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Heisenberg's Microscope
Heisenberg's microscope is a thought experiment proposed by Werner Heisenberg that has served as the nucleus of some commonly held ideas about quantum mechanics. In particular, it provides an argument for the uncertainty principle on the basis of the principles of classical optics. The concept was criticized by Heisenberg's mentor Niels Bohr, and theoretical and experimental developments have suggested that Heisenberg's intuitive explanation of his mathematical result might be misleading. While the act of measurement does lead to uncertainty, the loss of precision is less than that predicted by Heisenberg's argument when measured at the level of an individual state. The formal mathematical result remains valid, however, and the original intuitive argument has also been vindicated mathematically when the notion of disturbance is expanded to be independent of any specific state. Heisenberg's argument Heisenberg supposes that an electron is like a classical particle, moving in the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Thought Experiment
A thought experiment is a hypothetical situation in which a hypothesis, theory, or principle is laid out for the purpose of thinking through its consequences. History The ancient Greek ''deiknymi'' (), or thought experiment, "was the most ancient pattern of mathematical proof", and existed before Euclidean mathematics, where the emphasis was on the conceptual, rather than on the experimental part of a thought-experiment. Johann Witt-Hansen established that Hans Christian Ørsted was the first to use the German term ' (lit. thought experiment) circa 1812. Ørsted was also the first to use the equivalent term ' in 1820. By 1883 Ernst Mach used the term ' in a different way, to denote exclusively the conduct of a experiment that would be subsequently performed as a by his students. Physical and mental experimentation could then be contrasted: Mach asked his students to provide him with explanations whenever the results from their subsequent, real, physical experiment differed ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Planck Constant
The Planck constant, or Planck's constant, is a fundamental physical constant of foundational importance in quantum mechanics. The constant gives the relationship between the energy of a photon and its frequency, and by the mass-energy equivalence, the relationship between mass and frequency. Specifically, a photon's energy is equal to its frequency multiplied by the Planck constant. The constant is generally denoted by h. The reduced Planck constant, or Dirac constant, equal to the constant divided by 2 \pi, is denoted by \hbar. In metrology it is used, together with other constants, to define the kilogram, the SI unit of mass. The SI units are defined in such a way that, when the Planck constant is expressed in SI units, it has the exact value The constant was first postulated by Max Planck in 1900 as part of a solution to the ultraviolet catastrophe. At the end of the 19th century, accurate measurements of the spectrum of black body radiation existed, but the distribut ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Electromagnetic Radiation
In physics, electromagnetic radiation (EMR) consists of waves of the electromagnetic field, electromagnetic (EM) field, which propagate through space and carry momentum and electromagnetic radiant energy. It includes radio waves, microwaves, infrared, Light, (visible) light, ultraviolet, X-rays, and gamma rays. All of these waves form part of the electromagnetic spectrum. Classical electromagnetism, Classically, electromagnetic radiation consists of electromagnetic waves, which are synchronized oscillations of electric field, electric and magnetic fields. Depending on the frequency of oscillation, different wavelengths of electromagnetic spectrum are produced. In a vacuum, electromagnetic waves travel at the speed of light, commonly denoted ''c''. In homogeneous, isotropic media, the oscillations of the two fields are perpendicular to each other and perpendicular to the direction of energy and wave propagation, forming a transverse wave. The position of an electromagnetic wave w ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quantum Field Theory
In theoretical physics, quantum field theory (QFT) is a theoretical framework that combines classical field theory, special relativity, and quantum mechanics. QFT is used in particle physics to construct physical models of subatomic particles and in condensed matter physics to construct models of quasiparticles. QFT treats particles as excited states (also called Quantum, quanta) of their underlying quantum field (physics), fields, which are more fundamental than the particles. The equation of motion of the particle is determined by minimization of the Lagrangian, a functional of fields associated with the particle. Interactions between particles are described by interaction terms in the Lagrangian (field theory), Lagrangian involving their corresponding quantum fields. Each interaction can be visually represented by Feynman diagrams according to perturbation theory (quantum mechanics), perturbation theory in quantum mechanics. History Quantum field theory emerged from the wo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Uncertainty Principle
In quantum mechanics, the uncertainty principle (also known as Heisenberg's uncertainty principle) is any of a variety of mathematical inequalities asserting a fundamental limit to the accuracy with which the values for certain pairs of physical quantities of a particle, such as position, ''x'', and momentum, ''p'', can be predicted from initial conditions. Such variable pairs are known as complementary variables or canonically conjugate variables; and, depending on interpretation, the uncertainty principle limits to what extent such conjugate properties maintain their approximate meaning, as the mathematical framework of quantum physics does not support the notion of simultaneously well-defined conjugate properties expressed by a single value. The uncertainty principle implies that it is in general not possible to predict the value of a quantity with arbitrary certainty, even if all initial conditions are specified. Introduced first in 1927 by the German physicist Werner ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Schrödinger's Cat
In quantum mechanics, Schrödinger's cat is a thought experiment that illustrates a paradox of quantum superposition. In the thought experiment, a hypothetical cat may be considered simultaneously both alive and dead, while it is unobserved in a closed box, as a result of its fate being linked to a random subatomic event that may or may not occur. This thought experiment was devised by physicist Erwin Schrödinger in 1935, in a discussion with Albert Einstein, to illustrate what Schrödinger saw as the problems of the Copenhagen interpretation of quantum mechanics. The scenario is often featured in theoretical discussions of the interpretations of quantum mechanics, particularly in situations involving the measurement problem. Origin and motivation Schrödinger intended his thought experiment as a discussion of the EPR article—named after its authors Einstein, Podolsky, and Rosen—in 1935. The EPR article highlighted the counterintuitive nature of quantum superposition ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Philosophical Interpretation Of Classical Physics
Classical ''Newtonian'' physics has, formally, been replaced by quantum mechanics on the small scale and relativity on the large scale. Because most humans continue to think in terms of the kind of events we perceive in the human scale of daily life, it became necessary to provide a new philosophical interpretation of classical physics. Classical mechanics worked extremely well within its domain of observation but made inaccurate predictions at very small scale – atomic scale systems – and when objects moved very fast or were very massive. Viewed through the lens of quantum mechanics or relativity, we can now see that classical physics, imported from the world of our everyday experience, includes notions for which there is no actual evidence. For example, one commonly held idea is that there exists one absolute time shared by all observers. Another is the idea that electrons are discrete entities like miniature planets that circle the nucleus in definite orbits. The corresponden ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Interpretation Of Quantum Mechanics
An interpretation of quantum mechanics is an attempt to explain how the mathematical theory of quantum mechanics might correspond to experienced reality. Although quantum mechanics has held up to rigorous and extremely precise tests in an extraordinarily broad range of experiments, there exist a number of contending schools of thought over their interpretation. These views on interpretation differ on such fundamental questions as whether quantum mechanics is deterministic or stochastic, which elements of quantum mechanics can be considered real, and what the nature of measurement is, among other matters. Despite nearly a century of debate and experiment, no consensus has been reached among physicists and philosophers of physics concerning which interpretation best "represents" reality. History The definition of quantum theorists' terms, such as ''wave function'' and ''matrix mechanics'', progressed through many stages. For instance, Erwin Schrödinger originally viewed the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Basics Of Quantum Mechanics
Quantum mechanics is the study of matter and its interactions with energy on the scale of atomic and subatomic particles. By contrast, classical physics explains matter and energy only on a scale familiar to human experience, including the behavior of astronomical bodies such as the moon. Classical physics is still used in much of modern science and technology. However, towards the end of the 19th century, scientists discovered phenomena in both the large ( macro) and the small (micro) worlds that classical physics could not explain. The desire to resolve inconsistencies between observed phenomena and classical theory led to two major revolutions in physics that created a shift in the original scientific paradigm: the ''theory of relativity'' and the development of ''quantum mechanics''. This article describes how physicists discovered the limitations of classical physics and developed the main concepts of the quantum theory that replaced it in the early decades of the 20th cen ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quantum Mechanics
Quantum mechanics is a fundamental theory in physics that provides a description of the physical properties of nature at the scale of atoms and subatomic particles. It is the foundation of all quantum physics including quantum chemistry, quantum field theory, quantum technology, and quantum information science. Classical physics, the collection of theories that existed before the advent of quantum mechanics, describes many aspects of nature at an ordinary (macroscopic) scale, but is not sufficient for describing them at small (atomic and subatomic) scales. Most theories in classical physics can be derived from quantum mechanics as an approximation valid at large (macroscopic) scale. Quantum mechanics differs from classical physics in that energy, momentum, angular momentum, and other quantities of a bound system are restricted to discrete values ( quantization); objects have characteristics of both particles and waves (wave–particle duality); and there are limits to ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Atom Localization
Atom localization deals with estimating the position of an atom using techniques of quantum optics with increasing precision. This field finds its origins in the thought experiment by Werner Heisenberg called Heisenberg's microscope, which is commonly used as an illustration of Heisenberg's Uncertainty relation in quantum mechanics textbooks. The techniques have matured enough to offer atom localization along all three spatial dimensions in the subwavelength domain. Atom localization techniques have been applied to other fields requiring precise control or measurement of the position of atom-like entities such as microscopy, nanolithography, optical trapping of atoms, optical lattices, and atom optics. Atom localization is based on employing atomic coherence to determine the position of the atom to a precision smaller than the wavelength of the light being used. This seemingly surpasses the Rayleigh limit of resolution and opens up possibilities of super-resolution for a variety ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Probability Distribution
In probability theory and statistics, a probability distribution is the mathematical function that gives the probabilities of occurrence of different possible outcomes for an experiment. It is a mathematical description of a random phenomenon in terms of its sample space and the probabilities of events (subsets of the sample space). For instance, if is used to denote the outcome of a coin toss ("the experiment"), then the probability distribution of would take the value 0.5 (1 in 2 or 1/2) for , and 0.5 for (assuming that the coin is fair). Examples of random phenomena include the weather conditions at some future date, the height of a randomly selected person, the fraction of male students in a school, the results of a survey to be conducted, etc. Introduction A probability distribution is a mathematical description of the probabilities of events, subsets of the sample space. The sample space, often denoted by \Omega, is the set of all possible outcomes of a random phe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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