Talk about quantum physics

A brief history of quantum physics and its development

Although quantum mechanics was founded to describe the abstract atomic world far from our daily life experience, it has a great influence on daily life. Without quantum mechanics as a tool, chemistry, biology, medicine and other key disciplines will not make fascinating progress. Without quantum mechanics, there would be no global economy, because the electronic revolution, as a product of quantum mechanics, has brought us into the computer age. At the same time, the photonics revolution has brought us into the information age. The masterpiece of quantum physics has changed our world, and the scientific revolution has brought good news and potential threats to the world.

Perhaps the following information can best describe the unique position of this crucial but elusive theory: quantum theory is the most accurately tested theory and the most successful theory in the history of science. Quantum mechanics deeply troubled its founder. However, until today, when it is expressed in a universal form in essence, some scientific elites are still dissatisfied with its foundation and basic explanation, although they admit its great power.

Max Planck put forward the concept of quantum 100 years ago. In his classic paper on thermal radiation, Planck assumes that the total energy of a vibration system cannot change continuously, but jumps from one value to another in discontinuous energy sub-forms. The concept of energy quantum was so radical that Planck later shelved it. Later, Einstein realized the potential significance of light quantization in 1905 (an extraordinary year for him). But the concept of quantum is so bizarre that there is almost no fundamental progress later. The foundation of modern quantum theory was established by a new generation of physicists in more than 20 years.

Quantum physics actually includes two aspects. One is the material theory at the atomic level: quantum mechanics, which is the reason why we can understand and manipulate the material world; The other is quantum field theory, which plays a completely different role in science.

Old quantum theory

The fuse of quantum revolution is not the study of matter, but the radiation problem. The specific challenge is to understand the spectrum of blackbody (that is, some hot objects) radiation. People who bake too much are familiar with the phenomenon that a hot object will glow, and the hotter it is, the brighter it will be. The spectral range is very wide. When the temperature rises, the peak of the spectrum moves from the red line to the yellow line and then to the blue line (which we can't see directly).

It seems that combining the concepts of thermodynamics and electromagnetism can explain the shape of the spectrum, but all attempts have ended in failure. But Planck assumes that the energy of light radiated by vibrating electrons is quantized, and thus an expression is obtained, which is completely consistent with the experiment. But he is also fully aware of the absurdity of the theory itself, as he later said: "Quantization is just a desperate practice".

Planck applied his quantum hypothesis to the oscillator energy on the radiator surface. Without the rookie Albert Einstein, quantum physics might stop here. In 1905, he did not hesitate to conclude that if the energy of the oscillator is quantized, then the energy of the electromagnetic field that produces light should also be quantized. Although Maxwell's theory and authoritative experiments for more than a century show that light fluctuates, Einstein's theory still contains the particle behavior of light. The photoelectric effect experiments in the following ten years show that light energy can only be absorbed if it reaches a certain discrete order of magnitude, just like being carried by particles. The wave-particle duality of light depends on the focus of your observation, which is one of the headache examples throughout quantum physics and has become a theoretical problem in the next 20 years.

The radiation problem contributed to the first step towards quantum theory, and the material paradox contributed to the second step. As we all know, atoms contain particles with positive and negative charges, and different charges attract each other. According to the electromagnetic theory, the positive and negative charges will spiral together and radiate light with a wide spectrum until the atom collapses.

Then, another rookie, niels bohr, took a decisive step. In 19 13, Bohr put forward a radical hypothesis: the electrons in an atom can only be in a stationary state including the ground state, and the electrons jump between the two stationary states to change their energy, and at the same time emit light with a certain wavelength, and the wavelength of light depends on the energy difference between the stationary states. Combining the known laws with this strange hypothesis, Bohr solved the problem of atomic stability. Bohr's theory is full of contradictions, but it provides a quantitative description of the spectrum of hydrogen atoms. He realized the success and shortcomings of his model. With amazing foresight, he called a group of physicists to create new physics. It took a generation of young physicists 12 years to finally realize his dream.

At first, attempts to develop Bohr's quantum theory (traditionally known as the old quantum theory) failed repeatedly. Then a series of developments completely changed the way of thinking.

Quantum history of mechanics

1923, Louis de Broglie proposed in his doctoral thesis that the particle behavior of light and the fluctuation behavior of particles should exist correspondingly. He related the wavelength of particles to momentum: the greater the momentum, the shorter the wavelength. This is a fascinating idea, but no one knows what the fluctuation of particles means or what it has to do with the atomic structure. However, De Broglie's hypothesis is an important prelude, and many things are about to happen.

In the summer of 1924, another prelude appeared. Satyendra N. Bose put forward a new method to explain Planck's radiation law. He regards light as a gas composed of particles (now called photons) without (static) mass, and does not follow the classical Boltzmann statistical law, but follows a new statistical theory based on the indefiniteness (i.e. isotropy) of particles. Einstein immediately applied Bose reasoning to the actual gas with mass, and thus obtained a distribution law describing the number of particles in gas relative to energy, namely the famous Bose-Einstein distribution. However, under normal circumstances, the old and new theories will predict the same behavior of atomic gases. Einstein was no longer interested in this aspect, so these achievements were shelved for 10 years. However, its key idea-particle isotropy is extremely important.

Suddenly, a series of events followed, which finally triggered a scientific revolution. 1 month 1925 to 1 month 1928:

Wolfgang Pauli put forward the principle of incompatibility, which laid a theoretical foundation for the periodic table.

Werner Heisenberg, Max Born and pascual Jordan put forward the first version of quantum mechanics-matrix mechanics. People finally gave up the historical goal of understanding the movement of electrons in atoms by systematically sorting out the observable spectral lines.

Irving Schrodinger proposed the second form of quantum mechanics, wave mechanics. In wave mechanics, the state of the system is described by the solution of Schrodinger equation-wave function. Matrix mechanics and wave mechanics seem contradictory, but they are essentially equivalent.

Electrons have been proved to follow a new statistical law, Fermi-Dirac statistics. It is further recognized that all particles follow Fermi-Dirac statistics or bose-einstein statistics, and the basic properties of these two kinds of particles are quite different.

Heisenberg expounded the uncertainty principle.

Paul ·A·M· dirac proposed a relativistic wave equation to describe electrons, explain their spins and predict antimatter.

Dirac put forward the quantum description of electromagnetic field, which laid the foundation of quantum field theory.

Bohr put forward the complementary principle (a philosophical principle), trying to explain some obvious contradictions in quantum theory, especially the wave-particle duality.

The main founders of quantum theory are all young people. 1925, Pauli was 25, Heisenberg and Enrico Fermi were 24, Dirac and Jordan were 23. Schrodinger was a late bloomer, aged 36. Born and Bohr are older. It is worth mentioning that most of their contributions are explanatory. Einstein's reaction reflected the profundity and radicalization of quantum mechanics, which was an intellectual achievement: he rejected many key concepts that led to quantum theory, and his paper on bose-einstein statistics was his last contribution to theoretical physics and his last important contribution to physics.

It is not surprising that the creation of quantum mechanics needs a new generation of physicists. Sir Kelvin expressed the reason in a letter congratulating Bohr on his paper on hydrogen atom published in 19 13. He said there were many reasons in Bohr's paper that he couldn't understand. Kelvin believes that the basic new physics must come from an unrestrained mind.

1928, the revolution is over, and the foundation of quantum mechanics has been established in essence. Later, Abraham Pais recorded this frenzied revolution with anecdotes. There is a passage like this: 1925, Samuel Goodmitt and George Uhlenbeck put forward the concept of electron spin, which Bohr deeply doubted. On June+10, 5438, Bohr took a train to Leiden, the Netherlands, to attend the 50th birthday celebration of Hendrick A. Lorenz. Pauli met Bohr in Hamburg, Germany, and asked Bohr about the possibility of electron spin. Bohr replied with his famous low-key evaluation language that the proposal of spin was "very, very interesting". Later, Einstein and paul ehrenfest met Bohr in Leiden and discussed spin. Bohr explained his objection, but Einstein showed a way of spin, which made Bohr a supporter of spin. On Bohr's return trip, he met more discussants. When the train passed through Gottingen, Germany, Heisenberg and Jordan met at the station and asked his opinion. Paulie also made a special trip from Hamburg to Berlin airport. Bohr told them that the discovery of spin was a great progress.

The creation of quantum mechanics triggered the scientific gold rush. The early achievements are as follows: Heisenberg obtained the approximate solution of Schrodinger equation of helium atom in 1927, which laid the foundation of atomic structure theory; John Slater, Douglas Reina Hartree and Vladimir Fogg then put forward the general calculation skills of atomic structure; Fritz London and Walter Hai Telei solved the structure of hydrogen molecule. On this basis, linus pauling established theoretical chemistry. Sommerfeld and Pauli laid the foundation of metal electronic theory, and felix bloch founded the theory of energy band structure. Heisenberg explained the cause of ferromagnetism. 1928 George Gamow explained the mystery of the randomness of alpha radioactive decay, and he proved that alpha decay was caused by the tunneling effect of quantum mechanics. In the next few years, hans bethe laid the foundation of nuclear physics and explained the energy sources of stars. With these advances, atomic physics, molecular physics, solid state physics and nuclear physics have entered the era of modern physics.

Key points of quantum mechanics

Along with these advances, there are many arguments about the explanation and correctness of quantum mechanics. Bohr and Heisenberg are important members of the advocates. They believed in the new theory, but Einstein and Schrodinger were not satisfied with it.

Basic description: wave function. The behavior of the system is described by Schrodinger equation, and its solution is called wave function. The complete information of the system is expressed by its wave function, and any observable possible value can be calculated by wave function. The probability of finding an electron in a given volume of space is proportional to the square of the amplitude of Apollo function, so the position of particles is distributed in the volume where the wave function is located. The momentum of particles depends on the slope of Apollo function, and the steeper the wave function, the greater the momentum. The slope is variable, so the momentum is also distributed. In this way, it is necessary to abandon the classical image whose displacement and velocity can be determined with arbitrary accuracy and adopt the fuzzy probability image, which is also the core of quantum mechanics.

For the same system, the same careful measurement may not necessarily produce the same result. On the contrary, the results are scattered within the range described by wave function, so the specific position and momentum of electrons are meaningless. This can be expressed by the uncertainty principle as follows: in order to accurately measure the particle position, the wave function must be peak-shaped, however, the peak must have a steep slope, so the momentum distribution is in a large range; On the contrary, if the momentum distribution is small, the slope of wave function will be small, so the wave function distribution range is large, and the position of particles is even more uncertain.

Interference of waves. Whether waves are added or subtracted depends on their phases, and the amplitudes are added in phase and subtracted in opposite phase. When waves reach the receiver along several paths, such as double-slit interference of light, interference patterns generally appear. When particles follow the wave equation, there must be similar behavior, such as electron diffraction. At this point, analogy seems reasonable, unless we want to investigate the nature of waves. Waves are usually considered as disturbances in media. But there is no medium in quantum mechanics, and in a sense there is no wave at all. Wave function is essentially just a statement of system information.

Symmetry and isotropy. Helium atom consists of two electrons moving around the nucleus. The wave function of helium atom describes the position of each electron, but there is no way to distinguish which electron is which electron. So we can't see any changes in the system after the electronic exchange, that is to say, the probability of finding an electron at a given position remains unchanged. Because the probability depends on the square of the amplitude of Apollo function, the relationship between the wave function of the system after particle exchange and the original wave function can only be one of the following: either it is the same as the original wave function, or it changes its sign, that is, it is multiplied by-1. Who should I take?

An amazing discovery of quantum mechanics is that the wave function of electrons will change sign because of electron exchange. The result was dramatic. Two electrons are in the same quantum state, and the wave functions are opposite, so the total wave function is zero, which means that the probability of two electrons being in the same state is zero, which is the Pauli exclusion principle. All semi-integer spin particles (including electrons) follow this principle and are called fermions. The wave functions of particles (including photons) with integer spins are exchange-invariant, which is called boson. Electrons are fermions, so they are arranged in layers in atoms; Light is composed of bosons, so the laser presents a super-strong beam (essentially a quantum state). Recently, gas atoms have been cooled to quantum state, forming Bose-Einstein condensation. At this time, the system can emit a beam of high-energy substances and form an atomic laser.

This concept only applies to identical particles, because the wave functions of different particles are obviously different after exchange. Therefore, only when the particle system is identical particles will it behave like a boson or a fermion. The same particles are absolutely the same, which is one of the most mysterious aspects of quantum mechanics, and the achievement of quantum field theory will explain this.

Controversy and confusion

What does quantum mechanics mean? What exactly is a wave function? What does measurement mean? These problems caused a heated debate in the early days. Until 1930, Bohr and his colleagues more or less put forward the standard explanation of quantum mechanics, namely Copenhagen explanation; The key point is to describe matter and events in probability through Bohr's complementary principle and to reconcile the wave-particle duality contradiction of matter. Einstein did not accept quantum theory. He argued with Bohr about the basic principles of quantum mechanics until his death in 1955.

The focus of the debate in quantum mechanics is whether the wave function contains all the information of the system or whether there are hidden factors (hidden variables) that determine the specific measurement results. In the mid-1960s, John S. Bell proved that if there are hidden variables, the probability of experimental observation should be below a specific limit, which is Bell inequality. The experimental results of most groups are contrary to Bell inequality, and their data categorically deny the possibility of the existence of hidden variables. In this way, most scientists no longer doubt the correctness of quantum mechanics.

However, due to the magical power of quantum theory, its essence still attracts people's attention. The strange properties of quantum systems are caused by so-called entangled states. Simply put, quantum systems (such as atoms) can not only be in a series of steady states, but also be in their superposition states. Measure some properties (such as energy) of atoms in superposition state. Generally speaking, sometimes one value is obtained, and sometimes another value is obtained. So far, there is nothing weird.

However, it is possible to construct an entangled diatomic system so that two atoms have the same properties. When these two atoms are separated, the information of one atom is shared (or entangled) by the other atom. This behavior can only be explained by the language of quantum mechanics. This effect is so incredible that only a few active theoretical and experimental institutions are paying attention to it, and the topic is not limited to the study of principle, but the use of entangled States; Entangled states have been applied to quantum information systems and become the basis of quantum computers.

The second revolution

In the frenzied era when quantum mechanics was founded in the mid-1920s, another revolution was going on, and the foundation of quantum field theory, another branch of quantum physics, was being established. Different from the creation of quantum mechanics, the creation of quantum field theory has experienced a tortuous history and continues to this day. Although quantum field theory is difficult, its prediction accuracy is the most accurate in all physical disciplines, and it also provides an example for the exploration of some important theoretical fields.

The problem of quantum field theory is how atoms radiate light when electrons transition from excited state to ground state. 19 16 years, Einstein studied this process and called it spontaneous radiation, but he could not calculate the spontaneous radiation coefficient. To solve this problem, we must develop the relativistic quantum theory of electromagnetic field (that is, light). Quantum mechanics is a theory to explain matter, and quantum field theory, as its name implies, is a theory to study fields, not only electromagnetic fields, but also other fields discovered later.

In 1925, born, Heisenberg and Jordan published the preliminary idea of quantum field theory of light, but the key step was Dirac, a young and unknown physicist, who put forward the field theory alone in 1926. Dirac's theory has many defects: insurmountable computational complexity, infinite prediction and obvious violation of correspondence principle.

In the late 1940s, new progress was made in quantum field theory. Richard feynman, Julian Schwinger and Sinitro Youyong proposed quantum electrodynamics (QED). They avoid infinity by renormalization, the essence of which is to get limited results by subtracting an infinity. Because of the complexity of the equation, it is impossible to find an exact solution, so the approximate solution is usually obtained by series, but the series term is more and more difficult to calculate. Although the series terms decrease in turn, the total result begins to increase after a certain term, so the approximation process fails. Despite this danger, QED is still listed as one of the most successful theories in the history of physics. It is predicted that the intensity of interaction between electrons and magnetic field is only 2/ 1, 000,000,000,000,000.

Although QED has achieved remarkable success, it is still full of mystery. For void space, the theory seems to provide an absurd view that vacuum is not empty, and it is full of tiny electromagnetic fluctuations everywhere. These tiny fluctuations are the key to explain spontaneous emission, and they cause measurable changes in the properties of particles such as atomic energy and electrons. Although QED is eccentric, its effectiveness has been confirmed by many of the most accurate experiments.

For the low-energy world around us, quantum mechanics is accurate enough, but for the high-energy world, the effect of relativity is remarkable, which requires a more comprehensive method. The establishment of quantum field theory reconciled the contradiction between quantum mechanics and special relativity.

The outstanding function of quantum field theory is that it explains some of the most profound problems related to the nature of matter. It explains why there are two basic particles, boson and fermion, and what is the relationship between their properties and intrinsic spin. It can describe how particles (including photons, electrons, positrons or antielectrons) are produced and annihilated. It explains the mysterious isotropy in quantum mechanics. Identical particles is absolutely the same, because they come from the same basic field. It explains not only electrons, but also leptons such as muons, τ and their antiparticles.

QED is a theory about leptons, which cannot describe complex particles called hadrons, including protons, neutrons and a large number of mesons. For hadrons, a more general theory than QED is proposed, which is called Quantum Chromodynamics (QCD). QED and QCD have many similarities: electrons are the constituent elements of atoms and quarks are the constituent elements of hadrons; In QED, photon is the medium that transmits the interaction between charged particles, and in QCD, gluon is the medium that transmits the interaction between quarks. Although QED and QCD have many similarities, there are still significant differences between them. Unlike leptons and photons, quarks and gluons are always trapped in hadrons, unable to be liberated and exist in isolation.

QED and QCD constitute the cornerstone of the unified standard model. The standard model successfully explains all the particle experiments today, but many physicists think it is incomplete because the data of particle mass, charge and other properties still come from experiments; An ideal theory should be able to give all this.

Today, seeking the understanding of the ultimate essence of matter has become the focus of major scientific research, which makes people unconsciously think of the miraculous days when quantum mechanics was founded, and its achievements will have a far-reaching impact. Now we must try our best to find a quantum description of gravity. Half a century's efforts show that QED's masterpiece, the quantization program of electromagnetic field, is invalid for gravity field. This problem is very serious, because if both general relativity and quantum mechanics are true, they must provide essentially compatible descriptions of the same event. There will be no contradiction in the world around us, because gravity is so weak relative to electricity that its quantum effect can be ignored and the classical description is perfect enough; But there is no reliable way to predict the quantum behavior of a system with very strong gravity like a black hole.

A century ago, our understanding of the physical world was empirical; In the 20th century, quantum mechanics provided us with the theory of matter and field, which changed our world. Looking forward to 2 1 century, quantum mechanics will continue to provide basic concepts and important tools for all sciences. We make such confident predictions because quantum mechanics provides an accurate and complete theory for the world around us; However, today's physics is very similar to that of 1900: it still retains basic experience, and we can't completely predict the properties of the basic elements that make up matter, so we still need to measure them.

Perhaps superstring theory is the only theory that can explain this mystery. It is an extension of quantum field theory, which replaces point objects such as electrons with objects with length and eliminates all infinity. Whatever the outcome, the ultimate dream of understanding nature, which began at the dawn of science, will continue to be the driving force of new knowledge. A century later, we will continue to pursue this dream, and the result will make all our imaginations come true.