Special relativity

Special relativity implies a wide range of consequences, which have been experimentally verified,[2] including length contraction, time dilation, relativistic mass, mass–energy equivalence, a universal speed limit, and relativity of simultaneity. It has replaced the conventional notion of an absolute universal time with the notion of a time that is dependent on reference frame and spatial position. Rather than an invariant time interval between two events, there is an invariant spacetime interval. Combined with other laws of physics, the two postulates of special relativity predict the equivalence of mass and energy, as expressed in the mass–energy equivalence formula E = mc2, where c is the speed of light in vacuum.[3][4] A defining feature of special relativity is the replacement of the Galilean transformations of classical mechanics with the Lorentz transformations. Postulates Lack of an absolute reference frame Relativity theory depends on "reference frames". where we get Related:  Collection

Relativistic Doppler effect Diagram 1. A source of light waves moving to the right, relative to observers, with velocity 0.7c. The frequency is higher for observers on the right, and lower for observers on the left. The relativistic Doppler effect is the change in frequency (and wavelength) of light, caused by the relative motion of the source and the observer (as in the classical Doppler effect), when taking into account effects described by the special theory of relativity. The relativistic Doppler effect is different from the non-relativistic Doppler effect as the equations include the time dilation effect of special relativity and do not involve the medium of propagation as a reference point. They describe the total difference in observed frequencies and possess the required Lorentz symmetry. Visualization In Diagram 2, the blue point represents the observer, and the arrow represents the observer's velocity vector. Diagram 3. Analogy Motion along the line of sight away from him (where where and . to

Maxwell's equations Maxwell's equations are a set of partial differential equations that, together with the Lorentz force law, form the foundation of classical electrodynamics, classical optics, and electric circuits. These fields in turn underlie modern electrical and communications technologies. Maxwell's equations describe how electric and magnetic fields are generated and altered by each other and by charges and currents. They are named after the Scottish physicist and mathematician James Clerk Maxwell, who published an early form of those equations between 1861 and 1862. The equations have two major variants. The term "Maxwell's equations" is often used for other forms of Maxwell's equations. Since the mid-20th century, it has been understood that Maxwell's equations are not exact laws of the universe, but are a classical approximation to the more accurate and fundamental theory of quantum electrodynamics. Formulation in terms of electric and magnetic fields Flux and divergence

Kennedy–Thorndike experiment Figure 1. The Kennedy–Thorndike experiment Improved variants of the Kennedy–Thorndike experiment have been conducted using optical cavities or Lunar Laser Ranging. For a general overview of tests of Lorentz invariance, see Tests of special relativity. The experiment The original Michelson–Morley experiment was useful for testing the Lorentz–FitzGerald contraction hypothesis only. The principle on which this experiment is based is the simple proposition that if a beam of homogeneous light is split […] into two beams which after traversing paths of different lengths are brought together again, then the relative phases […] will depend […] on the velocity of the apparatus unless the frequency of the light depends […] on the velocity in the way required by relativity. Referring to Fig. 1, key optical components were mounted within vacuum chamber V on a fused quartz base of extremely low coefficient of thermal expansion. Theory Basic theory of the experiment Figure 2. where

Time dilation of moving particles Relation between the Lorentz factor γ and the time dilation of moving clocks. Time dilation of moving particles as predicted by special relativity can be measured in particle lifetime experiments. According to special relativity, the rate of clock C traveling between two synchronized laboratory clocks A and B is slowed with respect to the laboratory clock rates. This effect is called time dilation. Atmospheric tests a) View in S b) View in S′ c) Loedel diagram (In order to make the differences smaller, 0.7c was used instead of 0.995c) Theory The emergence of the muons is caused by the collision of cosmic rays with the upper atmosphere, after which the muons reach Earth. Time dilation and length contraction Length of the atmosphere: The contraction formula is given by , where L0 is the proper length of the atmosphere and L its contracted length. Decay time of muons: The time dilation formula is In S, muon-S′ has a longer decay time than muon-S. Minkowski diagram Experiments and

Ives–Stilwell experiment Ives–Stilwell experiment (1938). "Canal rays" (a mixture of mostly H2+ and H3+ ions) were accelerated through perforated plates charged from 6,788 to 18,350 volts. The beam and its reflected image were simultaneously observed with the aid of a concave mirror offset 7° from the beam.[1] (The offset in this illustration is exaggerated.) The Ives–Stilwell experiment tested the contribution of relativistic time dilation to the Doppler shift of light.[1][2] The result was in agreement with the formula for the transverse Doppler effect, and was the first direct, quantitative confirmation of the time dilation factor. Experiments with "canal rays" The experiment of 1938 Ives remarked that it is nearly impossible to measure the transverse Doppler effect with respect to light rays emitted by canal rays at right angles to the direction of motion of the canal rays (as it was considered earlier by Einstein), because the influence of the longitudinal effect can hardly be excluded.

Michelson–Morley experiment Figure 1. Michelson and Morley's interferometric setup, mounted on a stone slab and floating in a pool of mercury. The Michelson–Morley experiment was published in 1887 by Albert A. Michelson and Edward W. Michelson–Morley type experiments have been repeated many times with steadily increasing sensitivity. Detecting the aether Physics theories of the late 19th century assumed that just as surface water waves must have a supporting substance, i.e. a "medium", to move across (in this case water), and audible sound requires a medium to transmit its wave motions (such as air or water), so light must also require a medium, the "luminiferous aether", to transmit its wave motions. Figure 2. According to this hypothesis, Earth and the aether are in relative motion, implying that a so-called "aether wind" (Fig. 2) should exist. 1881 and 1887 experiments Michelson experiment (1881) Figure 3. Michelson–Morley experiment (1887) Figure 5. Figure 6. Figure 7. Figure 4.

cahier physique - physics workbook PART I click here (from Copernicus to Newton) movie to watch: greatest discoveries in Astronomy from discovery channel (42 minutes)Willam Herschel He gave up music for astronomy. Built huge telescopes and discovered Uranus and the milky way.+ other objects like comets.Here to learn more general relativity At the end of 19th century some problems with Newtonian Physics arose. watch that movie (from NOVA) Einstein's theory triumphed when the light from a star was observed to be curved during a solar eclipse.lNo matter ca go faster than the speed of light and the speed of light does not depend on theframe of reference it is measured in ! llight is made of particle waves = photons. galaxies, universe is expanding , big bang20s 1927 Edwin Hubble using the observatory at Mt Wilson understands that some of thesefuzzy clouds observed in the background of stars are in fact far away galaxies. radio waves from the center of the milky way are detected30s form WMAP pulsars?

Biologist warn of early stages of Earth's sixth mass extinction event -- ScienceDaily The planet's current biodiversity, the product of 3.5 billion years of evolutionary trial and error, is the highest in the history of life. But it may be reaching a tipping point. In a new review of scientific literature and analysis of data published in Science, an international team of scientists cautions that the loss and decline of animals is contributing to what appears to be the early days of the planet's sixth mass biological extinction event. Since 1500, more than 320 terrestrial vertebrates have become extinct. Populations of the remaining species show a 25 percent average decline in abundance. And while previous extinctions have been driven by natural planetary transformations or catastrophic asteroid strikes, the current die-off can be associated to human activity, a situation that the lead author Rodolfo Dirzo, a professor of biology at Stanford, designates an era of "Anthropocene defaunation." The scientists also detailed a troubling trend in invertebrate defaunation.

Markov process Markov process example Introduction A Markov process is a stochastic model that has the Markov property. It can be used to model a random system that changes states according to a transition rule that only depends on the current state. This article describes the Markov process in a very general sense, which is a concept that is usually specified further. Note that there is no definitive agreement in literature on the use of some of the terms that signify special cases of Markov processes. Markov processes arise in probability and statistics in one of two ways. Markov property The general case Let , for some (totally ordered) index set ; and let be a measurable space. adapted to the filtration is said to possess the Markov property with respect to the if, for each and each with s < t, A Markov process is a stochastic process which satisfies the Markov property with respect to its natural filtration. For discrete-time Markov chains In the case where Examples Gambling

Why Probability in Quantum Mechanics is Given by the Wave Function Squared One of the most profound and mysterious principles in all of physics is the Born Rule, named after Max Born. In quantum mechanics, particles don’t have classical properties like “position” or “momentum”; rather, there is a wave function that assigns a (complex) number, called the “amplitude,” to each possible measurement outcome. The Born Rule is then very simple: it says that the probability of obtaining any possible measurement outcome is equal to the square of the corresponding amplitude. (The wave function is just the set of all the amplitudes.) Born Rule: The Born Rule is certainly correct, as far as all of our experimental efforts have been able to discern. That’s right. The status of the Born Rule depends greatly on one’s preferred formulation of quantum mechanics. It’s an ungainly mess, we all agree. Of course we can do better, since “textbook quantum mechanics” is an embarrassment. Like the textbook formulation, Everettian quantum mechanics also comes with a list of postulates.

Random walk Example of eight random walks in one dimension starting at 0. The plot shows the current position on the line (vertical axis) versus the time steps (horizontal axis). A random walk is a mathematical formalization of a path that consists of a succession of random steps. Various different types of random walks are of interest. . is defined for the continuum of times . Lattice random walk A popular random walk model is that of a random walk on a regular lattice, where at each step the location jumps to another site according to some probability distribution. One-dimensional random walk An elementary example of a random walk is the random walk on the integer number line, , which starts at 0 and at each step moves +1 or −1 with equal probability. This walk can be illustrated as follows. All possible random walk outcomes after 5 flips of a fair coin Random walk in two dimensions with two million even smaller steps. To define this walk formally, take independent random variables and . of .

Astronomers discover complex organic matter exists throughout the universe -- ScienceDaily Astronomers report in the journal Nature that organic compounds of unexpected complexity exist throughout the Universe. The results suggest that complex organic compounds are not the sole domain of life but can be made naturally by stars. Prof. Sun Kwok and Dr. Yong Zhang of The University of Hong Kong show that an organic substance commonly found throughout the Universe contains a mixture of aromatic (ring-like) and aliphatic (chain-like) components. The researchers investigated an unsolved phenomenon: a set of infrared emissions detected in stars, interstellar space, and galaxies. Not only are stars producing this complex organic matter, they are also ejecting it into the general interstellar space, the region between stars. Most interestingly, this organic star dust is similar in structure to complex organic compounds found in meteorites. Prof.

Monte Carlo method Monte Carlo methods (or Monte Carlo experiments) are a broad class of computational algorithms that rely on repeated random sampling to obtain numerical results; typically one runs simulations many times over in order to obtain the distribution of an unknown probabilistic entity. They are often used in physical and mathematical problems and are most useful when it is difficult or impossible to obtain a closed-form expression, or infeasible to apply a deterministic algorithm. Monte Carlo methods are mainly used in three distinct problem classes: optimization, numerical integration and generation of draws from a probability distribution. The modern version of the Monte Carlo method was invented in the late 1940s by Stanislaw Ulam, while he was working on nuclear weapons projects at the Los Alamos National Laboratory. Immediately after Ulam's breakthrough, John von Neumann understood its importance and programmed the ENIAC computer to carry out Monte Carlo calculations. Introduction

Birth–death process The birth–death process is a special case of continuous-time Markov process where the state transitions are of only two types: "births", which increase the state variable by one and "deaths", which decrease the state by one. The model's name comes from a common application, the use of such models to represent the current size of a population where the transitions are literal births and deaths. Birth–death processes have many applications in demography, queueing theory, performance engineering, epidemiology or in biology. When a birth occurs, the process goes from state n to n + 1. and death rates Examples A pure birth process is a birth–death process where for all A pure death process is a birth–death process where A (homogeneous) Poisson process is a pure birth process where M/M/1 model and M/M/c model, both used in queueing theory, are birth–death processes used to describe customers in an infinite queue. Use in queueing theory /FIFO (in complete Kendall's notation) queue. . and

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