"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 set of equations that define how space and time coordinates transform between different inertial frames of reference.
Galilean transformations: The basic equations of the Galilean transformation and the limitations of its application in the context of relativistic problems.
Special Relativity: The fundamental principles of special relativity and its key features such as time dilation, length contraction, and the relativity of simultaneity.
Lorentz Transformation: Definition and derivation of the Lorentz Transformation equations, and their consequences for time and space measurements.
Minkowski spacetime: Introduction to four-dimensional spacetime and concepts such as the spacetime interval, the light cone, and the causal structure of events.
Relativity of simultaneity: The idea that simultaneity is relative to the observer's frame of reference and the implications for the measurement of events.
Time dilation: The concept that time is relative, and the time interval between two events depends on the observer's motion relative to those events.
Length contraction: The concept that the length of an object in motion is shorter when measured in the direction of motion than at rest.
Relativistic Doppler effect: The change in frequency of light or sound waves due to the motion of the source or the observer.
Mass-energy equivalence: The famous E=mc² equation and its significance in understanding the relationship between mass and energy.
General Relativity: Introduction to the theory of general relativity, its key principles, and the implications for the nature of gravity and the geometry of spacetime.
Gravitational time dilation: The effect of gravity on the flow of time and its implications for phenomena such as black holes and time travel.
Curved spacetime: The idea that the presence of matter and energy warps the geometry of spacetime, and the implications for the motion of objects in gravitational fields.
Einstein's field equations: The equations that describe the dynamics of the curvature of spacetime in general relativity.
Schwarzschild metric: The metric that describes the geometry of spacetime around a non-rotating, spherically symmetric object, such as a black hole.
Cosmology: The study of the large-scale structure and evolution of the universe, including the expanding universe, dark matter, and dark energy.
Boost: This transformation describes a change in velocity between two reference frames.
Rotation: This transformation describes a change in spatial orientation between two reference frames.
Time Dilation: This transformation describes the change in the rate at which time passes between two reference frames.
Length Contraction: This transformation describes the change in the length of objects moving relative to two reference frames.
Doppler Shift: This transformation describes the change in the frequency of a wave as it travels between two reference frames.
Gravitational Redshift: This transformation describes the change in the frequency of a wave as it travels through a gravitational field.
Time Delay: This transformation describes the delay in time between an event and its observation due to the finite speed of light.
Frame Dragging: This transformation describes the change in the spatial orientation of particles due to the rotation of the reference frame.
Weyl Transformation: This transformation involves a conformal transformation of the metric of space-time.
Inflationary Cosmology: This transformation describes the rapid expansion of the universe in the early stages of its existence.
"The transformations are named after the Dutch physicist Hendrik Lorentz."
"The most common form of the transformation, parametrized by the real constant v, representing a velocity confined to the x-direction, is expressed as..."
"...where γ = (√(1 - v^2/c^2))^-1 is the Lorentz factor."
"When speed v approaches c, γ (Lorentz factor) grows without bound."
"The value of v must be smaller than c for the transformation to make sense."
"Expressing the speed as β = v/c, an equivalent form of the transformation is..."
"Frames of reference can be divided into two groups: inertial (relative motion with constant velocity) and non-inertial (accelerating, moving in curved paths, rotational motion with constant angular velocity, etc.)."
"In each reference frame, an observer can use a local coordinate system to measure lengths, and a clock to measure time intervals."
"The transformations connect the space and time coordinates of an event as measured by an observer in each frame."
"Lorentz transformations supersede the Galilean transformation of Newtonian physics, which assumes an absolute space and time."
"The invariance of light speed is one of the postulates of special relativity."
"Historically, the transformations were the result of attempts by Lorentz and others to explain how the speed of light was observed to be independent of the reference frame, and to understand the symmetries of the laws of electromagnetism."
"Lorentz transformations preserve the spacetime interval between any two events. This property is the defining property of a Lorentz transformation."
"A rotation-free Lorentz transformation is called a Lorentz boost."
"In Minkowski space, the Lorentz transformations describe only the transformations in which the spacetime event at the origin is left fixed."
"The more general set of transformations that also includes translations is known as the Poincaré group."
"Minkowski space is the mathematical model of spacetime in special relativity."
"The Lorentz transformations are a six-parameter family of linear transformations."
"The Lorentz transformation is in accordance with Albert Einstein's special relativity, but was derived first." (Note: Due to the length of the paragraph, some questions may not have specific quotes that directly answer them. In these cases, I chose the most relevant quotes that provide relevant information)