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.[1] Relying on these methods, Pauli derived the hydrogen atom spectrum in 1926,[2] before the development of wave mechanics. Development of matrix mechanics[edit] In 1925, Werner Heisenberg, Max Born, and Pascual Jordan formulated the matrix mechanics representation of quantum mechanics. Epiphany at Helgoland[edit] 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[edit] After Heisenberg returned to Göttingen, he showed Wolfgang Pauli his calculations, commenting at one point:[4] In the paper, Heisenberg formulated quantum theory without sharp electron orbits. W.
Einselection In quantum mechanics, einselection, short for environment - induced superselection, is a name coined by Wojciech H. Zurek[1] for a process which explains the phenomenon of wavefunction collapse and the emergence of classical descriptions of reality from quantum descriptions. Classicality is an emergent property induced in open quantum systems by their environments. Since only quasi-local, essentially classical states survive the decoherence process, einselection can in many ways explain the emergence of a (seemingly) classical reality in a fundamentally quantum universe (at least to local observers). Definition[edit] corresponding to different pointer states become orthogonal: Details[edit] To study einselection, an operational definition of pointer states has been introduced.[4][5] This is the "predictability sieve" criterion, based on an intuitive idea: Pointer states can be defined as the ones which become minimally entangled with the environment in the course of their evolution. ). .
Quantum gauge theory Older approaches to quantization for Abelian models use the Gupta-Bleuler formalism with a "semi-Hilbert space" with an indefinite sesquilinear form. However, it is much more elegant to just work with the quotient space of vector field configurations by gauge transformations. An alternative approach using lattice approximations is covered in (Wick rotated) lattice gauge theory. To establish the existence of the Yang-Mills theory and a mass gap is one of the seven Millennium Prize Problems of the Clay Mathematics Institute. How Cosmic Inflation Creates an Infinity of Universes [Video] Give a Gift & Get a Gift - Free! Quantum teleportation Quantum teleportation is a process by which quantum information (e.g. the exact state of an atom or photon) can be transmitted (exactly, in principle) from one location to another, with the help of classical communication and previously shared quantum entanglement between the sending and receiving location. Because it depends on classical communication, which can proceed no faster than the speed of light, it cannot be used for superluminal transport or communication of classical bits. It also cannot be used to make copies of a system, as this violates the no-cloning theorem. Although the name is inspired by the teleportation commonly used in fiction, current technology provides no possibility of anything resembling the fictional form of teleportation. Non-technical summary[edit] Quantum teleportation provides a mechanism of moving a qubit from one location to another, without having to physically transport the underlying particle that a qubit is normally attached to. Protocol[edit] and
Applications From Eternity to Book Club: Chapter Eleven | Cosmic Variance Welcome to this week’s installment of the From Eternity to Here book club. Part Three of the book concludes with Chapter Eleven, “Quantum Time.” Excerpt: This distinction between “incomplete knowledge” and “intrinsic quantum indeterminacy” is worth dwelling on. Title notwithstanding, the point of the chapter is not that there’s some “quantum” version of time that we have to understand. However, we still need to talk about quantum mechanics for the purposes of this book, for one very good reason: we’ve been making a big deal about how the fundamental laws of physics are reversible, but wave function collapse (under the textbook Copenhagen interpretation) is an apparent counterexample. Along the way, I get to give my own perspective on what quantum mechanics really means. So I present a number of colorful examples of two-state systems involving cats and dogs.
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]
Pearltrees No-communication theorem In physics, the no-communication theorem is a no-go theorem from quantum information theory, which states that, during measurement of an entangled quantum state, it is not possible for one observer, making a measurement of a subsystem of the total state, to communicate information to another observer. The theorem is important because, in quantum mechanics, quantum entanglement is an effect by which certain widely separated events can be correlated in ways that suggest the possibility of instantaneous communication. The no-communication theorem gives conditions under which such transfer of information between two observers is impossible. In very rough terms, the theorem describes a situation that is analogous to two people, each with a radio receiver, listening to a common radio station: it is impossible for one of the listeners to use their radio receiver to send messages to the other listener. Informal Overview[edit] Formulation[edit] where Ti and Si are operators on HA and HB. The term
Macroscopic quantum phenomena Quantum mechanics is most often used to describe matter on the scale of molecules, atoms, or elementary particles. However some phenomena, particularly at low temperatures, show quantum behavior on a macroscopic scale. The best-known examples of macroscopic quantum phenomena are superfluidity and superconductivity; another example is the quantum Hall effect. Since 2000 there has been extensive experimental work on quantum gases, particularly Bose–Einstein Condensates. Between 1996 to 2003 four Nobel prizes were given for work related to macroscopic quantum phenomena.[1] Macroscopic quantum phenomena can be observed in superfluid helium and in superconductors,[2] but also in dilute quantum gases and in laser light. Although these media are very different, their behavior is very similar as they all show macroscopic quantum behavior. Consequences of the macroscopic occupation[edit] Fig.1 Left: only one particle; usually the small box is empty. with Ψ₀ the amplitude and the phase. 1. 2. 3. and
From Eternity to Book Club: Chapter Twelve | Cosmic Variance Welcome to this week’s installment of the From Eternity to Here book club. Part Four opens with Chapter Twelve, “Black Holes: The Ends of Time.” Excerpt: Unlike boxes full of atoms, we can’t make black holes with the same size but different masses. The size of a black hole is characterized by the “Schwarzschild radius,” which is precisely proportional to its mass. If you know the mass, you know the size; contrariwise, if you have a box of fixed size, there is a maximum mass black hole you can possibly fit into it. It’s not surprising to find a chapter about black holes in a book that talks about relativity and cosmology and all that. Black holes are important to our story for a couple of reasons. The other reason black holes are important, of course, is that the answer that Bekenstein and Hawking derive is somewhat surprising, and ultimately game-changing.