A theory of reality beyond Einstein's universe is taking shape – and a mysterious cosmic signal could soon fill in the blanks
IT WASN'T so long ago we thought space and time were the absolute and unchanging scaffolding of the universe. Then along came Albert Einstein, who showed that different observers can disagree about the length of objects and the timing of events. His theory of relativity unified space and time into a single entity - space-time. It meant the way we thought about the fabric of reality would never be the same again. "Henceforth space by itself, and time by itself, are doomed to fade into mere shadows," declared mathematician Hermann Minkowski. "Only a kind of union of the two will preserve an independent reality."
But did Einstein's revolution go far enough? Physicist Lee Smolin at the Perimeter Institute for Theoretical Physics in Waterloo, Ontario, Canada, doesn't think so. He and a trio of colleagues are aiming to take relativity to a whole new level, and they have space-time in their sights. They say we need to forget about the home Einstein invented for us: we live instead in a place called phase space.
If this radical claim is true, it could solve a troubling paradox about black holes that has stumped physicists for decades. What's more, it could set them on the path towards their heart's desire: a "theory of everything" that will finally unite general relativity and quantum mechanics.
So what is phase space? It is a curious eight-dimensional world that merges our familiar four dimensions of space and time and a four-dimensional world called momentum space.
Momentum space isn't as alien as it first sounds. When you look at the world around you, says Smolin, you don't ever observe space or time - instead you see energy and momentum. When you look at your watch, for example, photons bounce off a surface and land on your retina. By detecting the energy and momentum of the photons, your brain reconstructs events in space and time.
The same is true of physics experiments. Inside particle smashers, physicists measure the energy and momentum of particles as they speed toward one another and collide, and the energy and momentum of the debris that comes flying out. Likewise, telescopes measure the energy and momentum of photons streaming in from the far reaches of the universe. "If you go by what we observe, we don't live in space-time," Smolin says. "We live in momentum space."
And just as space-time can be pictured as a coordinate system with time on one axis and space - its three dimensions condensed to one - on the other axis, the same is true of momentum space. In this case energy is on one axis and momentum - which, like space, has three components - is on the other (see diagram).
Simple mathematical transformations exist to translate measurements in this momentum space into measurements in space-time, and the common wisdom is that momentum space is a mere mathematical tool. After all, Einstein showed that space-time is reality's true arena, in which the dramas of the cosmos are played out.
Smolin and his colleagues aren't the first to wonder whether that is the full story. As far back as 1938, the German physicist Max Born noticed that several pivotal equations in quantum mechanics remain the same whether expressed in space-time coordinates or in momentum space coordinates. He wondered whether it might be possible to use this connection to unite the seemingly incompatible theories of general relativity, which deals with space-time, and quantum mechanics, whose particles have momentum and energy. Maybe it could provide the key to the long-sought theory of quantum gravity.
Born's idea that space-time and momentum space should be interchangeable - a theory now known as "Born reciprocity" - had a remarkable consequence: if space-time can be curved by the masses of stars and galaxies, as Einstein's theory showed, then it should be possible to curve momentum space too.
At the time it was not clear what kind of physical entity might curve momentum space, and the mathematics necessary to make such an idea work hadn't even been invented. So Born never fulfilled his dream of putting space-time and momentum space on an equal footing.
That is where Smolin and his colleagues enter the story. Together with Laurent Freidel, also at the Perimeter Institute, Jerzy Kowalski-Glikman at the University of Wroclaw, Poland, and Giovanni Amelino-Camelia at Sapienza University of Rome in Italy, Smolin has been investigating the effects of a curvature of momentum space.
The quartet took the standard mathematical rules for translating between momentum space and space-time and applied them to a curved momentum space. What they discovered is shocking: observers living in a curved momentum space will no longer agree on measurements made in a unified space-time. That goes entirely against the grain of Einstein's relativity. He had shown that while space and time were relative, space-time was the same for everyone. For observers in a curved momentum space, however, even space-time is relative (see diagram).
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Sateesh.smart
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