Two entities are in causal contact if there may be an event that has affected both in a causal way. Every object of mass in space, for instance, exerts a field force on all other objects of mass, according to Newton'slaw of universal gravitation. Because this force exerted by one object affects the motion of the other, it can be said that these two objects are in causal contact.
The only objects not in causal contact are those for which there is no event in the history of the universe that could have sent a beam of light to both. For example, if the universe were not expanding and had existed for 10 billion years, anything more than 20 billion light-years away from the earth would not be in causal contact with it. Anything less than 20 billion light-years away would because an event occurring 10 billion years in the past that was 10 billion light-years away from both the earth and the object under question could have affected both.
A worldline through a light cone in 2D space plus a time dimension.
A good illustration of this principle is the light cone, which is constructed as follows. Taking as event a flash of light (light pulse) at time , all events that can be reached by this pulse from form the future light cone of , whilst those events that can send a light pulse to form the past light cone of .
Given an event , the light cone classifies all events in spacetime into 5 distinct categories:
Events on the future light cone of .
Events on the past light cone of .
Events inside the future light cone of are those affected by the beam of light emitted at .
Events inside the past light cone of are those that can emit a beam of light and affect what is happening at .
All other events are in the (absolute) elsewhere of and are those that will never affect and can never be affected by .
Faster-than-light travel and communication are the conjectural propagation of matter or information faster than the speed of light. The special theory of relativity implies that only particles with zero rest mass may travel at the speed of light, and that nothing may travel faster.
In physics, spacetime is a mathematical model that combines the three dimensions of space and one dimension of time into a single four-dimensional manifold. Spacetime diagrams can be used to visualize relativistic effects, such as why different observers perceive differently where and when events occur.
Radiation pressure is the mechanical pressure exerted upon any surface due to the exchange of momentum between the object and the electromagnetic field. This includes the momentum of light or electromagnetic radiation of any wavelength that is absorbed, reflected, or otherwise emitted by matter on any scale. The associated force is called the radiation pressure force, or sometimes just the force of light.
A gravitational singularity, spacetime singularity or simply singularity is a condition in which gravity is so intense that spacetime itself breaks down catastrophically. As such, a singularity is by definition no longer part of the regular spacetime and cannot be determined by "where" or "when". Gravitational singularities exist at a junction between general relativity and quantum mechanics; therefore, the properties of the singularity cannot be described without an established theory of quantum gravity. Trying to find a complete and precise definition of singularities in the theory of general relativity, the current best theory of gravity, remains a difficult problem. A singularity in general relativity can be defined by the scalar invariant curvature becoming infinite or, better, by a geodesic being incomplete.
In standard cosmology, comoving distance and proper distance are two closely related distance measures used by cosmologists to define distances between objects. Proper distance roughly corresponds to where a distant object would be at a specific moment of cosmological time, which can change over time due to the expansion of the universe. Comoving distance factors out the expansion of the universe, giving a distance that does not change in time due to the expansion of space.
Causality is the relationship between causes and effects. While causality is also a topic studied from the perspectives of philosophy and physics, it is operationalized so that causes of an event must be in the past light cone of the event and ultimately reducible to fundamental interactions. Similarly, a cause cannot have an effect outside its future light cone.
The world line of an object is the path that an object traces in 4-dimensional spacetime. It is an important concept in modern physics, and particularly theoretical physics.
The observable universe is a ball-shaped region of the universe comprising all matter that can be observed from Earth or its space-based telescopes and exploratory probes at the present time, because the electromagnetic radiation from these objects has had time to reach the Solar System and Earth since the beginning of the cosmological expansion. There may be 2 trillion galaxies in the observable universe, although that number was reduced in 2021 to only several hundred billion based on data from New Horizons. Assuming the universe is isotropic, the distance to the edge of the observable universe is roughly the same in every direction. That is, the observable universe is a spherical region centered on the observer and is unique for every unique observational position.
In mathematical physics, a closed timelike curve (CTC) is a world line in a Lorentzian manifold, of a material particle in spacetime, that is "closed", returning to its starting point. This possibility was first discovered by Willem Jacob van Stockum in 1937 and later confirmed by Kurt Gödel in 1949, who discovered a solution to the equations of general relativity (GR) allowing CTCs known as the Gödel metric; and since then other GR solutions containing CTCs have been found, such as the Tipler cylinder and traversable wormholes. If CTCs exist, their existence would seem to imply at least the theoretical possibility of time travel backwards in time, raising the spectre of the grandfather paradox, although the Novikov self-consistency principle seems to show that such paradoxes could be avoided. Some physicists speculate that the CTCs which appear in certain GR solutions might be ruled out by a future theory of quantum gravity which would replace GR, an idea which Stephen Hawking labeled the chronology protection conjecture. Others note that if every closed timelike curve in a given space-time passes through an event horizon, a property which can be called chronological censorship, then that space-time with event horizons excised would still be causally well behaved and an observer might not be able to detect the causal violation.
In special and general relativity, a light cone is the path that a flash of light, emanating from a single event and traveling in all directions, would take through spacetime.
In theoretical physics, a Penrose diagram is a two-dimensional diagram capturing the causal relations between different points in spacetime through a conformal treatment of infinity. It is an extension of a Minkowski diagram where the vertical dimension represents time, and the horizontal dimension represents a space dimension. Using this design, all light rays take a 45° path.. The biggest difference is that locally, the metric on a Penrose diagram is conformally equivalent to the actual metric in spacetime. The conformal factor is chosen such that the entire infinite spacetime is transformed into a Penrose diagram of finite size, with infinity on the boundary of the diagram. For spherically symmetric spacetimes, every point in the Penrose diagram corresponds to a 2-dimensional sphere .
The horizon problem is a cosmological fine-tuning problem within the Big Bang model of the universe. It arises due to the difficulty in explaining the observed homogeneity of causally disconnected regions of space in the absence of a mechanism that sets the same initial conditions everywhere. It was first pointed out by Wolfgang Rindler in 1956.
The Gödel metric, also known as the Gödel solution or Gödel universe, is an exact solution of the Einstein field equations in which the stress–energy tensor contains two terms, the first representing the matter density of a homogeneous distribution of swirling dust particles, and the second associated with a negative cosmological constant.
In general relativity, Kruskal–Szekeres coordinates, named after Martin Kruskal and George Szekeres, are a coordinate system for the Schwarzschild geometry for a black hole. These coordinates have the advantage that they cover the entire spacetime manifold of the maximally extended Schwarzschild solution and are well-behaved everywhere outside the physical singularity. There is no misleading coordinate singularity at the horizon.
The expansion of the universe is the increase in distance between any two given gravitationally unbound parts of the observable universe with time. It is an intrinsic expansion whereby the scale of space itself changes. The universe does not expand "into" anything and does not require space to exist "outside" it. This expansion involves neither space nor objects in space "moving" in a traditional sense, but rather it is the metric that changes in scale. As the spatial part of the universe's spacetime metric increases in scale, objects become more distant from one another at ever-increasing speeds. To any observer in the universe, it appears that all of space is expanding, and that all but the nearest galaxies recede at speeds that are proportional to their distance from the observer. While objects within space cannot travel faster than light, this limitation does not apply to the effects of changes in the metric itself. Objects that recede beyond the cosmic event horizon will eventually become unobservable, as no new light from them will be capable of overcoming the universe's expansion, limiting the size of our observable universe.
In general relativity, an absolute horizon is a boundary in spacetime, defined with respect to the external universe, inside which events cannot affect an external observer. Light emitted inside the horizon can never reach the observer, and anything that passes through the horizon from the observer's side is never seen again by the observer. An absolute horizon is thought of as the boundary of a black hole.
In cosmology, a Hubble volume (named for the astronomer Edwin Hubble) or Hubble sphere, subluminal sphere, causal sphere and sphere of causality is a spherical region of the observable universe surrounding an observer beyond which objects recede from that observer at a rate greater than the speed of light due to the expansion of the universe. The Hubble volume is approximately equal to 1031 cubic light years (or about 1079 cubic meters).
A spacetime diagram is a graphical illustration of the properties of space and time in the special theory of relativity. Spacetime diagrams allow a qualitative understanding of the corresponding phenomena like time dilation and length contraction without mathematical equations.
In mathematical physics, the causal structure of a Lorentzian manifold describes the causal relationships between points in the manifold.
In astrophysics, an event horizon is a boundary beyond which events cannot affect an observer. Wolfgang Rindler coined the term in the 1950s.
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