Quantum entanglement
Quantum entanglement is a physical phenomenon that occurs when pairs or groups of particles are generated or interact in ways such that the quantum state of each particle cannot be described independently – instead, a quantum state may be given for the system as a whole. Such phenomena were the subject of a 1935 paper by Albert Einstein, Boris Podolsky and Nathan Rosen,[1] describing what came to be known as the EPR paradox, and several papers by Erwin Schrödinger shortly thereafter.[2][3] Einstein and others considered such behavior to be impossible, as it violated the local realist view of causality (Einstein referred to it as "spooky action at a distance"),[4] and argued that the accepted formulation of quantum mechanics must therefore be incomplete. History[edit] However, they did not coin the word entanglement, nor did they generalize the special properties of the state they considered. Concept[edit] Meaning of entanglement[edit] Apparent paradox[edit] The hidden variables theory[edit]

Amplituhedron
An amplituhedron is a geometric structure that enables simplified calculation of particle interactions in some quantum field theories. In planar N = 4 supersymmetric Yang–Mills theory, an amplituhedron is defined as a mathematical space known as the positive Grassmannian. The connection between the amplituhedron and scattering amplitudes is at present a conjecture that has passed many non-trivial checks, including an understanding of how locality and unitarity arise as consequences of positivity. Research has been led by Nima Arkani-Hamed. Edward Witten described the work as “very unexpected" and said that "it is difficult to guess what will happen or what the lessons will turn out to be Description[edit] Using twistor theory, BCFW recursion relations involved in the scattering process may be represented as a small number of twistor diagrams. Implications[edit] See also[edit] References[edit] Notes[edit] Bibliography[edit] External links[edit]

Quantum geometry
In theoretical physics, quantum geometry is the set of new mathematical concepts generalizing the concepts of geometry whose understanding is necessary to describe the physical phenomena at very short distance scales (comparable to Planck length). At these distances, quantum mechanics has a profound effect on physics. Quantum gravity[edit] In an alternative approach to quantum gravity called loop quantum gravity (LQG), the phrase "quantum geometry" usually refers to the formalism within LQG where the observables that capture the information about the geometry are now well defined operators on a Hilbert space. In particular, certain physical observables, such as the area, have a discrete spectrum. It has also been shown that the loop quantum geometry is non-commutative[citation needed]. It is possible (but considered unlikely) that this strictly quantized understanding of geometry will be consistent with the quantum picture of geometry arising from string theory. See also[edit]

Quantum spacetime
In mathematical physics, the concept of quantum spacetime is a generalization of the usual concept of spacetime in which some variables that ordinarily commute are assumed not to commute and form a different Lie algebra. The choice of that algebra still varies from theory to theory. As a result of this change some variables that are usually continuous may become discrete. Often only such discrete variables are called "quantized"; usage varies. The idea of quantum spacetime was proposed in the early days of quantum theory by Heisenberg and Ivanenko as a way to eliminate infinities from quantum field theory. The germ of the idea passed from Heisenberg to Rudolf Peierls, who noted that electrons in a magnetic field can be regarded as moving in a quantum space-time, and to Robert Oppenheimer, who carried it to Hartland Snyder, who published the first concrete example.[1] Snyder's Lie algebra was made simple by C. The Lie algebra should be semisimple (Yang, I. for the spatial variables . .

Personal and Historical Perspectives of Hans Bethe
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. The density operator for this system is[1] By choosing a basis (which need not be orthogonal), one may resolve the density operator into the density matrix, whose elements are[1] For an operator (which describes an observable is given by[1] 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[edit] 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[edit] An example of pure and mixed states is light polarization. . and . . .

Planck constant
Plaque at the Humboldt University of Berlin: "Max Planck, discoverer of the elementary quantum of action h, taught in this building from 1889 to 1928." In 1905 the value (E), the energy of a charged atomic oscillator, was theoretically associated with the energy of the electromagnetic wave itself, representing the minimum amount of energy required to form an electromagnetic field (a "quantum"). Further investigation of quanta revealed behaviour associated with an independent unit ("particle") as opposed to an electromagnetic wave and was eventually given the term photon. The Planck relation now describes the energy of each photon in terms of the photon's frequency. This energy is extremely small in terms of ordinary experience. Since the frequency , wavelength λ, and speed of light c are related by λν = c, the Planck relation for a photon can also be expressed as The above equation leads to another relationship involving the Planck constant. Value[edit] Significance of the value[edit]

Atoms Reach Record Temperature, Colder than Absolute Zero
Absolute zero is often thought to be the coldest temperature possible. But now researchers show they can achieve even lower temperatures for a strange realm of "negative temperatures." Oddly, another way to look at these negative temperatures is to consider them hotter than infinity, researchers added. This unusual advance could lead to new engines that could technically be more than 100 percent efficient, and shed light on mysteries such as dark energy, the mysterious substance that is apparently pulling our universe apart. An object's temperature is a measure of how much its atoms move — the colder an object is, the slower the atoms are. Bizarro negative temperatures To comprehend the negative temperatures scientists have now devised, one might think of temperature as existing on a scale that is actually a loop, not linear. With positive temperatures, atoms more likely occupy low-energy states than high-energy states, a pattern known as Boltzmann distribution in physics.