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FQXI ARTICLE
October 23, 2014

Breaking the Universe’s Speed Limit
If we give up the idea that time exists and the speed of light is constant at the fundamental level, then we could find a theory of quantum gravity.
by Graeme Stemp-Morlock
FQXi Awardees: John Donoghue
April 21, 2011
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JOHN DONOGHUE
University of Massachusetts, Amherst
Imagine holding a Rubik’s cube in your hand. It’s square and has different colors. Maybe if you have been struggling with it for a while it is warm or a little slippery from your beads of frustrated sweat. The physics of this cube is simple: It has got a definite mass and it can’t travel faster than the speed of light. And no matter which way you turn the cube or where you take it, those laws remain the same.

But what happens if you zoom in on the Rubik’s cube until you can see the very atoms that make it up? Suddenly the laws of physics have changed completely. What we saw on the macroscale is not the same on this microscale.

Merging the vastly different laws that govern the macro and the micro has been a huge challenge for physics. Now, John Donoghue, a physicist at the University of Massachusetts, Amherst, thinks he may have the answer. Perhaps, he argues, the familiar view of spacetime as a four-dimensional fabric, which we inherited from Einstein, is not fundamental, but only emerges on large scales—just like our picture of a solid and symmetrical Rubik’s cube disappears and re-appears depending on the perspective that we look at it. If he is correct, physicists may have to rethink one of their more cherished beliefs: that the speed of light has always been constant.

This idea would change
99.9% of physics research.
- John Donoghue
Donoghue is aware that his idea of a varying universal speed limit—famously set by Einstein over a century ago—goes against the physics’ grain. "This is a very nonstandard idea," he admits. "It would really change 99.9 per cent of physics research."

However, there’s good reason to think that our understanding of spacetime and, in turn, the speed of light, may need to be rewritten. The two cornerstones of modern physics, Einstein’s general relativity, which explains the behavior of stars and planets on the largest scales, and quantum mechanics, which governs the interactions of subatomic particles, each paint a different picture of the role of space and time. General relativity weaves space and time together into a four-dimensional fabric that can be warped by matter, while the equations of quantum mechanics use an immutable absolute clock to measure out the regular ticks as time passes. This difference has led some physicists to ponder whether spacetime changes character on different scales.

Emerging Spacetime

Physicists use the term emergence to describe how the world can look different, depending on how much you zoom on it, explains Donoghue. In everyday life, for example, we encounter sound waves and water waves as the large-scale result of atoms interacting with each other at microscopic scales; sound waves and water waves are not themselves fundamental. However, it has been difficult to formulate a model in which a four-dimensional spacetime emerges from a very different underlying microphysics. The trouble is that alternative theories that have been proposed to describe physics on small scales do not neatly morph back into general relativity when they are supposed to. In particular, they inadvertently unshackle light, so that it no longer obeys a speed limit at large scales—defying the historic observations that confirmed the predictions made by general relativity.


THE SPEED OF GRAVITY
Artist’s impression of the gravitational waves caused by two
orbiting black holes.

Credit: K. Thorne & T. Carnahan, Caltech/NASA
However, Donoghue and his colleague Mohamed Anbar, at the University of Toronto, Ontario, recently showed that the speed of light, itself, could vary at high energies—such as those in the early universe—with a single, constant speed of light emerging only later, as the universe’s energy lowered. In this model, elementary particles and fields of different natures would each "see" a universe with a different speed of light, which means that the laws that govern the behavior of each type of particle and field would be slightly different. But, as the particles and fields interact with each other, the limiting velocities of light would even out, eventually reaching the constant speed we see today.

Jan Ambjørn, a physicist at the Niels Bohr Institute in Copenhagen, Denmark, is a fan of Donoghue’s work. Asking whether the speed of light is emergent is, "a totally legal question," he says. We still have trouble understanding what is happening in the early universe, so "it might be that some new perspective is needed," he adds.

Eleanor Knox, an expert on emergent theories of spacetime, at King’s College London agrees that Donoghue’s ideas are "a good way forward." However, she notes that until he and his colleagues have a more specific driving theory, it will be difficult to know where to look for evidence of an emerging speed of light.

Making Waves

With a grant of almost $90,000 from FQXi, Donoghue hopes to address that issue, by refining his theory so that he can make specific predictions about where to look for experimental signs of an emerging speed limit. Unfortunately, most of the effects of differing speeds of light would only be noticeable at extremely high energies—far greater than even the famed Large Hadron Collider, the particle accelerator in Geneva, Switzerland, can test.

Asking whether the speed
of light is emergent
is a totally legal question.
- Jan Ambjørn
But, according to Donoghue’s model, there may be a chance that the speed of gravity is larger than the speed of light. (Usually the two speeds are thought to be identical.) The Laser Interferometric Gravitational-wave Observatory, and other experiments, are already searching for signs of gravitational waves—ripples in the spacetime fabric—and could detect this speed mismatch. (Read more about the search for gravitational waves in the article, "The Quantum PlayStation.")

Other FQXi researchers are studying how different theories about character of spacetime should affect some high-energy particles. Cosmic rays and bursts of high-energy radiation, known as gamma rays, travel huge distances across the universe, and over the course of their long journey the tiny effects of unusual spacetime structure might accumulate to an observable level. Donoghue has a student looking at this too. "I’d like to be able to report that we found something that showed evidence, but we haven’t," he says. But the team has set a limit on how big any effects due to emergence could be. "That’s also a bit of progress because we’ve made a connection that people hadn’t thought of before," Donoghue says.

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