Multiple time dimensions

The possibility that there might be more than one dimension of time has occasionally been discussed in physics and philosophy.

Physics

Special relativity describes spacetime as a manifold whose metric tensor has a negative eigenvalue. This corresponds to the existence of a "timelike" direction. A modified metric with multiple negative eigenvalues would correspondingly imply a number of such timelike directions, but there is no consensus regarding the possible relationships of these extra "times" to time as conventionally understood.

If the special theory of relativity is generalized for the case of k-dimensional time (t1, t2, ..., tk) and n-dimensional space (xk + 1, xk + 2, ..., xk + n), then the (k + n)-dimensional interval, being invariant, is given by the expression

(dsk,n)2 = (cdt1)2 + ... + (cdtk)2 − (dxk+1)2 − … − (dxk+n)2.

The metric signature is then

(timelike sign convention)

or

(spacelike sign convention).

The transformations between the two inertial frames of reference K and K′, which are in a standard configuration (i.e., transformations without translations and/or rotations of the space axis in the hyperplane of space and/or rotations of the time axis in the hyperplane of time), are given as follows:[1]

where are the vectors of the velocities of K′ against K, defined accordingly in relation to the time dimensions t1, t2, ..., tk; σ = 1, 2, ..., k; λ = k+2, k+3, ..., k+n. Here δσθ is the Kronecker delta. These transformations are generalization of the Lorentz boost in a fixed space direction (xk+1) in the field of the multidimensional time and multidimensional space.

Causal structure of a space-time with two time dimensions and one space dimension
Causal structure of a space-time with two time dimensions and one space dimension

Denoting and where σ = 1, 2, ..., k; η = k+1, k+2, ..., k+n. The velocity-addition formula is then given by

where σ = 1, 2, ..., k; λ = k+2, k+3, ..., k+n.

For simplicity, consider only one spatial dimension x3 and the two time dimensions x1 and x2. (E. g., x1 = ct1, x2 = ct2, x3 = x.) Assuming that in point O, having coordinates x1 = 0, x2 = 0, x3 = 0, there has been an event E. Further assuming that a given interval of time has passed since the event E', the causal region connected to the event E includes the lateral surface of the right circular cone {(x1)2 + (x2)2 − (x3)2 = 0}, the lateral surface of the right circular cylinder {(x1)2 + (x2)2 = c2ΔT2} and the inner region bounded by these surfaces, i.e., the causal region includes all points (x1, x2, x3), for which the conditions

{(x1)2 + (x2)2 − (x3)2 = 0 and |x3| ≤ cΔT} or
{(x1)2 + (x2)2 = c2ΔT2 and |x3| ≤ cΔT} or
{(x1)2 + (x2)2 − (x3)2 > 0 and (x1)2 + (x2)2 < c2ΔT2}

are fulfilled.[1]

Theories with more than one dimension of time have sometimes been advanced in physics, whether as a serious description of reality or just as a curious possibility. Itzhak Bars's work on "two-time physics",[2] inspired by the SO(10,2) symmetry of the extended supersymmetry structure of M-theory, is the most recent and systematic development of the concept (see also F-theory). Walter Craig and Steven Weinstein proved the existence of a well-posed initial value problem for the ultrahyperbolic equation (a wave equation in more than one time dimension).[3] This showed that initial data on a mixed (spacelike and timelike) hypersurface obeying a particular nonlocal constraint evolves deterministically in the remaining time dimension.

Connection to the Planck length and the speed of light

The motion of a test particle may be described by coordinate

which is the canonical (1,3) spacetime vector with extended by an additional timelike coordinate . is then a second time parameter, describes the size of the second time dimension and is the characteristic velocity, thus the equivalent of . describes the shape of the second time dimension and is a normalization parameter such that is dimensionless. Decomposing with

and using the metric , the Lagrangian becomes

Applying the Euler-Lagrange Equations

the existence of the Planck length and the constancy of the speed of light can be derived.

As a consequence of this model it has been suggested that the speed of light may not have been constant in the early universe.[4]

Philosophy

Conceptual difficulties with multiple physical time dimensions have been raised in modern analytic philosophy.[5]

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, 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. At the end of the regress was a "superlative general observer" who existed in eternity.[6] He published his theory in relation to precognitive dreams in his 1927 book An Experiment with Time 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.[7][8]

See also

References

  1. ^ a b Velev, Milen (2012). "Relativistic mechanics in multiple time dimensions". Physics Essays. 25 (3): 403–438. Bibcode:2012PhyEs..25..403V. doi:10.4006/0836-1398-25.3.403.
  2. ^ Bars, Itzhak. "Two-Time Physics". Retrieved 8 December 2012.
  3. ^ Craig, Walter; Weinstein, Steven. "On determinism and well-posedness in multiple time dimensions". Proc. R. Soc. A vol. 465 no. 2110 3023-3046 (2008). Retrieved 5 December 2013.
  4. ^ Albrecht, A.; Magueijo, J. "A Time Varying Speed of Light as a Solution to Cosmological Puzzles". Phys. Rev. D vol. 59 043516 (1999). Missing or empty |url= (help)
  5. ^ Weinstein, Steven. "Many Times". Foundational Questions Institute. Retrieved 5 December 2013.
  6. ^ McDonald, John Q. (15 November 2006). "John's Book Reviews: An Experiment with Time". Retrieved 8 December 2012.
  7. ^ J.A. Gunn; The Problem of Time, Unwin, 1929.
  8. ^ J.B. Priestley, Man and Time, Aldus, 1964.

External links

A series and B series

In philosophy, A series and B series are two different descriptions of the temporal ordering relation among events. The two series differ principally in their use of tense to describe the temporal relation between events. The terms were introduced by the Scottish idealist philosopher John McTaggart in 1908 as part of his argument for the unreality of time, but since then they have become widely used terms of reference in modern discussions of the philosophy of time.

Astrarium

An astrarium, also called a planetarium, is the mechanical representation of the cyclic nature of astronomical objects in one timepiece. It is an astronomical clock.

BPL (time service)

BPL is the call sign of the official long-wave time signal service of the People's Republic of China, operated by the Chinese Academy of Sciences, broadcasting on 100 kHz from CAS's National Time Service Center in Pucheng County, Shaanxi at 34°56′54″N 109°32′34″E, roughly 70 km northeast of Lintong, along with NTSC's short-wave time signal BPM on 2.5, 5.0, 10.0, and 15.0 MHz.

BPL broadcasts LORAN-C compatible format signal from 5:30 to 13:30 UTC, using an 800 kW transmitter covering a radius up to 3000 km.

Chronometry

Chronometry (from Greek χρόνος chronos, "time" and μέτρον metron, "measure") is the science of the measurement of time, or timekeeping. Chronometry applies to electronic devices, while horology refers to mechanical devices.

It should not to be confused with chronology, the science of locating events in time, which often relies upon it.

Collision Course (Bayley novel)

Collision Course (a.k.a. Collision with Chronos) is the fourth novel by the science fiction author Barrington J. Bayley. The novel was inspired by the multiple time dimensions proposed by J. W. Dunne. The plot centers on the collision of two alternate "presents", with disastrous implications for reality.

Common year

A common year is a calendar year with 365 days, as distinguished from a leap year, which has 366. More generally, a common year is one without intercalation. The Gregorian calendar, (like the earlier Julian calendar), employs both common years and leap years to keep the calendar aligned with the tropical year, which does not contain an exact number of days.

The common year of 365 days has 52 weeks and one day, hence a common year always begins and ends on the same day of the week (for example, January 1 and December 31 fell on a Sunday in 2017) and the year following a common year will start on the subsequent day of the week. In common years, February has four weeks, so March will begin on the same day of the week. November will also begin on this day.

In the Gregorian calendar, 303 of every 400 years are common years. By comparison, in the Julian calendar, 300 out of every 400 years are common years, and in the Revised Julian calendar (used by Greece) 682 out of every 900 years are common years.

Endurantism

Endurantism or endurance theory is a philosophical theory of persistence and identity. According to the endurantist view, material objects are persisting three-dimensional individuals wholly present at every moment of their existence, which goes with an A-theory of time. This conception of an individual as always present is opposed to perdurantism or four dimensionalism, which maintains that an object is a series of temporal parts or stages, requiring a B-theory of time. The use of "endure" and "perdure" to distinguish two ways in which an object can be thought to persist can be traced to David Lewis.

Eternity

Eternity in common parlance is an infinitely long period of time. In classical philosophy, however, eternity is defined as what exists outside time while sempiternity is the concept that corresponds to the colloquial definition of eternity.

Eternity is an important concept in many religions, where the god or gods are said to endure eternally. Some, such as Aristotle, would say the same about the natural cosmos in regard to both past and future eternal duration, and like the eternal Platonic forms, immutability was considered essential.

Event (philosophy)

In philosophy, events are objects in time or instantiations of properties in objects.

Extra dimensions

In physics, extra dimensions are proposed additional space or time dimensions beyond the (3 + 1) typical of observed spacetime, such as the first attempts based on the Kaluza–Klein theory. Among theories proposing extra dimensions are:

Large extra dimension, mostly motivated by the ADD model, by Nima Arkani-Hamed, Savas Dimopoulos, and Gia Dvali in 1998, in an attempt to solve the hierarchy problem. This theory requires that the fields of the Standard Model are confined to a four-dimensional membrane, while gravity propagates in several additional spatial dimensions that are large compared to the Planck scale.

Warped extra dimensions, such as those proposed by the Randall–Sundrum model (RS), based on warped geometry where the universe is a five-dimensional anti-de Sitter space and the elementary particles except for the graviton are localized on a (3 + 1)-dimensional brane or branes.

Universal extra dimension, proposed and first studied in 2000, assume, at variance with the ADD and RS approaches, that all fields propagate universally in the extra dimensions.

Multiple time dimensions, i.e. the possibility that there might be more than one dimension of time, has occasionally been discussed in physics and philosophy, although those models have to deal with the problem of causality.

String theory has one notable feature that requires extra dimensions for mathematical consistency. Spacetime is 26-dimensional in bosonic string theory, 10-dimensional in superstring theory, and 11-dimensional in supergravity theory and M-theory.

HD2IOA

HD2IOA is the callsign of a time signal radio station operated by the Navy of Ecuador. The station is located at Guayaquil, Ecuador and transmits in the HF band on 3.81 and 7.6 MHz.The transmission is in AM mode with only the lower sideband (part of the time H3E and the rest H2B/H2D) and consists of 780 Hz tone pulses repeated every ten seconds and voice announcements in Spanish.

While sometimes this station is described as defunct, reception reports of this station on 3.81 MHz appear regularly at the Utility DX Forum.

Intercalation (timekeeping)

Intercalation or embolism in timekeeping is the insertion of a leap day, week, or month into some calendar years to make the calendar follow the seasons or moon phases. Lunisolar calendars may require intercalations of both days and months.

Minute

The minute is a unit of time or angle. As a unit of time, the minute is most of times equal to ​1⁄60 (the first sexagesimal fraction) of an hour, or 60 seconds. In the UTC time standard, a minute on rare occasions has 61 seconds, a consequence of leap seconds (there is a provision to insert a negative leap second, which would result in a 59-second minute, but this has never happened in more than 40 years under this system). As a unit of angle, the minute of arc is equal to ​1⁄60 of a degree, or 60 seconds (of arc). Although not an SI unit for either time or angle, the minute is accepted for use with SI units for both. The SI symbols for minute or minutes are min for time measurement, and the prime symbol after a number, e.g. 5′, for angle measurement. The prime is also sometimes used informally to denote minutes of time.

Perdurantism

Perdurantism or perdurance theory is a philosophical theory of persistence and identity. The perdurantist view is that an individual has distinct temporal parts throughout its existence. Perdurantism is usually presented as the antipode to endurantism, the view that an individual is wholly present at every moment of its existence.The use of "endure" and "perdure" to distinguish two ways in which an object can be thought to persist can be traced to David Kellogg Lewis (1986). However, contemporary debate has demonstrated the difficulties in defining perdurantism (and also endurantism). For instance, the work of Ted Sider (2001) has suggested that even enduring objects can have temporal parts, and it is more accurate to define perdurantism as being the claim that objects have a temporal part at every instant that they exist. Currently there is no universally acknowledged definition of perdurantism. Others argue that this problem is avoided by creating time as a continuous function, rather than a discrete one.

Perdurantism is also referred to as "four-dimensionalism" (by Ted Sider, in particular) but perdurantism also applies if one believes there are temporal but non-spatial abstract entities (like immaterial souls or universals of the sort accepted by David Malet Armstrong).

Philosophical presentism

Philosophical presentism is the view that neither the future nor the past exist. In some versions of presentism, this view is extended to timeless objects or ideas (such as numbers). According to presentism, events and entities that are wholly past or wholly future do not exist at all. Presentism contrasts with eternalism and the growing block theory of time which hold that past events, like the Battle of Waterloo, and past entities, like Alexander the Great's warhorse Bucephalus, really do exist, although not in the present. Eternalism extends to future events as well.

Static interpretation of time

The static interpretation of time is a view of time which arose in the early years of the 20th century from Einstein's special relativity and Hermann Minkowski's extension of special relativity in which time and space were famously united in physicists' thinking as spacetime.

Essentially the universe is regarded as akin to a reel of film – which is a wholly static physical object – but which when played through a movie projector conjures a world of movement, color, light and change. In the static view our whole universe – our past, present, and future are fixed parts of that reel of film, and the projector is our consciousness. But the 'happenings' of our consciousness have no objective significance – the objective universe does not happen, it simply exists in its entirety, albeit perceived from within as a world of changes.

The alternative, and commonly assumed view, is that the world unfolds in existence, that our present has some wider physical significance, because the universe evolves in step with it.

The static view is the simpler in that all that is held to exist is the physical ordering of the universe. All that there is at every time simply exists. The unfolding view requires an additional quality to the universe – that besides the physical ordering there is some quality of coming into and out of existence.

One can argue that the onus is therefore upon those who propose it, that the world unfolds, and that this additional quality they hold to (absent from special relativity) is indeed a physical feature of the world. There is however as yet no proof, experiment, or measurement, to show that our conscious experience of an unfolding present has any objective physical significance, or that the universe is anything other than static.

The static view is however commonly rejected for psychological, not scientific reasons, because it leads to a fatalistic or "fixed" conclusion about human existence – our 'past', 'present', and 'future' being what they are – there is no contingency in the world and no possibility of 'altering' or creating the future through some act of will – the future exists. It is simply that our consciousness has not yet reached it.

Steven Weinstein (philosopher)

Steven Weinstein is a philosopher at the University of Waterloo, noted particularly for his work on quantum gravity, time, and the interpretation of quantum mechanics.

Tomorrow (time)

Tomorrow is a temporal construct of the relative future; literally of the day after the current day (today), or figuratively of future periods or times. Tomorrow is usually considered just beyond the present and counter to yesterday. It is important in time perception because it is the first direction the arrow of time takes humans on Earth.

YVTO

YVTO is the callsign of the official time signal from the Juan Manuel Cagigal Naval Observatory in Caracas, Venezuela. The content of YVTO's signal, which is a continuous 1 kW amplitude modulated carrier wave at 5.000 MHz, is much simpler than that broadcast by some of the other time signal stations around the world, such as WWV.

The methods of time transmission from YVTO are very limited. The broadcast employs no form of digital time code. The time of day is given in Venezuelan Standard Time (VET), and is only sent using Spanish language voice announcements. YVTO also transmits 100 ms-long beeps of 1000 Hz every second, except for thirty seconds past the minute. The top of the minute is marked by a 0.5 second 800 Hz tone.The station previously broadcast on 6,100 MHz but appears to have changed to the current frequency by 1990.

Concepts
in time
Theories
of time
Related
articles

This page is based on a Wikipedia article written by authors (here).
Text is available under the CC BY-SA 3.0 license; additional terms may apply.
Images, videos and audio are available under their respective licenses.