Search FQXi


Steve Dufourny: "E=m(c²+Xl²)+Y=2 mc² the gravitation originates from the energies..." in The Noise of Gravitons

Cabal Owen: "I have learned this while my research - What are the types of BCI’s ..." in Expanding the Mind...

Georgina Woodward: "Compare: "Wild', existentially free particle, unmeasured, unperturbed, in..." in Quantum Physics and the...

Georgina Woodward: "1. The 'magic rabbit' does not come into being, upon the photo being seen...." in Quantum Physics and the...

Deserdi Chapas: "Report on ongoing Holographic Physics work at As humanity has..." in Alternative Models of...

umair zaheer: "Travel is the movement of people between distant geographical locations...." in Anatomy of spacetime and...

robin 435: "rsvsfascxseaczcfadv" in Anatomy of spacetime and...

David Vognar: "Electron Doping? by David Vognar I think it helps to visualize physics so..." in The Present State of...

click titles to read articles

The Entropic Price of Building the Perfect Clock: Q&A with Natalia Ares
Experiments investigating the thermodynamics of clocks can teach us about the origin of time's arrow.

Schrödinger’s A.I. Could Test the Foundations of Reality
Physicists lay out blueprints for running a 'Wigner's Friend' experiment using an artificial intelligence, built on a quantum computer, as an 'observer.'

Expanding the Mind (Literally): Q&A with Karim Jerbi and Jordan O'Byrne
Using a brain-computer interface to create a consciousness 'add-on' to help test Integrated Information Theory.

Quanthoven's Fifth
A quantum computer composes chart-topping music, programmed by physicists striving to understand consciousness.

The Math of Consciousness: Q&A with Kobi Kremnitzer
A meditating mathematician is developing a theory of conscious experience to help understand the boundary between the quantum and classical world.

December 9, 2022

The Times They Are A-Changin’
Investigating whether time has more than one dimension.
by Grace Stemp-Morlock
September 7, 2010
Bookmark and Share

University of Waterloo
A one-dimensional view is often dismissed as simplistic and narrow-minded. That’s certainly the outlook of some physicists, who are taking this philosophy to a whole new level—by applying it to time. They argue, against conventional wisdom, that time is multi-dimensional. If they are correct, then it could help to unify general relativity and quantum mechanics.

Today, we’re almost complacent about the possibility that there may be extra dimensions of space. String theory, for example, proposes that there may be ten or more spatial dimensions, most of which are curled up so that we do not experience them everyday. The notion that time could have more than one-dimension, however, is far more jarring and physicists have been reluctant to suggest that time could move sideways as well as forwards. But the times, they are a-changin’.

"Three dimensions doesn’t seem to be an essential property of space, it seems like a contingent property and could be otherwise," says FQXi member Steven Weinstein, at the University of Waterloo, Ontario. An assistant professor of both philosophy and physics, Weinstein is open to the possibility that time could have two or more dimensions.

Part of the thinking behind this comes from attempts to unify general relativity, which governs the behavior of large-scale objects in the cosmos, and quantum mechanics, which describes particles in the subatomic world. Both theories are extremely successful in their own domains, but have so far defied attempts to be brought together under one overarching theory. A universe with three dimensions of space and one of time, it seems, is not big enough for the both of them. String theory’s extra spatial dimensions help create a bit more room, but recently some physicists have been proposing that an extra dimension of time might also be needed.

Where to Begin?

To check what a multi-time-dimensional universe would look like and if it could be compatible with the world we see around us, Weinstein and his colleagues tried to model a simple physical theory in two dimensions of time. They wanted to investigate how a standard equation describing an electromagnetic wave would be modified in a two-time-dimensional universe, but they were not sure where to begin—quite literally. Weinstein realized that he did not know how to mark off an initial time in his model: When there are multiple values for time, what is time T=0?

Weinstein’s team addressed this by attempting to see how the wave evolved as both timelines changed at once. The trouble was this made the model too wide, with too many possibilities for how the wave would grow and change. The same initial conditions could give very different final answers. By contrast, in our world we can make predictions for how the universe evolves based on initial conditions, so it seemed that a model of two-dimensional time constructed in this particular way could not be right.

Three dimensions doesn’t seem
to be an essential property
of space, so why should time
only have one dimension?
"It’s very, very hard to make a deterministic theory, where you start with data and it determines what the future will be in a reasonable way," says Walter Craig, a mathematician at McMaster University in Hailton, Ontario, Canada, who helped Weinstein make sense of his multi-time model.

Weinstein and Craig realized that a model in which the second time dimension was handled in a different way might work. Initially, they set it to zero and evolved their wave in the other dimensions of time and space. Then—to account for the extra time dimension—they stepped the initial time forward in the extra time dimension and found the data produced by the model was perfectly well-behaved. (See Weinstein’s award-winning essay in FQXi’s Nature of Time contest for more details.)

This is good news for physicists trying to build multi-dimensional time models. One such physicist is Itzhak Bars at the University of Southern California in Los Angeles. For more than a decade, he has independently been developing a "two-time-physics" formulation, which includes a second time dimension and a fourth spatial dimension, and which grew out of his work in string theory and its extension M-theory. He believes that this extra wiggle room might help fix certain mathematical anomalies in our current understanding of particle physics.

Credit: Nikada
Any physicist dabbling with multiple time dimensions has to be cautious that they do not run into paradoxes, however. One problem that Bars has had to contend with is time travel. With a whole extra dimension of time kicking around, there would seem, at least naively, to be far more freedom for particles to navigate their way sideways and then backwards in time. In his own formulation, time travel is restricted; subatomic particles and the laws of physics may be influenced by these extra-dimensions, but we are constrained to move in a "shadow" world of three spatial dimensions and one time dimension, just as shadows are restricted to a two-dimensional wall of a three-dimensional room.

Another implication of playing with multiple time dimensions is that it dramatically changes our understanding of what it means to be an observer. "That’s a question we don’t often bother to analyze when we’re doing physics," says Weinstein. "I’m localized I can go here, or here, or here, and I can’t be in two places at the same time and you take all that for granted. But how do you represent experience in multiple times?"

But Bars argues that the biggest issue that Weinstein will have to look into is that his formulation is not open to "ghosts," that is, that it does not allow unphysical negative probabilities. "This is the main issue that stopped other physicists," he says.

Nonetheless, Weinstein hopes that more physicists will investigate multiple dimensions in time because the rewards in terms of unifying physics would be huge. But even if, in the end, Weinstein finds that time is simply one-dimensional, that will raise new questions. "That would be interesting too because in that way it would be essentially different from space," he says. And the philosopher in him can occupy himself with trying to work out why.

Comment on this Article

Please read the important Introduction that governs your participation in this community. Inappropriate language will not be tolerated and posts containing such language will be deleted. Otherwise, this is a free speech Forum and all are welcome!
  • Please enter the text of your post, then click the "Submit New Post" button below. You may also optionally add file attachments below before submitting your edits.

  • HTML tags are not permitted in posts, and will automatically be stripped out. Links to other web sites are permitted. For instructions on how to add links, please read the link help page.

  • You may use superscript (10100) and subscript (A2) using [sup]...[/sup] and [sub]...[/sub] tags.

  • You may use bold (important) and italics (emphasize) using [b]...[/b] and [i]...[/i] tags.

  • You may also include LateX equations into your post.

Insert LaTeX Equation [hide]

LaTeX equations may be displayed in FQXi Forum posts by including them within [equation]...[/equation] tags. You may type your equation directly into your post, or use the LaTeX Equation Preview feature below to see how your equation will render (this is recommended).

For more help on LaTeX, please see the LaTeX Project Home Page.

LaTeX Equation Preview

preview equation
clear equation
insert equation into post at cursor

Your name: (optional)

Recent Comments

Every book spends space to time

And now is where you look.

The eye supplies your history

And that is where you must be.

This interchange of time and space

May seem a strange interlace

But Einstein's thoughts nicely comply

With this arrangement's how and why.

Me, transcribed within some book,

Needs someone else to look

So I must wonder who, what is reading,

A question where curiosity

Becomes most exceeding.

I knew time had two dimensions fifty years ago when I was 12. I drew a diagram to explain it to my mother but she had no idea what I was talking about ;)

read all article comments

Please enter your e-mail address:
Note: Joining the FQXi mailing list does not give you a login account or constitute membership in the organization.