Is God rolling dice?

"In any case, I am convinced that God will not roll the dice." Over the years, Einstein's words have become a symbol of his opposition to quantum mechanics and its randomness, but people actually misunderstood him.

"God doesn't roll the dice"-Einstein's famous saying is rarely quoted so much. People naturally take this famous saying as evidence that he categorically denies quantum mechanics, because quantum mechanics regards randomness as an inherent attribute of the physical world.

In the public mind, the story is like this. Einstein refused to accept the fact that some things are uncertain-they happen when they happen, and people can never find the reason. Among his contemporaries, he is almost the only one who still holds this belief: he firmly believes that the universe is classical physics, ticking mechanically like a clock, and every moment determines the next. This dice line symbolizes the other side of his life: the physical revolutionary who put forward the theory of relativity sadly became a conservative, and he was "behind the times" in quantum theory, just as niels bohr commented.

However, over the years, many historians, philosophers and physicists have questioned this story. After studying Einstein's original words, they found that Einstein's thinking about indeterminism was far more radical and nuanced than most people thought. Don A. Howard, a historian at the University of Notre Dame in the United States, said, "It has become our mission to correctly understand this matter. "After digging deep into the literature, we see that the facts are completely different from the general narrative, which is surprising." As he and others have proved, Einstein actually admitted the uncertainty of quantum mechanics-and it should be, because he discovered the uncertainty in quantum mechanics. What he can't accept is that indeterminism is the basic principle of nature. Indeterminism implies that there is a deeper physical reality in all aspects, which cannot be explained by quantum theory. Einstein's criticism is not mysterious. On the contrary, some scientific problems he is concerned about have not been solved yet.

Whether the universe is like a clockwork or a dice table touches the core of physics. In our view, physics is to find hidden simple principles in the complicated nature. If something happens for no reason, it means that our rational exploration has reached its limit here. "If uncertainty is a basic principle, it will mean the end of science," said Andrew S. Friedman, a cosmologist at MIT, worriedly.

But philosophers in history have assumed that indeterminism is a prerequisite for human free will. Either we are all gears in the clockwork, then everything is doomed; Either we are the masters of our own destiny, then the universe is not deterministic after all. It is of great practical significance to distinguish this binary opposition, which can help the society decide how much responsibility people should bear for their actions. In our legal system, the assumption of free will can be seen everywhere: to accuse a person of a crime, he must be intentional. To this end, the court has been trying to determine whether the defendant is innocent or not, whether it is only driven by insanity, the impulse of teenagers or the degenerate social background.

However, when people talk about binary opposition, they usually try to prove it wrong. In fact, many philosophers think it is meaningless to argue whether the universe follows determinism or indeterminism, because it depends on the size or complexity of the object of study: particles, atoms, molecules, cells, organisms, ideas and communities. "The difference between determinism and indeterminism depends on a specific level," said Christian Liszt, a philosopher at the London School of Economics and Political Science. "If a certain level is certain, it is uncertain at both higher and lower levels." The movement pattern of atoms in the brain is completely certain, but we can still enjoy the freedom of action because atoms and initiative operate at different levels. Similarly, Einstein is also trying to find a kind of determinism at the quantum level, while ensuring that the quantum level is still probabilistic.

1. What did Einstein object to?

How Einstein was labeled as "anti-quantum mechanics" is as great a mystery as quantum mechanics itself. The concept of "quantum"-a discontinuous energy unit-was the crystallization of his thought in 1905, but in fact, in the following 15 years, he was the only one who supported the idea of energy quantization. Einstein put forward the basic characteristics of quantum mechanics, which is generally accepted today. For example, light can behave like particles and waves, while Erwin Schr?dinger? The most commonly used expression of quantum theory established by Schrodinger in the 1920s is also based on Einstein's thinking on wave physics. Einstein was not against quantum mechanics, nor against randomness. In 19 16, he proved that when an atom emits photons, the emission time and angle are random. "This is just the opposite of Einstein's public image of opposing randomness," said Jan von Plato, a philosopher at the University of Helsinki.

But Einstein and his contemporaries are faced with a serious problem: quantum phenomena are random, while quantum theory is not: Schrodinger equation 100% obeys determinism. This equation uses the so-called "wave function" to describe a particle or system, which embodies the wave nature of particles and explains the possible waveforms of particle groups. Equation can predict every moment of wave function with complete certainty. Schrodinger equation is more definite than Newton's law of motion in many aspects: it will not cause chaos, such as singularity (the physical quantity becomes infinite, so it cannot be described) or chaos (the motion is unpredictable).

The tricky thing is that the certainty of Schrodinger equation is the certainty of wave function, but the wave function is not directly observable like the position and velocity of particles. It only clarifies which physical quantities can be observed and the possibility of each result being observed. Quantum theory does not answer the question of what wave function is and whether it can be considered as true wave. Therefore, whether the randomness we observe is the intrinsic essence of nature or the superficial phenomenon remains to be solved. "People say that quantum mechanics is uncertain, but it is too early to draw this conclusion," said Christian Wüthrich, a philosopher at the University of Geneva in Switzerland.

Werner Heisenberg, another pioneer of early quantum mechanics, imagined the wave function as a fog, which covered some physical reality. If the position of a particle cannot be accurately found by the wave function, it is actually because it is not anywhere. Only when you observe a particle will it exist somewhere. The wave function may have been scattered in a huge space, but at the moment of observation, it suddenly collapsed to a peak somewhere, so particles appeared here. When you observe a particle, it no longer shows certainty, but suddenly jumps to a certain result, just like a child grabbing a seat in a chair game. No law can govern the collapse, no equation can describe the collapse, it just happened, that's all.

Wave function collapse is the core of Copenhagen explanation, which is named after Bohr and the city where his research institute is located, and Heisenberg also completed most of his early work here (ironically, Bohr himself never accepted the view of wave function collapse). The Copenhagen school regards the randomness observed as the surface property of quantum mechanics, which cannot be further explained. Most physicists accept this statement only because of the psychological "anchoring effect": this explanation is good enough and the earliest one.

Although Einstein did not oppose quantum mechanics, he certainly opposed the Copenhagen interpretation. He doesn't like the idea that measurement will make the physical system constantly evolve and jump, which is the background that he began to question "God rolls the dice". "Einstein regretted such specific problems in 1926, but he did not metaphysically assert that determinism must be the absolute necessary condition for quantum mechanics," Howard said. "He paid special attention to whether the collapse of wave function caused discontinuity."

Einstein thought that wave function collapse could not be a real process. This requires a certain instantaneous action at a distance-some mysterious mechanism-to ensure that the left and right sides of the wave function collapse to the same peak, even if there is no external force. Not only Einstein, but also every physicist of his time thought that such a process was impossible, because it would exceed the speed of light and obviously violate the theory of relativity. In fact, quantum mechanics doesn't give you the chance to roll the dice freely at all. It lets you roll the dice in pairs, and the points of the two dice are always the same, even if you roll one dice in Las Vegas and the other rolls the other in Vega. For Einstein, this obviously means that the dice contain some hidden properties and their results can be corrected in advance. However, the Copenhagen school denies the existence of similar things and suggests that dice can really interact in distant space.

The magic of measurement endowed by Copenhagen School further troubled Einstein. What exactly is measurement? Can only a conscious life or a tenured professor measure it? Heisenberg and other Copenhagen scholars failed to explain this point in detail. Some people think that our observations create reality-this idea sounds poetic, but it may be a bit too poetic. The Copenhagen school thinks that quantum mechanics is complete and the ultimate theory that will never be replaced, but Einstein thinks this idea is too frivolous. He regards all theories, including his own, as stepping stones to higher theories.

2. random thoughts

Einstein believes that if we grasp the problem that Copenhagen School can't explain, we will find that quantum randomness, like all other types of randomness in physics, is the result of some deeper processes behind it. Einstein believed that the dust flying in the sun exposed the complex motion of invisible air molecules, and the process of photon emission by radioactive nuclei was similar. Then quantum mechanics may be just a rough theory, which can explain the overall behavior of the basic components of nature, but the resolution is not enough to explain individuals. A deeper and more complete theory may fully explain this movement without introducing any mysterious "jumping".

According to this view, the wave function is a collective description, just like saying that if a fair dice is thrown repeatedly, each face should be roughly the same number of times. Wave function collapse is not a physical process, but the acquisition of knowledge. If a six-sided dice is rolled, the upward side is 4, then the possibility of 1 pair 6 will "collapse" to the actual result, that is, 4. If there is an omnipotent devil who has the ability to track all the tiny details that affect the dice-the precise way you roll the dice on the table-it will never describe the process as "collapse".

Einstein's intuition comes from his early work on molecular collective effect, which belongs to a branch of physics called statistical mechanics, in which he proved that physics can be probabilistic even if the reality behind it is deterministic. 1935, Einstein wrote to the philosopher karl popper: "In your paper, you suggested that it is impossible to draw statistical conclusions from a deterministic theory, but I think you are wrong. Just consider classical statistical mechanics (gas theory or Brownian motion theory). "

The probability in Einstein's eyes is as objective as that in Copenhagen's interpretation. Although they do not appear in the basic laws of motion, they show other characteristics of the world, so they are not the products of human ignorance. Einstein gave an example in his letter to Popper: a particle moving in a uniform circle, and the probability that the particle appears on an arc reflects the symmetry of the particle trajectory. Similarly, the probability that the dice face up is one in six, because all six faces are the same. "He knows that the details of probability in statistical mechanics contain great physical significance. In this respect, he really knows better than most people in that era. " Howard said.

Another inspiration of statistical mechanics is that the physical quantities we observe do not necessarily exist at a deeper level. For example, a mass of gas has a temperature, but a single gas molecule does not. Through analogy, Einstein began to believe that a "quantum theory" should be significantly different from quantum theory. He wrote in 1936: "There is no doubt that quantum mechanics has grasped the wonderful corner of truth ... but I don't believe that quantum mechanics is the starting point for finding basic principles, just as people can't start from thermodynamics (or statistical mechanics) to find the basis of mechanics." In order to describe the deeper level, Einstein tried to find a unified field theory, in which particles will be derived from structures completely different from particles. In a word, the traditional view misunderstood Einstein, and Einstein did not deny the randomness of quantum physics. He tried to explain randomness instead of eliminating it through explanation.

3. Hierarchical structure

Although Einstein's overall plan failed, his basic intuition about randomness still holds: indeterminism can be deduced from determinism. Quantum and sub-quantum energy levels-or other paired energy levels in nature-all contain unique structures, so they also obey different laws. The laws governing one level can allow true randomness, even if the laws of the next level are completely orderly. "The microphysics of determinism will not lead to the macrophysics of determinism," said Jeremy butterfield, a philosopher at Cambridge University.

Consider an atomic dice. Its atomic structure can have countless possibilities, which cannot be distinguished by the naked eye. When you roll the dice, if you trace any structure, you will observe a specific result, which is completely certain. Some configurations will cause the die 1 to face up, some other configurations will cause the die 2 to face up, and so on. Therefore, a single macro condition (thrown) can lead to many possible macro results (one of the six faces is facing up). "If we describe dice at the macro level, we can regard it as a stochastic system that allows probability to exist objectively." Liszt, who studies hierarchical participation with mathematician Marcus Pivato of Sergey-Pontoise University, said.

Although the higher level is constructed (in terminology, it is "attached" to the lower level), it operates independently. In order to describe dice, you need to work hard at the level of dice, and when you do, you can only ignore atoms and their dynamics. If you jump from one level to another, then you have a "category error", in the words of David Z. Albert, a philosopher at Columbia University, just like asking about the political position of tuna sandwiches. "If there is a phenomenon that can be described at multiple levels, then we should be very cautious in concept to avoid confusion at different levels." Liszt said.

Hierarchical logic also works in reverse: the micro-physics of indeterminism can lead to the macro-physics of determinism. The atoms that make up baseball move randomly, but the trajectory of baseball is completely predictable because the quantum randomness is averaged out. Similarly, molecules in gas have complex motions (which are actually uncertain), but the temperature and other characteristics of gas can be described by very simple laws. There is even bolder speculation: some physicists, such as Robert Labrin of Stanford University, think that lower energy levels are completely irrelevant. No matter what the basic components are, they can have the same collective behavior. After all, systems as diverse as molecules in water, stars in galaxies and cars on highways obey the laws of fluid motion.

When you think from a hierarchical perspective, the worry that indeterminism marks the end of science disappears. There is no wall around us that separates the whole universe that obeys the laws of physics from other parts that don't. On the contrary, the world is a layered cake composed of determinism and indeterminism, and human beings exist in this layered cake. Even if all the behaviors of particles are doomed, our choices can still be completely decided by ourselves, because the low-level laws governing particle behaviors are different from the high-level laws governing human consciousness. This view solves the dilemma between determinism and free will. ?

In fact, Howard thinks Einstein would be happy to consider indeterminism as long as his questions can be answered-for example, if someone can clearly explain what measurement is, how particles can stay related without distance. There are some signs that Einstein did not take determinism as the primary requirement: he asked the determinism theory explained by Copenhagen to explain the above two problems, and rejected these alternative theories. Another historian, Arthur Fine from the University of Washington, thinks that Howard exaggerated Einstein's acceptance of indeterminism, but compared with the story of craps that was misunderstood by several generations of physicists, Fine thinks that Howard's idea is more valid.