of great goodness." Now, apart from the sentence about good and evil, mathematicians have clearly understood how correct he is.