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| title | chunk | source | category | tags | date_saved | instance |
|---|---|---|---|---|---|---|
| Absolute space and time | 2/2 | https://en.wikipedia.org/wiki/Absolute_space_and_time | reference | science, encyclopedia | 2026-05-05T11:14:58.980985+00:00 | kb-cron |
== Mathematical definitions == Space, as understood in Newtonian mechanics, is three-dimensional and Euclidean, with a fixed orientation. It is denoted E3. If some point O in E3 is fixed and defined as an origin, the position of any point P in E3 is uniquely determined by its radius vector
r
=
O
P
→
{\displaystyle \mathbf {r} ={\vec {OP}}}
(the origin of this vector coincides with the point O and its end coincides with the point P). The three-dimensional linear vector space R3 is a set of all radius vectors. The space R3 is endowed with a scalar product ⟨ , ⟩. Time is a scalar which is the same in all space E3 and is denoted as t. The ordered set { t } is called a time axis. Motion (also path or trajectory) is a function r : Δ → R3 that maps a point in the interval Δ from the time axis to a position (radius vector) in R3. The above four concepts are the "well-known" objects mentioned by Isaac Newton in his Principia:
I do not define time, space, place and motion, as being well known to all.
== Special relativity == The concepts of space and time were separate in physical theory prior to the advent of special relativity theory, which connected the two and showed both to be dependent upon the reference frame's motion. In Einstein's theories, the ideas of absolute time and space were superseded by the notion of spacetime in special relativity, and curved spacetime in general relativity. Absolute simultaneity refers to the concurrence of events in time at different locations in space in a manner agreed upon in all frames of reference. The theory of relativity does not have a concept of absolute time because there is a relativity of simultaneity. An event that is simultaneous with another event in one frame of reference may be in the past or future of that event in a different frame of reference, which negates absolute simultaneity.
== Einstein ==
Quoted below from his later papers, Einstein identified the term aether with "properties of space", a terminology that is not widely used. Einstein stated that in general relativity the "aether" is not absolute anymore, as the geodesic and therefore the structure of spacetime depends on the presence of matter.
To deny the ether is ultimately to assume that empty space has no physical qualities whatever. The fundamental facts of mechanics do not harmonize with this view. For the mechanical behaviour of a corporeal system hovering freely in empty space depends not only on relative positions (distances) and relative velocities, but also on its state of rotation, which physically may be taken as a characteristic not appertaining to the system in itself. In order to be able to look upon the rotation of the system, at least formally, as something real, Newton objectivises space. Since he classes his absolute space together with real things, for him rotation relative to an absolute space is also something real. Newton might no less well have called his absolute space “Ether”; what is essential is merely that besides observable objects, another thing, which is not perceptible, must be looked upon as real, to enable acceleration or rotation to be looked upon as something real. Because it was no longer possible to speak, in any absolute sense, of simultaneous states at different locations in the aether, the aether became, as it were, four-dimensional, since there was no objective way of ordering its states by time alone. According to special relativity too, the aether was absolute, since its influence on inertia and the propagation of light was thought of as being itself independent of physical influence....The theory of relativity resolved this problem by establishing the behaviour of the electrically neutral point-mass by the law of the geodetic line, according to which inertial and gravitational effects are no longer considered as separate. In doing so, it attached characteristics to the aether which vary from point to point, determining the metric and the dynamic behaviour of material points, and determined, in their turn, by physical factors, namely the distribution of mass/energy. Thus the aether of general relativity differs from those of classical mechanics and special relativity in that it is not ‘absolute’ but determined, in its locally variable characteristics, by ponderable matter.
== General relativity == Special relativity eliminates absolute time (although Gödel and others suspect absolute time may be valid for some forms of general relativity) and general relativity further reduces the physical scope of absolute space and time through the concept of geodesics. There appears to be absolute space in relation to the distant stars because the local geodesics eventually channel information from these stars, but it is not necessary to invoke absolute space with respect to any system's physics, as its local geodesics are sufficient to describe its spacetime.
== See also ==
== References and notes ==
== External links == Media related to Absolute space and time at Wikimedia Commons