"In physics, spacetime is any mathematical model that fuses the three dimensions of space and the one dimension of time into a single four-dimensional continuum."
A fusion of the three dimensions of space with one dimension of time into a single four-dimensional space-time continuum.
Special Relativity: Special relativity is a theory that describes the laws of physics in a frame of reference that is moving at a constant velocity relative to an observer. It introduces the concept of spacetime and establishes that the laws of physics are the same in all inertial frames of reference.
General Relativity: General relativity is the theory of gravity that describes the curvature of spacetime caused by the presence of massive objects. It replaces Newton's law of gravitation with a new concept of gravity that is based on the geometry of spacetime.
Space and Time: The concepts of space and time are fundamental to understanding relativity. Relativity introduces the concept of curved spacetime, which means that space and time are no longer separate entities but are part of a single four-dimensional manifold.
The Lorentz Transformation: The Lorentz transformation is a mathematical equation used to describe how measurements of time and distance change between two frames of reference that are moving relative to each other.
The Twins Paradox: The twins paradox is a thought experiment in which one twin travels at relativistic speeds while the other twin stays on Earth. Due to time dilation, the traveling twin ages less than the non-traveling twin upon their reunion.
Black Holes: Black holes are predicted by general relativity and are regions of spacetime where the gravitational pull is so strong that nothing, including light, can escape. They are important for understanding the extreme end states of astrophysical systems.
Cosmology: Cosmology is the study of the universe as a whole, including its origin, evolution, and current properties. General relativity is essential for understanding the large-scale structure of the universe and the behavior of massive objects such as galaxies and clusters of galaxies.
Gravitational Waves: Gravitational waves are ripples in spacetime that are produced by accelerating massive objects. They were predicted by general relativity and were recently observed for the first time, opening up a new window in astronomy.
Time Travel: Relativity allows for the possibility of time travel, although it is subject to various paradoxes and causality violations.
Quantum Gravity: Quantum gravity is the field of study that attempts to reconcile general relativity with quantum mechanics, two theories that are currently incompatible. It is an active area of research in theoretical physics.
Flat Spacetime: This is a theoretical concept that describes the uncurved space-time that exists in regions where there is no mass, energy, or gravitational fields. Flat spacetime is used as a baseline for comparing other curved spacetimes.
Minkowski Spacetime: This is a flat spacetime with a special metric that describes the four dimensions of space-time. It is commonly used in special relativity, which describes the laws of physics in a uniform motion.
Schwarzschild Spacetime: This is a curved spacetime that describes the gravitational field outside a non-rotating, spherically symmetric body. It is commonly used in general relativity and forms the basis for the modern understanding of black holes.
Friedmann-Lemaître-Robertson-Walker (FLRW) Spacetime: This is a curved spacetime that describes the expanding universe. It is used as the mathematical framework for cosmology, and it describes the large-scale structure and formation of galaxies and galaxy clusters.
Kerr Spacetime: This is a curved spacetime that describes rotating black holes. It is a solution to Einstein's field equations in which the black hole has both mass and angular momentum.
Anti de Sitter (AdS) Spacetime: This is a curved spacetime that has negative curvature and a cosmological constant. It has been used to describe the holographic principle, which is a property of quantum gravity that relates the quantum properties of a system to its classical properties in a higher dimensional space.
de Sitter Spacetime: This is a curved spacetime with a positive cosmological constant that describes the accelerating expansion of the universe. It is also used as a background for studying inflationary cosmology.
"Spacetime diagrams are useful in visualizing and understanding relativistic effects such as how different observers perceive where and when events occur."
"Until the turn of the 20th century, the assumption had been that the three-dimensional geometry of the universe was distinct from time."
"Space and time took on new meanings with the Lorentz transformation and special theory of relativity."
"In 1908, Hermann Minkowski presented a geometric interpretation of special relativity."
"Hermann Minkowski fused time and the three spatial dimensions of space into a single four-dimensional continuum."
"A single four-dimensional continuum now known as Minkowski space."
"This interpretation proved vital to the general theory of relativity."
"In the general theory of relativity, wherein spacetime is curved by mass and energy."
"Fusing the three dimensions of space and the one dimension of time into a single four-dimensional continuum."
"Understanding relativistic effects such as how different observers perceive where and when events occur."
"Space and time took on new meanings with the Lorentz transformation and special theory of relativity."
"Hermann Minkowski presented a geometric interpretation of special relativity."
"Hermann Minkowski fused time and the three spatial dimensions of space into a single four-dimensional continuum."
"Minkowski space is a geometric interpretation of special relativity."
"The general theory of relativity states that spacetime is curved by mass and energy."
"The fusion of space and time into a single four-dimensional continuum."
"Spacetime diagrams are useful in visualizing and understanding relativistic effects."
"Spacetime is curved by mass and energy."
"The assumption had been that the three-dimensional geometry of the universe was distinct from time."