In astronomy, aberration is a phenomenon where celestial objects exhibit an apparent motion about their true positions based on the velocity of the observer: It causes objects to appear to be displaced towards the observer's direction of motion. The change in angle is of the order of where is the speed of light and the velocity of the observer. In the case of "stellar" or "annual" aberration, the apparent position of a star to an observer on Earth varies periodically over the course of a year as the Earth's velocity changes as it revolves around the Sun, by a maximum angle of approximately 20 arcseconds in right ascension or declination.
The Doppler effect is the change in the frequency of a wave in relation to an observer who is moving relative to the source of the wave. The Doppler effect is named after the physicist Christian Doppler, who described the phenomenon in 1842. A common example of Doppler shift is the change of pitch heard when a vehicle sounding a horn approaches and recedes from an observer. Compared to the emitted frequency, the received frequency is higher during the approach, identical at the instant of passing by, and lower during the recession.
In physics, the Lorentz transformations are a six-parameter family of linear transformations from a coordinate frame in spacetime to another frame that moves at a constant velocity relative to the former. The respective inverse transformation is then parameterized by the negative of this velocity. The transformations are named after the Dutch physicist Hendrik Lorentz.
In physics, a redshift is an increase in the wavelength, and corresponding decrease in the frequency and photon energy, of electromagnetic radiation. The opposite change, a decrease in wavelength and increase in frequency and energy, is known as a blueshift, or negative redshift. The terms derive from the colours red and blue which form the extremes of the visible light spectrum. The main causes of electromagnetic redshift in astronomy and cosmology are the relative motions of radiation sources, which give rise to the relativistic Doppler effect, and gravitational potentials, which gravitationally redshift escaping radiation. All sufficiently distant light sources show cosmological redshift corresponding to recession speeds proportional to their distances from Earth, a fact known as Hubble's law that implies the universe is expanding.
In physics, the special theory of relativity, or special relativity for short, is a scientific theory of the relationship between space and time. In Albert Einstein's 1905 paper, On the Electrodynamics of Moving Bodies, the theory is presented as being based on just two postulates:
- The laws of physics are invariant (identical) in all inertial frames of reference. This is known as the principle of relativity.
- The speed of light in vacuum is the same for all observers, regardless of the motion of light source or observer. This is known as the principle of light constancy, or the principle of light speed invariance.
In physics, spacetime, also called the space-time continuum, is a mathematical model that fuses the three dimensions of space and the one dimension of time into a single four-dimensional continuum. Spacetime diagrams are useful in visualizing and understanding relativistic effects, such as how different observers perceive where and when events occur.
The invariant mass, rest mass, intrinsic mass, proper mass, or in the case of bound systems simply mass, is the portion of the total mass of an object or system of objects that is independent of the overall motion of the system. More precisely, it is a characteristic of the system's total energy and momentum that is the same in all frames of reference related by Lorentz transformations. If a center-of-momentum frame exists for the system, then the invariant mass of a system is equal to its total mass in that "rest frame". In other reference frames, where the system's momentum is nonzero, the total mass of the system is greater than the invariant mass, but the invariant mass remains unchanged.
Time dilation is the difference in elapsed time as measured by two clocks, either because of a relative velocity between them, or a difference in gravitational potential between their locations. When unspecified, "time dilation" usually refers to the effect due to velocity.
Length contraction is the phenomenon that a moving object's length is measured to be shorter than its proper length, which is the length as measured in the object's own rest frame. It is also known as Lorentz contraction or Lorentz–FitzGerald contraction and is usually only noticeable at a substantial fraction of the speed of light. Length contraction is only in the direction in which the body is travelling. For standard objects, this effect is negligible at everyday speeds, and can be ignored for all regular purposes, only becoming significant as the object approaches the speed of light relative to the observer.
In astronomy, superluminal motion is the apparently faster-than-light motion seen in some radio galaxies, BL Lac objects, quasars, blazars and recently also in some galactic sources called microquasars. Bursts of energy moving out along the relativistic jets emitted from these objects can have a proper motion that appears greater than the speed of light. All of these sources are thought to contain a black hole, responsible for the ejection of mass at high velocities. Light echoes can also produce apparent superluminal motion.
The relativistic Doppler effect is the change in frequency, wavelength and amplitude of light, caused by the relative motion of the source and the observer, when taking into account effects described by the special theory of relativity.
The Kerr metric or Kerr geometry describes the geometry of empty spacetime around a rotating uncharged axially symmetric black hole with a quasispherical event horizon. The Kerr metric is an exact solution of the Einstein field equations of general relativity; these equations are highly non-linear, which makes exact solutions very difficult to find.
The word "mass" has two meanings in special relativity: invariant mass is an invariant quantity which is the same for all observers in all reference frames, while the relativistic mass is dependent on the velocity of the observer. According to the concept of mass–energy equivalence, invariant mass is equivalent to rest energy, while relativistic mass is equivalent to relativistic energy.
In physics, a wave vector is a vector used in describing a wave, with a typical unit being cycle per metre. It has a magnitude and direction. Its magnitude is the wavenumber of the wave, and its direction is perpendicular to the wavefront. In isotropic media, this is also the direction of wave propagation.
In physics, relativistic beaming is the process by which relativistic effects modify the apparent luminosity of emitting matter that is moving at speeds close to the speed of light. In an astronomical context, relativistic beaming commonly occurs in two oppositely-directed relativistic jets of plasma that originate from a central compact object that is accreting matter. Accreting compact objects and relativistic jets are invoked to explain x-ray binaries, gamma-ray bursts, and, on a much larger scale, (AGN) active galactic nuclei.
In relativistic physics, a velocity-addition formula is an equation that specifies how to combine the velocities of objects in a way that is consistent with the requirement that no object's speed can exceed the speed of light. Such formulas apply to successive Lorentz transformations, so they also relate different frames. Accompanying velocity addition is a kinematic effect known as Thomas precession, whereby successive non-collinear Lorentz boosts become equivalent to the composition of a rotation of the coordinate system and a boost.
In physics, the Ives–Stilwell experiment tested the contribution of relativistic time dilation to the Doppler shift of light. 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. Since then many Ives–Stilwell type experiments have been performed with increased precision. Together with the Michelson–Morley and Kennedy–Thorndike experiments it forms one of the fundamental tests of special relativity theory. Other tests confirming the relativistic Doppler effect are the Mössbauer rotor experiment and modern Ives–Stilwell experiments.
Gullstrand–Painlevé coordinates are a particular set of coordinates for the Schwarzschild metric – a solution to the Einstein field equations which describes a black hole. The ingoing coordinates are such that the time coordinate follows the proper time of a free-falling observer who starts from far away at zero velocity, and the spatial slices are flat. There is no coordinate singularity at the Schwarzschild radius. The outgoing ones are simply the time reverse of ingoing coordinates.
A spacetime diagram is a graphical illustration of locations in space at various times, especially in the special theory of relativity. Spacetime diagrams can show the geometry underlying phenomena like time dilation and length contraction without mathematical equations.
The photoacoustic Doppler effect is a type of Doppler effect that occurs when an intensity modulated light wave induces a photoacoustic wave on moving particles with a specific frequency. The observed frequency shift is a good indicator of the velocity of the illuminated moving particles. A potential biomedical application is measuring blood flow.
