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FQXI ARTICLE

December 14, 2017

The Times They Are A-Changin’

Investigating whether time has more than one dimension.

September 7, 2010

STEVEN WEINSTEIN

University of Waterloo

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

Three dimensions doesn’t seem

to be an essential property

of space, so why should time

only have one dimension?

to be an essential property

of space, so why should time

only have one dimension?

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.

DOUBLING-UP TIME’S DIMENSIONS

Credit: Nikada

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.

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GEORGINA WOODWARD wrote on May 16, 2017

The temporal non-homogeneity of the content of the product of information processing would only be obvious if there are very large distances such as astronomical distances included in the observation, if the information is EM frequency and intensity; Due to the very high speed of light. It would be shown more clearly for "Earth-bound" distances if the information was frequency and intensity carried by sound waves or olfactory information carried on air currents.

The temporal non-homogeneity of the content of the product of information processing would only be obvious if there are very large distances such as astronomical distances included in the observation, if the information is EM frequency and intensity; Due to the very high speed of light. It would be shown more clearly for "Earth-bound" distances if the information was frequency and intensity carried by sound waves or olfactory information carried on air currents.

GEORGINA WOODWARD wrote on May 16, 2017

Hi MJGeddes, I think i may be thinking about this in a different way to what you are imagining. What do*you* mean by movement through 2 dimensions of time? I'm not sure how you are drawing the slope. If I have it related to distance and hence info transmission time it gets less steep because of the way the values are set along the x.

What if the y was replicated so there is a new one for each x value, corresponding roughly to the time it takes to updating the info. processing...

Hi MJGeddes, I think i may be thinking about this in a different way to what you are imagining. What do

What if the y was replicated so there is a new one for each x value, corresponding roughly to the time it takes to updating the info. processing...

GEORGINA WOODWARD wrote on May 16, 2017

Hi MJGeddes, by "physical" do you meant what exists materially or something else? By computational time do you mean what a person or device computes giving an experienced present or product, or do you mean something else?

You could define *time flow* as the slope of the line but is that name helpful? Is it really*time* flow. If you are talking about existence and product of information processing, the slope relates to information transfer time (varying with distance) and processing...

Hi MJGeddes, by "physical" do you meant what exists materially or something else? By computational time do you mean what a person or device computes giving an experienced present or product, or do you mean something else?

You could define *time flow* as the slope of the line but is that name helpful? Is it really

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