How to understand quantum mechanics. Quantum physics for dummies: the essence in simple words

What is quantum mechanics?

Quantum mechanics (QM; also known as quantum physics or quantum theory), including quantum field theory, is a branch of physics that studies the laws of nature that occur at small distances and at low energies of atoms and subatomic particles. Classical physics - physics that existed before quantum mechanics, follows from quantum mechanics as its limiting transition, valid only at large (macroscopic) scales. Quantum mechanics differs from classical physics in that energy, momentum, and other quantities are often limited to discrete values ​​(quantization), objects have characteristics of both particles and waves (wave-particle duality), and there are limits to the precision with which quantities can be measured. determined (uncertainty principle).

Quantum mechanics follows successively from Max Planck's 1900 solution to the black-body radiation problem (published 1859) and Albert Einstein's 1905 work proposing quantum theory to explain the photoelectric effect (published 1887). Early quantum theory was deeply rethought in the mid-1920s.

The rethought theory is formulated in the language of specially developed mathematical formalisms. In one, a mathematical function (wave function) provides information about the probability amplitude of the particle's position, momentum, and other physical characteristics.

Important areas of application of quantum theory are: quantum chemistry, superconducting magnets, light-emitting diodes, as well as laser, transistor and semiconductor devices such as the microprocessor, medical and research imaging such as magnetic resonance imaging and electron microscopy, and explanations of many biological and physical phenomena.

History of quantum mechanics

Scientific research into the wave nature of light began in the 17th and 18th centuries, when scientists Robert Hooke, Christian Huygens and Leonhard Euler proposed the wave theory of light based on experimental observations. In 1803, Thomas Young, an English general scientist, conducted the famous double-slit experiment, which he later described in a paper entitled The Nature of Light and Colors. This experiment played an important role in the general acceptance of the wave theory of light.

In 1838, Michael Faraday discovered cathode rays. These studies were followed by Gustav Kirchhoff's formulation of the blackbody radiation problem in 1859, Ludwig Boltzmann's proposal in 1877 that the energy states of a physical system could be discrete, and Max Planck's quantum hypothesis in 1900. Planck's hypothesis that energy is emitted and absorbed in a discrete "quantum" (or packets of energy) matches exactly the observed patterns of blackbody radiation.

In 1896, Wilhelm Wien empirically determined the law of distribution of black body radiation, named after him, Wien's law. Ludwig Boltzmann independently came to this result by analyzing Maxwell's equations. However, the law only applied at high frequencies and underestimated radiation at low frequencies. Planck later corrected this model with a statistical interpretation of Boltzmann's thermodynamics and proposed what is now called Planck's law, which led to the development of quantum mechanics.

Following Max Planck's solution in 1900 to the problem of black body radiation (published 1859), Albert Einstein proposed quantum theory to explain the photoelectric effect (1905, published 1887). In the years 1900-1910, atomic theory and the corpuscular theory of light began to be widely accepted as scientific fact for the first time. Accordingly, these latter theories can be considered quantum theories of matter and electromagnetic radiation.

Among the first to study quantum phenomena in nature were Arthur Compton, C. W. Raman, and Peter Zeeman, each of whom has several quantum effects named after them. Robert Andrews Millikan studied the photoelectric effect experimentally, and Albert Einstein developed a theory for it. At the same time, Ernest Rutherford experimentally discovered the nuclear model of the atom, according to which Niels Bohr developed his theory of atomic structure, which was later confirmed by the experiments of Henry Moseley. In 1913, Peter Debye expanded Niels Bohr's theory of atomic structure by introducing elliptical orbits, a concept also proposed by Arnold Sommerfeld. This stage in the development of physics is known as old quantum theory.

According to Planck, the energy (E) of a radiation quantum is proportional to the radiation frequency (v):

where h is Planck's constant.

Planck was careful to insist that this was simply a mathematical expression of the processes of absorption and emission of radiation and had nothing to do with the physical reality of radiation itself. In fact, he considered his quantum hypothesis to be a mathematical trick performed in order to get the right answer, rather than a major fundamental discovery. However, in 1905, Albert Einstein gave Planck's quantum hypothesis a physical interpretation and used it to explain the photoelectric effect, in which shining light on certain substances can cause electrons to be emitted from the substance. For this work, Einstein received the 1921 Nobel Prize in Physics.

Einstein then expanded on this idea to show that an electromagnetic wave, which is what light is, can also be described as a particle (later called a photon), with discrete quantum energy that depends on the frequency of the wave.

During the first half of the 20th century, Max Planck, Niels Bohr, Werner Heisenberg, Louis de Broglie, Arthur Compton, Albert Einstein, Erwin Schrödinger, Max Born, John von Neumann, Paul Dirac, Enrico Fermi, Wolfgang Pauli, Max von Laue, Freeman Dyson, David Hilbert, Wilhelm Wien, Shatyendranath Bose, Arnold Sommerfeld and others laid the foundations of quantum mechanics. Niels Bohr's Copenhagen interpretation has received universal recognition.

In the mid-1920s, developments in quantum mechanics led to it becoming the standard formulation for atomic physics. In the summer of 1925, Bohr and Heisenberg published results that closed the old quantum theory. Out of respect for their particle-like behavior in certain processes and measurements, light quanta came to be called photons (1926). From Einstein's simple postulate arose a flurry of discussions, theoretical constructions and experiments. Thus, entire fields of quantum physics emerged, leading to its widespread recognition at the Fifth Solvay Congress in 1927.

It was found that subatomic particles and electromagnetic waves are neither simply particles nor waves, but have certain properties of each. This is how the concept of wave-particle duality arose.

By 1930, quantum mechanics was further unified and formulated in the work of David Hilbert, Paul Dirac, and John von Neumann, which placed great emphasis on measurement, the statistical nature of our knowledge of reality, and philosophical reflections on the “observer.” It has subsequently penetrated into many disciplines, including quantum chemistry, quantum electronics, quantum optics, and quantum information science. Her theoretical modern developments include string theory and theories of quantum gravity. It also provides a satisfying explanation of many features of the modern periodic table of elements and describes the behavior of atoms in chemical reactions and the movement of electrons in computer semiconductors, and therefore plays a crucial role in many modern technologies.

Although quantum mechanics was built to describe the microscopic world, it is also needed to explain some macroscopic phenomena such as superconductivity and superfluidity.

What does the word quantum mean?

The word quantum comes from the Latin "quantum", which means "how much" or "how much". In quantum mechanics, a quantum means a discrete unit associated with certain physical quantities, such as the energy of an atom at rest. The discovery that particles are discrete packets of energy with wave-like properties led to the creation of the branch of physics that deals with atomic and subatomic systems, which is now called quantum mechanics. It provides the mathematical foundation for many areas of physics and chemistry, including condensed matter physics, solid state physics, atomic physics, molecular physics, computational physics, computational chemistry, quantum chemistry, particle physics, nuclear chemistry, and nuclear physics. Some fundamental aspects of the theory are still being actively studied.

The meaning of quantum mechanics

Quantum mechanics is essential for understanding the behavior of systems at atomic and smaller distance scales. If the physical nature of the atom were described solely by classical mechanics, then the electrons should not orbit the nucleus, since orbital electrons should emit radiation (due to circular motion) and eventually collide with the nucleus due to the loss of energy through radiation. Such a system could not explain the stability of atoms. Instead, electrons reside in uncertain, non-deterministic, smeared, probabilistic wave-particle orbitals around the nucleus, contrary to traditional concepts of classical mechanics and electromagnetism.

Quantum mechanics was originally developed to better explain and describe the atom, especially the differences in the spectra of light emitted by different isotopes of the same chemical element, as well as to describe subatomic particles. In short, the quantum mechanical model of the atom has been amazingly successful in an area where classical mechanics and electromagnetism have failed.

Quantum mechanics includes four classes of phenomena that classical physics cannot explain:

• quantization of individual physical properties
• quantum entanglement
• uncertainty principle
• wave-particle duality

Mathematical foundations of quantum mechanics

In the mathematically rigorous formulation of quantum mechanics developed by Paul Dirac, David Hilbert, John von Neumann, and Hermann Weyl, the possible states of a quantum mechanical system are symbolized by unit vectors (called state vectors). Formally, they belong to the complex separable Hilbert space - otherwise, the state space or the associated Hilbert space of the system, and are defined up to the product of a complex number with unit modulus (phase factor). In other words, possible states are points in the projective space of Hilbert space, typically called complex projective space. The exact nature of this Hilbert space depends on the system - for example, the state space of position and momentum is the space of square-integrable functions, while the state space for the spin of a single proton is just the direct product of two complex planes. Each physical quantity is represented by a hypermaximally Hermitian (more precisely: self-adjoint) linear operator acting on the state space. Each eigenstate of a physical quantity corresponds to an eigenvector of the operator, and its associated eigenvalue corresponds to the value of the physical quantity in that eigenstate. If the spectrum of the operator is discrete, the physical quantity can only take discrete eigenvalues.

In the formalism of quantum mechanics, the state of a system at a given moment is described by a complex wave function, also called a state vector in a complex vector space. This abstract mathematical object allows you to calculate the probabilities of the outcomes of specific experiments. For example, it allows you to calculate the probability of an electron being in a certain area around the nucleus at a certain time. Unlike classical mechanics, simultaneous predictions with arbitrary precision can never be made for conjugate variables such as position and momentum. For example, electrons can be assumed to be (with some probability) located somewhere within a given region of space, but their exact location is unknown. You can draw regions of constant probability, often called “clouds,” around the nucleus of an atom to represent where the electron is most likely to be. The Heisenberg uncertainty principle quantifies the inability to accurately localize a particle with a given momentum, which is the conjugate of position.

According to one interpretation, as a result of the measurement, the wave function containing information about the probability of the state of the system decays from a given initial state to a certain eigenstate. Possible results of the measurement are the eigenvalues ​​of the operator representing the physical quantity - which explains the choice of the Hermitian operator, in which all eigenvalues ​​are real numbers. The probability distribution of a physical quantity in a given state can be found by calculating the spectral decomposition of the corresponding operator. The Heisenberg uncertainty principle is represented by a formula in which operators corresponding to certain quantities do not commute.

Measurement in quantum mechanics

The probabilistic nature of quantum mechanics thus follows from the act of measurement. This is one of the most difficult aspects of quantum systems to understand, and was a central theme in Bohr's famous debate with Einstein, in which both scientists attempted to clarify these fundamental principles through thought experiments. In the decades following the formulation of quantum mechanics, the question of what constitutes a “measurement” was widely studied. New interpretations of quantum mechanics have been formulated to do away with the concept of wave function collapse. The basic idea is that when a quantum system interacts with a measuring apparatus, their respective wave functions become entangled, so that the original quantum system ceases to exist as an independent entity.

The probabilistic nature of quantum mechanics predictions

As a rule, quantum mechanics does not assign specific values. Instead, it makes a prediction using a probability distribution; that is, it describes the probability of obtaining possible results from the measurement of a physical quantity. Often these results are distorted, like probability density clouds, by many processes. Probability density clouds are an approximation (but better than the Bohr model) in which the location of the electron is given by a probability function, wave functions corresponding to the eigenvalues, such that the probability is the square of the modulus of the complex amplitude, or quantum state of nuclear attraction. Naturally, these probabilities will depend on the quantum state at the “moment” of measurement. Consequently, uncertainty is introduced into the measured value. There are, however, some states that are associated with certain values ​​of a particular physical quantity. They are called eigenstates (eigenstates) of a physical quantity ("eigen" can be translated from German as "inherent" or "inherent").

It is natural and intuitive that everything in everyday life (all physical quantities) has its own values. Everything seems to have a certain position, a certain moment, a certain energy, and a certain time of occurrence. However, quantum mechanics does not specify the precise values ​​of a particle's position and momentum (since these are conjugate pairs) or its energy and time (since they are also conjugate pairs); more precisely, it provides only the range of probabilities with which that particle can have a given momentum and the probability of momentum. Therefore, it is advisable to distinguish between states that have uncertain values ​​and states that have definite values ​​(eigenstates). As a rule, we are not interested in a system in which the particle does not have its own value of a physical quantity. However, when measuring a physical quantity, the wave function instantly takes on the eigenvalue (or "generalized" eigenvalue) of that quantity. This process is called wave function collapse, a controversial and much discussed process in which the system under study is expanded by adding a measuring device to it. If you know the corresponding wave function immediately before the measurement, you can calculate the probability that the wave function will go to each of the possible eigenstates. For example, the free particle in the previous example typically has a wave function, which is a wave packet centered around some average position x0 (having no position and momentum eigenstates). When the position of a particle is measured, it is impossible to predict the result with certainty. It is likely, but not certain, that it will be near x0, where the amplitude of the wave function is large. After performing a measurement, having obtained some result x, the wave function collapses into its own function of the position operator centered at x.

Schrödinger equation in quantum mechanics

The time evolution of a quantum state is described by the Schrödinger equation, in which the Hamiltonian (the operator corresponding to the total energy of the system) generates the time evolution. The time evolution of wave functions is deterministic in the sense that - given what the wave function was at the initial time - one can make a clear prediction of what the wave function will be at any time in the future.

On the other hand, during the measurement, the change from the original wave function to another, later wave function will not be deterministic, but will be unpredictable (i.e. random). An emulation of time evolution can be seen here.

Wave functions change over time. The Schrödinger equation describes the change in wave functions over time, and plays a role similar to the role of Newton's second law in classical mechanics. The Schrödinger equation, applied to the above example of a free particle, predicts that the center of the wave packet will move through space at a constant speed (like a classical particle in the absence of forces acting on it). However, the wave packet will also spread out over time, meaning the position becomes more uncertain over time. This also has the effect of turning the position eigenfunction (which can be thought of as an infinitely sharp peak of the wave packet) into an extended wave packet that no longer represents the (defined) position eigenvalue.

Some wave functions produce probability distributions that are constant or independent of time—for example, when in a stationary state with constant energy, time disappears from the modulus of the square of the wave function. Many systems that are considered dynamic in classical mechanics are described in quantum mechanics by such “static” wave functions. For example, a single electron in an unexcited atom is represented classically as a particle moving in a circular path around the atomic nucleus, while in quantum mechanics it is described by a static, spherically symmetric wave function surrounding the nucleus (Fig. 1) (note, however, that only the lowest states of orbital angular momentum, denoted s, are spherically symmetric).

The Schrödinger equation acts on the entire probability amplitude, and not just on its absolute value. While the absolute value of the probability amplitude contains information about probabilities, its phase contains information about the mutual influence between quantum states. This gives rise to "wave-like" behavior of quantum states. As it turns out, analytical solutions to the Schrödinger equation are possible only for a very small number of Hamiltonians of relatively simple models, such as the quantum harmonic oscillator, the particle in a box, the hydrogen molecule ion and the hydrogen atom - these are the most important representatives of such models. Even the helium atom, which contains only one more electron than the hydrogen atom, has defied any attempt at a purely analytical solution.

However, there are several methods for obtaining approximate solutions. An important technique known as perturbation theory uses an analytical result obtained for a simple quantum mechanical model and from this generates a result for a more complex model that differs from the simpler model (for example) by adding weak potential field energy. Another approach is the "quasi-classical approximation" method, which is applied to systems for which quantum mechanics applies only to weak (small) deviations from classical behavior. These deviations can then be calculated from the classical motion. This approach is especially important when studying quantum chaos.

Mathematically equivalent formulations of quantum mechanics

There are numerous mathematically equivalent formulations of quantum mechanics. One of the oldest and most commonly used formulations is the "transformation theory" proposed by Paul Dirac, which combines and generalizes the two earliest formulations of quantum mechanics - matrix mechanics (created by Werner Heisenberg) and wave mechanics (created by Erwin Schrödinger).

Given that Werner Heisenberg was awarded the Nobel Prize in Physics in 1932 for the development of quantum mechanics, Max Born's role in the development of QM was overlooked until he was awarded the Nobel Prize in 1954. This role is mentioned in a 2005 biography of Born, which talks about his role in the matrix formulation of quantum mechanics, as well as the use of probability amplitudes. In 1940, Heisenberg himself admitted in a commemorative volume in honor of Max Planck that he learned about matrices from Born. In the matrix formulation, the instantaneous state of a quantum system determines the probabilities of its measurable properties or physical quantities. Examples of quantities include energy, position, momentum, and orbital momentum. Physical quantities can be either continuous (eg the position of a particle) or discrete (eg the energy of an electron bound to a hydrogen atom). Feynman path integrals are an alternative formulation of quantum mechanics in which the quantum mechanical amplitude is considered to be the sum over all possible classical and non-classical trajectories between the initial and final states. This is the quantum mechanical analogue of the principle of least action in classical mechanics.

Laws of quantum mechanics

The laws of quantum mechanics are fundamental. It is stated that the state space of a system is Hilbertian, and the physical quantities of that system are Hermitian operators acting on that space, although it is not stated which exactly these Hilbert spaces are or which exactly these operators are. They can be selected accordingly to obtain a quantitative characteristic of the quantum system. An important guideline for making these decisions is the correspondence principle, which states that the predictions of quantum mechanics reduce to classical mechanics when the system moves into the region of high energies or, equivalently, into the region of large quantum numbers, that is, while an individual particle has a certain degree of randomness; in systems containing millions of particles, average values ​​predominate and, when approaching the high-energy limit, the statistical probability of random behavior tends to zero. In other words, classical mechanics is simply the quantum mechanics of large systems. This "high energy" limit is known as the classical or correspondence limit. Thus, the solution can even begin with an established classical model of a particular system, and then try to guess the underlying quantum model that would generate such a classical model when passing to the matching limit.

When quantum mechanics was originally formulated, it was applied to models whose limit of correspondence was non-relativistic classical mechanics. For example, the well-known quantum harmonic oscillator model uses an explicitly non-relativistic expression for the kinetic energy of the oscillator and is thus a quantum version of the classical harmonic oscillator.

Interaction with other scientific theories

Early attempts to combine quantum mechanics with special relativity involved replacing the Schrödinger equation with covariant equations such as the Klein-Gordon equation or the Dirac equation. Although these theories were successful in explaining many experimental results, they had certain unsatisfactory qualities arising from the fact that they did not take into account the relativistic creation and destruction of particles. A fully relativistic quantum theory required the development of a quantum field theory that involves quantizing a field (rather than a fixed set of particles). The first full-fledged quantum field theory, quantum electrodynamics, provides a complete quantum description of electromagnetic interaction. The full apparatus of quantum field theory is often not required to describe electrodynamic systems. A simpler approach, used since the creation of quantum mechanics, is to consider charged particles as quantum mechanical objects that are subject to a classical electromagnetic field. For example, the elementary quantum model of the hydrogen atom describes the electric field of the hydrogen atom using the classical expression for the Coulomb potential:

E2/(4πε0r)

This “quasi-classical” approach does not work if quantum fluctuations of the electromagnetic field play an important role, for example, when photons are emitted by charged particles.

Quantum field theories for strong and weak nuclear forces were also developed. The quantum field theory for strong nuclear interactions is called quantum chromodynamics and describes the interactions of subnuclear particles such as quarks and gluons. The weak nuclear and electromagnetic forces were unified in their quantized forms into a unified quantum field theory (known as the electroweak force) by physicists Abdus Salam, Sheldon Glashow and Steven Weinberg. For this work, all three received the Nobel Prize in Physics in 1979.

It has proven difficult to build quantum models for the fourth remaining fundamental force, gravity. Semiclassical approximations have been performed, leading to predictions such as Hawking radiation. However, the formulation of a complete theory of quantum gravity is hampered by apparent incompatibilities between general relativity (which is the most accurate theory of gravity currently known) and some of the fundamental tenets of quantum theory. Resolving these incompatibilities is an area of ​​active research and theory, such as string theory, one of the possible candidates for a future theory of quantum gravity.

Classical mechanics was also extended into the complex field, with complex classical mechanics beginning to behave similarly to quantum mechanics.

The connection between quantum mechanics and classical mechanics

The predictions of quantum mechanics have been confirmed experimentally with a very high degree of accuracy. According to the correspondence principle between classical and quantum mechanics, all objects obey the laws of quantum mechanics, and classical mechanics is only an approximation for large systems of objects (or statistical quantum mechanics for a large set of particles). Thus, the laws of classical mechanics follow from the laws of quantum mechanics as a statistical average when tending to a very large limiting value of the number of elements of the system or the values ​​of quantum numbers. However, chaotic systems lack good quantum numbers, and quantum chaos studies the connection between classical and quantum descriptions of these systems.

Quantum coherence is an essential difference between classical and quantum theories, exemplified by the Einstein–Podolsky–Rosen (EPR) paradox, and has become an attack on the established philosophical interpretation of quantum mechanics by appealing to local realism. Quantum interference involves the addition of probability amplitudes, while classical "waves" involve the addition of intensities. For microscopic bodies, the extent of the system is much less than the coherence length, which leads to entanglement over long distances and other nonlocal phenomena characteristic of quantum systems. Quantum coherence does not usually appear on macroscopic scales, although an exception to this rule may occur at extremely low temperatures (i.e., near absolute zero), at which quantum behavior can appear on a macroscopic scale. This is in accordance with the following observations:

Many macroscopic properties of a classical system are a direct consequence of the quantum behavior of its parts. For example, the stability of the bulk of matter (consisting of atoms and molecules, which under the influence of electrical forces alone would quickly collapse), the rigidity of solids, as well as the mechanical, thermal, chemical, optical and magnetic properties of matter are the result of the interaction of electric charges in accordance with rules of quantum mechanics.

While the seemingly "exotic" behavior of matter postulated by quantum mechanics and relativity becomes more apparent when dealing with very small particles or traveling at speeds approaching the speed of light, the laws of classical, often called "Newtonian" physics remain accurate when predicting the behavior of the overwhelming number of “large” objects (on the order of the size of large molecules or even larger) and at speeds much lower than the speed of light.

What is the difference between quantum mechanics and classical mechanics?

Classical and quantum mechanics are very different in that they use very different kinematic descriptions.

According to the well-established opinion of Niels Bohr, the study of quantum mechanical phenomena requires experiments with a complete description of all the devices of the system, preparatory, intermediate and final measurements. Descriptions are presented in macroscopic terms expressed in ordinary language, supplemented by concepts of classical mechanics. The initial conditions and final state of the system are respectively described by a position in configuration space, such as coordinate space, or some equivalent space such as momentum space. Quantum mechanics does not allow for a completely accurate description, both in terms of position and momentum, of an exact deterministic and causal prediction of the final state from the initial conditions or "state" (in the classical sense of the word). In this sense, promoted by Bohr in his mature works, a quantum phenomenon is a process of transition from an initial to a final state, and not an instantaneous "state" in the classical sense of the word. Thus, there are two types of processes in quantum mechanics: stationary and transient. For stationary processes, the initial and final positions are the same. For transitional ones, they are different. It is obvious by definition that if only the initial condition is given, then the process is not defined. Given the initial conditions, prediction of the final state is possible, but only on a probabilistic level, since the Schrödinger equation is deterministic for the evolution of the wave function, and the wave function describes the system only in a probabilistic sense.

In many experiments it is possible to take the initial and final state of the system as a particle. In some cases, it turns out that there are potentially multiple spatially distinct paths or trajectories along which a particle can transition from an initial to a final state. An important feature of the quantum kinematic description is that it does not allow us to unambiguously determine which of these paths produces the transition between states. Only the initial and final conditions are defined, and, as stated in the previous paragraph, they are defined only as accurately as the description by spatial configuration or its equivalent allows. In every case for which a quantum kinematic description is needed, there is always a good reason for this limitation of kinematic accuracy. The reason is that for a particle to be experimentally found in a certain position, it must be motionless; to experimentally detect a particle with a certain momentum, it must be in free motion; these two requirements are logically incompatible.

Initially, classical kinematics does not require an experimental description of its phenomena. This makes it possible to completely accurately describe the instantaneous state of the system by position (point) in phase space - the Cartesian product of configuration and momentum spaces. This description simply assumes, or imagines, the state as a physical entity, without worrying about its experimental measurability. This description of the initial state, together with Newton's laws of motion, allows an accurate deterministic and cause-and-effect prediction of the final state, along with a defined trajectory of the system's evolution, to be made. For this purpose, Hamiltonian dynamics can be used. Classical kinematics also allows a description of the process, similar to the description of the initial and final state used by quantum mechanics. Lagrangian mechanics allows us to do this. For processes in which it is necessary to take into account the magnitude of the action of the order of several Planck constants, classical kinematics is not suitable; this requires the use of quantum mechanics.

General theory of relativity

Even though the defining postulates of general relativity and Einstein's quantum theory are unequivocally supported by rigorous and repeatable empirical evidence, and although they do not contradict each other theoretically (at least in relation to their primary statements), they have proven extremely difficult to integrate into one coherent , a single model.

Gravity can be neglected in many areas of particle physics, so the unification between general relativity and quantum mechanics is not a pressing issue in these particular applications. However, the lack of a correct theory of quantum gravity is an important issue in physical cosmology and physicists' search for an elegant "Theory of Everything" (TV). Therefore, resolving all the inconsistencies between both theories is one of the main goals for 20th and 21st century physics. Many eminent physicists, including Stephen Hawking, have labored over the years in an attempt to discover the theory behind it all. This TV will combine not only different models of subatomic physics, but also derive the four fundamental forces of nature - the strong force, electromagnetism, the weak force and gravity - from a single force or phenomenon. While Stephen Hawking initially believed in TV, after considering Gödel's incompleteness theorem, he concluded that such a theory was not feasible and stated this publicly in his lecture "Gödel and the End of Physics" (2002).

Basic theories of quantum mechanics

The quest to unify fundamental forces through quantum mechanics is still ongoing. Quantum electrodynamics (or "quantum electromagnetism"), which is currently (at least in the perturbative regime) the most accurate tested physical theory in rivalry with general relativity, successfully unifies the weak nuclear forces into the electroweak force and is currently being worked on to combine the electroweak and strong interactions into the electrostrong interaction. Current predictions state that around 1014 GeV the three above-mentioned forces merge into a single unified field. In addition to this "grand unification", it is proposed that gravity can be unified with the other three gauge symmetries, which is expected to occur at about 1019 GeV. However - and while special relativity is carefully incorporated into quantum electrodynamics - extended general relativity, currently the best theory describing gravitational forces, is not fully incorporated into quantum theory. One of the people developing a coherent theory of everything, Edward Witten, a theoretical physicist, formulated M-theory, which is an attempt to expound supersymmetry on the basis of superstring theory. M-theory suggests that our apparent 4-dimensional space is actually an 11-dimensional space-time continuum, containing ten space dimensions and one time dimension, although the 7 space dimensions at low energies are completely "densified" (or infinitely curved) and are not easily measured or researched.

Another popular theory is Loop quantum gravity (LQG), a theory first proposed by Carlo Rovelli that describes the quantum properties of gravity. It is also a theory of quantum space and quantum time, since in general relativity the geometric properties of space-time are a manifestation of gravity. LQG is an attempt to unify and adapt standard quantum mechanics and standard general relativity. The main result of the theory is a physical picture in which space is granular. Graininess is a direct consequence of quantization. It has the same granularity of photons in quantum theory of electromagnetism or discrete energy levels of atoms. But here the space itself is discrete. More precisely, space can be considered as an extremely thin fabric or network, “woven” from finite loops. These loop networks are called spin networks. The evolution of a spin network over time is called spin foam. The predicted size of this structure is the Planck length, which is approximately 1.616 × 10-35 m. According to theory, there is no point in a shorter length than this. Therefore, LQG predicts that not only matter, but also space itself, has an atomic structure.

Philosophical aspects of quantum mechanics

Since its inception, the many paradoxical aspects and results of quantum mechanics have given rise to intense philosophical debate and a variety of interpretations. Even fundamental questions, such as Max Born's basic rules regarding probability amplitude and probability distribution, took decades to be appreciated by society and many leading scientists. Richard Feynman once said, “I think I can safely say that no one understands quantum mechanics.” In the words of Steven Weinberg, “There is, in my opinion, no completely satisfactory interpretation of quantum mechanics now.

The Copenhagen interpretation - largely thanks to Niels Bohr and Werner Heisenberg - remains the most acceptable among physicists for 75 years after its proclamation. According to this interpretation, the probabilistic nature of quantum mechanics is not a temporary feature that will eventually be replaced by a deterministic theory, but should be seen as a final rejection of the classical idea of ​​"causation". In addition, it is believed that any well-defined applications of quantum mechanical formalism must always make reference to the experimental design due to the interconnected nature of the evidence obtained in different experimental situations.

Albert Einstein, while one of the founders of quantum theory, himself did not accept some of the more philosophical or metaphysical interpretations of quantum mechanics, such as the rejection of determinism and causation. His most quoted famous response to this approach is: “God doesn’t play dice.” He rejected the concept that the state of a physical system depends on the experimental measurement setup. He believed that natural phenomena occur according to their own laws, regardless of whether and how they are observed. In this regard, it is supported by the currently accepted definition of a quantum state, which remains invariant under an arbitrary choice of the configuration space for its representation, that is, the method of observation. He also believed that the basis of quantum mechanics should be a theory that carefully and directly expresses a rule that rejects the principle of action at a distance; in other words, he insisted on the principle of locality. He considered, but theoretically justifiably rejected, the particular idea of ​​hidden variables to avoid uncertainty or lack of cause-and-effect relationships in quantum mechanical measurements. He believed that quantum mechanics was valid at that time, but not the final and unshakable theory of quantum phenomena. He believed that its future replacement would require deep conceptual advances and that it would not happen quickly or easily. The Bohr-Einstein discussions provide a clear critique of the Copenhagen interpretation from an epistemological point of view.

John Bell showed that this "EPR" paradox led to experimentally testable differences between quantum mechanics and theories that rely on the addition of hidden variables. Experiments have been carried out to prove the accuracy of quantum mechanics, thereby demonstrating that quantum mechanics cannot be improved by adding hidden variables. Alain Aspect's initial experiments in 1982 and many subsequent experiments since then have definitively confirmed quantum entanglement.

Entanglement, as Bell's experiments showed, does not violate cause-and-effect relationships, since no information transfer occurs. Quantum entanglement forms the basis of quantum cryptography, which is proposed for use in highly secure commercial applications in banking and government.

Everett's many-worlds interpretation, formulated in 1956, holds that all the possibilities described by quantum theory simultaneously arise in a multiverse consisting primarily of independent parallel universes. This is not achieved by introducing some “new axiom” into quantum mechanics, but on the contrary, it is achieved by removing the wave packet decay axiom. All possible sequential states of the measured system and the measuring device (including the observer) are present in a real physical - and not just a formal mathematical, as in other interpretations - quantum superposition. Such a superposition of successive combinations of states of different systems is called an entangled state. While the multiverse is deterministic, we perceive non-deterministic behavior, random in nature, since we can only observe the universe (i.e., the contribution of a compatible state to the above superposition) in which we, as observers, inhabit. Everett's interpretation fits perfectly with John Bell's experiments and makes them intuitive. However, according to the theory of quantum decoherence, these “parallel universes” will never be accessible to us. Inaccessibility can be understood this way: once a measurement is made, the system being measured becomes entangled with both the physicist who measured it and with a huge number of other particles, some of which are photons, flying away at the speed of light to the other end of the universe. To prove that the wave function has not decayed, it is necessary to bring all these particles back and measure them again along with the system that was originally measured. Not only is this completely impractical, but even if it could theoretically be done, it would have to destroy any evidence that the original measurement took place (including the physicist's memory). In light of these Bell experiments, Cramer formulated his transactional interpretation in 1986. In the late 1990s, relational quantum mechanics emerged as a modern derivative of the Copenhagen interpretation.

Quantum mechanics has had enormous success in explaining many features of our Universe. Quantum mechanics is often the only tool available that can reveal the individual behavior of the subatomic particles that make up all forms of matter (electrons, protons, neutrons, photons, etc.). Quantum mechanics has greatly influenced string theory, a contender for the Theory of Everything.

Quantum mechanics is also critical to understanding how individual atoms form covalent bonds to form molecules. The application of quantum mechanics to chemistry is called quantum chemistry. Relativistic quantum mechanics can, in principle, describe most chemistry mathematically. Quantum mechanics can also provide a quantitative understanding of the processes of ionic and covalent bonding by explicitly showing which molecules energetically match with other molecules and at what energy values. In addition, most calculations in modern computational chemistry rely on quantum mechanics.

In many industries, modern technologies operate at scales where quantum effects are significant.

Quantum physics in electronics

Many modern electronic devices are designed using quantum mechanics. For example, laser, transistor (and thus microchip), electron microscope and magnetic resonance imaging (MRI). The study of semiconductors led to the invention of the diode and transistor, which are indispensable components of modern electronic systems, computers and telecommunications devices. Another application is the light-emitting diode, which is a highly efficient light source.

Many electronic devices operate under the influence of quantum tunneling. It is even present in a simple switch. The switch would not work if electrons could not quantum tunnel through the oxide layer on the metal contact surfaces. Flash memory chips, the main component of USB storage devices, use quantum tunneling to erase information in their cells. Some negative differential resistance devices, such as the resonant tunnel diode, also use the quantum tunneling effect. Unlike classical diodes, the current in it flows under the influence of resonant tunneling through two potential barriers. Its mode of operation with negative resistance can only be explained by quantum mechanics: as the energy of the state of bound carriers approaches the Fermi level, the tunneling current increases. As you move away from the Fermi level, the current decreases. Quantum mechanics is vital to understanding and designing these types of electronic devices.

Quantum cryptography

Researchers are currently looking for reliable methods to directly manipulate quantum states. Efforts are being made to fully develop quantum cryptography, which theoretically will guarantee the secure transmission of information.

Quantum computing

A more distant goal is the development of quantum computers, which are expected to perform certain computational tasks exponentially faster than classical computers. Instead of classical bits, quantum computers use qubits, which can exist in a superposition of states. Another active research topic is quantum teleportation, which deals with methods for transmitting quantum information over arbitrary distances.

Quantum effects

While quantum mechanics primarily applies to atomic systems with smaller amounts of matter and energy, some systems exhibit quantum mechanical effects on larger scales. Superfluidity, the ability of a fluid to move without friction at a temperature near absolute zero, is one well-known example of such effects. Closely related to this phenomenon is the phenomenon of superconductivity - a flow of electron gas (electric current) moving without resistance in a conductive material at sufficiently low temperatures. The fractional quantum Hall effect is a topological ordered state that corresponds to models of quantum entanglement operating over long distances. States with different topological order (or different long-range entanglement configurations) cannot introduce state changes into each other without phase transformations.

Quantum theory

Quantum theory also contains precise descriptions of many previously unexplained phenomena, such as blackbody radiation and the stability of orbital electrons in atoms. It also provided insight into the workings of many different biological systems, including olfactory receptors and protein structures. Recent research into photosynthesis has shown that quantum correlations play an important role in this fundamental process occurring in plants and many other organisms. However, classical physics can often provide good approximations to the results obtained by quantum physics, usually in conditions of large numbers of particles or large quantum numbers. Because classical formulas are much simpler and easier to compute than quantum formulas, the use of classical approximations is preferred when the system is large enough to make the effects of quantum mechanics negligible.

Movement of a free particle

For example, consider a free particle. In quantum mechanics, wave-particle duality is observed, so that the properties of a particle can be described as the properties of a wave. Thus, a quantum state can be represented as a wave of arbitrary shape and extending through space as a wave function. The position and momentum of a particle are physical quantities. The uncertainty principle states that position and momentum cannot be accurately measured at the same time. However, it is possible to measure the position (without measuring momentum) of a moving free particle by creating a position eigenstate with a wave function (Dirac delta function) that is very large at a certain position x, and zero at other positions. If you perform a position measurement with such a wave function, then the result will be x with a probability of 100% (that is, with complete confidence, or with complete accuracy). This is called the eigenvalue (state) of the position or, specified in mathematical terms, the eigenvalue of the generalized coordinate (eigendistribution). If a particle is in its own state of position, then its momentum is absolutely indeterminable. On the other hand, if the particle is in its own state of momentum, then its position is completely unknown. In an eigenstate of a pulse whose eigenfunction is in the form of a plane wave, it can be shown that the wavelength is equal to h/p, where h is Planck's constant and p is the momentum of the eigenstate.

Rectangular potential barrier

This is a model of the quantum tunneling effect, which plays an important role in the production of modern technological devices such as flash memory and scanning tunneling microscopes. Quantum tunneling is a central physical process occurring in superlattices.

Particle in a one-dimensional potential box

A particle in a one-dimensional potential box is the simplest mathematical example in which spatial constraints lead to quantization of energy levels. A box is defined as having zero potential energy everywhere inside a certain region and infinite potential energy everywhere outside that region.

Final potential well

A finite potential well is a generalization of the infinite potential well problem, which has a finite depth.

The problem of a finite potential well is mathematically more complex than the problem of a particle in an infinite potential box, since the wave function does not vanish at the walls of the well. Instead, the wave function must satisfy more complex mathematical boundary conditions since it is nonzero in the region outside the potential well.

Nobody in this world understands what quantum mechanics is. This is perhaps the most important thing you need to know about her. Of course, many physicists have learned to use laws and even predict phenomena based on quantum computing. But it is still unclear why the observer of the experiment determines the behavior of the system and forces it to accept one of two states.

Here are several examples of experiments with results that will inevitably change under the influence of the observer. They show that quantum mechanics practically deals with the intervention of conscious thought into material reality.

There are many interpretations of quantum mechanics today, but the Copenhagen interpretation is perhaps the most famous. In the 1920s, its general postulates were formulated by Niels Bohr and Werner Heisenberg.

The Copenhagen interpretation is based on the wave function. This is a mathematical function containing information about all possible states of a quantum system in which it exists simultaneously. According to the Copenhagen Interpretation, the state of a system and its position relative to other states can only be determined by observation (the wave function is used only to mathematically calculate the probability of the system being in one state or another).

We can say that after observation, a quantum system becomes classical and immediately ceases to exist in states other than the one in which it was observed. This conclusion found its opponents (remember Einstein’s famous “God does not play dice”), but the accuracy of the calculations and predictions still had their effect.

However, the number of supporters of the Copenhagen interpretation is declining, and the main reason for this is the mysterious instantaneous collapse of the wave function during the experiment. Erwin Schrödinger's famous thought experiment with the poor cat should demonstrate the absurdity of this phenomenon. Let's remember the details.

Inside the black box sits a black cat, along with a vial of poison and a mechanism that can release the poison randomly. For example, a radioactive atom may break a bubble during decay. The exact time of atomic decay is unknown. Only the half-life is known, during which decay occurs with a probability of 50%.

Obviously, to an outside observer, the cat inside the box is in two states: it is either alive, if everything went well, or dead, if decay has occurred and the bottle has broken. Both of these states are described by the cat's wave function, which changes over time.

The more time has passed, the greater the likelihood that radioactive decay has occurred. But as soon as we open the box, the wave function collapses, and we immediately see the results of this inhumane experiment.

In fact, until the observer opens the box, the cat will endlessly balance between life and death, or be both alive and dead. Its fate can only be determined by the actions of the observer. Schrödinger pointed out this absurdity.

According to a survey of famous physicists conducted by The New York Times, the electron diffraction experiment is one of the most amazing studies in the history of science. What is its nature? There is a source that emits a beam of electrons onto a light-sensitive screen. And there is an obstacle in the way of these electrons, a copper plate with two slits.

What kind of picture can we expect on the screen if electrons usually appear to us as small charged balls? Two stripes opposite the slots in the copper plate. But in fact, a much more complex pattern of alternating white and black stripes appears on the screen. This is due to the fact that when passing through a slit, electrons begin to behave not only as particles, but also as waves (photons or other light particles that can be a wave at the same time behave in the same way).

These waves interact in space, colliding and reinforcing each other, and as a result, a complex pattern of alternating light and dark stripes is displayed on the screen. At the same time, the result of this experiment does not change even if the electrons pass one after another - even one particle can be a wave and pass through two slits simultaneously. This postulate was one of the main ones in the Copenhagen interpretation of quantum mechanics, where particles can simultaneously exhibit their “ordinary” physical properties and exotic properties as a wave.

But what about the observer? It is he who makes this confusing story even more confusing. When physicists, during similar experiments, tried to determine with the help of instruments which slit the electron actually passed through, the picture on the screen changed dramatically and became “classical”: with two illuminated sections exactly opposite the slits, without any alternating stripes.

The electrons seemed reluctant to reveal their wave nature to the watchful eye of observers. It looks like a mystery shrouded in darkness. But there is a simpler explanation: observation of the system cannot be carried out without physical influence on it. We will discuss this later.

2. Heated fullerenes

Experiments on particle diffraction were carried out not only with electrons, but also with other, much larger objects. For example, fullerenes, large and closed molecules consisting of several dozen carbon atoms, were used. Recently, a group of scientists from the University of Vienna, led by Professor Zeilinger, tried to incorporate an element of observation into these experiments. To do this, they irradiated moving fullerene molecules with laser beams. Then, heated by an external source, the molecules began to glow and inevitably display their presence to the observer.

Along with this innovation, the behavior of molecules also changed. Before such comprehensive observations began, fullerenes were quite successful in avoiding obstacles (exhibiting wave properties), similar to the previous example with electrons hitting the screen. But with the presence of an observer, fullerenes began to behave like completely law-abiding physical particles.

3. Cooling dimension

One of the most famous laws in the world of quantum physics is the Heisenberg uncertainty principle, according to which it is impossible to determine the speed and position of a quantum object at the same time. The more accurately we measure a particle's momentum, the less accurately we can measure its position. However, in our macroscopic real world, the validity of quantum laws acting on tiny particles usually goes unnoticed.

The recent experiments of Professor Schwab from the USA make a very valuable contribution to this field. Quantum effects in these experiments were demonstrated not at the level of electrons or fullerene molecules (the approximate diameter of which is 1 nm), but on larger objects, a tiny aluminum strip. This tape was fixed on both sides so that its middle was suspended and could vibrate under external influence. In addition, a device was placed nearby that could accurately record the position of the tape. The experiment revealed several interesting things. First, any measurement related to the position of the object and observation of the tape influenced it; after each measurement, the position of the tape changed.

The experimenters determined the coordinates of the tape with high accuracy, and thus, in accordance with the Heisenberg principle, changed its speed, and therefore its subsequent position. Secondly, and quite unexpectedly, some measurements led to cooling of the tape. Thus, an observer can change the physical characteristics of objects simply by his presence.

4. Freezing particles

As is known, unstable radioactive particles decay not only in experiments with cats, but also on their own. Each particle has an average lifespan, which, as it turns out, can increase under the watchful eye of an observer. This quantum effect was predicted back in the 60s, and its brilliant experimental proof appeared in a paper published by a team led by Nobel laureate physicist Wolfgang Ketterle from the Massachusetts Institute of Technology.

In this work, the decay of unstable excited rubidium atoms was studied. Immediately after preparing the system, the atoms were excited using a laser beam. The observation took place in two modes: continuous (the system was constantly exposed to small light pulses) and pulsed (the system was irradiated from time to time with more powerful pulses).

The results obtained were fully consistent with theoretical predictions. External light effects slow down the decay of particles, returning them to their original state, which is far from the state of decay. The magnitude of this effect was also consistent with predictions. The maximum lifetime of unstable excited rubidium atoms increased by 30 times.

5. Quantum mechanics and consciousness

Electrons and fullerenes cease to show their wave properties, aluminum plates cool down, and unstable particles slow down their decay. The watchful eye of the observer literally changes the world. Why can't this be proof of the involvement of our minds in the workings of the world? Perhaps Carl Jung and Wolfgang Pauli (Austrian physicist, Nobel Prize winner, pioneer of quantum mechanics) were right, after all, when they said that the laws of physics and consciousness should be seen as complementary to each other?

We are one step away from recognizing that the world around us is simply an illusory product of our mind. The idea is scary and tempting. Let's try to turn to physicists again. Especially in recent years, when fewer and fewer people believe the Copenhagen interpretation of quantum mechanics with its mysterious wave function collapses, turning to the more mundane and reliable decoherence.

The point is that in all these observational experiments, the experimenters inevitably influenced the system. They lit it with a laser and installed measuring instruments. They shared an important principle: you cannot observe a system or measure its properties without interacting with it. Any interaction is a process of modification of properties. Especially when a tiny quantum system is exposed to colossal quantum objects. Some eternally neutral Buddhist observer is impossible in principle. This is where the term “decoherence” comes into play, which is irreversible from a thermodynamic point of view: the quantum properties of a system change when it interacts with another large system.

During this interaction, the quantum system loses its original properties and becomes classical, as if “submitting” to the larger system. This also explains the paradox of Schrödinger's cat: a cat is too big a system, so it cannot be isolated from the rest of the world. The very design of this thought experiment is not entirely correct.

In any case, if we assume the reality of the act of creation by consciousness, decoherence seems to be a much more convenient approach. Perhaps even too convenient. With this approach, the entire classical world becomes one big consequence of decoherence. And as the author of one of the most famous books in this field stated, this approach logically leads to statements like “there are no particles in the world” or “there is no time at a fundamental level.”

What is the truth: the creator-observer or powerful decoherence? We need to choose between two evils. Nevertheless, scientists are increasingly convinced that quantum effects are a manifestation of our mental processes. And where observation ends and reality begins depends on each of us.

There are many places to start this discussion, and this one is as good as any: everything in our Universe is both particle and wave in nature. If one could say of magic, “It's all waves and nothing but waves,” that would be a wonderfully poetic description of quantum physics. In fact, everything in this universe has a wave nature.

Of course, also everything in the Universe is of the nature of particles. It sounds strange, but it is.

Describing real objects as particles and waves at the same time will be somewhat inaccurate. Strictly speaking, the objects described by quantum physics are not particles and waves, but rather belong to the third category, which inherits the properties of waves (frequency and wavelength, along with propagation in space) and some properties of particles (they can be counted and localized to a certain degree ). This leads to a lively debate in the physics community about whether it is even correct to talk about light as a particle; not because there is a controversy about whether light has a particle nature, but because calling photons “particles” rather than “quantum field excitations” is misleading to students. However, this also applies to whether electrons can be called particles, but such disputes will remain in purely academic circles.

This “third” nature of quantum objects is reflected in the sometimes confusing language of physicists who discuss quantum phenomena. The Higgs boson was discovered at the Large Hadron Collider as a particle, but you've probably heard the phrase "Higgs field," that delocalized thing that fills all of space. This occurs because under certain conditions, such as particle collision experiments, it is more appropriate to discuss excitations of the Higgs field rather than defining the characteristics of a particle, while under other conditions, such as general discussions of why certain particles have mass, it is more appropriate to discuss physics in terms of interactions with quantum a field of universal proportions. These are simply different languages ​​that describe the same mathematical objects.

Quantum physics is discrete

It's all in the name of physics - the word "quantum" comes from the Latin "how much" and reflects the fact that quantum models always involve something coming in discrete quantities. The energy contained in a quantum field comes in multiples of some fundamental energy. For light, this is associated with the frequency and wavelength of the light—high-frequency, short-wavelength light has enormous characteristic energy, while low-frequency, long-wavelength light has little characteristic energy.

In both cases, however, the total energy contained in a separate light field is an integer multiple of this energy - 1, 2, 14, 137 times - and there are no strange fractions like one and a half, "pi" or the square root of two. This property is also observed in discrete energy levels of atoms, and energy zones are specific - some energy values ​​are allowed, others are not. Atomic clocks work thanks to the discreteness of quantum physics, using the frequency of light associated with the transition between two allowed states in cesium, which allows time to be kept at the level necessary for the “second jump” to occur.

Ultra-precision spectroscopy can also be used to search for things like dark matter and remains part of the motivation for the Low Energy Fundamental Physics Institute.

This is not always obvious - even some things that are quantum in principle, like black body radiation, are associated with continuous distributions. But upon closer examination and when deep mathematical apparatus is involved, quantum theory becomes even stranger.

Quantum physics is probabilistic

One of the most surprising and (historically, at least) controversial aspects of quantum physics is that it is impossible to predict with certainty the outcome of a single experiment with a quantum system. When physicists predict the outcome of a particular experiment, their prediction takes the form of the probability of finding each of the particular possible outcomes, and comparisons between theory and experiment always involve deriving a probability distribution from many repeated experiments.

The mathematical description of a quantum system typically takes the form of a "wave function" represented by the Greek beech psi equations: Ψ. There is a lot of debate about what exactly a wave function is, and it has divided physicists into two camps: those who see the wave function as a real physical thing (ontic theorists), and those who believe that the wave function is purely an expression of our knowledge (or lack thereof) regardless of the underlying state of an individual quantum object (epistemic theorists).

In each class of underlying model, the probability of finding a result is determined not by the wave function directly, but by the square of the wave function (roughly speaking, it's all the same; the wave function is a complex mathematical object (and therefore includes imaginary numbers like the square root or its negative version), and the operation of obtaining the probability is a little more complicated, but the “square of the wave function” is enough to understand the basic essence of the idea). This is known as Born's rule, after the German physicist Max Born, who first calculated it (in a footnote to a 1926 paper) and surprised many people with its ugly incarnation. Active work is underway to try to derive the Born rule from a more fundamental principle; but so far none of them has been successful, although they have generated a lot of interesting things for science.

This aspect of the theory also leads us to particles being in multiple states at the same time. All we can predict is a probability, and before measuring with a specific result, the system being measured is in an intermediate state - a state of superposition that includes all possible probabilities. But whether a system really exists in multiple states or is in one unknown depends on whether you prefer an ontic or an epistemic model. Both of these lead us to the next point.

Quantum physics is non-local

The latter was not widely accepted as such, mainly because he was wrong. In a 1935 paper, along with his young colleagues Boris Podolky and Nathan Rosen (EPR work), Einstein provided a clear mathematical statement of something that had been bothering him for some time, what we call "entanglement."

EPR's work argued that quantum physics recognized the existence of systems in which measurements made at widely separated locations can correlate so that the outcome of one determines the other. They argued that this meant that the results of measurements must be determined in advance by some common factor, since otherwise the result of one measurement would have to be transmitted to the site of another at speeds exceeding the speed of light. Therefore, quantum physics must be incomplete, an approximation of a deeper theory (the "hidden local variable" theory, in which the results of individual measurements are not dependent on something that is further from the place of measurement than a signal traveling at the speed of light can cover (locally), but rather is determined by some factor common to both systems in the entangled pair (hidden variable).

This was all considered an obscure footnote for over 30 years as there seemed to be no way to test it, but in the mid-60s Irish physicist John Bell worked out the implications of EPR in more detail. Bell showed that you can find circumstances in which quantum mechanics will predict correlations between distant measurements that will be stronger than any possible theory like those proposed by E, P and R. This was tested experimentally in the 70s by John Kloser and Alain Aspect in the early 80s. x - they showed that these entangled systems could not potentially be explained by any local hidden variable theory.

The most common approach to understanding this result is to assume that quantum mechanics is nonlocal: that the results of measurements made at a specific location can depend on the properties of a distant object in a way that cannot be explained using signals traveling at the speed of light. This, however, does not allow information to be transmitted at superluminal speeds, although many attempts have been made to overcome this limitation using quantum nonlocality.

Quantum physics is (almost always) concerned with very small

Quantum physics has a reputation for being strange because its predictions are radically different from our everyday experience. This is because its effects become less pronounced the larger the object - you will hardly see the wave behavior of the particles and how the wavelength decreases with increasing torque. The wavelength of a macroscopic object like a walking dog is so ridiculously small that if you magnified every atom in the room to the size of the solar system, the dog's wavelength would be the size of one atom in that solar system.

This means that quantum phenomena are mostly limited to the scale of atoms and fundamental particles whose masses and accelerations are small enough that the wavelength remains so small that it cannot be observed directly. However, a lot of effort is being made to increase the size of the system demonstrating quantum effects.

Quantum physics is not magic

The previous point leads us quite naturally to this: no matter how strange quantum physics may seem, it is clearly not magic. What it postulates is strange by the standards of everyday physics, but it is strictly limited by well-understood mathematical rules and principles.

So if someone comes to you with a "quantum" idea that seems impossible - infinite energy, magical healing powers, impossible space engines - it is almost certainly impossible. This doesn't mean we can't use quantum physics to do incredible things: we're constantly writing about incredible breakthroughs using quantum phenomena that have already surprised humanity, it just means we won't go beyond the laws of thermodynamics and common sense .

If the above points do not seem enough to you, consider this just a useful starting point for further discussion.

If you suddenly realized that you have forgotten the basics and postulates of quantum mechanics or don’t even know what kind of mechanics it is, then it’s time to refresh your memory of this information. After all, no one knows when quantum mechanics may be useful in life.

It’s in vain that you grin and sneer, thinking that you will never have to deal with this subject in your life. After all, quantum mechanics can be useful to almost every person, even those infinitely far from it. For example, you have insomnia. For quantum mechanics this is not a problem! Read the textbook before going to bed - and you will fall into a deep sleep on the third page. Or you can call your cool rock band that. Why not?

Jokes aside, let's start a serious quantum conversation.

Where to begin? Of course, starting with what quantum is.

Quantum

Quantum (from the Latin quantum - “how much”) is an indivisible portion of some physical quantity. For example, they say - a quantum of light, a quantum of energy or a quantum of field.

What does it mean? This means that it simply cannot be less. When they say that some quantity is quantized, they understand that this quantity takes on a number of specific, discrete values. Thus, the energy of an electron in an atom is quantized, light is distributed in “portions”, that is, in quanta.

The term "quantum" itself has many uses. The quantum of light (electromagnetic field) is a photon. By analogy, quanta are particles or quasiparticles corresponding to other interaction fields. Here we can recall the famous Higgs boson, which is a quantum of the Higgs field. But we are not going into these jungles yet.

How can mechanics be quantum?

As you have already noticed, in our conversation we mentioned particles many times. You may be accustomed to the fact that light is a wave that simply propagates at speed With . But if you look at everything from the point of view of the quantum world, that is, the world of particles, everything changes beyond recognition.

Quantum mechanics is a branch of theoretical physics, a component of quantum theory that describes physical phenomena at the most elementary level - the level of particles.

The effect of such phenomena is comparable in magnitude to Planck's constant, and Newton's classical mechanics and electrodynamics turned out to be completely unsuitable for describing them. For example, according to classical theory, an electron, rotating at high speed around a nucleus, should radiate energy and eventually fall onto the nucleus. This, as we know, does not happen. That is why quantum mechanics was invented - the discovered phenomena had to be explained somehow, and it turned out to be precisely the theory within which the explanation was the most acceptable, and all experimental data “converged”.

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A little history

The birth of quantum theory occurred in 1900, when Max Planck spoke at a meeting of the German Physical Society. What did Planck say then? And the fact that the radiation of atoms is discrete, and the smallest portion of the energy of this radiation is equal to

Where h is Planck's constant, nu is the frequency.

Then Albert Einstein, introducing the concept of “quantum of light”, used Planck’s hypothesis to explain the photoelectric effect. Niels Bohr postulated the existence of stationary energy levels in the atom, and Louis de Broglie developed the idea of ​​wave-particle duality, that is, that a particle (corpuscle) also has wave properties. Schrödinger and Heisenberg joined the cause, and in 1925 the first formulation of quantum mechanics was published. Actually, quantum mechanics is far from a complete theory; it is actively developing at the present time. It should also be recognized that quantum mechanics, with its assumptions, does not have the ability to explain all the questions it faces. It is quite possible that it will be replaced by a more advanced theory.

During the transition from the quantum world to the world of things familiar to us, the laws of quantum mechanics are naturally transformed into the laws of classical mechanics. We can say that classical mechanics is a special case of quantum mechanics, when the action takes place in our familiar and familiar macroworld. Here bodies move calmly in non-inertial frames of reference at a speed much lower than the speed of light, and in general everything around is calm and clear. If you want to know the position of a body in a coordinate system, no problem; if you want to measure the impulse, you’re welcome.

Quantum mechanics has a completely different approach to the issue. In it, the results of measurements of physical quantities are probabilistic in nature. This means that when a certain value changes, several results are possible, each of which has a certain probability. Let's give an example: a coin is spinning on the table. While it is spinning, it is not in any specific state (heads-tails), but only has the probability of ending up in one of these states.

Here we are gradually approaching Schrödinger equation And Heisenberg uncertainty principle.

According to legend, Erwin Schrödinger, in 1926, speaking at a scientific seminar on the topic of wave-particle duality, was criticized by a certain senior scientist. Refusing to listen to his elders, after this incident Schrödinger actively began developing the wave equation to describe particles within the framework of quantum mechanics. And he did it brilliantly! The Schrödinger equation (the basic equation of quantum mechanics) is:

This type of equation, the one-dimensional stationary Schrödinger equation, is the simplest.

Here x is the distance or coordinate of the particle, m is the mass of the particle, E and U are its total and potential energies, respectively. The solution to this equation is the wave function (psi)

The wave function is another fundamental concept in quantum mechanics. So, any quantum system that is in some state has a wave function that describes this state.

For example, when solving the one-dimensional stationary Schrödinger equation, the wave function describes the position of the particle in space. More precisely, the probability of finding a particle at a certain point in space. In other words, Schrödinger showed that probability can be described by a wave equation! Agree, we should have thought of this before!

But why? Why do we have to deal with these incomprehensible probabilities and wave functions, when, it would seem, there is nothing simpler than just taking and measuring the distance to a particle or its speed.

Everything is very simple! Indeed, in the macrocosm this is indeed the case - we measure distances with a certain accuracy with a tape measure, and the measurement error is determined by the characteristics of the device. On the other hand, we can almost accurately determine by eye the distance to an object, for example, to a table. In any case, we accurately differentiate its position in the room relative to us and other objects. In the world of particles, the situation is fundamentally different - we simply physically do not have measurement tools to accurately measure the required quantities. After all, the measuring instrument comes into direct contact with the object being measured, and in our case, both the object and the instrument are particles. It is this imperfection, the fundamental impossibility of taking into account all the factors acting on the particle, as well as the very fact of changing the state of the system under the influence of measurement, that underlies the Heisenberg uncertainty principle.

Let us give its simplest formulation. Let's imagine that there is a certain particle, and we want to know its speed and coordinate.

In this context, the Heisenberg Uncertainty Principle states that it is impossible to accurately measure the position and velocity of a particle at the same time. . Mathematically it is written like this:

Here delta x is the error in determining the coordinate, delta v is the error in determining the speed. Let us emphasize that this principle says that the more accurately we determine the coordinate, the less accurately we will know the speed. And if we determine the speed, we will not have the slightest idea of ​​where the particle is.

There are many jokes and anecdotes on the topic of the uncertainty principle. Here is one of them:

A policeman stops a quantum physicist.
- Sir, do you know how fast you were moving?
- No, but I know exactly where I am.

And, of course, we remind you! If, for some reason, solving the Schrödinger equation for a particle in a potential well keeps you awake, turn to professionals who were raised with quantum mechanics on their lips!

Welcome to the blog! I am very glad to see you!

You've probably heard it many times about the inexplicable mysteries of quantum physics and quantum mechanics. Its laws fascinate with mysticism, and even physicists themselves admit that they do not fully understand them. On the one hand, it is interesting to understand these laws, but on the other hand, there is no time to read multi-volume and complex books on physics. I understand you very much, because I also love knowledge and the search for truth, but there is sorely not enough time for all the books. You are not alone, many curious people type in the search bar: “quantum physics for dummies, quantum mechanics for dummies, quantum physics for beginners, quantum mechanics for beginners, basics of quantum physics, basics of quantum mechanics, quantum physics for children, what is quantum Mechanics". This publication is exactly for you.

You will understand the basic concepts and paradoxes of quantum physics. From the article you will learn:

• What is interference?
• What is spin and superposition?
• What is "measurement" or "wavefunction collapse"?
• What is Quantum Entanglement (or Quantum Teleportation for Dummies)? (see article)
• What is the Schrödinger's Cat thought experiment? (see article)

What is quantum physics and quantum mechanics?

Quantum mechanics is a part of quantum physics.

Why is it so difficult to understand these sciences? The answer is simple: quantum physics and quantum mechanics (part of quantum physics) study the laws of the microworld. And these laws are absolutely different from the laws of our macrocosm. Therefore, it is difficult for us to imagine what happens to electrons and photons in the microcosm.

An example of the difference between the laws of the macro- and microworlds: in our macroworld, if you put a ball in one of 2 boxes, then one of them will be empty, and the other will have a ball. But in the microcosm (if there is an atom instead of a ball), an atom can be in two boxes at the same time. This has been confirmed experimentally many times. Isn't it hard to wrap your head around this? But you can't argue with the facts.

One more example. You took a photograph of a fast racing red sports car and in the photo you saw a blurry horizontal stripe, as if the car was located at several points in space at the time of the photo. Despite what you see in the photo, you are still sure that the car was in one specific place in space. In the micro world, everything is different. An electron that rotates around the nucleus of an atom does not actually rotate, but is located simultaneously at all points of the sphere around the nucleus of an atom. Like a loosely wound ball of fluffy wool. This concept in physics is called "electronic cloud" .

A short excursion into history. Scientists first thought about the quantum world when, in 1900, German physicist Max Planck tried to figure out why metals change color when heated. It was he who introduced the concept of quantum. Until then, scientists thought that light traveled continuously. The first person to take Planck's discovery seriously was the then unknown Albert Einstein. He realized that light is not just a wave. Sometimes he behaves like a particle. Einstein received the Nobel Prize for his discovery that light is emitted in portions, quanta. A quantum of light is called a photon ( photon, Wikipedia) .

To make it easier to understand the laws of quantum physicists And mechanics (Wikipedia), we must, in a sense, abstract from the laws of classical physics that are familiar to us. And imagine that you dived, like Alice, into the rabbit hole, into Wonderland.

And here is a cartoon for children and adults. Describes the fundamental experiment of quantum mechanics with 2 slits and an observer. Lasts only 5 minutes. Watch it before we dive into the fundamental questions and concepts of quantum physics.

Quantum physics for dummies video. In the cartoon, pay attention to the “eye” of the observer. It has become a serious mystery for physicists.

What is interference?

At the beginning of the cartoon, using the example of a liquid, it was shown how waves behave - alternating dark and light vertical stripes appear on the screen behind a plate with slits. And in the case when discrete particles (for example, pebbles) are “shot” at the plate, they fly through 2 slits and land on the screen directly opposite the slits. And they “draw” only 2 vertical stripes on the screen.

Interference of light- This is the “wave” behavior of light, when the screen displays many alternating bright and dark vertical stripes. Also these vertical stripes called interference pattern.

In our macrocosm, we often observe that light behaves like a wave. If you place your hand in front of a candle, then on the wall there will be not a clear shadow from your hand, but with blurry contours.

So, it's not all that complicated! It is now quite clear to us that light has a wave nature and if 2 slits are illuminated with light, then on the screen behind them we will see an interference pattern. Now let's look at the 2nd experiment. This is the famous Stern-Gerlach experiment (which was carried out in the 20s of the last century).

The installation described in the cartoon was not shined with light, but “shot” with electrons (as individual particles). Then, at the beginning of the last century, physicists around the world believed that electrons are elementary particles of matter and should not have a wave nature, but the same as pebbles. After all, electrons are elementary particles of matter, right? That is, if you “throw” them into 2 slits, like pebbles, then on the screen behind the slits we should see 2 vertical stripes.

But... The result was stunning. Scientists saw an interference pattern - many vertical stripes. That is, electrons, like light, can also have a wave nature and can interfere. On the other hand, it became clear that light is not only a wave, but also a bit of a particle - a photon (from the historical background at the beginning of the article, we learned that Einstein received the Nobel Prize for this discovery).

Maybe you remember, at school we were told in physics about "wave-particle duality"? It means that when we are talking about very small particles (atoms, electrons) of the microcosm, then They are both waves and particles

Today you and I are so smart and we understand that the 2 experiments described above - shooting with electrons and illuminating slits with light - are the same thing. Because we shoot quantum particles at the slits. We now know that both light and electrons are of a quantum nature, that they are both waves and particles at the same time. And at the beginning of the 20th century, the results of this experiment were a sensation.

Attention! Now let's move on to a more subtle issue.

We shine a stream of photons (electrons) onto our slits and see an interference pattern (vertical stripes) behind the slits on the screen. It is clear. But we are interested in seeing how each of the electrons flies through the slot.

Presumably, one electron flies into the left slot, the other into the right. But then 2 vertical stripes should appear on the screen directly opposite the slots. Why does an interference pattern occur? Maybe the electrons somehow interact with each other already on the screen after flying through the slits. And the result is a wave pattern like this. How can we keep track of this?

We will throw electrons not in a beam, but one at a time. Let's throw it, wait, let's throw the next one. Now that the electron is flying alone, it will no longer be able to interact with other electrons on the screen. We will register each electron on the screen after the throw. One or two, of course, will not “paint” a clear picture for us. But when we send a lot of them into the slits one at a time, we will notice... oh horror - they again “drew” an interference wave pattern!

We are slowly starting to go crazy. After all, we expected that there would be 2 vertical stripes opposite the slots! It turns out that when we threw photons one at a time, each of them passed, as it were, through 2 slits at the same time and interfered with itself. Fantastic! Let's return to explaining this phenomenon in the next section.

What is spin and superposition?

We now know what interference is. This is the wave behavior of micro particles - photons, electrons, other micro particles (for simplicity, let's call them photons from now on).

As a result of the experiment, when we threw 1 photon into 2 slits, we realized that it seemed to fly through two slits at the same time. Otherwise, how can we explain the interference pattern on the screen?

But how can we imagine a photon flying through two slits at the same time? There are 2 options.

• 1st option: a photon, like a wave (like water) “floats” through 2 slits at the same time
• 2nd option: a photon, like a particle, flies simultaneously along 2 trajectories (not even two, but all at once)

In principle, these statements are equivalent. We arrived at the “path integral”. This is Richard Feynman's formulation of quantum mechanics.

By the way, exactly Richard Feynman there is a well-known expression that We can confidently say that no one understands quantum mechanics

But this expression of his worked at the beginning of the century. But now we are smart and know that a photon can behave both as a particle and as a wave. That he can, in some way incomprehensible to us, fly through 2 slits at the same time. Therefore, it will be easy for us to understand the following important statement of quantum mechanics:

Strictly speaking, quantum mechanics tells us that this photon behavior is the rule, not the exception. Any quantum particle is, as a rule, in several states or at several points in space simultaneously.

Objects of the macroworld can only be in one specific place and in one specific state. But a quantum particle exists according to its own laws. And she doesn’t even care that we don’t understand them. That's the point.

We just have to admit, as an axiom, that the “superposition” of a quantum object means that it can be on 2 or more trajectories at the same time, in 2 or more points at the same time

The same applies to another photon parameter – spin (its own angular momentum). Spin is a vector. A quantum object can be thought of as a microscopic magnet. We are accustomed to the fact that the magnet vector (spin) is either directed up or down. But the electron or photon again tells us: “Guys, we don’t care what you’re used to, we can be in both spin states at once (vector up, vector down), just like we can be on 2 trajectories at the same time or at 2 points at the same time!

What is "measurement" or "wavefunction collapse"?

There is little left for us to understand what “measurement” is and what “wave function collapse” is.

Wave function is a description of the state of a quantum object (our photon or electron).

Suppose we have an electron, it flies to itself in an indefinite state, its spin is directed both up and down at the same time. We need to measure his condition.

Let's measure using a magnetic field: electrons whose spin was directed in the direction of the field will deviate in one direction, and electrons whose spin is directed against the field - in the other. More photons can be directed into a polarizing filter. If the spin (polarization) of the photon is +1, it passes through the filter, but if it is -1, then it does not.

Stop! Here you will inevitably have a question: Before the measurement, the electron did not have any specific spin direction, right? He was in all states at the same time, wasn't he?

This is the trick and sensation of quantum mechanics. As long as you do not measure the state of a quantum object, it can rotate in any direction (have any direction of the vector of its own angular momentum - spin). But at the moment when you measured his state, he seems to be making a decision which spin vector to accept.

This quantum object is so cool - it makes decisions about its state. And we cannot predict in advance what decision it will make when it flies into the magnetic field in which we measure it. The probability that he will decide to have a spin vector “up” or “down” is 50 to 50%. But as soon as he decides, he is in a certain state with a specific spin direction. The reason for his decision is our “dimension”!

This is called " collapse of the wave function". The wave function before the measurement was uncertain, i.e. the electron spin vector was simultaneously in all directions; after the measurement, the electron recorded a certain direction of its spin vector.

Attention! An excellent example for understanding is an association from our macrocosm:

Spin a coin on the table like a spinning top. While the coin is spinning, it does not have a specific meaning - heads or tails. But as soon as you decide to “measure” this value and slam the coin with your hand, that’s when you get the specific state of the coin - heads or tails. Now imagine that this coin decides which value to “show” you - heads or tails. The electron behaves in approximately the same way.

Now remember the experiment shown at the end of the cartoon. When photons were passed through the slits, they behaved like a wave and showed an interference pattern on the screen. And when scientists wanted to record (measure) the moment of photons flying through the slit and placed an “observer” behind the screen, the photons began to behave not like waves, but like particles. And they “drew” 2 vertical stripes on the screen. Those. at the moment of measurement or observation, quantum objects themselves choose what state they should be in.

Fantastic! Is not it?

But that is not all. Finally we We got to the most interesting part.

But... it seems to me that there will be an overload of information, so we will consider these 2 concepts in separate posts:

• What's happened ?
• What is a thought experiment.

Now, do you want the information to be sorted out? Watch the documentary produced by the Canadian Institute of Theoretical Physics. In it, in 20 minutes, you will be very briefly and in chronological order told about all the discoveries of quantum physics, starting with Planck’s discovery in 1900. And then they will tell you what practical developments are currently being carried out on the basis of knowledge in quantum physics: from the most accurate atomic clocks to super-fast calculations of a quantum computer. I highly recommend watching this film.

See you!

I wish everyone inspiration for all their plans and projects!

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