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How Time Flies: Tracking the Arrow of Time

We all intuitively perceive that time flows in only one direction – from past to future – and Templeton Frontiers Fellow Flavio Mercati is developing an innovative point of view on this so-called arrow of time.

Time marches on.

We’re not entirely sure, mind you, why time strides steadily forward without making an about-face and backtracking from whence it came. No matter where you are in the universe, though, clocks go “tick tock” instead of “tock tick.”

Physicists call it the arrow of time, and much theorizing has gone into why it’s not a boomerang.

A prevailing explanation is called the “past hypothesis,” which presumes that the universe began with a very special low-entropy state – that is, a tidy scenario in which the baby universe was nicely ordered before getting progressively messier.

According to the past hypothesis, the arrow of time can be ascribed to a trend in the universe toward increased messiness, according to the second law of thermodynamics.

But our universe doesn’t seem to get messier as it evolves; quite the contrary, observations suggest it evolved from a very messy state in the past (a “plasma soup” close to thermal equilibrium) into the beautifully ordered structures seen today (galaxies, solar systems, people).

A popular way to reconcile the cherished second law of thermodynamics with the observations is to assume that, while the matter in the universe seems to get more ordered, the gravitational field itself increases in entropy, compensating the entropy of matter so that the overall entropy ends up increasing. However, attempts at defining a notion of entropy for the gravitational field have been so far unsuccessful.

Moreover, the past hypothesis makes too many unreasonable assumptions about the early universe, says Flavio Mercati.

“The only explanations so far are that we are the result of a colossal statistical fluke or an implausibly special initial condition of the universe,” he says.

“These are not satisfactory explanations.”

A more satisfactory explanation, he and a pair of colleagues suggest, isn’t about entropy at all, but rather about complexity.

“The universe is a structure whose complexity is growing,” says Mercati. “The universe is made up of big galaxies separated by vast voids. In the distant past, they were more clumped together. Our conjecture is that our perception of time is the result of a law that determines an irreversible growth of complexity.”

That is, Mercati and collaborators Julian Barbour and Tim Koslowski linked the arrow of time to the universe’s “clumpiness” (a term they employed in their recent paper on the subject, “A Gravitational Origin of the Arrows of Time”).

It turns out that growth of complexity is accompanied by growth of local information – an observation that connects the problem of time with the topic of information theory.

This realization is at the basis of a research project that secured Mercati and Koslowski (a former Perimeter postdoctoral researcher) a grant from the Foundational Questions Institute (FQXi) worth $140,000 over two years, giving them the ability to dive deeply into the topic.

“We realized that there is a possible explanation for the arrow of time that doesn’t need special conditions for the origin of the universe,” explains Mercati. “The answer is just sitting there in gravity itself.”

Since there can be no complex things like galaxies or planets without a high level of complexity – and since we know the early universe was a very uncomplex plasma soup – the researchers deduced that our perception of the past is linked to states of low-complexity in the universe.

The model Mercati and collaborators studied exhibits an irreversible growth of complexity in all its solutions, which implies that the flow of time streams necessarily from past to future.

Of course, their work is based on simplified models of the universe – the so-called n-body problem – which is a good approximation, but doesn’t quite reflect the universe in all its variety.   

“We studied an excellent toy model,” says Mercati. “But the universe is more than an n-body problem. The universe has a lot of stuff – matter, radiation. It’s complex.”

Still, Mercati explains, their toy model captures some key features of gravity which are likely to remain in more elaborate models and to give rise to an analogue arrow of time.

“What we have is – so far as we know – a totally new way to explain the arrow of time, which works very well in the n-body problem and opens a novel approach to the problem for the universe as a whole.”



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