# How many dimensions does time have?

As phrased in the title, How many dimensions does time have?

If one considers time by itself (in isolation from other putative phenomena such as space or spacetime), what can be said about the dimensionality of time? Is it similar to or unlike other things, like space, that are said to have a certain dimensionality?

• It's typically taken to be one dimension, and most physical models will take that view. Some physical models have more than 1 time dimension.
– TKoL
Dec 21, 2023 at 17:59
• The distinction between space-like and time-like dimensions does not require that each dimension be equally "navigable". Just because you can't change your direction or speed (relativity aside) doesn't mean that one dimension is not sufficient to model time. Time is one-dimensional because you only need one label to identify a point in time; space is three-dimensional because you need three numbers (x, y, and z coordinates, for example) to identify a point in space. Dec 22, 2023 at 20:13
• Can you say how this is about Philosophy rather than, for instance, Physics? Dec 22, 2023 at 23:19
• @RobbieGoodwin I believe the nature of time to be a philosophical question. All of the sciences were, in the past, more honestly named philosophy, for example "natural philosophy" is the 19th century term for the field of physics. Dec 22, 2023 at 23:39
• Pygosceles that belief is your choice and clearly, no few Members here have been sucked into it… Your basis for believing the nature of time is a Question of philosophy looks to be decades or centuries out of date. Can you put it in modern terms? 'Natural philosophy' is a 19th century term. What, in your book, should we use today? How might the naming of sciences in the past matter here? Dec 23, 2023 at 0:27

The time variable in spacetime can be rolled into the algebra like a spatial quantity but gets marked with a sign (+/-) opposite that of the spatial variables so the math will work out. This is routinely done in what is called a space-time diagram, the mastery of which is a prerequisite to the study of Minkowski space (3 dimensions of space + one of time).

In the real world we inhabit, moving "sideways" in 2-dimensional time has no physical meaning, but a plane extending perpendicularly away from the time axis in a spacetime diagram touches all points in space that are experiencing that particular instant in time. sliding around on that plane would allow you to reach any location in space experiencing that instant, in zero time- which is not how the RWOT (real world out there) works.

The reasons why can be worked out algebraically within the spacetime diagram using the concept of the light cone which is used to trace causality (or its impossibility) as time advances. Rather than attempt to do a spacetime diagram tutorial in this forum I would advise finding one on-line or reposting this question on the physics stack exchange, which is where I normally lurk.

• What ends up being required is that the time coordinate has an opposite sign to the spatial coordinates in the metric, not that it has to be negative. See metric signature. Dec 22, 2023 at 15:36
• @galen, will edit. -NN Dec 22, 2023 at 18:09
• Great point about the difference between the hyper-navigable algebraic model and the RWOT. Since the question pertains more to the RWOT, this would really benefit from being fleshed out more. I believe it is worth mentioning for example that the algebraic model is limited to purely deterministic (or probabilistic, but still known-distribution) and time-reversible equations and simulations. Dec 28, 2023 at 17:30
• @pygosceles, will try an edit- please review. -NN Dec 28, 2023 at 17:56
• When you speak of moving in 2-dimensional time having no physical meaning is that another way of saying that time moves only forwards, but it helps the model to pretend that it can also move backwards, or did I miss something? Jan 19 at 21:09

According to Kant, "Time is one-dimensional," is a synthetical proposition, which means that the concept of time by itself doesn't decide any specific dimensionality, but this must be found out by/in temporal intuition. Suppose, then, that we can imagine temporal manifolds of higher dimensionality, and distinguish between imagined manifolds and physical ones like we distinguish imagined spatial manifolds from physical space. (This will smack of some measure of dualism, but oh well...) Thus far, the imaginary manifolds will in themselves have whatever dimensionality we attribute to them a priori, even perhaps infinitely many dimensions (if we so see fit to think through the matter).

For a less fanciful theory involving at least two-dimensional time, see Bars[00]. For something more recent, see Merali[22]. For an even more fanciful theory, see about the musings of J. W. Dunne.

• +1 For digging up J. W. Dunne's proposal. It seems an attempt to add the subjectivity of perceived time to the consensual objective time. This sort of seems like the notion of a tensor space to me, where you can nest time inside of time.
– J D
Dec 22, 2023 at 16:06

First, the physical study of time is but one aspect of understanding time (SEP) philosophically. One can study time through natural language tense and aspect, or can study how time is constructed by the mind, as Daniel Dennett does in his Consciousness Explained. This would be a psychological interpretation of time, since time has a subjective aspect called perception of time.

However, in physics, time is a variable and is measured by the real numbers. As such, it has only one dimension, because dimensions in mathematical models are represented as variables. Thus, time in such models of physical reality often carries with it the same properties as reals, for instance, it is well-ordered under Newtonian notions of time and space. With the advent of Minkowski space, the model gets more complicated, but time is still one dimension, though it becomes localized and therefore dilates relative to the observer. There are accompanying philosophical interpretations of relativistic models (SEP) some of which are quite complex.

See also the Conventionality of Simultaneity (SEP) and Space and Time: Inertial Frames (SEP). A modern philosophical interpretation of physical time is viewed through the twin lenses of quantum mechanics (SEP) and general relativity.

• "because dimensions in mathematical models are represented as variables" << The only way I can make sense of this is by mentally replacing the word "variables" with "degrees of freedom"; is that what you meant?
– Stef
Dec 22, 2023 at 11:41
• I think there is some thinking to be had here. I would offer that space in the Minkowski model has 3 dimensions of space, but 5 degrees of freedom (the 2 rotational degrees in addition to the 3 linear ones). In that conceptualization, it would seem to me that a degree is in some sense a 'linear basis' for modeling motion? I'm happy to hear an argument of why degrees of freedom is superior to variables which are existential as (Ex in R where R is linear). @Stef
– J D
Dec 22, 2023 at 16:13
• Well I'm not arguing that degrees of freedom is "superior to variables", I'm just trying to understand what you mean by "variables". A punctual position in space has only 3 degrees of freedom. Yes, an object which is not punctual has more than 3 degrees of freedom if you add its orientation in addition to its position. And if you add its inertial direction then it has even more degrees of freedom. And I'm sure with more imagination we could come up with more and more and more degrees of freedom for an object to have. But I would argue that in a certain sense, "just space" itself only gives 3.
– Stef
Dec 22, 2023 at 17:46
• @Stef In a technical sense, a variable is a reference whose referent varies. A logical variable is a constituent in a domain of discourse that allows references to refer to senses which are normally called values. Discourse is broken into compositional elements of segments. So, in reference to conversation about space, a variable is either the length, width, or depth of an applied coordinate system. In physics, we use reals to constrain our sense when we refer to length, width, or depth. Thus, Minkowski space (as opposed to Netwonian or tensor space, for instance) has three variables.
– J D
Dec 22, 2023 at 17:56
• From etymonline, "dimension" literally evolves in natural language from measuring (-mension) in two directions (di-). Thus, in a classic conception, a dimension is a number system applied to the perception of a line which starting with Euclid has an established linear basis requiring three distinct and orthogonal lines. Do you have a different understanding of dimension in physics?
– J D
Dec 22, 2023 at 17:59

What you describe as time 'lumped in' to a four-dimensional spacetime certainly is accurate, in the sense that it is a model that is an extremely good fit to reality. Curved spacetime is the current mainstream explanation of gravitational attraction. In 'flat' spacetime- which is described by special relativity- your time axis is at right angles to your three spatial axes, so that you can move along your time axis without changing your spatial coordinates. In curved spacetime, as you coast along your curved time axis, your spatial coordinates necessarily change so that you accelerate in space, and that gives the appearance of a force acting upon you, which we call gravity.

Also in Einstein’s Theory of Relativity time is one-dimensional like a line.

The new concept of 4-dimensional spacetime fuses the three-dimensional space and the one-dimensional time. The new and surprising property of spacetime is the fact that space and time lose their absolute property. The splitting of the 4-dimensional spacetime into 3-dimensional space and 1-dimensional time is not unique but has a certain arbitrariness.

You are right that space and time have different properties, which can be studied best from the viewpoint of spacetime. For an introduction see Spacetime.

Time has an order, therefore it is one dimensional.

Events can occur both simultaneously and in sequence, but this sequence (including the coincidences) is universal. When an observer might notice these events is subject to change based on where they are and how fast they're moving in which direction, but with the math of special relativity, we can interpret events to understand that sequence from any perspective (location and velocity).

Intrinsically, 1 comes before 2. When we examine complex numbers (2d), quaternions (4d), octonions (8d), etc..., we find that these numbers do not have any ordering: we cannot say whether 1+2i is bigger or smaller than 2+i, or even whether 1 intrinsically comes before -20-40i. Vectors (multi-dimensional objects) generally do not have an ordering.

For more information on number systems and their properties, see the Cayley-Dickson construction.

Don't think of time as "having dimensions". We have mathematical models of physics that use a single dimension to model time, and they are very useful. If we used zero dimensions for time, the models would be much less useful. We could create models that used more dimensions for time, and they'd be just as accurate, but they wouldn't be any more accurate, so why increase the complexity?

This is a question about coordinate systems. Humans invent coordinate systems in which the specified dimensions may or may not be orthogonal. Orthogonal coordinates are perpendicular to each other at coordinate points. Orthogonality holds for space dimensions designated metric, polar, cylindrical, and spherical coordinate systems.

Time is the inverse of frequency of a resonant system called a time-base oscillator or of a periodic system such as uniform rotational motion. If we count the periods or sub-periods of the time-base oscillator or uniform periodic motion - then we translate the frequency or motion into a clock that measures and specifies elapsed time. The clock enables each independent observer to measure and specify time in one dimension. I am not aware of definitions of coordinates where time is orthogonal to one or more distinct dimensions of time. We usually map space using orthogonal space coordinates.

Is time orthogonal to space?

https://physics.stackexchange.com/questions/87105/can-we-show-that-time-is-orthogonal-to-space

Is the time axis really perpendicular to spacial axis in Minkowski diagrams and Special Relativity?

https://youtu.be/rceYwLCUgwo

Einstein and the clock - an intro to special relativity:

https://youtu.be/dht4OTVxpDw

How does an inertial observer assign space and time coordinates:

https://youtu.be/D1dKihovkJ4

Historically Galileo performed a thought experiment called Galileo's Ship. Three distinct Observers exist in three distinct locations in space. There is Observer 1 on the shore. There is Observer 2 on the deck of the ship, which sails by the shore at a perpendicular angle to Observer 1 on shore, and there is Observer 3 in the closed cabin of the ship with no doors, windows, etc. Galileo assumes that the ship sails in a straight line on a perfectly smooth sea at uniform speed with no pitching, rocking, or rolling motion. Observer 3 inside the closed cabin cannot perform any experiment (known to Galileo) to determine whether the ship is at rest on the shore or moving in a straight line at uniform speed!

If a ball falls from the ship's mast then Observer 1 maps a parabolic path of independent (orthogonal) vertical and horizontal motion but Observer 2 maps only the straight vertical path of motion. There is one event, a falling ball, and two distinct frames of reference. Observer 1 and 2 might be using two distinct frequencies of time-base oscillators for their respective clocks. So the specified path and rate of motion, given by the respective math model, would differ based on the choice of clock and imposed reference frame.

Britannica - https://www.britannica.com/science/Galilean-relativity - According to the principle of Galilean relativity, if Newton's laws are true in any reference frame, they are also true in any other frame moving at constant velocity with respect to the first one.

In Classical Physics there are resonant systems and/or periodic events such as the rotation of Earth about its axis. If the rotational speed of Earth is uniform it provides the time-base for an astrological clock. This means time is a change in the configuration of objects in space or some other change in a physical system distributed in space. Humans transform periodic or resonant systems (changes in systems distributed in space) to a dimension that we call time. Time is the inverse of frequency. The frequency of some systems used as a clock will vary with relative velocity under the assumption that the speed of light is constant for every observer moving with a clock and measuring stick to measure the wavelength of light.

We have good reasons to invent time from the human perspective, in part because we age and die, but the matter-energy in the Universe persists forever independent of our efforts to measure and specify periods of elapsed time. Both time and eternity are physical properties.

Philosophically, time is not so much an issue of spatial movement but of change or, more specifically evolution.

The universe is constantly self-actualizing out of necessity. And to our human minds the perception of this change and the memories of past stages of evolution are what we call time.

I think dimension of time is a misguided concept under these axioms because we are not moving through time but we are simply evolving, changing.

If we insist in looking for a time dimension I might answer that time is half-dimentional(?) because we are only moving in one direction (we can't go back on evolution).

• Really? How could that work, please? Philosophically or physically, what difference do you see between 'spatial movement' and any other kind of change? In such contexts, how is evolution different? Dec 27, 2023 at 0:11
• Spatial movement is a change in position while evolution is a change in the configuration of matter. Dec 28, 2023 at 14:14

Practically speaking, time is half-dimensional.

A typical dimensional axis consists of a line, extending infinitely in both directions. However, the navigability of time is constrained to the forward direction, unlike the spatial dimensions:

If we assume we can evaluate the past robustly, we could in theory view a timeline as a true one-dimensional line extending into both the past and future rather than as a one-directional ray--but the evaluation as a full dimension would necessarily be speculative or read-only. In terms of interactivity and consequence, time, being causal unlike other dimensions, only points in the forward direction.

Applications for full one-dimensional time are limited to exotic deterministic simulations having strict invertibility properties, and hypothetical models of state in an infinite past (hypothetical since all observational systems have a definite starting point beyond or before which they cannot measure). In general and for interactive observation, control and dynamical systems in the real world and in computing, the half-dimensional paradigm would be the valid one. This includes the vast majority of applications.

One reason to require navigability for consideration as a full dimension is that even in mathematical terms (linear algebra), it is not possible to span or touch any point in the past using only the current time value and remaining future as the basis vector. The past is unreachable, therefore in general, time cannot be considered as a full dimension.

• Interesting. Would it be possible to make sense of other fractional dimensions? What would 1/4-dimensional or 2/3-dimensional mean?
– Stef
Dec 22, 2023 at 11:43
• I"m not downvoting because I like the speculative nature of your answer, but 'half-dimensional' seems to me that you claim time is ordered fowards, but not backwards. If you treat time as a ray geometrically, rays still lie in a line, and therefore have all the properties of a line except that they are in someway bounded. If you take away half a dimension for a ray as opposed to a line because of the boundary, that would suggest that a segment is 0 dimensional like a point, and that points and line segments are in the same class.
– J D
Dec 22, 2023 at 15:58
• @JD Great comment, I have added some clarification about the effects of navigability and why that matters for time in particular. The boundedness affects navigability, one of the intrinsic properties of a valid dimension--time is inherently causal and therefore precludes backwards navigability. One could select a span of time that is bounded on both ends as a basis function, but of course its span would be limited to an infinitesimal space relative to the entire domain. Maybe I wouldn't call a bounded nondegenerate line segment zero-dimensional, but epsilon-dimensional. Dec 22, 2023 at 21:34
• @Stef I am not sure what that would look like, but let's try to construct a hypothetical scenario that could quantitatively satisfy such a metric--As J D pointed out, a line segment is far from being even half-dimensional (it would be some finite number divided by infinity), so what if we were to say for example that every even hour is navigable and odd hours are not? Then we would have 1/4 of a dimension, in some sense--in that half of the future is navigable, and none of the past is, leaving us with a variable that is 1/4-dimensional. There might be other ways to do this. Dec 22, 2023 at 21:36
• @pygosceles Well, you've given me something to think about. I would have concerns that time itself is literally not navigable, which rather is a conceptual metaphor we might use to make the notion meaningful based on literal navigation through space. We can think about the models of time and causality as moving back and forth along a continuum, but in a very physical ontology, the notion that time can be moved through might create some metaphysical problems.
– J D
Dec 22, 2023 at 21:51