Interpretations of quantum mechanics An interpretation of quantum mechanics is a set of statements which attempt to explain how quantum mechanics informs our understanding of nature. Although quantum mechanics has held up to rigorous and thorough experimental testing, many of these experiments are open to different interpretations. There exist a number of contending schools of thought, differing over whether quantum mechanics can be understood to be deterministic, which elements of quantum mechanics can be considered "real", and other matters. This question is of special interest to philosophers of physics, as physicists continue to show a strong interest in the subject. History of interpretations Main quantum mechanics interpreters An early interpretation has acquired the label Copenhagen interpretation, and is often used. Nature of interpretation An interpretation of quantum mechanics is a conceptual or argumentative way of relating between: Two qualities vary among interpretations: Concerns of Einstein
EPR paradox Albert Einstein The EPR paradox is an early and influential critique leveled against the Copenhagen interpretation of quantum mechanics. Albert Einstein and his colleagues Boris Podolsky and Nathan Rosen (known collectively as EPR) designed a thought experiment which revealed that the accepted formulation of quantum mechanics had a consequence which had not previously been noticed, but which looked unreasonable at the time. The scenario described involved the phenomenon that is now known as quantum entanglement. According to quantum mechanics, under some conditions, a pair of quantum systems may be described by a single wave function, which encodes the probabilities of the outcomes of experiments that may be performed on the two systems, whether jointly or individually. At the time the EPR article discussed below was written, it was known from experiments that the outcome of an experiment sometimes cannot be uniquely predicted. History of EPR developments Einstein's opposition
X 4, 041013 (2014) - Quantum Phenomena Modeled by Interactions between Many Classical Worlds We investigate whether quantum theory can be understood as the continuum limit of a mechanical theory, in which there is a huge, but finite, number of classical “worlds,” and quantum effects arise solely from a universal interaction between these worlds, without reference to any wave function. Here, a “world” means an entire universe with well-defined properties, determined by the classical configuration of its particles and fields. In our approach, each world evolves deterministically, probabilities arise due to ignorance as to which world a given observer occupies, and we argue that in the limit of infinitely many worlds the wave function can be recovered (as a secondary object) from the motion of these worlds.
Winter Temperatures and the Arctic Oscillation If you live nearly anywhere in North America, Europe, or Asia, it’s no news that December 2009 and early January 2010 were cold. This image illustrates how cold December was compared to the average of temperatures recorded in December between 2000 and 2008. Blue points to colder than average land surface temperatures, while red indicates warmer temperatures. Much of the Northern Hemisphere experienced cold land surface temperatures, but the Arctic was exceptionally warm. This weather pattern is a tale-tell sign of the Arctic Oscillation. The Arctic Oscillation is a climate pattern that influences winter weather in the Northern Hemisphere. Throughout December 2009, the North Atlantic Oscillation was strongly negative, said the National Weather Service. ReferencesClimate Prediction Center. (2010, January 8). NASA Earth Observatory image by Kevin Ward, based on data provided by the NASA Earth Observations (NEO) Project. Instrument(s): Terra - MODIS
Applications Matrix mechanics Matrix mechanics is a formulation of quantum mechanics created by Werner Heisenberg, Max Born, and Pascual Jordan in 1925. In some contrast to the wave formulation, it produces spectra of energy operators by purely algebraic, ladder operator, methods. Relying on these methods, Pauli derived the hydrogen atom spectrum in 1926, before the development of wave mechanics. Development of matrix mechanics In 1925, Werner Heisenberg, Max Born, and Pascual Jordan formulated the matrix mechanics representation of quantum mechanics. Epiphany at Helgoland In 1925 Werner Heisenberg was working in Göttingen on the problem of calculating the spectral lines of hydrogen. "It was about three o' clock at night when the final result of the calculation lay before me. The Three Fundamental Papers After Heisenberg returned to Göttingen, he showed Wolfgang Pauli his calculations, commenting at one point: In the paper, Heisenberg formulated quantum theory without sharp electron orbits. W.
Quantum Chaos Editor's Note: This feature was originally published in our January 1992 issue. We are posting it because of recent discussions of the connections between chaos and quantum mechanics. In 1917 Albert Einstein wrote a paper that was completely ignored for 40 years. In it he raised a question that physicists have only, recently begun asking themselves: What would classical chaos, which lurks everywhere in our world, do to quantum mechanics, the theory describing the atomic and subatomic worlds? The effects of classical chaos, of course, have long been observed-Kepler knew about the motion of the moon around the earth and Newton complained bitterly about the phenomenon. At the end of the 19th century the American astronomer William Hill demonstrated that the irregularity is the result entirely of the gravitational pull of the sun. Perhaps the single most outstanding feature of the quantum world is its smooth and wavelike nature. Such a highly excited atom is called a Rydberg atom.
Cell Size and Scale Some cells are visible to the unaided eye The smallest objects that the unaided human eye can see are about 0.1 mm long. That means that under the right conditions, you might be able to see an ameoba proteus, a human egg, and a paramecium without using magnification. Smaller cells are easily visible under a light microscope. To see anything smaller than 500 nm, you will need an electron microscope. Adenine The label on the nucleotide is not quite accurate. How can an X chromosome be nearly as big as the head of the sperm cell? No, this isn't a mistake. The X chromosome is shown here in a condensed state, as it would appear in a cell that's going through mitosis. A chromosome is made up of genetic material (one long piece of DNA) wrapped around structural support proteins (histones). Carbon The size of the carbon atom is based on its van der Waals radius.
Density matrix Explicitly, suppose a quantum system may be found in state with probability p1, or it may be found in state with probability p2, or it may be found in state with probability p3, and so on. By choosing a basis (which need not be orthogonal), one may resolve the density operator into the density matrix, whose elements are For an operator (which describes an observable is given by In words, the expectation value of A for the mixed state is the sum of the expectation values of A for each of the pure states Mixed states arise in situations where the experimenter does not know which particular states are being manipulated. Pure and mixed states In quantum mechanics, a quantum system is represented by a state vector (or ket) . is called a pure state. and a 50% chance that the state vector is . A mixed state is different from a quantum superposition. Example: Light polarization The incandescent light bulb (1) emits completely random polarized photons (2) with mixed state density matrix .
Relationship between string theory and quantum field theory Many first principles in quantum field theory are explained, or get further insight, in string theory: Note: formally, gauge symmetries in string theory are (at least in most cases) a result of the existence of a global symmetry together with the profound gauge symmetry of string theory, which is the symmetry of the worldsheet under a local change of coordinates and scales. SelfOrganizingQuantumJul08.pdf