Quantum physics includes two parts: one isquantum mechanicsIt is a physical theory at the atomic level and a theory to explain the laws of material movement in the micro world;SecondQuantum field theoryIt is the basic law of the research field and reveals some profound problems related to the essence of matter.[1]
Quantum mechanics is not only one of the basic theories of modern physics, but also widely used in chemistry and many modern technologies[2]。In the 20th century, quantum mechanics provided us with a theory of matter and field, which changed our world;Looking forward to the 21st century, quantum mechanics will continue to provide basic concepts and important tools for all sciences.
althoughquantum mechanicsIt was created to describe the abstract atomic world far away from our daily life experience, but it has a tremendous impact on our daily life.Without quantum mechanics as a tool, there can be no fascinating progress in chemistry, biology, medicine and every other key discipline.Without quantum mechanics, there would be no global economy, because the electronics revolution, as the product of quantum mechanics, has brought us into the computer age[3]。At the same time, the revolution of photonics also brings usInformation Age。The masterpiece of quantum physics has changed our world,scientific revolutionThe good news brought to the world has also brought potential threats.
The concept of quantum is so confusing that there has been almost no fundamental progress in the 20 years since it was introduced. Later, a small group of physicists spent three years creating quantum mechanics.these ones herescientistI am troubled by what I have done, and sometimes I am disappointed in what I have done.Perhaps the following observation can best describe the unique position of this crucial but elusive theory: quantum theory is the most accurate theory that can be tested by experiments in the history of science and the most successful theory in the history of science.Quantum mechanics has deeply troubled its founder. However, 75 years later, some elites in the scientific community are still dissatisfied with its foundation and basic interpretation, although they admit its powerful power.
1918 Nobel Prize Winner in PhysicsMax Planck (Max Planck) proposed in 1900Planck radiation lawQuantum theory was born.In his classic paper on thermal radiation, Planck assumed that the total energy of the vibration system could not be changed continuously, but jumped from one value to another in the form of discontinuous energy sub.The concept of energy son was so radical that Planck put it aside later.Later, in 1905, which was an extraordinary year for Einstein, Einstein realized the potential significance of quantum quantization.However, the concept of quantum is too strange, and there was almost no fundamental progress later.The creation of modern quantum theory is the crystallization of a new generation of physicists who spent more than 20 years.
By comparing the fields of physics before and after the birth of quantum theory, we can realize that quantum physics has had a revolutionary impact on physics.The physics journal papers from 1890 to 1900 were basically articles about atomic spectrum and other basic measurable properties of matter, such as viscosity, elasticity, conductivity, thermal conductivity, expansion coefficient, refractive index and thermal elastic coefficient.Stimulated by the development of Victorian working mechanism and sophisticated experimental methods, knowledge has accumulated at a tremendous speed.However, the most remarkable thing for contemporary people is that the concise description of material properties is basically empirical.Thousands of pages of spectral data list the exact wavelength values of a large number of elements, but no one knows why spectral lines appear, let alone the information they convey.The model interpretation of thermal conductivity and conductivity is only consistent with about half of the facts.Although there are countless empirical laws, they are difficult to satisfy.For example, the Dulong Petit law establishes a simple relationship between the specific heat and the atomic weight of matter, but it sometimes works well and sometimes does not.In most cases, the mass ratio of gas with the same volume satisfies a simple integer relationship.periodic table of ele mentsAlthough it provides key organizational rules for the prosperity of chemistry, there is no theoretical basis.
Among many great revolutionary developments, quantum mechanics provides a quantitative theory of matter.In principle, we can understand every detail of atomic structure;The periodic table can also be explained simply and naturally;The huge spectral alignment also incorporates an elegant theoretical framework.Quantum mechanics facilitates the quantitative understanding of molecules, fluids and solids, conductors and semiconductors.It can explain strange phenomena such as superfluids and superconductors, and strange forms of matter aggregation such as neutron stars and Bose Einstein condensation (in this phenomenon, all atoms in the gas behave like a single super atom).Quantum mechanics provides a key tool for all branches of science and every high technology.
Quantum physics actually includes two aspects.One is the material theory at the atomic level: quantum mechanics;It is this that we can understand and manipulate the material world.The other isQuantum field theoryIt plays a completely different role in science, and we will return to it later.
Old quantum theory
The fuse of the quantum revolution is not the study of matter, but radiation.The specific challenge is to understand the spectrum of radiation from a blackbody (that is, a hot object).People who have baked are familiar with such a phenomenon: hot objects emit light, and the hotter the light, the brighter the light.The spectrum has a wide range. When the temperature rises, the peak of the spectrum moves from the red line to the yellow line, and then to the blue line (these are not directly visible).
Combine thermodynamics andelectromagneticsThe concept of "0" seems to explain the shape of the spectrum, but all attempts failed.However, Planck assumed that the energy of the light radiated by the vibrating electron was quantized, so an expression was obtained, which was in perfect agreement with the experiment.But he also fully realized that the theory itself was absurd, as he later said: "Quantization is just a desperate practice".
Planck applied his quantum hypothesis to the energy of the surface oscillator of the radiator. If there was no newcomer Albert Einstein, quantum physics would have ended 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.althoughMaxwell theoryAs well as more than a century of authoritative experiments have shown that light has volatility, Einstein's theory still contains the particle behavior of light.Later, more than ten years of photoelectric effect experiments showed that light energy can be absorbed only when it reaches some discrete values, as if it were carried by particles.PhotogenicWave particle dualityDepending on the focus of your observation, this is one of the headache examples throughout quantum physics, and it will become a theoretical problem in the next 20 years.
The radiation problem led to the first step to quantum theory, and the material paradox led to the second step.As is known to all, atoms contain particles with positive and negative charges, and different sign charges attract each other.According to electromagnetic theory, positive and negative charges will spiral close to each other, emitting light with a wide spectrum until the atom collapses.Then, another rookie, Niels Bohr, took a decisive step.In 1913, 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 can change their energy by transiting between two stationary states. At the same time, they emit light of a certain wavelength, whose wavelength depends on the energy difference between the stationary states.Combining the known law with this strange hypothesis, Bohr cleared up the problem of atomic stability.Bohr's theory is full of contradictions, butAtomic hydrogen spectroscopyProvides a quantitative description.He recognized the successes and shortcomings of his model.With his amazing foresight, he gathered a group of physicists to create new physics.It took a generation of young physicists 12 years to finally realize his dream.
At the beginning, attempts to develop Bohr's quantum theory (traditionally called the old quantum theory) suffered repeated failures.Then a series of developments completely changed the process of thinking.
History of Quantum Mechanics
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In 1923, Louis de Broglie put forward in his doctoral thesis that the particle behavior of light should correspond to the wave behavior of particles.He linked the wavelength of a particle to its 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 how it relates to atomic structure.However, de Broglie's hypothesis is an important prelude, and many things are about to happen.
In the summer of 1924, there was another Qiancai.Satyendra N. Bose proposed a new method to explainPlanck radiation law。He regards light as a gas composed of particles (now called photons) without (static) mass, which does not follow the classicalBoltzmann statisticsAnd follows a new statistical theory based on the indistinguishable properties of particles (i.e., isotropy).Einstein immediately applied Bose's reasoning to the actual gas with mass to obtain a distribution law describing the number of particles in the gas with respect to energy, namely the famous Bose Einstein distribution[4]。However, in general, the old and new theories will predict the same behavior of atomic gases.Einstein was no longer interested in this aspect, so these results were shelved for more than 10 years.However, its key idea, the isotropy of particles, is extremely important.Suddenly, a series of events came one after another, leading to ascientific revolution。From January 1925 to January 1928:
Wolfgang Pauli proposed the incompatibility principle, which laid a theoretical foundation for the periodic table.
Weiner·Heisenberg (Werner Heisenberg), Max Born and Pascal Jordan proposed the first version of quantum mechanics, matrix mechanics.People have finally abandoned the historical goal of understanding the movement of electrons in atoms by arranging observable spectral lines in a systematic way.
Erwin Schrodinger proposed the second form of quantum mechanics,Wave dynamics。In wave dynamics, the state of the system isSchrodinger equationThe wave function.Matrix mechanics and wave dynamics seem to be contradictory, but they are essentially equivalent.
The electron is proved to follow a new statistical law, Fermi Dirac statistics.It is further recognized that all particles either follow Fermi Dirac statistics or Bose Einstein statistics, and the basic properties of these two types of particles are very different.
Heisenberg expounded the uncertainty principle.
Paul A. M. Dirac proposed a relativistic wave equation to describe electrons, explain the spin of electrons and predict antimatter.
Dirac proposed the quantum description of electromagnetic field and established the basis of quantum field theory.
Bohr proposed the principle of complementarity (a philosophical principle), trying to explain some obvious contradictions in quantum theory, especiallyWave particle duality。
The main founders of quantum theory are young people.In 1925, Pauli was 25, Heisenberg and Enrico Fermi were 24, and Dirac and Dang were about 23.Schrodinger was a late bloomer, 36 years old.Born and Bohr are older. It is worth mentioning that their contributions are mostly interpretive.Einstein's reaction reflects the profound and radical attribute of quantum mechanics, an intellectual achievement: he rejects many key concepts that lead to quantum theory, and his paper on Bose Einstein statistics is his contribution toTheoretical physicsThis is the last important contribution to physics.
It is not surprising that the creation of quantum mechanics requires a new generation of physicists. Sir Kelvin expressed the reason in a letter congratulating Bohr on his 1913 paper on hydrogen atom.He said that there were many truths in Bohr's paper that he could not understand.Kelvin believed that the basic new physics must come from an unrestrained mind.
In 1928, after the revolution, the foundation of quantum mechanics was essentially established.Later, Abraham Pais recorded this revolution in a fanatical rhythm with an anecdote.In one paragraph, Samuel Goudsmit and George Uhlenbeck put forward the concept of electron spin in 1925, which Bohr deeply doubted.In October, Bohr took a train to Leiden, Netherlands, to attend the 50th birthday celebration of Hendrik A. Lorentz. Pauli met Bohr in Hamburg, Germany, and asked Bohr's opinion on the possibility of electron spin;Bohr replied in his famous low-key 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 and made Bohr a supporter of spin.During Bohr's return journey, he met more discussants.When the train passed by Gottingen, a German taxi, Heisenberg and Jordan met him at the station and asked his opinion. Pauli also went from Hamburg to Berlin to meet him.Bohr told them that the discovery of spin was a major step forward.
The creation of quantum mechanics triggered the gold rush of science.Early achievements include:
In 1927, Heisenberg obtained the helium atomSchrodinger equationThe basis of the atomic structure theory is established;John Slater, Douglas Rayner Hartree and Vladimir Fock subsequently put forward the general calculation skills of atomic structure;Fritz London and Walter Heitler solved the structure of hydrogen molecule. On this basis, Linus Pauling established theoretical chemistry;Arnold Sommerfeld and Pauli established the basis of metal electron theory, and Felix Bloch established the theory of energy band structure;Heisenberg explained the origin of ferromagnetism.
In 1928, George Gamow explained the mystery of the random nature of alpha radioactive decay, and he showed that alpha decay is caused by quantum mechanicsTunnel effectCaused by.In the following years, Hans Bethe established the basis of nuclear physics and explained the energy source of stars.With these developments, atomic physics, molecular physics, solid state physics and nuclear physics have entered the era of modern physics.
Key points of quantum mechanics
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With these developments, there have been many debates about the interpretation and correctness of quantum mechanics.Bohr and Heisenberg are important members of the advocates, who believe in new theories, while Einstein and Schrodinger are dissatisfied with the new theories.To understand the causes of these confusion, we must master the key features of quantum theory, which are summarized as follows[5]。(For simplicity, we only describeSchrodingerWave mechanics.)
wave function
The behavior of the systemSchrodinger equationThe solution of the equation is called wave function.The complete information of the system is expressed by its wave function, through which the possible value of any observable quantity can be calculated.The probability of finding an electron in a given volume of space is proportional to the square of the amplitude of the wave function, so the position of particles is distributed in the volume of the wave function.The momentum of the particle depends on the slope of the wave function. The steeper the wave function, the greater the momentum.The slope is variable, so momentum is also distributed.In this way, it is necessary to give up the classical image that displacement and velocity can be determined to any precision and adopt a fuzzy probability image, which is also the core of quantum mechanics.
The same careful measurement of the same systems may not produce the same results. On the contrary, the results are scattered in the range described by the wave function. Therefore, the specific position and momentum of the electron are meaningless.This can be expressed by the uncertainty principle as follows: in order to measure the position of particles accurately, the wave function must be spike type, however, the spike must have a very steep slope, so the momentum is distributed in a large range;On the contrary, if the momentum has a small distribution, the slope of the wave function must be very small, so the wave function is distributed in a large range, so the position of the particles is more uncertain.
Interference of waves
The addition or subtraction of waves depends on their phases. Amplitudes are added when they are in phase and subtracted when they are out of phase.When waves follow several paths from the wave source to the receiver, such as the double slit interference of light, interference patterns will generally be generated.If a particle follows the wave equation, it must have similar behavior, such as electron diffraction.So far, analogy seems reasonable, unless the nature of waves is investigated.Wave is usually considered as a disturbance in the medium. However, there is no medium in quantum mechanics. In a sense, there is no wave at all. In essence, wave function is just a statement of system information.
Symmetry and Homogeneity
A helium atom consists of two electrons moving around a nucleus.The wave function of the helium atom describes the position of each electron, but there is no way to distinguish which electron is which electron. Therefore, after the exchange of electrons, no change in the system can be seen, that is, the probability of finding an electron at a given position remains unchanged.Since the probability depends on the square of the amplitude of the wave 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 the same as the original wave function, or change the sign, that is, multiply by - 1.Who should I take?
One surprising discovery of quantum mechanics is that the wave function of the electron changes the sign for electron exchange.The result is dramatic. Two electrons are in the same quantum state, and their wave functions are opposite, so the total wave function is zero, that is, the probability of two electrons being in the same state is 0, which isPauli exclusion principle。All semi integer spin particles (including electrons) follow this principle and are called fermions.For particles (including photons) with integral spinwave functionFor the exchange invariant sign, it is called boson.Electrons are fermions, so they are arranged in layers in atoms;Light is composed of bosons, so the laser light presents an ultra intense beam (essentially a quantum state).Recently, gas atoms have been cooled to quantum state to form Bose Einstein condensation. At this time, the system can emit ultra strong matter beams to form atomic lasers.
This concept is only applicable to identical particles, because the wave functions of different particles are obviously different after exchange.Therefore, only when the particle system is identical can it show the behavior of boson or fermion.The same particle is absolutely the same, which is one of the most mysterious aspects of quantum mechanics. The achievements of quantum field theory will explain this.
Dispute and confusion
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What does quantum mechanics mean?What is a wave function?What does measurement mean?These issues were hotly debated in the early days.Until 1930, Bohr and his colleagues more or less put forward the standard interpretation of quantum mechanics, namely the Copenhagen interpretation;The key point is to describe the probability of matter and events through Bohr's complementarity principle, and reconcile matterWave particle dualityThe contradiction of[6]。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 on 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 results of specific measurements.In the mid-1960s, John S. Bell proved that if there were hidden variables, the probability observed in the experiment should be below a specific limit, that isBell inequality。The experimental results of most groups contradict Bell's 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 arise from the so-called entangled states. In short, quantum systems (such as atoms) can not only be in a series of stationary states, but also in their superposition states.To measure certain properties (such as energy) of atoms in superposition state, generally speaking, sometimes this value is obtained, and sometimes another value is obtained.So far, nothing strange has appeared.
However, it is possible to construct a two atom system in an entangled state, so that the two atoms share the same properties.When the two atoms are separated, the information of one atom is shared (or entangled) by the other.This behavior can only be explained in the language of quantum mechanics.This effect is so incredible that only a few active theoretical and experimental institutions are focusing on it. The topic is not limited to the study of principles, but the use of entangled states;Entangled states have been applied toQuantum informationSystem, also known asquantum computerThe foundation of.
Second Revolution
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In the feverish era when quantum mechanics was founded in the mid-1920s, another revolution was also under way, and the foundation of quantum field theory, another branch of quantum physics, was being established.Unlike the creation of quantum mechanics, which is just like a storm, the creation of quantum field theory has gone through a tortuous history, which continues to this day.Although quantum field theory is difficult, its prediction accuracy is the most accurate among all physical disciplines. At the same time, it also provides examples for the exploration of some important theoretical fields.
The problem of quantum field theory proposed by excitation is how the atom radiates light when the electron transitions from the excited state to the ground state.In 1916, Einstein studied this process and called it spontaneous emission, but he was unable to calculate the coefficient of spontaneous emission.To solve this problem, we need to develop the relativistic quantum theory of electromagnetic field (i.e. light).Quantum mechanics is the theory that explains matter, and quantum field theory, as its name suggests, is the theory that studies 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 the field theory independently proposed by young and unknown physicist Dirac in 1926.Dirac's theory has many defects: it is difficult to overcome the computational complexity, predict an infinite number, and obviously contradicts the correspondence principle.
In the late 1940s, new progress was made in quantum field theory. Richard Feynman, Julian Schwinger and Sinitro Tomonaga proposedQuantum electrodynamics(abbreviated as QED).They avoid infinity by renormalization, whose essence is to obtain finite results by subtracting an infinity.Due to the complexity of the equation, the exact solution cannot be found, so the approximate solution is usually obtained by series, but the series term is increasingly difficult to calculate.Although the series term decreases in turn, the total result starts to increase after a certain term, so that the approximation process fails.Despite this danger, QED is still listed as one of the most successful theories in the history of physics. The difference between the predicted interaction intensity of electron and magnetic field and the experimental reliable value is only 2/10000000000000.
Despite its extraordinary success, QED is still full of mysteries.For the empty space (vacuum), the theory seems to provide an absurd view. It shows that vacuum is not empty, and it is full of small electromagnetic fluctuations.These small fluctuations are the key to explain spontaneous emission, and they can cause measurable changes in atomic energy and properties of particles such as 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 relativistic effect is significant and needs a more comprehensive approach. The creation of quantum field theory reconciles quantum mechanics andSpecial relativityThe contradiction of.
The outstanding role 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 kinds of basic particles, boson and fermion, and how their properties are related to the intrinsic spin;It can describe how particles (including photons, electrons, positrons or antielectrons) are generated and annihilated;It explains the mysterious homogeneity in quantum mechanics. Identical particles are absolutely the same because they come from the same basic field;It not only explains electrons, but also leptons such as muons, tauons and their antiparticles.
QED is aboutLeptonIt cannot describe the complex particles called hadrons, which include protons, neutrons and a large number of mesons.For hadrons, a more general theory than QED, calledQuantum chromodynamics（QCD）。There are many similarities between QED and QCD: electrons are elements of atoms, quarks are elements of hadrons;In QED, photons are the medium to transfer the interaction between charged particles, and in QCD, gluons are the medium to transfer the interaction between quarks.Although there are many correspondences between QED and QCD, they still have significant differences.Unlike leptons and photons, quarks and gluons are forever confined inside hadrons, and they cannot be liberated to exist in isolation.
QED and QCD constitute the cornerstone of the unified standard model.The Standard Model successfully explains all particle experiments today, but many physicists believe that it is incomplete, because the data of particle mass, charge and other properties also come from experiments;An ideal theory should give all this.
Today, seeking to understand the ultimate nature of matter has become the focus of major scientific research, which makes people unconsciously think of the crazy miracle days of creating quantum mechanics, and the impact of its achievements will be more far-reaching.We must strive 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 gravitational field.The problem is serious, because if both general relativity and quantum mechanics are true, they must provide essentially consistent 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;However, we have no reliable way to predict the quantum behavior of black holes, which have very strong gravity.
A century ago, the physical world we understood was empirical;We make such confident predictions because quantum mechanics provides accurate and complete theories for the world around us;However, today's physics has a lot in common with the physics of 1900: it still retains the basic empiricism. We cannot completely predict the attributes of the basic elements that make up matter, and we still need to measure them.Perhaps,Superstring theoryIt is the only theory that can explain this mystery. It is an extension of quantum field theory. It eliminates all infinity by replacing dot objects such as electrons with objects of length.Whatever the outcome, the dream of the ultimate understanding of nature from the dawn of science will continue to be the driving force of new knowledge.One century from now, we will continue to pursue this dream, and the result will make all our imaginations come true.
