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The problem is what Konstantin Tsiolkovsky discovered 100 years ago: as speed increases, the mass required (in fuel) increases exponentially. This relation, specifically, is
$$
\Delta v=v_e\ln\left(\frac{m_i}{m_f}\right)
$$
where $v_e$ is the exhaust velocity, $m_i$ the initial mass and $m_f$ the...
The dawn of a new year, 2015, now approaches, or has already approached, either way it means that it is now time to reset our Community Promotion Ads!
What are Community Promotion Ads?
Community Promotion Ads are community-vetted advertisements that will show up on the main site, in the right s...
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A way to understand this, is to imagine that light actually follows all paths. However, most paths experience destructive interference with other paths. The only paths that do not experience destructive interference are those in the neighbourhood of paths with stationary (e.g., minimal) action (t...
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QED: The Strange Theory of Light and Matter is an adaptation for the general reader of four lectures on quantum electrodynamics (QED) by Richard Feynman (1918-1988).
QED was designed to be a popular science book, written in a witty style, and containing just enough quantum-mechanical mathematics to allow the solving of very basic problems in quantum electrodynamics by an educated lay audience. It is unusual for a popular science book in the level of mathematical detail it goes into, actually allowing the reader to solve simple optics problems, as might be found in an actual textbook. But unlike...
In quantum mechanics, a probability amplitude is a complex number used in describing the behaviour of systems. The modulus squared of this quantity represents a probability or probability density.
Probability amplitudes provide a relationship between the wave function (or, more generally, of a quantum state vector) of a system and the results of observations of that system, a link first proposed by Max Born. Interpretation of values of a wave function as the probability amplitude is a pillar of the Copenhagen interpretation of quantum mechanics. In fact, the properties of the space of wave functions...
The path integral formulation of quantum mechanics is a description of quantum theory which generalizes the action principle of classical mechanics. It replaces the classical notion of a single, unique trajectory for a system with a sum, or functional integral, over an infinity of possible trajectories to compute a quantum amplitude.
The basic idea of the path integral formulation can be traced back to Norbert Wiener, who introduced the Wiener integral for solving problems in diffusion and Brownian motion. This idea was extended to the use of the Lagrangian in quantum mechanics by P. A. M. Dirac...
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The double-slit experiment is a demonstration that light and matter can display characteristics of both classically defined waves and particles; moreover, it displays the fundamentally probabilistic nature of quantum mechanical phenomena. This experiment is sometimes referred to as Young's experiment. The experiment belongs to a general class of "double path" experiments, in which a wave is split into two separate waves that later combine back into a single wave. Changes in the path lengths of both waves result in a phase shift, creating an interference pattern. Another version is the Mach–Zehnder...
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