Uncertainty principle isHeisenberg The principle of physics proposed in 1927.It pointed out that:It is impossible to accurately determine the position and momentum of an elementary particle at the same time.[8]The product of the uncertainty of particle position and momentum must be greater than or equal toPlanck constant(Planck constant) divided by 4π[9](Formula: Δ x Δ p ≥ h/4 π).This shows that the behavior of particles in the micro world is very different from that of macro matter.In addition, the principle of uncertainty involves many profound philosophical problems. In Heisenberg's own words, "in the statement of the law of causality, that is, 'if you know exactly the present, you can foresee the future', what you get is not a conclusion, but a premise. We cannot know all the details of the present, which is a matter of principle."
The uncertainty principle proposed by German physicist Heisenberg in 1927, including the uncertainty principle between two mechanical quantities and the uncertainty principle of energy and time, means that quantum mechanics has not only a complete mathematical form, but also a reasonable theoretical explanation.[10]The uncertainty principle proposed by Heisenberg isquantum mechanicsThe product of.This principle states that there are limits to the precise determination of the position and momentum of electrons around a particle, such as an atom.This uncertainty comes from two factors. First, the behavior of measuring something will inevitably disturb that thing, thus changing itsstate；Secondly, because the quantum world is not specific, but based on probability, there are more profound and fundamental restrictions on accurately determining the state of a particle.
Heisenberg uncertainty principle is demonstrated by some experiments.Imagine using aGamma rayThe microscope is used to observe the coordinates of an electron. Because the resolution ability of the gamma ray microscope is limited by the wavelength λ, the shorter the wavelength λ of the light used, the higher the resolution of the microscope, so as to determine the uncertainty of the electronic coordinates
The smaller it is, so
。On the other hand, when light shines on electrons, it can be seen as the collision between light quanta and electrons. The shorter the wavelength λ is, the greater the momentum of light quanta will be
。
Another example is to measure the position and speed of a particle by shining light on it. Some light waves are scattered by the particle, indicating its position.However, it is impossible to determine the position of particles to a smaller extent than the distance between the two peaks of light, so in order to accurately determine the position of particles, short wavelength light must be used.
butPlonkAccording to the quantum hypothesis of, people cannot use any small amount of light: people must use at least one quantum of light.This quantum will disturb the particle and change its speed in an unpredictable way.
So, in brief, if you want to determine the exact position of a quantum, you need to use a wave with the shortest wavelength. In this way, the greater the disturbance to the quantum, the less accurate the velocity measurement will be;If you want to accurately measure the speed of a quantum, you need to use a wave with a longer wavelength, and you cannot accurately measure its position[1]。
Then, after some reasoning and calculation, Heisenberg obtained: △ q △ p ≥ħ/2（ħ=h/2π）。Heisenberg He wrote: "At the moment when the position is measured, that is, when the photon is deflected by the electron, the momentum of the electron has a discontinuous change. Therefore, at the moment when the position of the electron is determined, we can only know the degree of its momentum corresponding to the size of its discontinuous change. Therefore, the more accurate the position is measured, the less accurate the measurement of momentum is, and vice versa."[1]
Heisenberg also determinedAtomic magnetic momentOfStern Gallach experimentThe analysis of shows that the longer it takes △ T for the atom to pass through the deflection, the smaller the uncertainty △ E in the energy measurement.PlusDe Broglie relationshipλ=h/p，Heisenberg got △ E △ T ≥ h/4 π, and made a conclusion: "The accurate measurement of energy can only be obtained by the corresponding uncertainty of time."
brief introduction
In quantum mechanics,Uncertainty principle(Uncertainty principle) indicates that the position of particles ismomentumIt cannot be determined at the same time, and the uncertainty of position and momentum obey inequality
Werner Heisenberg In 1927, he published a paper giving the original heuristic exposition of this principle, so this principle is also called“Heisenberg Uncertainty Principle ”。According to Heisenberg's statement, the action of measurement inevitably disturbed the motion state of the measured particles, thus generating uncertainty.Later that year,Earl Kennard(Earl Kennard) gives another expression.The next year,Hermann Weyl This result is also obtained independently.According to Kennard's statement, the uncertainty of position and momentum is the nature of particles, which cannot be suppressed below a certain limit relationship at the same time, and has nothing to do with the action of measurement.Thus, there are two completely different expressions of uncertainty principle.In the final analysis, the two expressions are equivalent, and the other expression can be derived from any one of them.[2]
For a long time, the uncertainty principle is similar to another physical effect (calledObserver effect）They are often confused.The observer effect points out that the measurement of a system will inevitably affect the system.In order to explain quantum uncertainty, Heisenberg's statement refers to the observer effect at the quantum level.Later, physicists gradually found that the uncertainty principle involved in Kennard's statement was the intrinsic property of all wave like systems, and it appeared in quantum mechanics because of theWave particle dualityIt actually shows the basic properties of quantum system, rather than the quantitative evaluation of the observation ability of scientific and technological experiments today.It is emphasized here that measurement is not a process involving only experimental observers, but the interaction between classical objects and quantum objects, regardless of whether any observers participate in this process.
Similar uncertainty relations also exist between energy and time, angular momentum, angle and other physical quantities.Since the uncertainty principle is an important result of quantum mechanics, many general experiments often involve some problems about it.Some experiments will specifically test this principle or similar principles.For example, the "digital phase uncertainty principle" occurring in superconducting systems or quantum optical systems is tested.The research on uncertainty principle can be used to develop the low-noise technology required by gravitational wave interferometer.[3]
Law influence
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This principle shows that some of thephysical quantity(e.g. position and momentum, orazimuthAndMoment of momentum, as well as time and energy), it is impossible to have certain values at the same time. The more certain one quantity is, the greater the uncertainty of the other quantity is.Measure a pairConjugate quantityThe product of the error (standard deviation) of must be greater than the constant h/4 π (h isPlanck constant）It was first proposed by Heisenberg in 1927. It reflects the basic law of the movement of microscopic particles -probabilityAmplitude function（wave function）CompositionFourier transformation yes;And the basic relationship of quantum mechanics（
）Is another important principle in physics.[4]
Development History
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Old quantum theory
Following Hans Kramers' pioneering work, in June 1925,Werner Heisenberg He published the paper Quantum Theoretical Re interpretation of Kinematic and Mechanical Relations and founded matrix mechanics.Old quantum theoryGradually declining, modern quantum mechanics officially opened.Matrix mechanics boldly assumes that the classical concept of motion does not apply to the quantum hierarchy.The electrons in an atom do not move in a clear orbit, but in a vague and unobservable orbital region;Its Fourier transform of time only involves discrete frequencies observed from quantum transitions.
In his paper, Heisenberg proposed that only physical quantities that can be observed in experiments can have physical meaning and can be used to describe their physical behavior in theory. Others are nonsense.Therefore, he avoids any detailed calculation involving the movement orbit of particles, such as the exact movement position of particles changing with time.Because, the motion orbit cannot be observed directly.Instead, he focused on the discrete frequency and intensity of light emitted during electron transitions.He calculated an infinite matrix representing position and momentum.These matrices can correctly predict the intensity of light waves emitted by electronic transitions.
In June of the same year, Max Born, Heisenberg's boss, after reading the paper Heisenberg gave him for publication, found that there was a significant relationship between the position and the infinite matrix of momentum - they were not reciprocal.This relationship is called regular commutation relationship, which is expressed as:
At that time, physicists had not been able to clearly understand this important result, and they could not give a reasonable interpretation.[3]
question
Ozawa's inequality and its verification
With the progress of science and technology, since the 1980s, voices have begun to point out that this law is not omnipotent.JapanNagoya University professorOzawa integrityIn 2003, he proposed "Ozawa's inequality" and thought that the "uncertainty principle" might have its defects.For this reason, its scientific research team made precise measurements of the two values related to the "rotation" tendency of the neutrons that make up the atom, and successfully measured the accuracy of the two values that exceed the so-called "limit", making Ozawa's inequality tenable, and also proving the contradiction with the "uncertainty principle".
The scientific research team of Masayoshi Ozawa, a professor of Nagoya University in Japan, and Yuji Hasegawa, an associate professor of Vienna University of Technology in Austria, found through experiments that the uncertainty principle, a basic law proposed about 80 years ago to explain quantum mechanics in the micro world, has its flaws.This discovery is the first in the world.This discovery was published in the British scientific journal Natural Physics (electronic edition) on January 15, 2012, which was said to be forced by the application of high-speed cryptographic communication technology and the change of textbooks.[4]
Weak measurement technology
University of TorontoLee Rozema of the Quantum Optics Research Group of the University of Toronto designed an instrument to measure physical properties, and his research results were published in the weekly Physical Review Letters on September 7, 2012.
In order to achieve this goal, it is necessary to measure photons before they enter the instrument, but this process will also cause interference.In order to solve this problem, Rozema and his colleagues used a weak measurement technology to make the measured object suffer little interference. Before each photon enters the instrument, researchers measure its weak point, then measure it with the instrument, and then compare the two results.The interference caused by the discovery is not as large as that inferred in Heisenberg's principle.
This discovery challenges Heisenberg's theory.2010, AustraliaGriffith University Scientists A.P. Lund and Howard Wiseman of Griffith University found that weak measurement can be used to measure quantum systems, but a microquantum computerBut this kind of computer is difficult to produce.Rozema's experiments include the application of weak measurement and the simplification of quantum computing through "cluster quantum computing" technology. By combining the two, he found a way to test Lund and Wiseman's ideas in the laboratory.
Modern inequality
Heisenberg and Bohr jointly discuss issues
In 1926, Heisenberg was employed as a lecturer at Niels Bohr Institute of Copenhagen University, helping Niels Bohr do research.There, Heisenberg expressed the uncertainty principle, which laid a solid foundation for the later well-known Copenhagen interpretation.Heisenberg proved that the uncertainty can be derived from the commutation relationship, or, using Bohr's term, complementarity: it is impossible to observe any two non commutative variables at the same time;If you know one variable more accurately, you must know the other variable more inaccurately.
In his famous 1927 paper, Heisenberg wrote the following formula
This formula gives the minimum unavoidable momentum uncertainty caused by any position measurement.Although he mentioned that the formula can be derived from the commutation relationship, he did not write the relevant mathematical theory nor give a precise definition.He only gave reasonable estimates for a few cases (Gaussian wave packets).In Heisenberg's Chicago handout, he further improved the relationship:
In 1927, Earl Kennard first proved the modern inequality:
Among them,
Is the position standard deviation,
Is the standard deviation of momentum,
Is the reduced Planck constant.
In 1929, Howard Robertson proposed how to obtain the uncertainty relation from the commutation relation.
name
For a long time, the uncertainty principle was called the "uncertainty principle", but in fact, for the intrinsic nature of the wave like system, the uncertainty principle has no direct relationship with the accuracy of the measurement (please refer to the previous section onObserver effectTherefore, the translation does not correctly express the connotation of this principle.In addition, English calls this principle "Uncertainty Principle", which is literally translated as "Uncertainty Principle". There is no such statement as "Uncertainty Principle". Other languages are similar to English. Except Chinese, there is no word "Uncertainty Principle".Today, in textbooks in mainland China, the official translation of this principle has also been changed to "Uncertainty Relationship".
Theoretical background
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Heisenberg
Heisenberg
When Heisenberg founded matrix mechanics, he took a negative attitude towards visualized images.However, he still needs to use words such as "coordinate" and "speed" in his expression. Of course, these words are no longer equivalent to those in classical theory.However, how should we understand the new physical meaning of these words?Heisenberg grasped the problem of observing electron tracks in cloud chamber experiments to think.He tried to use matrix mechanics to make mathematical representations of electron tracks, but failed.This put Heisenberg in trouble.He thought it over and over and realized that the key lies in the formulation of the electron orbit itself.The track people see is not the real orbit of the electron, but the fog track formed by the string of water drops. The water drop is far larger than the electron, so people may only observe the uncertain position of a series of electrons, rather than the exact orbit of the electron.Therefore, in quantum mechanics, an electron can only be in a certain position with a certain uncertainty, and also can only have a certain speed with a certain uncertainty.These uncertainties can be limited to the minimum range, but cannot be equal to zero.This is Heisenberg's initial thinking on uncertainty.According to Heisenberg's memory in his later years, Einstein was inspired by a conversation in 1926.When Einstein and Heisenberg discussed whether the electron orbit could be considered, he asked Heisenberg: "Do you seriously believe that only observable quantities should be included in physical theory?" Heisenberg replied, "Isn't that the way you deal with relativity? You stressed that absolute time is not allowed, just because absolute time cannot be observed."Einstein admitted this, but said: "It will be instructive and helpful for a person to keep in mind what he actually observed... In principle, it is totally wrong to try to build a theory solely on observable quantities.In fact, on the contrary, it is theory that determines what we can observe... Only theory, that is, knowledge about the laws of nature, can enable us to infer basic phenomena from sensory impressions. "[5]
At the beginning of his 1927 paper, Heisenberg said: "If anyone wants to clarify the meaning of the phrase 'the position of an object' (such as the position of an electron), he must describe an experiment that can measure 'the position of an electron', otherwise the phrase would be meaningless." Heisenberg talked about such things as position and momentum,Or the uncertainty relationship between energy and time, such as some regular conjugate quantities, said: "This uncertainty is the fundamental reason for the emergence of statistical relations in quantum mechanics."
Debate with Bohr
Heisenberg's uncertainty principle was supported by Bohr, but Bohr disagreed with his reasoning method and thought that the basic concepts he used to establish uncertainty relations were problematic.There was a heated argument between the two sides.Bohr's view is that the foundation of uncertainty lies in wave particle duality. He said: "This is the core of the problem." Heisenberg said: "We have a consistent mathematical reasoning method, which tells people everything we observe. There is nothing in nature that cannot be described by this mathematical reasoning method."Bohr said: "The complete physical explanation should be absolutely higher than the mathematical formal system."
Bohr theory
Bohr paid more attention to philosophical considerations.In 1927, Bohr made a speech titled "Quantum postulates and new progress in atomic theory", and put forward the famous principle of complementarity.He pointed out that in physical theory, people usually think that we can observe the object without interfering with it, but from the perspective of quantum theory, it is impossible, because any observation of atomic system will involve that the object observed has changed in the observation process, so it is impossible to have a single definition, and the so-called causality no longer exists.Different properties that are mutually exclusive to classical theory have become complementary aspects in quantum theory.Wave particle duality is an important manifestation of complementarity.The uncertainty principle and other quantum mechanics conclusions can also be explained here.
viewpoint
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determinism
The success of scientific theories, especially Newton's theory of gravity, led the French scientist Marquis Laplace to conclude at the beginning of the 19th century that the universe was completely determined.He believes that there is a set of scientific laws. As long as we fully know the state of the universe at a certain time, we can predict any event that will happen in the universe according to this.For example, if we know the position and speed of the sun and planets at a certain time, we can use Newton's law to calculate the state of the solar system at any other time.The fatalism in this case is obvious. Laplace further assumes that there are certain laws that similarly restrict everything else, including human behavior.The essence of the uncertainty principle is a kind of more affirmation of causality. It is conceivable that any kind of tiny observation can change the state of the object, so that the system of the original object can enter a new state quantity, but its state quantity will develop along a direction of its own action before it is interfered with,(Of course, its direction is uncertain to us, and this uncertainty is essentially for our observation.) However, the interference (observation) makes it start a "new era", and the interference result is certain to the object, which will make the object start a new state. Of course, this new result will act on other systems,So as to affect the whole universe.In short, it can be said that because of your sneeze, the air flow has a strong movement. Through the force between the air flows, a cloud in the United States has finally reached the conditions for precipitation. Because of your sneeze, the United States has a rain!Without your sneeze, the movement of that cloud is also certain, and precipitation is impossible.The so-called butterfly effect, in fact, is also the same reason. The butterfly flapped its wings in the Pacific Ocean, and the other side may have a typhoon.[6]
It is ridiculous to try to calculate future events through the laws of physics. From the perspective of computer science, this calculation is an infinite recursion. The condition for terminating recursion is to get the state at a certain time in the future, but the algorithm needs to know the impact of the computor on the environment (must be considered) after it gets the results, so it falls into recursion, because the termination condition cannot be reached,Therefore, the algorithm cannot be completed.From the perspective of feasibility, the world we live in is like a 400 mips computer environment. It is impossible to simulate a 500 mips virtual machine.So the future is unknowable.
Fatalism
Many people strongly resist this scientific determinism. They feel that it violates the freedom of "God" or mysterious forces to interfere in the world. Until the beginning of the 20th century, this concept was still considered as the standard assumption of science.An initial sign that this belief must be abandoned is the calculation made by British scientists Lord Rayleigh and Sir James Kings, who pointed out that a hot object - such as a star - must radiate energy at an infinite rate.According to the law that we believed at that time, a hot body must emit electromagnetic waves (such as radio waves, visible light or X-rays) equally in all frequency bands.For example, a hot body emits waves of the same energy between 1 trillion Hz and 2 trillion Hz and between 2 trillion Hz and 3 trillion Hz.Since the spectrum of waves is infinite, this means that the total energy radiated must be infinite.
Quantum hypothesis
To avoid this apparently absurd result, German scientistsMax Planck In 1900, it was proposed that light waves, X-rays and other waves cannot radiate at any rate, but must be emitted in a form called quantum.Moreover, each quantum has a certain energy. The higher the frequency of the wave, the greater its energy.Thus, at a sufficiently high frequency, the energy required to radiate a single quantum is more than can be obtained.Therefore, radiation is reduced at high frequencies, and the rate at which objects lose energy becomes limited.[7]
Meaning of quantum hypothesis
The quantum hypothesis can explain the observed emissivity of the hot body very well. It was not until 1926 when another German scientist Weiner Heisenberg put forward the famous uncertainty principle that its meaning to fatalism was realized.In order to predict the future position and velocity of a particle, people must be able to accurately measure its current position and velocity.The obvious way is to shine light on the particle, and part of the light wave is scattered by the particle, thus indicating its position.However, it is impossible to determine the position of particles to a smaller extent than the distance between the two peaks of light, so it is necessary to use short wavelength light to measure the position of particles.The particle position can be measured through the "hexagonal mirror"."Hexagonal mirror": one observation mirror at the top and bottom, one observation mirror at the left and right, one observation mirror at the front and one observation mirror at the back.According to Planck's quantum hypothesis, people cannot use any small amount of light, but at least one quantum of light.This quantum will disturb the particle and change its speed in an unpredictable way.Moreover, the more accurate the position measurement is, the shorter the wavelength required is, and the greater the energy of individual quantum is, so the velocity of particles will be disturbed more severely.In other words, the more accurate you measure the position of particles, the less accurate you measure the velocity, and vice versa.Heisenberg pointed out that the uncertainty of particle position multiplied by particle mass and then multiplied by speed cannot be less than a certain quantity Planck constant.Moreover, this limit does not depend on the method of measuring the position and velocity of particles, nor does it depend on the type of particles.Heisenberg uncertainty principle is a basic and unavoidable property of the world.
influence
The uncertainty principle has a very profound impact on our world outlook.Even more than 50 years later, it has not been appreciated by many philosophers and is still the subject of many controversies.The uncertainty principle brings to an end Laplace's scientific theory, that is, the dream of a completely deterministic universe model: if people cannot even accurately measure the current state of the universe, then they cannot accurately predict future events (denying that observers can determine the future)!But objectively speaking, the current state of the universe is certain (admitting the certainty of the objective future).We can still imagine that for some supernatural creatures, there is a set of laws that completely determine events. These creatures can observe their state without disturbing the universe.However, for all of us, such a cosmic model is not very interesting, because for us observers, the future is indeed unpredictable.It seems that it is better to use the economic principle called Aokeng Razor to cut off all features that cannot be observed in the theory.The 1920s.On the basis of the uncertainty principle, Heisenberg, Irving Schrodinger and Paul Dirac used this method to re express mechanics into a new theory called quantum mechanics.In this theory, the particle no longer has a well defined position and velocity that can be observed at the same time, but instead has a quantum state of a combination of position and velocity.
quantum mechanics
In general, quantum mechanics does not predict a single deterministic result for a single observation.Instead, it predicts a set of different possible outcomes and tells us the probability of each outcome.That is to say, if we make the same measurement for a large number of similar systems, and each system starts in the same way, we will find that the measurement result is that A occurs a certain number of times, and B occurs a different number of times, etc.People can predict that the result is an approximation of the number of occurrences of A or B, but cannot predict the specific results of individual measurements.Therefore, quantum mechanics introduces the inevitable unpredictability or contingency to science.Although Einstein played a great role in developing these ideas, he strongly opposed them.The reason why he gotNobel PrizeBecause of his contribution to quantum theory.Even so, he never accepted the view that the universe was controlled by opportunities;His feeling can be expressed in his famous assertion: "God does not play dice." However, most other scientists are willing to accept quantum mechanics because it is in perfect agreement with the experiment.It has indeed become an extremely successful theory, and has become the basis of almost all modern science and technology.It restricts the behavior of transistors and integrated circuits, which are the basic elements of electronic devices such as televisions and computers.It is also the foundation of modern chemistry and biology.The only fields that physical science does not allow quantum mechanics to enter are gravity and the large-scale structure of the universe.
