Matrix Theory and Linear Algebra (Несколько текстов для зачёта), страница 9

In this hypothetical experiment the scientists do not measure the spin of each particle right away. They send the two particles, called an entangled pair, off in opposite directions until they are far apart from each other. The scientists then measure the spin of one of the particles, fixing its value. Instantaneously, the spin of the other particle becomes known and fixed. It is no longer a fuzzy probability but must be the opposite of the other particle, so that their spins will add to zero. It is as though the first particle communicated with the second. This apparent instantaneous passing of information from one particle to the other would violate the rule that nothing, not even information, can travel faster than the speed of light. The two particles do not, however, communicate with each other. Physicists can instantaneously know the spin of the second particle because they set the total spin of the system to be zero at the beginning of the experiment. In 1997 Austrian researchers performed an experiment similar to the hypothetical experiment of the 1930s, confirming the effect of measurement on a quantum system.

The first great achievement of quantum theory was to explain how atoms work. Physicists found explaining the structure of the atom with classical physics to be impossible. Atoms consist of negatively charged electrons bound to a positively charged nucleus. The nucleus of an atom contains positively charged particles called protons and may contain neutral particles called neutrons. Protons and neutrons are about the same size but are much larger and heavier than electrons are. Classical physics describes a hydrogen atom as an electron orbiting a proton, much as the Moon orbits Earth. By the rules of classical physics, the electron has a property called inertia that makes it want to continue traveling in a straight line. The attractive electrical force of the positively charged proton overcomes this inertia and bends the electron’s path into a circle, making it stay in a closed orbit. The classical theory of electromagnetism says that charged particles (such as electrons) radiate energy when they bend their paths. If classical physics applied to the atom, the electron would radiate away all of its energy. It would slow down and its orbit would collapse into the proton within a fraction of a second. However, physicists know that atoms can be stable for centuries or longer.

Quantum theory gives a model of the atom that explains its stability. It still treats atoms as electrons surrounding a nucleus, but the electrons do not orbit the nucleus like moons orbiting planets. Quantum mechanics gives the location of an electron as a probability instead of pinpointing it at a certain position. Even though the position of an electron is uncertain, quantum theory prohibits the electron from being at some places. The easiest way to describe the differences between the allowed and prohibited positions of electrons in an atom is to think of the electron as a wave. The wave-particle duality of quantum theory allows electrons to be described as waves, using the electron’s de Broglie wavelength.

If the electron is described as a continuous wave, its motion may be described as that of a standing wave. Standing waves occur when a continuous wave occupies one of a set of certain distances. These distances enable the wave to interfere with itself in such a way that the wave appears to remain stationary. Plucking the string of a musical instrument sets up a standing wave in the string that makes the string resonate and produce sound. The length of the string, or the distance the wave on the string occupies, is equal to a whole or half number of wavelengths. At these distances, the wave bounces back at either end and constructively interferes with itself, which strengthens the wave. Similarly, an electron wave occupies a distance around the nucleus of an atom, or a circumference, that enables it to travel a whole or half number of wavelengths before looping back on itself. The electron wave therefore constructively interferes with itself and remains stable:

An electron wave cannot occupy a distance that is not equal to a whole or half number of wavelengths. In a distance such as this, the wave would interfere with itself in a complicated way, and would become unstable:

An electron has a certain amount of energy when its wave occupies one of the allowed circumferences around the nucleus of an atom. This energy depends on the number of wavelengths in the circumference, and it is called the electron’s energy level. Because only certain circumferences, and therefore energy levels, are allowed, physicists say that the energy levels are quantized. This quantization means that the energies of the levels can only take on certain values.

The regions of space in which electrons are most likely to be found are called orbitals. Orbitals look like fuzzy, three-dimensional shapes. More than one orbital, meaning more than one shape, may exist at certain energy levels. Electron orbitals are also quantized, meaning that only certain shapes are allowed in each energy level. The quantization of electron orbitals and energy levels in atoms explains the stability of atoms. An electron in an energy level that allows only one wavelength is at the lowest possible energy level. An atom with all of its electrons in their lowest possible energy levels is said to be in its ground state. Unless it is affected by external forces, an atom will stay in its ground state forever.

The quantum theory explanation of the atom led to a deeper understanding of the periodic table of the chemical elements. The periodic table of elements is a chart of the known elements. Scientists originally arranged the elements in this table in order of increasing atomic number (which is equal to the number of protons in the nuclei of each element’s atoms) and according to the chemical behavior of the elements. They grouped elements that behave in a similar way together in columns. Scientists found that elements that behave similarly occur in a periodic fashion according to their atomic number. For example, a family of elements called the noble gases all share similar chemical properties. The noble gases include neon, xenon, and argon. They do not react easily with other elements and are almost never found in chemical compounds. The atomic numbers of the noble gases increase from one element to the next in a periodic way. They belong to the same column at the far right edge of the periodic table.

Quantum theory showed that an element’s chemical properties have little to do with the nucleus of the element’s atoms, but instead depend on the number and arrangement of the electrons in each atom. An atom has the same number of electrons as protons, making the atom electrically neutral. The arrangement of electrons in an atom depends on two important parts of quantum theory. The first is the quantization of electron energy, which limits the regions of space that electrons can occupy. The second part is a rule called the Pauli exclusion principle, first proposed by Austrian-born Swiss physicist Wolfgang Pauli.

The Pauli exclusion principle states that no electron can have exactly the same characteristics as those of another electron. These characteristics include orbital, direction of rotation (called spin), and direction of orbit. Each energy level in an atom has a set number of ways these characteristics can combine. The number of combinations determines how many electrons can occupy an energy level before the electrons have to start filling up the next level.

An atom is the most stable when it has the least amount of energy, so its lowest energy levels fill with electrons first. Each energy level must be filled before electrons begin filling up the next level. These rules, and the rules of quantum theory, determine how many electrons an atom has in each energy level, and in particular, how many it has in its outermost level. Using the quantum mechanical model of the atom, physicists found that all the elements in the same column of the periodic table also have the same number of electrons in the outer energy level of their atoms. Quantum theory shows that the number of electrons in an atom’s outer level determines the atom’s chemical properties, or how it will react with other atoms.

The number of electrons in an atom’s outer energy level is important because atoms are most stable when their outermost energy level is filled, which is the case for atoms of the noble gases. Atoms imitate the noble gases by donating electrons to, taking electrons from, or sharing electrons with other atoms. If an atom’s outer energy level is only partially filled, it will bond easily with atoms that can help it fill its outer level. Atoms that are missing the same number of electrons from their outer energy level will react similarly to fill their outer energy level.

Quantum theory also explains why different atoms emit and absorb different wavelengths of light. An atom stores energy in its electrons. An atom with all of its electrons at their lowest possible energy levels has its lowest possible energy and is said to be in its ground state. One of the ways atoms can gain more energy is to absorb light in the form of photons, or particles of light. When a photon hits an atom, one of the atom’s electrons absorbs the photon. The photon’s energy makes the electron jump from its original energy level up to a higher energy level. This jump leaves an empty space in the original inner energy level, making the atom less stable. The atom is now in an excited state, but it cannot store the new energy indefinitely, because atoms always seek their most stable state. When the atom releases the energy, the electron drops back down to its original energy level. As it does, the electron releases a photon.

Quantum theory defines the possible energy levels of an atom, so it defines the particular jumps that an electron can make between energy levels. The difference between the old and new energy levels of the electron is equal to the amount of energy the atom stores. Because the energy levels are quantized, atoms can only absorb and store photons with certain amounts of energy. The photon’s energy is related to its frequency, or color. As the frequency of photons increases, their energy increases. Atoms can only absorb certain amounts of energy, so only certain frequencies of light can excite atoms. Likewise, atoms only emit certain frequencies of light when they drop to their ground state. The different frequencies available to different atoms help astronomers, for example, determine the chemical makeup of a star by observing which wavelengths are especially weak or strong in the star’s light. See also Spectroscopy.

The development of quantum theory began with German physicist Max Planck’s proposal in 1900 that matter can emit or absorb energy only in small, discrete packets, called quanta. This idea introduced the particle nature of light. In 1905 German-born American physicist Albert Einstein used Planck’s work to explain the photoelectric effect, in which light hitting a metal makes the metal emit electrons. British physicist Ernest Rutherford proved that atoms consisted of electrons bound to a nucleus in 1911. In 1913 Danish physicist Niels Bohr proposed that classical mechanics could not explain the structure of the atom and developed a model of the atom with electrons in fixed orbits. Bohr’s model of the atom proved difficult to apply to all but the simplest atoms.

In 1923 French physicist Louis de Broglie suggested that matter could be described as a wave, just as light could be described as a particle. The wave model of the electron allowed Austrian physicist Erwin Schrödinger to develop a mathematical method of determining the probability that an electron will be at a particular place at a certain time. Schrödinger published his theory of wave mechanics in 1926. Around the same time, German physicist Werner Heisenberg developed a way of calculating the characteristics of electrons that was quite different from Schrödinger’s method but yielded the same results. Heisenberg’s method was called matrix mechanics.

In 1925 Austrian-born Swiss physicist Wolfgang Pauli developed the Pauli exclusion principle, which allowed physicists to calculate the structure of the quantum atom for the first time. In 1926 Heisenberg and two of his colleagues, German physicists Max Born and Ernst Pascual Jordan, published a theory that combined the principles of quantum theory with the classical theory of light (called electrodynamics). Heisenberg made another important contribution to quantum theory in 1927 when he introduced the Heisenberg uncertainty principle.

Since these first breakthroughs in quantum mechanical research, physicists have focused on testing and refining quantum theory, further connecting the theory to other theories, and finding new applications. In 1928 British physicist Paul Dirac refined the theory that combined quantum theory with electrodynamics. He developed a model of the electron that was consistent with both quantum theory and Einstein’s special theory of relativity, and in doing so he created a theory that came to be known as quantum electrodynamics, or QED. In the early 1950s Japanese physicist Tomonaga Shin’ichirō and American physicists Richard Feynman and Julian Schwinger each independently improved the scientific community’s understanding of QED and made it an experimentally testable theory that successfully predicted or explained the results of many experiments.

At the turn of the 21st century, physicists were still finding new problems to study with quantum theory and new applications for quantum theory. This research will probably continue for many decades. Quantum theory is technically a fully formulated theory—any questions about the physical world can be calculated using quantum mechanics, but some are too complicated to solve in practice. The attempt to find quantum explanations of gravitation and to find a unified description of all the forces in nature are promising and active areas of research. Researchers try to find out why quantum theory explains the way nature works—they may never find an answer, but the effort to do so is underway. Physicists also study the complicated area of overlap between classical physics and quantum mechanics and work on the applications of quantum mechanics.