Grand Unified Theory

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. Relativity and quantum mechanics 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[edit] Main quantum mechanics interpreters An early interpretation has acquired the label Copenhagen interpretation, and is often used. Nature of interpretation[edit] An interpretation of quantum mechanics is a conceptual or argumentative way of relating between: Two qualities vary among interpretations: Concerns of Einstein[edit]

Attempt at a unified field theory Schwinger–Dyson equation The Schwinger–Dyson equations (SDEs), also known as the Dyson–Schwinger equations, named after Julian Schwinger and Freeman Dyson, are general relations between Green functions in quantum field theories (QFTs). They are also referred to as the Euler–Lagrange equations of quantum field theories, since they are the equations of motion of the corresponding Green's function. They form a set of infinitely many functional differential equations, all coupled to each other, sometimes referred to as the infinite tower of SDEs. In his paper "The S-Matrix in Quantum electrodynamics",[1] Dyson derived relations between different S-matrix elements, or more specific "one-particle Green's functions", in quantum electrodynamics, by summing up infinitely many Feynman diagrams, thus working in a perturbative approach. Schwinger also derived an equation for the two-particle irreducible Green functions,[2] which is nowadays referred to as the inhomogeneous Bethe–Salpeter equation. Derivation[edit] , we have

Quantum mechanics and classical physics 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. 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. The routine explanation of this effect was, at that time, provided by Heisenberg's uncertainty principle. The EPR paper, written in 1935, was intended to illustrate that this explanation is inadequate. History of EPR developments[edit] Quantum mechanics and its interpretation[edit] Einstein's opposition[edit]

Applications