## Spacetime |

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Spacetime |
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Classical gravity |

In **spacetime** is any *where* and *when* events occur.

Until the turn of the 20th century, the assumption had been that the three-dimensional geometry of the universe (its spatial expression in terms of coordinates, distances, and directions) was independent of one-dimensional time. However, in 1905,

The logical consequence of taking these postulates together is the inseparable joining together of the four dimensions, hitherto assumed as independent, of space and time. Many counterintuitive consequences emerge: in addition to being independent of the motion of the light source, *the speed of light has the same speed regardless of the frame of reference in which it is measured*; the distances and even temporal ordering of pairs of events change when measured in different

Einstein framed his theory in terms of

In 1908,

Minkowski's geometric interpretation of relativity was to prove vital to Einstein's development of his 1915 *curve**flat* spacetime to a *Pseudo Riemannian* manifold

- introduction
- spacetime in special relativity
- basic mathematics of spacetime
- beyond the basics
- introduction to curved spacetime
- technical topics
- see also
- notes
- additional details
- references
- further reading
- external links

Non-relativistic ^{[1]} Furthermore, it assumes that space is Euclidean, which is to say, it assumes that space follows the geometry of common sense.^{[2]}

In the context of

In ordinary space, a position is specified by three numbers, known as *event*, and requires four numbers to be specified: the three-dimensional location in space, plus the position in time (Fig. 1). Spacetime is thus *x*, *y*, *z* and *t*.

The word "event" used in relativity should not be confused with the use of the word "event" in normal conversation, where it might refer to an "event" as something such as a concert, sporting event, or a battle. These are not mathematical "events" in the way the word is used in relativity, because they have finite durations and extents. Unlike the analogies used to explain events, such as firecrackers or lightning bolts, mathematical events have zero duration and represent a single point in spacetime.

The path of a particle through spacetime can be considered to be a succession of events. The series of events can be linked together to form a line which represents a particle's progress through spacetime. That line is called the particle's *world line*.^{[3]}^{:105}

Mathematically, spacetime is a * manifold*, which is to say, it appears locally "flat" near each point in the same way that, at small enough scales, a globe appears flat.

In special relativity, an observer will, in most cases, mean a frame of reference from which a set of objects or events are being measured. This usage differs significantly from the ordinary English meaning of the term. Reference frames are inherently nonlocal constructs, and according to this usage of the term, it does not make sense to speak of an observer as having a location. In Fig. 1‑1, imagine that the frame under consideration is equipped with a dense lattice of clocks, synchronized within this reference frame, that extends indefinitely throughout the three dimensions of space. Any specific location within the lattice is not important. The latticework of clocks is used to determine the time and position of events taking place within the whole frame. The term *observer* refers to the entire ensemble of clocks associated with one inertial frame of reference.^{[6]}^{:17–22} In this idealized case, every point in space has a clock associated with it, and thus the clocks register each event instantly, with no time delay between an event and its recording. A real observer, however, will see a delay between the emission of a signal and its detection due to the speed of light. To synchronize the clocks, in the

In many books on special relativity, especially older ones, the word "observer" is used in the more ordinary sense of the word. It is usually clear from context which meaning has been adopted.

Physicists distinguish between what one *measures* or *observes* (after one has factored out signal propagation delays), versus what one visually sees without such corrections. Failure to understand ^{[7]}

By the mid-1800s, various experiments such as the observation of the ^{[8]} Propagation of waves was then assumed to require the existence of a medium which *waved*: in the case of light waves, this was considered to be a hypothetical ^{[note 1]} However, the various attempts to establish the properties of this hypothetical medium yielded contradictory results. For example, the *simultaneously* flows at different speeds for different colors of light.^{[9]} The famous ^{[5]}

By 1904, Lorentz had expanded his theory such that he had arrived at equations formally identical with those that Einstein were to derive later (i.e. the ^{[10]}^{:163–174} Lorentz's equations predicted a quantity that he called *local time*, with which he could explain the

Other physicists and mathematicians at the turn of the century came close to arriving at what is currently known as spacetime. Einstein himself noted, that with so many people unraveling separate pieces of the puzzle, "the special theory of relativity, if we regard its development in retrospect, was ripe for discovery in 1905."^{[11]}

An important example is ^{[12]}^{[13]}^{:73–80,93–95} who in 1898 argued that the simultaneity of two events is a matter of convention.^{[14]}^{[note 2]} In 1900, he recognized that Lorentz's "local time" is actually what is indicated by moving clocks by applying an explicitly *operational definition* of clock synchronization assuming constant light speed.^{[note 3]} In 1900 and 1904, he suggested the inherent undetectability of the aether by emphasizing the validity of what he called the ^{[15]} he mathematically perfected Lorentz's theory of electrons in order to bring it into accordance with the postulate of relativity. While discussing various hypotheses on Lorentz invariant gravitation, he introduced the innovative concept of a 4-dimensional space-time by defining various ^{[16]}^{[17]} He did not pursue the 4-dimensional formalism in subsequent papers, however, stating that this line of research seemed to "entail great pain for limited profit", ultimately concluding "that three-dimensional language seems the best suited to the description of our world".^{[17]} Furthermore, even as late as 1909, Poincaré continued to believe in the dynamical interpretation of the Lorentz transform.^{[10]}^{:163–174} For these and other reasons, most historians of science argue that Poincaré did not invent what is now called special relativity.^{[13]}^{[10]}

In 1905, Einstein introduced special relativity (even though without using the techniques of the spacetime formalism) in its modern understanding as a theory of space and time.^{[13]}^{[10]} While his results are mathematically equivalent to those of Lorentz and Poincaré, it was Einstein who showed that the Lorentz transformations are not the result of interactions between matter and aether, but rather concern the nature of space and time itself. He obtained all of his results by recognizing that the entire theory can be built upon two postulates: The principle of relativity and the principle of the constancy of light speed.

Einstein performed his analyses in terms of ^{[18]}^{[note 4]}

In addition, Einstein in 1905 superseded previous attempts of an ^{[20]}^{:219} in the further development of general relativity Einstein fully incorporated the spacetime formalism.

When Einstein published in 1905, another of his competitors, his former mathematics professor ^{[21]}

“ | I went to Cologne, met Minkowski and heard his celebrated lecture 'Space and Time' delivered on 2 September 1908. […] He told me later that it came to him as a great shock when Einstein published his paper in which the equivalence of the different local times of observers moving relative to each other was pronounced; for he had reached the same conclusions independently but did not publish them because he wished first to work out the mathematical structure in all its splendor. He never made a priority claim and always gave Einstein his full share in the great discovery. | ” |

Minkowski had been concerned with the state of electrodynamics after Michelson's disruptive experiments at least since the summer of 1905, when Minkowski and ^{[22]}

On November 5, 1907 (a little more than a year before his death), Minkowski introduced his geometric interpretation of spacetime in a lecture to the Göttingen Mathematical society with the title, *The Relativity Principle* (*Das Relativitätsprinzip*).^{[note 5]} On September 21, 1908, Minkowski presented his famous talk, *Space and Time* (*Raum und Zeit*),^{[23]} to the German Society of Scientists and Physicians. The opening words of *Space and Time* include Minkowski's famous statement that "Henceforth, space for itself, and time for itself shall completely reduce to a mere shadow, and only some sort of union of the two shall preserve independence." *Space and Time* included the first public presentation of spacetime diagrams (Fig. 1‑4), and included a remarkable demonstration that the concept of the *invariant interval* (discussed below), along with the empirical observation that the speed of light is finite, allows derivation of the entirety of special relativity.^{[note 6]}

The spacetime concept and the Lorentz group are closely connected to certain types of ^{[note 7]}

Einstein, for his part, was initially dismissive of Minkowski's geometric interpretation of special relativity, regarding it as *überflüssige Gelehrsamkeit* (superfluous learnedness). However, in order to complete his search for general relativity that started in 1907, the geometric interpretation of relativity proved to be vital, and in 1916, Einstein fully acknowledged his indebtedness to Minkowski, whose interpretation greatly facilitated the transition to general relativity.^{[10]}^{:151–152} Since there are other types of spacetime, such as the curved spacetime of general relativity, the spacetime of special relativity is today known as *Minkowski spacetime.*

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latviešu: Laiktelpa

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Nederlands: Ruimtetijd

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norsk nynorsk: Tidrom

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shqip: Hapësirë-koha

Simple English: Space-time

slovenčina: Časopriestor

slovenščina: Prostor-čas

کوردی: کاتجێ

српски / srpski: Простор-време

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粵語: 時空

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