The possibility that there might be more than one dimension of time has occasionally been discussed in
physics
Physics is the scientific study of matter, its Elementary particle, fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of knowledge whi ...
and
philosophy
Philosophy ('love of wisdom' in Ancient Greek) is a systematic study of general and fundamental questions concerning topics like existence, reason, knowledge, Value (ethics and social sciences), value, mind, and language. It is a rational an ...
. Similar ideas appear in folklore and fantasy literature.
Physics
Speculative theories with more than one time dimension have been explored in physics. The additional dimensions may be similar to conventional time,
compactified like the additional spatial dimensions in
string theory
In physics, string theory is a theoretical framework in which the point-like particles of particle physics are replaced by one-dimensional objects called strings. String theory describes how these strings propagate through space and intera ...
, or components of a
complex
Complex commonly refers to:
* Complexity, the behaviour of a system whose components interact in multiple ways so possible interactions are difficult to describe
** Complex system, a system composed of many components which may interact with each ...
time (sometimes referred to as kime).
Itzhak Bars has proposed models of a two-time physics, noting in 2001 that "The 2T-physics approach
in ''d'' + 2 dimensions offers a highly symmetric and unified version of the phenomena described by 1T-physics in ''d'' dimensions."
F-theory
In theoretical physics, F-theory is a branch of string theory developed by Iranian-American physicist Cumrun Vafa. The new vacua described by F-theory were discovered by Vafa and allowed string theorists to construct new realistic vacua — in ...
, a branch of modern
string theory
In physics, string theory is a theoretical framework in which the point-like particles of particle physics are replaced by one-dimensional objects called strings. String theory describes how these strings propagate through space and intera ...
, describes a 12-dimensional spacetime having two dimensions of time, giving it the
metric signature
In mathematics, the signature of a metric tensor ''g'' (or equivalently, a real quadratic form thought of as a real symmetric bilinear form on a finite-dimensional vector space) is the number (counted with multiplicity) of positive, negative and z ...
(10,2).
The existence of a well-posed initial value problem for the
ultrahyperbolic equation (a wave equation in more than one time dimension) demonstrates that initial data on a mixed (spacelike and timelike) hypersurface, obeying a particular nonlocal constraint, evolves deterministically in the remaining time dimension.
Like other
complex number
In mathematics, a complex number is an element of a number system that extends the real numbers with a specific element denoted , called the imaginary unit and satisfying the equation i^= -1; every complex number can be expressed in the for ...
variables, complex time is two-dimensional, comprising one
real time dimension and one
imaginary time dimension, changing time from a real number line into a complex plane.
Introducing it into
Minkowski spacetime
In physics, Minkowski space (or Minkowski spacetime) () is the main mathematical description of spacetime in the absence of gravitation. It combines inertial space and time manifolds into a four-dimensional model.
The model helps show how a s ...
allows a generalization of
Kaluza–Klein theory
In physics, Kaluza–Klein theory (KK theory) is a classical unified field theory of gravitation and electromagnetism built around the idea of a fifth dimension beyond the common 4D of space and time and considered an important precursor to ...
.
Max Tegmark
Max Erik Tegmark (born 5 May 1967) is a Swedish-American physicist, machine learning researcher and author. He is best known for his book ''Life 3.0'' about what the world might look like as artificial intelligence continues to improve. Tegmark i ...
has argued that, if there is more than one time dimension, then the behavior of physical systems could not be predicted reliably from knowledge of the relevant
partial differential equation
In mathematics, a partial differential equation (PDE) is an equation which involves a multivariable function and one or more of its partial derivatives.
The function is often thought of as an "unknown" that solves the equation, similar to ho ...
s. In such a universe, intelligent life capable of manipulating technology could not emerge. Moreover
proton
A proton is a stable subatomic particle, symbol , Hydron (chemistry), H+, or 1H+ with a positive electric charge of +1 ''e'' (elementary charge). Its mass is slightly less than the mass of a neutron and approximately times the mass of an e ...
s and
electron
The electron (, or in nuclear reactions) is a subatomic particle with a negative one elementary charge, elementary electric charge. It is a fundamental particle that comprises the ordinary matter that makes up the universe, along with up qua ...
s would be unstable and could decay into particles having greater mass than themselves. (This is not a problem if the particles have a sufficiently low temperature.)
Philosophy
Multiple time dimensions appear to allow the breaking or re-ordering of cause-and-effect in the flow of any one dimension of time. This and conceptual difficulties with multiple physical time dimensions have been raised in modern
analytic philosophy
Analytic philosophy is a broad movement within Western philosophy, especially English-speaking world, anglophone philosophy, focused on analysis as a philosophical method; clarity of prose; rigor in arguments; and making use of formal logic, mat ...
.
As a solution to the problem of the subjective passage of time,
J. W. Dunne proposed an infinite hierarchy of time dimensions, inhabited by a similar hierarchy of levels of consciousness. Dunne suggested that, in the context of a "block" spacetime as modelled by
General Relativity
General relativity, also known as the general theory of relativity, and as Einstein's theory of gravity, is the differential geometry, geometric theory of gravitation published by Albert Einstein in 1915 and is the current description of grav ...
, a second dimension of time was needed in order to measure the speed of one's progress along one's own timeline. This in turn required a level of the conscious self existing at the second level of time. But the same arguments then applied to this new level, requiring a third level, and so on in an
infinite regress
Infinite regress is a philosophical concept to describe a series of entities. Each entity in the series depends on its predecessor, following a recursive principle. For example, the epistemic regress is a series of beliefs in which the justi ...
. At the end of the regress was a "superlative general observer" who existed in
eternity
Eternity, in common parlance, is an Infinity, infinite amount of time that never ends or the quality, condition or fact of being everlasting or eternal. Classical philosophy, however, defines eternity as what is timeless or exists outside tim ...
. He published his theory in relation to
precognitive
Precognition (from the Latin 'before', and 'acquiring knowledge') is the purported psychic phenomenon of seeing, or otherwise becoming directly aware of, events in the future.
There is no accepted scientific evidence that precognition is a ...
dreams in his 1927 book ''
An Experiment with Time
''An Experiment with Time'' is a book by the British soldier, aeronautical engineer and philosopher J. W. Dunne (1875–1949) about his precognitive dreams and a theory of time which he later called "Serialism". First published in March 1927 ...
'' and went on to explore its relevance to contemporary physics in ''The Serial Universe'' (1934). His infinite regress was criticised as logically flawed and unnecessary, although writers such as
J. B. Priestley acknowledged the possibility of his second time dimension.
The
Esoteric
Western esotericism, also known as the Western mystery tradition, is a wide range of loosely related ideas and movements that developed within Western society. These ideas and currents are united since they are largely distinct both from orthod ...
J. G. Bennett described three dimensions or aspects of time: a) Time – Causal or determinate influences on the present moment, b) Eternity – The influences of forms and values, c) Hyparxis – The influences of the Will (freedom) to choose within the present Moment. The physical world, life and consciousness lie in intermediate zones between these dimensions. Physicist
David Bohm
David Joseph Bohm (; 20 December 1917 – 27 October 1992) was an American scientist who has been described as one of the most significant Theoretical physics, theoretical physicists of the 20th centuryDavid Peat Who's Afraid of Schrödinger' ...
corresponded with Bennett and they influenced each other's ideas.
Fiction
Multiple independent timeframes, in which time passes at different rates, have long been a feature of stories.
Fantasy writers such as
J. R. R. Tolkien
John Ronald Reuel Tolkien (, 3 January 1892 – 2 September 1973) was an English writer and philologist. He was the author of the high fantasy works ''The Hobbit'' and ''The Lord of the Rings''.
From 1925 to 1945, Tolkien was the Rawlinson ...
and
C. S. Lewis
Clive Staples Lewis (29 November 1898 – 22 November 1963) was a British writer, literary scholar and Anglican lay theologian. He held academic positions in English literature at both Magdalen College, Oxford (1925–1954), and Magdalen ...
have made use of these and other multiple time dimensions, such as those proposed by Dunne, in some of their most well-known stories.
It has been argued that Tolkien borrowed his ideas for
Lórien time in
The Lord of the Rings
''The Lord of the Rings'' is an Epic (genre), epic high fantasy novel written by English author and scholar J. R. R. Tolkien. Set in Middle-earth, the story began as a sequel to Tolkien's 1937 children's book ''The Hobbit'' but eventually d ...
,
[Flieger, V.; ''A Question of Time: JRR Tolkien's Road to Faerie'', Kent State University Press, 1997.] and that Lewis adopted them for his
Chronicles of Narnia.
Science fiction author
H. Beam Piper, in his
Paratime series of short stories and novel that
multiple timelines exist as "worlds of alternate
probability on the lateral dimension of time."
[
]
See also
*
Dimensions of spacetime relating to the anthropic principle.
*
Multiverse
The multiverse is the hypothetical set of all universes. Together, these universes are presumed to comprise everything that exists: the entirety of space, time, matter, energy, information, and the physical laws and constants that describ ...
, parallel universes
*
Time Cube, a pseudoscientific crank theory of time
References
External links
*
{{Time in philosophy , state=collapsed
Time
Spacetime
Theories of time
Dimension