Some people cite randomness in quantum mechanics to support the theory of free will, but first, there is still an insurmountable distance between this randomness on the micro scale and macro free will in the usual sense; Secondly, it is difficult to prove whether this randomness is irreducible, because people's observation ability on the micro scale is still limited. Whether nature is really random is still an open question. Planck's constant is the decisive factor of this gap. Many examples of random events in statistics are strictly decisive.
[Edit this paragraph] A brief history of the development of quantum mechanics
Quantum mechanics is developed on the basis of the old quantum theory. The old quantum theory includes Planck's quantum hypothesis, Einstein's light quantum theory and Bohr's atomism.
1900, Planck put forward the radiation quantum hypothesis, assuming that the energy exchange between electromagnetic field and matter is realized in a discontinuous form (energy quantum), and the size of the energy quantum is proportional to the radiation frequency, and the proportional constant is called Planck constant, thus obtaining the energy distribution formula of blackbody radiation and successfully explaining the blackbody radiation phenomenon.
1905, Einstein introduced the concept of photon, gave the relationship between the energy and momentum of photon and the frequency and wavelength of radiation, and successfully explained the photoelectric effect. Later, he proposed that the vibration energy of solids is also quantized, thus explaining the specific heat of solids at low temperatures.
19 13, Bohr established the quantum theory of atoms on the basis of Rutherford's nuclear atom model. According to this theory, electrons in atoms can only move in discrete orbits, and when they move in orbits, they neither absorb energy nor release energy. An atom has definite energy, and its state is called "steady state". Only when the atom moves from one steady state to another, can it absorb or radiate energy. Although this theory has many successes, there are still many difficulties in further explaining the experimental phenomena.
After people realized that light has the duality of fluctuation and particles, in order to explain some phenomena that cannot be explained by classical theory, French physicist De Broglie put forward the concept of matter wave in 1923. People think that all microscopic particles are accompanied by a wave, which is called de Broglie wave.
De Broglie's equation of matter wave: E=? Ω, p=h/λ, where? = h/2π, which can be expressed by E=p? /2m gives λ = √ (h? /2mE).
Because microscopic particles have wave-particle duality, they follow different motion laws from macroscopic objects, and quantum mechanics describing the motion laws of microscopic particles is also different from classical mechanics describing the motion laws of macroscopic objects. When the particle size changes from micro to macro, the law it follows also changes from quantum mechanics to classical mechanics.
The difference between quantum mechanics and classical mechanics lies in the description of the state of particles, mechanical quantities and their changing laws. In quantum mechanics, the state of particles is described by wave function, which is a complex function of coordinates and time. In order to describe the law of microscopic particle state changing with time, it is necessary to find out the motion equation satisfied by wave function. This equation was first discovered by Schrodinger in 1926, and it is called Schrodinger equation.
When microscopic particles are in a certain state, their mechanical quantities (such as coordinates, momentum, angular momentum, energy, etc. Generally, there are a series of possible values, and each possible value appears with a certain probability. When the state of the particle is determined, the probability that the mechanical quantity has a certain possible value is completely determined. This is the uncertainty relation obtained by Heisenberg in 1927. At the same time, Bohr put forward the principle of union, which further explained quantum mechanics.
The combination of quantum mechanics and special relativity produces relativistic quantum mechanics. Quantum electrodynamics was developed through the work of Dirac, Heisenberg (also known as Heisenberg, the same below) and Pauli. Quantum field theory, which describes various particle fields, has been formed since 1930s, and it forms the theoretical basis for describing basic particle phenomena.
Quantum mechanics was developed and established after the establishment of the old quantum theory. In order to explain some phenomena in the microscopic field, the old quantum theory artificially revised or attached some conditions to the classical physical theory. Because the old quantum theory is not satisfactory, people have established quantum mechanics from two different paths when looking for the laws in the microscopic field.
1925, Heisenberg only dealt with the knowledge of observable measurement based on physical theory, abandoned the concept of unobservable orbit, and established matrix mechanics based on observable radiation frequency and intensity with Born and Iordan. 1926, Schrodinger found the equation of motion of the micro-system based on the knowledge that quantum is the reflection of the fluctuation of the micro-system, thus establishing wave mechanics, and proved the mathematical equivalence between wave mechanics and matrix mechanics shortly thereafter; Dirac and Iordan independently developed a universal transformation theory and gave a concise and perfect mathematical expression of quantum mechanics.
Heisenberg also put forward the uncertainty principle, the formula of which is as follows: Δ x Δ p ≥/2.
[Edit this paragraph] The basic content of quantum mechanics
The basic principles of quantum mechanics include the concept of quantum state, the corresponding rules and physical principles between motion equations, theoretical concepts and observed physical quantities.
In quantum mechanics, the state of a physical system is represented by state functions, and the arbitrary linear superposition of state functions still represents a possible state of the system. The change of state with time follows a linear differential equation, which predicts the behavior of the system. Physical quantities are represented by operators that meet certain conditions and represent some operation. The operation of measuring the physical quantity of a physical system in a certain state corresponds to the effect of the operator representing the quantity on its state function; The possible value of measurement is determined by the eigenequation of the operator, and the expected value of measurement is calculated by the integral equation containing the operator.
The square of the state function represents the probability that a physical quantity is its variable. According to these basic principles and other necessary assumptions, quantum mechanics can explain various phenomena of atoms and subatomics.
According to Dirac symbol, the state function is expressed by and the probability density of the state function is expressed by ρ =
The state function can be expressed as a state vector expanded in an orthogonal space set, such as | ψ (x) >; =∑|ρ_ I & gt； , where | ρ _ i > Is a space basis vector orthogonal to each other, < m | n & gt=δm, and n is a Dirac function, which satisfies the orthogonal normalization property.
The state function satisfies Schrodinger wave equation, I? (d/dt)| m & gt； = H | m> After the variables are separated, the temporal evolution equation H | m > can be obtained. = En | m>, En is the energy eigenvalue and h is the Hamiltonian energy operator.
Therefore, the quantization of classical physical quantities comes down to the solution of Schrodinger wave equation.
The explanation of quantum mechanics involves many philosophical problems, the core of which is causality and physical reality. According to the causality in the sense of dynamics, the motion equation of quantum mechanics is also the causality equation. When the state of the system at a certain moment is known, its future and past state at any moment can be predicted according to the equation of motion.
However, the prediction of quantum mechanics is essentially different from that of classical physical equations of motion (particle motion equation and wave equation). In the classical physics theory, the measurement of a system will not change its state, but it only changes and evolves according to the equation of motion. Therefore, the equation of motion can clearly predict the mechanical quantities that determine the state of the system.
But in quantum mechanics, there are two changes in the state of the system. One is that the state of the system evolves according to the equation of motion, which is a reversible change; The other is to measure irreversible changes that change the state of the system. Therefore, quantum mechanics can not give a definite prediction about the physical quantity that determines the state, but can only give the probability of taking the value of the physical quantity. In this sense, the causal law of classical physics has failed in the microscopic field.
Based on this, some physicists and philosophers assert that quantum mechanics abandons the law of causality, while others believe that the law of causality of quantum mechanics reflects a new law of causality-probabilistic causality. In quantum mechanics, the wave function representing the quantum state is defined in the whole space, and the change of any state is realized in the whole space at the same time.
Since the 1970s, experiments on the correlation of distant particles have shown that space-like separation events are related to the predictions of quantum mechanics. This correlation contradicts the view of special relativity, which holds that the physical interaction between objects can only propagate at a speed not greater than the speed of light. Therefore, in order to explain the existence of this correlation, some physicists and philosophers have proposed that there is a global causality or global causality in the quantum world, which is different from the local causality based on special relativity and can determine the behavior of related systems as a whole.
Quantum mechanics uses the concept of quantum state to represent the state of microscopic system, which deepens people's understanding of physical reality. The properties of microscopic systems are always shown in the interaction with other systems, especially observation instruments.
When people describe the observation results in the language of classical physics, it is found that the microscopic system is mainly characterized by fluctuating images or particle behaviors under different conditions. The concept of quantum state expresses the possibility of waves or particles generated by the interaction between microscopic systems and instruments.
Quantum mechanics shows that micro-physical reality is neither wave nor particle, and the real reality is quantum state. The decomposition of real state into hidden state and explicit state is caused by measurement, and only explicit state here conforms to the meaning of classical physical real. The reality of micro-system is also reflected in its inseparability. Quantum mechanics regards the research object and its environment as a whole, and it is not allowed to regard the world as composed of separate and independent parts. The experimental results of long-distance particle correlation also quantitatively support the inseparability of quantum States. Uncertainty means that economic actors can't know the result of their own decisions accurately in advance. In other words, as long as the decision of economic actors has more than one possible outcome, uncertainty will arise.
Uncertainty also refers to the uncertainty of quantum motion in quantum mechanics. Because the observation interferes with some quantities, the quantity associated with it (* * * yoke quantity) is inaccurate. This is the source of uncertainty.
Uncertainty, the concept of risk management in economics, means that economic subjects cannot know the distribution range and state of future economic conditions (especially gains and losses).
In quantum mechanics, uncertainty refers to the uncertainty of measuring physical quantities, because under certain conditions, some mechanical quantities can only be in their eigenstates, and the displayed values are discrete, so it is possible to get different values at different times, and there will be uncertain values, that is, when you measure, you may get this value or that value, and the obtained values are uncertain. Only by measuring the eigenstate of this mechanical quantity can we get an accurate value.
In classical physics, the position and momentum of a particle can be used to accurately describe its motion. At the same time, knowing the acceleration, we can even predict the position and momentum of the particle at any time in the future, thus drawing the trajectory. But in microphysics, uncertainty tells us that if we want to measure the position of particles more accurately, the measured momentum will be more inaccurate. In other words, it is impossible to accurately measure the position and momentum of a particle at the same time, so it is impossible to describe the motion of a particle by trajectory. This is the concrete explanation of the uncertainty principle.
Bohr Bohr is an outstanding contributor to quantum mechanics. He pointed out the concept of electron orbital quantization. Bohr thinks that the nucleus has a certain energy level. When an atom absorbs energy, it will jump to a higher energy level or excited state. When an atom releases energy, it will jump to a lower energy level or ground state. Whether the atomic energy level jumps depends on the difference between the two energy levels. According to this theory, Rydberg's common sense can be calculated theoretically, which is in good agreement with the experiment. But Bohr's theory also has limitations. For larger atoms, the error of calculation results is very large. Bohr still retains the concept of orbit in the macro world. In fact, the coordinates of electrons appearing in space are uncertain, and there are many electrons gathered, which shows that the probability of electrons appearing here is high, and vice versa. Many electrons gather together, which can be called an electron cloud.
[Edit this paragraph] Interpretation of quantum mechanics: particle vibration
Four-dimensional quantum theory on Hawking thin films
"String theory" is similar to 10 dimension or 1 1 dimension = vibrating string, and tiny objects are vibrating like strings.
Modern interpretation of the quantum theory of the four-dimensional world in Hawking's films (Deng Yu et al.,1980);
Vibration quantum (wave quantum = quantum ghost wave) = vibration of translational particles; Vibrating particles; Tiny objects like quantum (particle) are oscillating.
Fluctuation quantum = quantum fluctuation = particle translation+vibration
= translation+vibration
= vector sum
Deng's explanation of quantum ghost wave: vector sum of translation and vibration of microscopic particles (quantum)
Particle wave, quantum wave = vibration of particles (vibration of translational particles)