Infrared spectroscopy involves the interaction of infrared radiation with matter. It covers a range of techniques based on absorption spectroscopy; as with all spectroscopic techniques, it can be used to study chemicals. Samples may be liquid, or gas; the method or technique of infrared spectroscopy is conducted with an instrument called an infrared spectrometer to produce an infrared spectrum. An IR spectrum can be visualized in a graph of infrared light absorbance on the vertical axis vs. frequency or wavelength on the horizontal axis. Typical units of frequency used in IR spectra are reciprocal centimeters, with the symbol cm−1. Units of IR wavelength are given in micrometers, symbol μm, which are related to wave numbers in a reciprocal way. A common laboratory instrument that uses this technique is a Fourier transform infrared spectrometer. Two-dimensional IR is possible as discussed below; the infrared portion of the electromagnetic spectrum is divided into three regions. The higher-energy near-IR 14000–4000 cm−1 can excite overtone or harmonic vibrations.
The mid-infrared 4000–400 cm−1 may be used to study the fundamental vibrations and associated rotational-vibrational structure. The far-infrared 400–10 cm−1, lying adjacent to the microwave region, has low energy and may be used for rotational spectroscopy; the names and classifications of these subregions are conventions, are only loosely based on the relative molecular or electromagnetic properties. Infrared spectroscopy exploits the fact that molecules absorb frequencies that are characteristic of their structure; these absorptions occur at resonant frequencies, i.e. the frequency of the absorbed radiation matches the vibrational frequency. The energies are affected by the shape of the molecular potential energy surfaces, the masses of the atoms, the associated vibronic coupling. In particular, in the Born–Oppenheimer and harmonic approximations, i.e. when the molecular Hamiltonian corresponding to the electronic ground state can be approximated by a harmonic oscillator in the neighborhood of the equilibrium molecular geometry, the resonant frequencies are associated with the normal modes corresponding to the molecular electronic ground state potential energy surface.
The resonant frequencies are related to the strength of the bond and the mass of the atoms at either end of it. Thus, the frequency of the vibrations are associated with a particular normal mode of motion and a particular bond type. In order for a vibrational mode in a sample to be "IR active", it must be associated with changes in the dipole moment. A permanent dipole is not necessary. A molecule can vibrate in many ways, each way is called a vibrational mode. For molecules with N number of atoms, linear molecules have 3N – 5 degrees of vibrational modes, whereas nonlinear molecules have 3N – 6 degrees of vibrational modes; as an example H2O, a non-linear molecule, will have 3 × 3 – 6 = 3 degrees of vibrational freedom, or modes. Simple diatomic molecules have only one vibrational band. If the molecule is symmetrical, e.g. N2, the band is not observed in the IR spectrum, but only in the Raman spectrum. Asymmetrical diatomic molecules, e.g. CO, absorb in the IR spectrum. More complex molecules have many bonds, their vibrational spectra are correspondingly more complex, i.e. big molecules have many peaks in their IR spectra.
The atoms in a CH2X2 group found in organic compounds and where X can represent any other atom, can vibrate in nine different ways. Six of these vibrations involve only the CH2 portion: symmetric and antisymmetric stretching, rocking and twisting, as shown below. Structures that do not have the two additional X groups attached have fewer modes because some modes are defined by specific relationships to those other attached groups. For example, in water, the rocking and twisting modes do not exist because these types of motions of the H represent simple rotation of the whole molecule rather than vibrations within it; these figures do not represent the "recoil" of the C atoms, though present to balance the overall movements of the molecule, are much smaller than the movements of the lighter H atoms. The simplest and most important or fundamental IR bands arise from the excitations of normal modes, the simplest distortions of the molecule, from the ground state with vibrational quantum number v = 0 to the first excited state with vibrational quantum number v = 1.
In some cases, overtone bands are observed. An overtone band arises from the absorption of a photon leading to a direct transition from the ground state to the second excited vibrational state; such a band appears at twice the energy of the fundamental band for the same normal mode. Some excitations, so-called combination modes, involve simultaneous excitation of more than one normal mode; the phenomenon of Fermi resonance can arise. The infrared spectrum of a sample is recorded by passing a beam of infrared light through the sample; when the frequency of the IR is the same as the vibrational frequency of a bond or collection of bonds, absorption occurs. Examination of the transmitted light reveals; this mea
Frequency is the number of occurrences of a repeating event per unit of time. It is referred to as temporal frequency, which emphasizes the contrast to spatial frequency and angular frequency; the period is the duration of time of one cycle in a repeating event, so the period is the reciprocal of the frequency. For example: if a newborn baby's heart beats at a frequency of 120 times a minute, its period—the time interval between beats—is half a second. Frequency is an important parameter used in science and engineering to specify the rate of oscillatory and vibratory phenomena, such as mechanical vibrations, audio signals, radio waves, light. For cyclical processes, such as rotation, oscillations, or waves, frequency is defined as a number of cycles per unit time. In physics and engineering disciplines, such as optics and radio, frequency is denoted by a Latin letter f or by the Greek letter ν or ν; the relation between the frequency and the period T of a repeating event or oscillation is given by f = 1 T.
The SI derived unit of frequency is the hertz, named after the German physicist Heinrich Hertz. One hertz means. If a TV has a refresh rate of 1 hertz the TV's screen will change its picture once a second. A previous name for this unit was cycles per second; the SI unit for period is the second. A traditional unit of measure used with rotating mechanical devices is revolutions per minute, abbreviated r/min or rpm. 60 rpm equals one hertz. As a matter of convenience and slower waves, such as ocean surface waves, tend to be described by wave period rather than frequency. Short and fast waves, like audio and radio, are described by their frequency instead of period; these used conversions are listed below: Angular frequency denoted by the Greek letter ω, is defined as the rate of change of angular displacement, θ, or the rate of change of the phase of a sinusoidal waveform, or as the rate of change of the argument to the sine function: y = sin = sin = sin d θ d t = ω = 2 π f Angular frequency is measured in radians per second but, for discrete-time signals, can be expressed as radians per sampling interval, a dimensionless quantity.
Angular frequency is larger than regular frequency by a factor of 2π. Spatial frequency is analogous to temporal frequency, but the time axis is replaced by one or more spatial displacement axes. E.g.: y = sin = sin d θ d x = k Wavenumber, k, is the spatial frequency analogue of angular temporal frequency and is measured in radians per meter. In the case of more than one spatial dimension, wavenumber is a vector quantity. For periodic waves in nondispersive media, frequency has an inverse relationship to the wavelength, λ. In dispersive media, the frequency f of a sinusoidal wave is equal to the phase velocity v of the wave divided by the wavelength λ of the wave: f = v λ. In the special case of electromagnetic waves moving through a vacuum v = c, where c is the speed of light in a vacuum, this expression becomes: f = c λ; when waves from a monochrome source travel from one medium to another, their frequency remains the same—only their wavelength and speed change. Measurement of frequency can done in the following ways, Calculating the frequency of a repeating event is accomplished by counting the number of times that event occurs within a specific time period dividing the count by the length of the time period.
For example, if 71 events occur within 15 seconds the frequency is: f = 71 15 s ≈ 4.73 Hz If the number of counts is not large, it is more accurate to measure the time interval for a predetermined number of occurrences, rather than the number of occurrences within a specified time. The latter method introduces a random error into the count of between zero and one count, so on average half a count; this is called gating error and causes an average error in the calculated frequency of Δ f = 1 2 T
Black-body radiation is the thermal electromagnetic radiation within or surrounding a body in thermodynamic equilibrium with its environment, or emitted by a black body. It has a specific spectrum and intensity that depends only on the body's temperature, assumed for the sake of calculations and theory to be uniform and constant; the thermal radiation spontaneously emitted by many ordinary objects can be approximated as black-body radiation. A insulated enclosure, in thermal equilibrium internally contains black-body radiation and will emit it through a hole made in its wall, provided the hole is small enough to have negligible effect upon the equilibrium. A black-body at room temperature appears black, as most of the energy it radiates is infra-red and cannot be perceived by the human eye; because the human eye cannot perceive light waves at lower frequencies, a black body, viewed in the dark at the lowest just faintly visible temperature, subjectively appears grey though its objective physical spectrum peak is in the infrared range.
When it becomes a little hotter, it appears dull red. As its temperature increases further it becomes yellow and blue-white. Although planets and stars are neither in thermal equilibrium with their surroundings nor perfect black bodies, black-body radiation is used as a first approximation for the energy they emit. Black holes are near-perfect black bodies, in the sense that they absorb all the radiation that falls on them, it has been proposed that they emit black-body radiation, with a temperature that depends on the mass of the black hole. The term black body was introduced by Gustav Kirchhoff in 1860. Black-body radiation is called thermal radiation, cavity radiation, complete radiation or temperature radiation. Black-body radiation has a characteristic, continuous frequency spectrum that depends only on the body's temperature, called the Planck spectrum or Planck's law; the spectrum is peaked at a characteristic frequency that shifts to higher frequencies with increasing temperature, at room temperature most of the emission is in the infrared region of the electromagnetic spectrum.
As the temperature increases past about 500 degrees Celsius, black bodies start to emit significant amounts of visible light. Viewed in the dark by the human eye, the first faint glow appears as a "ghostly" grey. With rising temperature, the glow becomes visible when there is some background surrounding light: first as a dull red yellow, a "dazzling bluish-white" as the temperature rises; when the body appears white, it is emitting a substantial fraction of its energy as ultraviolet radiation. The Sun, with an effective temperature of 5800 K, is an approximate black body with an emission spectrum peaked in the central, yellow-green part of the visible spectrum, but with significant power in the ultraviolet as well. Black-body radiation provides insight into the thermodynamic equilibrium state of cavity radiation. All normal matter emits electromagnetic radiation; the radiation represents a conversion of a body's internal energy into electromagnetic energy, is therefore called thermal radiation.
It is a spontaneous process of radiative distribution of entropy. Conversely all normal matter absorbs electromagnetic radiation to some degree. An object that absorbs all radiation falling on it, at all wavelengths, is called a black body; when a black body is at a uniform temperature, its emission has a characteristic frequency distribution that depends on the temperature. Its emission is called black-body radiation; the concept of the black body is an idealization. Graphite and lamp black, with emissivities greater than 0.95, are good approximations to a black material. Experimentally, black-body radiation may be established best as the stable steady state equilibrium radiation in a cavity in a rigid body, at a uniform temperature, opaque and is only reflective. A closed box of graphite walls at a constant temperature with a small hole on one side produces a good approximation to ideal black-body radiation emanating from the opening. Black-body radiation has the unique stable distribution of radiative intensity that can persist in thermodynamic equilibrium in a cavity.
In equilibrium, for each frequency the total intensity of radiation, emitted and reflected from a body is determined by the equilibrium temperature, does not depend upon the shape, material or structure of the body. For a black body there is no reflected radiation, so the spectral radiance is due to emission. In addition, a black body is a diffuse emitter. Black-body radiation may be viewed as the radiation from a black body at thermal equilibrium. Black-body radiation becomes a visible glow of light if the temperature of the object is high enough; the Draper point is the temperature at which all solids glow a dim red, about 798 K. At 1000 K, a small opening in the wall of a large uniformly heated opaque-walled cavity, viewed from outside, looks red. No matter how the oven is constructed, or of what material, as long as it is built so that all light entering is absorbed by its walls, it will contain a good approximation to black-body radiation; the spectrum, therefore color, of the light that comes out will be a function of
Edward Teller was a Hungarian-American theoretical physicist, known colloquially as "the father of the hydrogen bomb", although he did not care for the title. He made numerous contributions to nuclear and molecular physics and surface physics, his extension of Enrico Fermi's theory of beta decay, in the form of Gamow–Teller transitions, provided an important stepping stone in its application, while the Jahn–Teller effect and the Brunauer–Emmett–Teller theory have retained their original formulation and are still mainstays in physics and chemistry. Teller made contributions to Thomas–Fermi theory, the precursor of density functional theory, a standard modern tool in the quantum mechanical treatment of complex molecules. In 1953, along with Nicholas Metropolis, Arianna Rosenbluth, Marshall Rosenbluth, Augusta Teller, Teller co-authored a paper, a standard starting point for the applications of the Monte Carlo method to statistical mechanics. Throughout his life, Teller was known both for his scientific ability and for his difficult interpersonal relations and volatile personality.
Teller emigrated to the United States in the 1930s. He was an early member of the Manhattan Project, charged with developing the first atomic bomb. After his controversial testimony in the security clearance hearing of his former Los Alamos Laboratory superior, J. Robert Oppenheimer, Teller was ostracized by much of the scientific community, he continued to find support from the U. S. government and military research establishment for his advocacy for nuclear energy development, a strong nuclear arsenal, a vigorous nuclear testing program. He was a co-founder of Lawrence Livermore National Laboratory, was both its director and associate director for many years. In his years, Teller became known for his advocacy of controversial technological solutions to both military and civilian problems, including a plan to excavate an artificial harbor in Alaska using thermonuclear explosive in what was called Project Chariot, he was a vigorous advocate of Ronald Reagan's Strategic Defense Initiative. Ede Teller was born on January 1908, in Budapest, Austria-Hungary, into a Jewish family.
His parents were Ilona, a pianist, Miksa Teller, an attorney. He learned in the Fasori Lutheran Gymnasium in the Minta Gymnasium in Budapest. Jewish of origin in life Teller became an agnostic Jew. "Religion was not an issue in my family", he wrote, "indeed, it was never discussed. My only religious training came because the Minta required that all students take classes in their respective religions. My family celebrated the Day of Atonement, when we all fasted, yet my father said prayers for his parents on all the Jewish holidays. The idea of God that I absorbed was that it would be wonderful if He existed: We needed Him but had not seen Him in many thousands of years." Like Einstein and Feynman, Teller was a late talker. He developed the ability to speak than most children, but became interested in numbers, would calculate large numbers in his head for fun. Teller left Hungary in 1926 due to the discriminatory numerus clausus rule under Miklós Horthy's regime; the political climate and revolutions in Hungary during his youth instilled a lingering animosity for both Communism and Fascism in Teller.
When he was a young student, his right foot was severed in a streetcar accident in Munich, requiring him to wear a prosthetic foot, leaving him with a lifelong limp. Werner Heisenberg said that it was the hardiness of Teller's spirit, rather than stoicism, that allowed him to cope so well with the accident. Teller graduated in chemical engineering at the University of Karlsruhe, received in 1930 his Ph. D. in physics under Werner Heisenberg at the University of Leipzig. Teller's dissertation dealt with one of the first accurate quantum mechanical treatments of the hydrogen molecular ion. In 1930 he befriended Russian physicists Lev Landau. Teller's lifelong friendship with a Czech physicist, George Placzek, was very important for his scientific and philosophical development, it was Placzek who arranged a summer stay in Rome with Enrico Fermi in 1932, thus orienting Teller's scientific career in nuclear physics. In 1930, Teller moved to the University of Göttingen one of the world's great centers of physics due to the presence of Max Born and James Franck, but after Adolf Hitler became Chancellor of Germany in January 1933, Germany became unsafe for Jewish people, he left through the aid of the International Rescue Committee.
He went to England, moved for a year to Copenhagen, where he worked under Niels Bohr. In February 1934, he married his long-time girlfriend Augusta Maria "Mici" Harkanyi, the sister of a friend, he returned to England in September 1934. Mici had been a student in Pittsburgh, wanted to return to the United States, her chance came in 1935, thanks to George Gamow, Teller was invited to the United States to become a Professor of Physics at George Washington University, where he worked with Gamow until 1941. At George Washington University in 1937, Teller predicted the Jahn–Teller effect, which distorts molecules in certain situations. Teller and Hermann Arthur Jahn analyzed it as a piece of purely mathematical physics. In collaboration with
Erich Armand Arthur Joseph Hückel was a German physicist and physical chemist. He is known for two major contributions: The Debye–Hückel theory of electrolytic solutions The Hückel method of approximate molecular orbital calculations on π electron systems. Hückel was born in the Charlottenburg suburb of Berlin, he studied mathematics from 1914 to 1921 at the University of Göttingen. On receiving his doctorate, he became an assistant at Göttingen, but soon became an assistant to Peter Debye at Zürich, it was there that he and Debye developed their theory of electrolytic solutions, elucidating the behavior of strong electrolytes by considering interionic forces, in order to account for their electrical conductivity and their thermodynamic activity coefficients. After spending 1928 and 1929 in England and Denmark, working with Niels Bohr, Hückel joined the faculty of the Technische Hochschule in Stuttgart. In 1935, he moved to Phillips University in Marburg, where he was named Full Professor a year before his retirement 1961.
He was a member of the International Academy of Quantum Molecular Science. Hückel is most famous for developing the Hückel method of approximate molecular orbital calculations on π electron systems, a simplified quantum-mechanical method to deal with planar unsaturated organic molecules. In 1930 he proposed a σ/π separation theory to explain the restricted rotation of alkenes; this model extended a 1929 interpretation of the bonding in triplet oxygen by Lennard-Jones. According to Hückel, only the ethene σ bond is axially symmetric about the C-C axis, but the π bond is not. In 1931 he generalized his analysis by formulating both valence bond and molecular orbital descriptions of benzene and other cycloconjugated hydrocarbons. Although undeniably a cornerstone of organic chemistry, Hückel's concepts were undeservedly unrecognized for two decades, his lack of communication skills contributed. The famous Hückel 4n+2 rule for determining whether ring molecules composed of C=C bonds would show aromatic properties was first stated by Doering in a 1951 article on tropolone.
Tropolone had been recognised as an aromatic molecule by Dewar in 1945. In 1936, Hückel developed the theory of π-conjugated biradicals; the first example, known as the Schlenk-Brauns hydrocarbon, had been discovered in the same year. The credit for explaining such biradicals is given to Christopher Longuet-Higgins in 1950. In 1937 Hückel refined his MO theory of pi electrons in unsaturated organic molecules; this is still used as an approximation, though the more precise PPP Pariser–Parr–Pople method succeeded it in 1953. "Extended Hückel MO theory" applies to both sigma and pi electrons, has its origins in work by William Lipscomb and Roald Hoffmann for nonplanar molecules in 1962. According to Felix Bloch, Erich Hückel "incited and helped" the students at the University of Zurich to write poems about their great professors; the poem about Erwin Schrödinger went like this: Gar Manches rechnet Erwin schon Mit seiner Wellenfunktion. Nur wissen möcht' man gerne wohl Was man sich dabei soll, it was translated by Felix Bloch: Erwin with his psi can do Calculations quite a few.
But one thing has not been seen: Just what does psi mean? 1965 Otto Hahn Prize for Chemistry and Physics Hückel, E.. "Zur Quantentheorie der Doppelbindung". Zeitschrift für Physik. 60: 423–456. Bibcode:1930ZPhy...60..423H. Doi:10.1007/BF01341254. Hückel, E.. "Quantentheoretische Beiträge zum Benzolproblem". Zeitschrift für Physik. 70: 204–286. Bibcode:1931ZPhy...70..204H. Doi:10.1007/BF01339530. Hückel, E.. "Quantum-theoretical contributions to the benzene problem. I; the electron configuration of benzene and related compounds". Z. Phys. 70: 204–86. Bibcode:1931ZPhy...70..204H. Doi:10.1007/BF01339530. Hückel, E.. "Quantum theoretical contributions to the problem of aromatic and non-saturated compounds". Z. Phys. 76: 628. Bibcode:1932ZPhy...76..628H. Doi:10.1007/BF01341936. Hückel, E.. "The theory of unsaturated and aromatic compounds". Z. Elektrochem. Angew. Physik. Chem. 42: 752 and 827. Hückel, E.. "Theory of the magnetism of so-called biradicals". Z. Phys. Chem. B34: 339. Pariser, R.. G.. "A semi-empirical theory of the electronic spectra and electronic structure of complex unsaturated molecules".
J. Chem. Phys. 21: 466–71. Bibcode:1953JChPh..21..466P. Doi:10.1063/1.1698929. Pople, J. A.. "Electron interaction in unsaturated hydrocarbons". Trans. Faraday Soc. 49: 1375–85. Doi:10.1039/tf9534901375. Hoffmann, R.. "Theory of polyhedral molecules. I. Physical factorizations of the secular equation". J. Chem. Phys. 36: 2179–89. Bibcode:1962JChPh..36.2179H. Doi:10.1063/1.1732849. E. Hückel, Ein Gelehrtenleben: Ernst u. Satire. A. Karachalios, Erich Hückel: From Physics to Quantum Chemistry
An experiment is a procedure carried out to support, refute, or validate a hypothesis. Experiments provide insight into cause-and-effect by demonstrating what outcome occurs when a particular factor is manipulated. Experiments vary in goal and scale, but always rely on repeatable procedure and logical analysis of the results. There exists natural experimental studies. A child may carry out basic experiments to understand gravity, while teams of scientists may take years of systematic investigation to advance their understanding of a phenomenon. Experiments and other types of hands-on activities are important to student learning in the science classroom. Experiments can raise test scores and help a student become more engaged and interested in the material they are learning when used over time. Experiments can vary from personal and informal natural comparisons, to controlled. Uses of experiments vary between the natural and human sciences. Experiments include controls, which are designed to minimize the effects of variables other than the single independent variable.
This increases the reliability of the results through a comparison between control measurements and the other measurements. Scientific controls are a part of the scientific method. Ideally, all variables in an experiment are controlled and none are uncontrolled. In such an experiment, if all controls work as expected, it is possible to conclude that the experiment works as intended, that results are due to the effect of the tested variable. In the scientific method, an experiment is an empirical procedure that arbitrates competing models or hypotheses. Researchers use experimentation to test existing theories or new hypotheses to support or disprove them. An experiment tests a hypothesis, an expectation about how a particular process or phenomenon works. However, an experiment may aim to answer a "what-if" question, without a specific expectation about what the experiment reveals, or to confirm prior results. If an experiment is conducted, the results either support or disprove the hypothesis.
According to some philosophies of science, an experiment can never "prove" a hypothesis, it can only add support. On the other hand, an experiment that provides a counterexample can disprove a theory or hypothesis, but a theory can always be salvaged by appropriate ad hoc modifications at the expense of simplicity. An experiment must control the possible confounding factors—any factors that would mar the accuracy or repeatability of the experiment or the ability to interpret the results. Confounding is eliminated through scientific controls and/or, in randomized experiments, through random assignment. In engineering and the physical sciences, experiments are a primary component of the scientific method, they are used to test theories and hypotheses about how physical processes work under particular conditions. Experiments in these fields focus on replication of identical procedures in hopes of producing identical results in each replication. Random assignment is uncommon. In medicine and the social sciences, the prevalence of experimental research varies across disciplines.
When used, experiments follow the form of the clinical trial, where experimental units are randomly assigned to a treatment or control condition where one or more outcomes are assessed. In contrast to norms in the physical sciences, the focus is on the average treatment effect or another test statistic produced by the experiment. A single study does not involve replications of the experiment, but separate studies may be aggregated through systematic review and meta-analysis. There are various differences in experimental practice in each of the branches of science. For example, agricultural research uses randomized experiments, while experimental economics involves experimental tests of theorized human behaviors without relying on random assignment of individuals to treatment and control conditions. One of the first methodical approaches to experiments in the modern sense is visible in the works of the Arab mathematician and scholar Ibn al-Haytham, he conducted his experiments in the field of optics - going back to optical and mathematical problems in the works of Ptolemy - by controlling his experiments due to factors such as self-criticality, reliance on visible results of the experiments as well as a criticality in terms of earlier results.
He counts as one of the first scholars using an inductive-experimental method for achieving results. In his book "Optics" he describes the fundamentally new approach to knowledge and research in an experimental sense: "We should, that is, recommence the inquiry into its principles and premisses, beginning our investigation with an inspection of the things that exist and a survey of the conditions of visible objects. We should distinguish the properties of particulars, gather by induction what pertains to the eye when vision takes place and what is found in the manner of sensation to be uniform, unchanging and not subject to doubt. After which we should ascend in our inquiry and reasonings and orderly, criticizing premisses and exercising caution in regard to conclusions – our aim in all that we make subject to inspect
Vladimir Aleksandrovich Fock was a Soviet physicist, who did foundational work on quantum mechanics and quantum electrodynamics. He was born in Russia. In 1922 he graduated from Petrograd University continued postgraduate studies there, he became a professor there in 1932. In 1919–1923 and 1928–1941 he collaborated with the Vavilov State Optical Institute, in 1924–1936 with the Leningrad Institute of Physics and Technology, in 1934–1941 and 1944–1953 with the Lebedev Physical Institute, his primary scientific contribution lies in the development of quantum physics and the theory of gravitation, although he contributed to the fields of mechanics, theoretical optics, physics of continuous media. In 1926, he derived the Klein–Gordon equation, he gave his name to Fock space, the Fock representation and Fock state, developed the Hartree–Fock method in 1930. He made many subsequent scientific contributions, during the rest of his life. Fock developed the electromagnetic methods for geophysical exploration in a book The theory of the study of the rocks resistance by the carottage method.
Fock made significant contributions to general relativity theory for the many body problems. Fock criticised on scientific grounds both Einstein's general principle of relativity as being devoid of physical substance and the equivalence principle as interpreted as the equivalence of gravitation and acceleration as having only a local validity. In Leningrad, Fock created a scientific school in theoretical physics and raised the physics education in the USSR through his books, he wrote the first textbook on quantum mechanics Fundamentals of Quantum Mechanics and a influential monograph The Theory of Space and Gravitation. Historians of science, such as Loren Graham, see Fock as a representative and proponent of Einstein's theory of relativity within the Soviet world. At a time when most Marxist philosophers objected to relativity theory, Fock emphasized a materialistic understanding of relativity that coincided philosophically with Marxism, he was a full member of the USSR Academy of Sciences and a member of the International Academy of Quantum Molecular Science.
List of things named after Vladimir Fock Graham, L.. "The reception of Einstein's ideas: Two examples from contrasting political cultures." In Holton, G. and Elkana, Y. Albert Einstein: Historical and cultural perspectives. Princeton, NJ: Princeton UP, pp. 107–136 Fock, V. A.. "The Theory of Space and Gravitation". Macmillan