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Those laws are exquisitely accurate. Einstein mastered gravity with his theory of general relativity, and the equations of quantum theory capture every nuance of matter and other forces, from the attractive power of magnets to the subatomic glue that holds an atom’s nucleus together.


But the laws can’t be complete. Einstein’s theory of gravity and quantum theory don’t fit together. Some piece is missing in the picture puzzle of physical reality.

Bars thinks one of the missing pieces is a hidden dimension of time.

Bizarre is not a powerful enough word to describe this idea, but it is a powerful idea nevertheless. With two times, Bars believes, many of the mysteries of today’s laws of physics may disappear.

Of course, it’s not as simple as that. An extra dimension of time is not enough. You also need an additional dimension of space.

It sounds like a new episode of “The Twilight Zone,” but it’s a familiar idea to most physicists. In fact, extra dimensions of space have become a popular way of making gravity and quantum theory more compatible.

Extra space dimensions aren’t easy to imagine — in everyday life, nobody ever notices more than three. Any move you make can be described as the sum of movements in three directions — up-down, back and forth, or sideways. Similarly, any location can be described by three numbers (on Earth, latitude, longitude and altitude), corresponding to space’s three dimensions.

Other dimensions could exist, however, if they were curled up in little balls, too tiny to notice. If you moved through one of those dimensions, you’d get back to where you started so fast you’d never realize that you had moved.

“An extra dimension of space could really be there, it’s just so small that we don’t see it,” said Bars, a professor of physics and astronomy.

Something as tiny as a subatomic particle, though, might detect the presence of extra dimensions. In fact, Bars said, certain properties of matter’s basic particles, such as electric charge, may have something to do with how those particles interact with tiny invisible dimensions of space.

In this view, the Big Bang that started the baby universe growing 14 billion years ago blew up only three of space’s dimensions, leaving the rest tiny. Many theorists today believe that 6 or 7 such unseen dimensions await discovery.

Only a few, though, believe that more than one dimension of time exists. Bars pioneered efforts to discern how a second dimension of time could help physicists better explain nature.

“Itzhak Bars has a long history of finding new mathematical symmetries that might be useful in physics,” said Joe Polchinski, a physicist at the Kavli Institute for Theoretical Physics at UC Santa Barbara. “This two-time idea seems to have some interesting mathematical properties.”

If Bars is on the right track, some of the most basic processes in physics will need re-examination. Something as simple as how particles move, for example, could be viewed in a new way. In classical physics (before the days of quantum theory), a moving particle was completely described by its momentum (its mass times its velocity) and its position. But quantum physics says you can never know those two properties precisely at the same time.

Bars alters the laws describing motion even more, postulating that position and momentum are not distinguishable at a given instant of time. Technically, they can be related by a mathematical symmetry, meaning that swapping position for momentum leaves the underlying physics unchanged (just as a mirror switching left and right doesn’t change the appearance of a symmetrical face).

In ordinary physics, position and momentum differ because the equation for momentum involves velocity. Since velocity is distance divided by time, it requires the notion of a time dimension. If swapping the equations for position and momentum really doesn’t change anything, then position needs a time dimension too.

“If I make position and momentum indistinguishable from one another, then something is changing about the notion of time,” said Bars. “If I demand a symmetry like that, I must have an extra time dimension.”

The bananas may be small, but will, as a rule, be almost as sweetly flavoured as those allowed to develop on the plant. Yet the superfine aesthetic essence is not for the delight of those to whom the fruit is tendered after it has undergone a sea voyage. Let there be no misunderstanding with respect to the desirableness of the coastal tract of North Queensland as a territory capable of supporting a large, prosperous and healthful population. It is no part of the present purpose to extol the mineral or the pastoral districts. They lie apart. But in North Queensland agriculture is almost solely confined to the coast and is essentially tropical. The tropics represent that portion of the earth’s surface wherein man may live with the minimum of exertion, where actual wants are few, and wherein ample comforts may be enjoyed by those who seek them with a quiet mind and easy understanding. Although the question may be perhaps beyond proof, it might be safely asserted that a larger proportion of men of the yeomen class, represented by those who have succeeded in tropical agriculture in North Queensland, are independent to-day, than of the men in Victoria and New South Wales, who devoted their energies to sheep-farming, wheat-growing and dairying. Out of the comparatively few sugar-cane farmers in North Queensland, a considerable percentage have acquired independence, and many wealth. Few have failed. Fortunes have been made and are being made out of sugar lands; immense profits have been earned and are being earned in the production of bananas, and from other easily grown tropical fruits, good incomes are realised. When private enterprise invests many thousands of pounds in the building of jetties and tram-lines to facilitate the shipment of fruit, evidence in support of these statements is unnecessary. The prosperity of the farmer and fruit-grower in North Queensland does not unhaply depend upon himself, but upon the existence of large populations within reasonable range.