Editing Spacetime (section)

== Fundamentals ==
{{anchor|Introduction}}
{{anchor|Definitions}}

=== Definitions ===
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Non-relativistic [[classical mechanics]] treats [[time]] as a universal quantity of measurement that is uniform throughout, is separate from space, and is agreed on by all observers. Classical mechanics assumes that time has a constant rate of passage, independent of the [[observer (special relativity)|observer's]] state of [[motion (physics)|motion]], or anything external.<ref>{{cite web|last1=Rynasiewicz|first1=Robert|title=Newton's Views on Space, Time, and Motion|url=https://plato.stanford.edu/entries/newton-stm/|website=Stanford Encyclopedia of Philosophy|publisher=Metaphysics Research Lab, Stanford University|date=August 12, 2004|access-date=24 March 2017|archive-date=16 July 2012|archive-url=https://archive.today/20120716191122/http://plato.stanford.edu/entries/newton-stm/|url-status=live}}</ref> It assumes that space is [[Euclidean space|Euclidean]]: it assumes that space follows the geometry of common sense.<ref>{{cite book|last1=Davis|first1=Philip J.|title=Mathematics & Common Sense: A Case of Creative Tension|date=2006|publisher=A.K. Peters|location=Wellesley, Massachusetts|isbn=978-1-4398-6432-6|page=86}}</ref>

In the context of [[special relativity]], time cannot be separated from the three dimensions of space, because the observed rate at which time passes for an object depends on the object's [[velocity]] relative to the observer.<ref name="Schutz"/>{{rp|214–217}} [[General relativity]] provides an explanation of how [[gravitational field]]s can slow the passage of time for an object as seen by an observer outside the field.

In ordinary space, a position is specified by three numbers, known as [[dimension#In physics|dimensions]]. In the [[Cartesian coordinate system]], these are often called ''x'', ''y'' and ''z''. A point in spacetime is called an ''event'', and requires four numbers to be specified: the three-dimensional location in space, plus the position in time (Fig.&nbsp;1). An event is represented by a set of coordinates ''x'', ''y'', ''z'' and ''t''.<ref name="Fock_1966">{{cite book |last1=Fock |first1=V. |title=The Theory of Space, Time and Gravitation |date=1966 |publisher=Pergamon Press Ltd. |location=New York |isbn=0-08-010061-9 |page=33 |edition=2nd |url=https://books.google.com/books?id=X7A3BQAAQBAJ&q=Fock,+v+the+theory+of+space,+time+and+gravitation |access-date=14 October 2023}}</ref> Spacetime is thus [[Four-dimensional space|four-dimensional]].

Unlike the analogies used in popular writings to explain events, such as firecrackers or sparks, mathematical events have zero duration and represent a single point in spacetime.<ref name="Lawden_1982">{{cite book |last1=Lawden |first1=D. F. |title=Introduction to Tensor Calculus, Relativity and Cosmology |date=1982 |publisher=Dover Publications |location=Mineola, New York |isbn=978-0-486-42540-5 |page=7 |edition=3rd |url=https://www.researchgate.net/publication/41167745}}</ref> Although it is possible to be in motion relative to the popping of a firecracker or a spark, it is not possible for an observer to be in motion relative to an event.

The path of a particle through spacetime can be considered to be a sequence of events. The series of events can be linked together to form a curve that represents the particle's progress through spacetime. That path is called the particle's ''world line''.<ref name="Collier" />{{rp|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, the surface of a globe appears to be flat.<ref>{{cite web |last1=Rowland |first1=Todd |title=Manifold |url=http://mathworld.wolfram.com/Manifold.html |website=Wolfram Mathworld |publisher=Wolfram Research |access-date=24 March 2017 |archive-date=13 March 2017 |archive-url=https://web.archive.org/web/20170313111306/http://mathworld.wolfram.com/Manifold.html |url-status=live }}</ref> A scale factor, <math>c</math> (conventionally called the ''speed-of-light'') relates distances measured in space to distances measured in time. The magnitude of this scale factor (nearly {{convert|300000|km|disp=or||}} in space being equivalent to one second in time), along with the fact that spacetime is a manifold, implies that at ordinary, non-relativistic speeds and at ordinary, human-scale distances, there is little that humans might observe that is noticeably different from what they might observe if the world were Euclidean. It was only with the advent of sensitive scientific measurements in the mid-1800s, such as the [[Fizeau experiment]] and the [[Michelson–Morley experiment]], that puzzling discrepancies began to be noted between observation versus predictions based on the implicit assumption of Euclidean space.<ref name="French">{{cite book |last1=French |first1=A. P. |title=Special Relativity |date=1968 |publisher=[[CRC Press]] |isbn=0-7487-6422-4 |location=[[Boca Raton, Florida]] |pages=35–60 |language=en-us}}</ref>

{{anchor|Figure 1-1}}
[[File:Observer in special relativity.svg|thumb|Figure 1-1. Each location in spacetime is marked by four numbers defined by a [[frame of reference]]: the position in space, and the time, which can be visualized as the reading of a clock located at each position in space. The 'observer' synchronizes the clocks according to their own reference frame.]]

In special relativity, an observer will, in most cases, mean a frame of reference from which a set of objects or events is 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.<ref name="Taylor"/>

In Fig.&nbsp;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 whole ensemble of clocks associated with one inertial frame of reference.<ref name="Taylor">{{cite book|url=https://archive.org/details/spacetime_physics/|title=Spacetime Physics: Introduction to Special Relativity|last1=Taylor|first1=Edwin F.|last2=Wheeler|first2=John Archibald|date=1992|publisher=Freeman|isbn=0-7167-0336-X|edition=2nd|location=San Francisco, California|access-date=14 April 2017}}</ref>{{rp|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 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 [[data reduction]] following an experiment, the time when a signal is received will be corrected to reflect its actual time were it to have been recorded by an idealized lattice of clocks.<ref name="Taylor"/>{{rp|17–22}}

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. Failing to understand [[Special relativity#Measurement versus visual appearance|the difference between what one measures and what one sees]] is the source of much confusion among students of relativity.<ref>{{cite journal|last1=Scherr|first1=Rachel E.|author1-link=Rachel Scherr|last2=Shaffer|first2=Peter S.|last3=Vokos|first3=Stamatis|title=Student understanding of time in special relativity: Simultaneity and reference frames|journal=[[American Journal of Physics]]|publisher=[[American Association of Physics Teachers]]|location=College Park, Maryland|date=July 2001|volume=69|issue=S1|pages=S24–S35|doi=10.1119/1.1371254|url=https://arxiv.org/ftp/physics/papers/0207/0207109.pdf|access-date=11 April 2017|bibcode=2001AmJPh..69S..24S|arxiv=physics/0207109|s2cid=8146369|archive-date=28 September 2018|archive-url=https://web.archive.org/web/20180928122701/https://arxiv.org/ftp/physics/papers/0207/0207109.pdf|url-status=live}}</ref>