"In physics, the special theory of relativity, or special relativity for short, is a scientific theory of the relationship between space and time."
The application of Special Relativity to the study of the behaviour of particles in motion.
Introduction to Special Relativity: The basic principles and postulates of special relativity, including time dilation, length contraction, and the equivalence of mass and energy.
Lorentz Transformations: The mathematical equations that describe how time, space, and energy transform between different reference frames.
Relativistic Energy and Momentum: The equations that describe the energy and momentum of particles in relativistic settings, including the famous E=mc2 formula.
Relativistic Doppler Effect: The way that the frequency and wavelength of light change in relativistic settings, including the redshift and blueshift effects.
Twin Paradox: A thought experiment that illustrates the different effects of time dilation on a pair of twins who travel at different speeds.
Mass-Energy Equivalence: The principle that mass and energy are interchangeable, and that a massive object can be thought of as having a certain amount of stored energy.
Gravitational Time Dilation: The way that time is affected by gravity, and how clocks run differently at different points in a gravitational field.
Black Holes: Objects with such a strong gravitational field that they cause time to stop, and light cannot escape.
Friedmann-Lemaître-Robertson-Walker Metric: The mathematical framework used to describe the large-scale structure and evolution of the universe.
General Covariance: The principle that physical laws should be the same in all reference frames, regardless of their motion or orientation.
General Relativity: The theory of gravity that describes how matter and energy warp the fabric of space-time, and how this warp influences the motion of other objects.
Equivalence Principle: The idea that the effects of gravitational fields are equivalent to the effects of acceleration, and that an object in free fall cannot distinguish between the two.
Schwarzschild Metric: The mathematical framework used to describe the space-time around a non-rotating, spherically symmetric object like a planet or a star.
Gravitational Waves: Ripples in the fabric of space-time caused by the motion of massive objects, like black holes or neutron stars.
Cosmological Consequences: The implications of general relativity for the large-scale structure and history of the universe, including the Big Bang, the expanding universe, and the cosmic microwave background.
Time dilation: Time dilation is a relativistic effect that occurs when time appears to slow down for an object that is moving at high speeds relative to an observer at rest. This effect is caused by the curvature of spacetime, which causes time to vary according to the velocity and gravitational potential of the object in question.
Length contraction: Length contraction is a relativistic effect that occurs when an object appears to shorten in length as it moves at high speeds relative to an observer at rest. This effect is caused by the contraction of space itself, which varies according to the velocity of the object in question.
Lorentz transformation: The Lorentz transformation is a mathematical formula that describes how measurements of time and space change according to relativistic effects. This formula is used extensively in special relativity, where it forms the basis for all calculations of relativistic kinematics.
Time-space diagrams: Time-space diagrams are graphical representations of relativistic motion, showing how time and space are affected by the curvature of spacetime. These diagrams are useful tools for visualizing complex relativistic effects.
Space-time intervals: Space-time intervals are a way of measuring the distance between two events in relativity, taking into account both the spatial and temporal components of the events. These intervals are invariant under the Lorentz transformation, meaning that they are always the same for all observers, regardless of their relative velocities.
Four-momentum: Four-momentum is a relativistic concept that combines the energy and momentum of a particle into a single four-dimensional vector. This concept is useful for describing the behavior of particles moving at high speeds, and is often used in particle physics and astrophysics.
Gravitational redshift: Gravitational redshift is a relativistic effect that occurs when light is emitted from a massive object, such as a star or a black hole. This effect causes the light to lose energy and appear redder than it would if it were emitted from a lighter object, such as a planet or a moon.
Perihelion precession: Perihelion precession is a relativistic effect that occurs when the orbit of a planet or other celestial object is affected by the curvature of spacetime caused by a nearby massive object, such as the Sun. This effect causes the orbit to slowly shift over time, resulting in a change in the object's closest approach (or perihelion) to the central object.
Gravitational lensing: Gravitational lensing is a relativistic effect that occurs when the path of light is bent by the gravitational field of a massive object, such as a galaxy or a black hole. This effect can distort the appearance of distant objects, and is used by astronomers to study the distribution of dark matter in the universe.
Time dilation in gravitational fields: Time dilation also occurs in gravitational fields, whereby time moves slower in a stronger gravitational field. This effect is described by the metric tensor in general relativity and is an important factor in phenomena such as gravitational redshift and black holes.
"The laws of physics are invariant (identical) in all inertial frames of reference (that is, frames of reference with no acceleration)." "The speed of light in vacuum is the same for all observers, regardless of the motion of light source or observer."
"In Albert Einstein's 1905 treatment, the theory is presented as being based on just two postulates."
"The laws of physics are invariant (identical) in all inertial frames of reference (that is, frames of reference with no acceleration)."
"The speed of light in vacuum is the same for all observers, regardless of the motion of light source or observer."
"The special theory of relativity [...] is a scientific theory of the relationship between space and time."
"The laws of physics are invariant (identical) in all inertial frames of reference."
"The laws of physics are invariant (identical) in all inertial frames of reference."
"The laws of physics are invariant (identical) in all inertial frames of reference (that is, frames of reference with no acceleration)."
"In Albert Einstein's 1905 treatment, the theory is presented as being based on just two postulates."
"The laws of physics are invariant (identical) in all inertial frames of reference." "The speed of light in vacuum is the same for all observers, regardless of the motion of light source or observer."
The paragraph does not provide information about general relativity.
The paragraph does not provide information about the impact on the concept of time.
The paragraph does not provide information about specific applications.
The paragraph does not provide information about additional theories.
The laws of physics are invariant (identical) in all inertial frames of reference.
The paragraph does not provide information about the nature of space.
"The speed of light in vacuum is the same for all observers, regardless of the motion of light source or observer."
The paragraph does not mention specific experiments or observations.
The paragraph does not provide information about the impact on our understanding of the universe.