Spacetime in the context of Schwarzschild coordinates

The past is the set of all events that occurred before a given point in time. The past is contrasted with and defined by the present and the future. The concept of the past is derived from the linear fashion in which human observers experience time, and is accessed through memory and recollection. In addition, human beings have recorded the past since the advent of written language.

In English, the word past was one of the many variant forms and spellings of passed, the past participle of the Middle English verb passen (whence Modern English pass), among ypassed, ypassyd, i-passed, passyd, passid, pass'd, paste, etc. It developed into an adjective and preposition in the 14th century, and a noun (as in the past or a past, through ellipsis with the adjective past) in the 15th century.

Space is a three-dimensional continuum containing positions and directions. In classical physics, physical space is often conceived in three linear dimensions. Modern physicists usually consider it, with time, to be part of a boundless four-dimensional continuum known as spacetime. The concept of space is considered to be of fundamental importance to an understanding of the physical universe. However, disagreement continues between philosophers over whether it is itself an entity, a relationship between entities, or part of a conceptual framework.

In the 19th and 20th centuries mathematicians began to examine geometries that are non-Euclidean, in which space is conceived as curved, rather than flat, as in the Euclidean space. According to Albert Einstein's theory of general relativity, space around gravitational fields deviates from Euclidean space. Experimental tests of general relativity have confirmed that non-Euclidean geometries provide a better model for the shape of space.

Time is the continuous progression of existence that occurs in an apparently irreversible succession from the past, through the present, and into the future. Time dictates all forms of action, age, and causality, being a component quantity of various measurements used to sequence events, to compare the duration of events (or the intervals between them), and to quantify rates of change of quantities in material reality or in the conscious experience. Time is often referred to as a fourth dimension, along with three spatial dimensions.

Time is primarily measured in linear spans or periods, ordered from shortest to longest. Practical, human-scale measurements of time are performed using clocks and calendars, reflecting a 24-hour day collected into a 365-day year linked to the astronomical motion of the Earth. Scientific measurements of time instead vary from Planck time at the shortest to billions of years at the longest. Measurable time is believed to have effectively begun with the Big Bang 13.8 billion years ago, encompassed by the chronology of the universe. Modern physics understands time to be inextricable from space within the concept of spacetime described by general relativity. Time can therefore be dilated by velocity and matter to pass faster or slower for an external observer, though this is considered negligible outside of extreme conditions, namely relativistic speeds or the gravitational pulls of black holes.

In physics, radiation is the emission or transmission of energy in the form of waves or particles through space or a material medium. This includes:

• electromagnetic radiation consisting of photons, such as radio waves, microwaves, infrared, visible light, ultraviolet, x-rays, and gamma radiation (γ)
• particle radiation consisting of particles of non-zero rest energy, such as alpha radiation (α), beta radiation (β), proton radiation and neutron radiation
• acoustic radiation, such as ultrasound, sound, and seismic waves, all dependent on a physical transmission medium
• gravitational radiation, in the form of gravitational waves, ripples in spacetime

Radiation is often categorized as either ionizing or non-ionizing depending on the energy of the radiated particles. Ionizing radiation carries more than 10 electron volts (eV), which is enough to ionize atoms and molecules and break chemical bonds. This is an important distinction due to the large difference in harmfulness to living organisms. A common source of ionizing radiation is radioactive materials that emit α, β, or γ radiation, consisting of helium nuclei, electrons or positrons, and photons, respectively. Other sources include X-rays from medical radiography examinations and muons, mesons, positrons, neutrons and other particles that constitute the secondary cosmic rays that are produced after primary cosmic rays interact with Earth's atmosphere.

Materialism is a form of philosophical monism in metaphysics, according to which matter is the fundamental substance in nature, and all things, including mental states and consciousness, are results of material interactions. According to philosophical materialism, mind and consciousness are caused by physical processes, such as the neurochemistry of the human brain and nervous system, without which they cannot exist. Materialism directly contrasts with monistic idealism, according to which consciousness is the fundamental substance of nature.

Materialism is closely related to physicalism—the view that all that exists is ultimately physical. Philosophical physicalism has evolved from materialism with the theories of the physical sciences to incorporate forms of physicality in addition to ordinary matter (e.g. spacetime, physical energies and forces, and exotic matter). Thus, some prefer the term physicalism to materialism, while others use them as synonyms. Materialism is also related to naturalism—the position that only natural laws and forces operate in the universe.

In celestial mechanics, an orbit is the curved trajectory of an object under the influence of an attracting force. Known as an orbital revolution, examples include the trajectory of a planet around a star, a natural satellite around a planet, or an artificial satellite around an object or position in space such as a planet, moon, asteroid, or Lagrange point. Normally, orbit refers to a regularly repeating trajectory, although it may also refer to a non-repeating trajectory. To a close approximation, planets and satellites follow elliptic orbits, with the center of mass being orbited at a focal point of the ellipse, as described by Kepler's laws of planetary motion.

For most situations, orbital motion is adequately approximated by Newtonian mechanics, which explains gravity as a force obeying an inverse-square law. However, Albert Einstein's general theory of relativity, which accounts for gravity as due to curvature of spacetime, with orbits following geodesics, provides a more accurate calculation and understanding of the exact mechanics of orbital motion.

In physics, the fundamental interactions or fundamental forces are interactions in nature that appear not to be reducible to more basic interactions. There are four fundamental interactions known to exist: gravity, electromagnetism, weak interaction, and strong interaction. The gravitational and electromagnetic interactions produce long-range forces whose effects can be seen directly in everyday life. The strong and weak interactions produce forces at subatomic scales and govern nuclear interactions inside atoms. Some scientists hypothesize that a fifth force might exist, but these hypotheses remain speculative.

Each of the known fundamental interactions can be described mathematically as a field. The gravitational interaction is attributed to the curvature of spacetime, described by Einstein's general theory of relativity. The other three are discrete quantum fields, and their interactions are mediated by elementary particles described by the Standard Model of particle physics.

General relativity, also known as the general theory of relativity, and as Einstein's theory of gravity, is the geometric theory of gravitation published by Albert Einstein in 1916 and is the accepted description of gravitation in modern physics. General relativity generalizes special relativity and refines Newton's law of universal gravitation, providing a unified description of gravity as a geometric property of space and time, or four-dimensional spacetime. In particular, the curvature of spacetime is directly related to the energy, momentum and stress of whatever is present, including matter and radiation. The relation is specified by the Einstein field equations, a system of second-order partial differential equations.

Newton's law of universal gravitation, which describes gravity in classical mechanics, can be seen as a prediction of general relativity for the almost flat spacetime geometry around stationary mass distributions. Some predictions of general relativity, however, are beyond Newton's law of universal gravitation in classical physics. These predictions concern the passage of time, the geometry of space, the motion of bodies in free fall, and the propagation of light, and include gravitational time dilation, gravitational lensing, the gravitational redshift of light, the Shapiro time delay and singularities/black holes. So far, all tests of general relativity have been in agreement with the theory. The time-dependent solutions of general relativity enable us to extrapolate the history of the universe into the past and future, and have provided the modern framework for cosmology, thus leading to the discovery of the Big Bang and cosmic microwave background radiation. Despite the introduction of a number of alternative theories, general relativity continues to be the simplest theory consistent with experimental data.

The theory of relativity usually encompasses two interrelated physics theories by Albert Einstein: special relativity and general relativity, proposed and published in 1905 and 1915, respectively. Special relativity applies to all physical phenomena in the absence of gravity. General relativity explains the law of gravitation and its relation to the forces of nature. It applies to the cosmological and astrophysical realm, including astronomy.

The theory transformed theoretical physics and astronomy during the 20th century, superseding a 200-year-old theory of mechanics created primarily by Isaac Newton. It introduced concepts including 4-dimensional spacetime as a unified entity of space and time, relativity of simultaneity, kinematic and gravitational time dilation, and length contraction. In the field of physics, relativity improved the science of elementary particles and their fundamental interactions, along with ushering in the nuclear age. With relativity, cosmology and astrophysics predicted extraordinary astronomical phenomena such as neutron stars, black holes, and gravitational waves.

In logic, a reference is a relationship between objects in which one object designates, or acts as a means by which to connect to or link to, another object. The first object in this relation is said to refer to the second object. It is called a name for the second object. The next object, the one to which the first object refers, is called the referent of the first object. A name is usually a phrase or expression, or some other symbolic representation. Its referent may be anything – a material object, a person, an event, an activity, or an abstract concept.

References can take on many forms, including: a thought, a sensory perception that is audible (onomatopoeia), visual (text), olfactory, or tactile, emotional state, relationship with other, spacetime coordinates, symbolic or alpha-numeric, a physical object, or an energy projection. In some cases, methods are used that intentionally hide the reference from some observers, as in cryptography.

In philosophy (metaphysics), physicalism or physical logicism is the view that "everything is physical", that there is "nothing over and above" the physical, or that everything supervenes on the physical. It is opposed to idealism, according to which the world arises from the mind. Physicalism is a form of ontological monism—a "one substance" view of the nature of reality, unlike "two-substance" (mind–body dualism) or "many-substance" (pluralism) views. Both the definition of "physical" and the meaning of physicalism have been debated. Physicalism is often treated as equivalent to naturalism but there are important distinctions between them.

Physicalism is closely related to materialism, and has evolved from materialism with advancements in the physical sciences in explaining observed phenomena. The terms "physicalism" and "materialism" are often used interchangeably, but can be distinguished on the basis that physics describes more than just matter. Physicalism encompasses matter, but also energy, physical laws, space, time, spacetime, exotic matter, structure, physical processes, information, state, and forces, among other things, as described by physics and other sciences, all within a monistic framework.

In physics and mathematics, the dimension of a mathematical space (or object) is informally defined as the minimum number of coordinates needed to specify any point within it. Thus, a line has a dimension of one (1D) because only one coordinate is needed to specify a point on it – for example, the point at 5 on a number line. A surface, such as the boundary of a cylinder or sphere, has a dimension of two (2D) because two coordinates are needed to specify a point on it – for example, both a latitude and longitude are required to locate a point on the surface of a sphere. A two-dimensional Euclidean space is a two-dimensional space on the plane. The inside of a cube, a cylinder or a sphere is three-dimensional (3D) because three coordinates are needed to locate a point within these spaces.

In classical mechanics, space and time are different categories and refer to absolute space and time. That conception of the world is a four-dimensional space but not the one that was found necessary to describe electromagnetism. The four dimensions (4D) of spacetime consist of events that are not absolutely defined spatially and temporally, but rather are known relative to the motion of an observer. Minkowski space first approximates the universe without gravity; the pseudo-Riemannian manifolds of general relativity describe spacetime with matter and gravity. 10 dimensions are used to describe superstring theory (6D hyperspace + 4D), 11 dimensions can describe supergravity and M-theory (7D hyperspace + 4D), and the state-space of quantum mechanics is an infinite-dimensional function space.

Gravitational waves are waves of spacetime distortion and curvature that propagate at the speed of light; these are produced by relative motion between gravitating masses. They were proposed by Oliver Heaviside in 1893 and then later by Henri Poincaré in 1905 as the gravitational equivalent of electromagnetic waves. In 1916, Albert Einstein demonstrated that gravitational waves result from his general theory of relativity as "ripples in spacetime".

Gravitational waves transport energy as gravitational radiation, a form of radiant energy similar to electromagnetic radiation. Newton's law of universal gravitation, part of classical mechanics, does not provide for their existence, instead asserting that gravity has instantaneous effect everywhere. Gravitational waves therefore stand as an important relativistic phenomenon that is absent from Newtonian physics.

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:

1. The laws of physics are invariant (identical) in all inertial frames of reference (that is, frames of reference with no acceleration). This is known as the principle of relativity.
2. 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.

The first postulate was first formulated by Galileo Galilei (see Galilean invariance).

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.

The most common form of the transformation, parametrized by the real constant ${\displaystyle v,}$ representing a velocity confined to the x-direction, is expressed as$${\displaystyle {\begin{aligned}t'&=\gamma \left(t-{\frac {vx}{c^{2}}}\right)\\x'&=\gamma \left(x-vt\right)\\y'&=y\\z'&=z\end{aligned}}}$$where (t, x, y, z) and (t′, x′, y′, z′) are the coordinates of an event in two frames with the spatial origins coinciding at t = t′ = 0, where the primed frame is seen from the unprimed frame as moving with speed v along the x-axis, where c is the speed of light, and $${\displaystyle \gamma ={\frac {1}{\sqrt {1-v^{2}/c^{2}}}}}$$is the Lorentz factor. When speed v is much smaller than c, the Lorentz factor is negligibly different from 1, but as v approaches c, ${\displaystyle \gamma }$ grows without bound. The value of v must be smaller than c for the transformation to make sense.