Faster Than Light

Good science needs heretics—people who aren’t afraid of seemingly mad ideas that may end up leading us to new truths. Once in awhile, their crazy proposals make the transition from taboo to—if not quite the mainstream—the respectable fringes of physics, with a host of associated offshoots by independent researchers. This is what has happened to cosmologist João Magueijo’s speculation, just over a decade ago, that the speed of light isn’t the physical constant we take it to be.

The constancy of the speed of light in a vacuum—pinpointed to 299,792,458 meters per second by hundreds of experiments—is a basic tenet of modern physics. In his theory of relativity, Einstein used light’s invariance as a yardstick to define how space and time expand or shrink according to the relative motions of an object and its observer. The speed of light sets the universe’s speed limit for how fast energy, matter, and information can travel; of all the supposed physical constants that are under scrutiny, the speed of light seems least likely to crumble. Yet today, research on the idea that the speed of light may vary is so prolific Magueijo admits he can’t keep up with it. It’s even receiving a new boost from two candidate models of fundamental physics: string theory and loop quantum gravity. So what is behind this surge in popularity?

Magueijo, at Imperial College London, UK, and his colleague, cosmologist Andreas Albrecht, a member of FQXi now at UC Davis, first came up with their varying speed of light (VSL) model in early 1997. The idea resolves two of the biggest problems with Big Bang cosmology: explaining the smoothness of the universe’s background radiation that we see today, called the horizon problem, and explaining the dynamics of expansion and the shape of the universe, which relates to its density, known as the flatness problem.

Expanding Horizons

To understand the horizon problem, imagine looking out at the background radiation that permeates the universe, a relic of the Big Bang explosion, due north and due south. The furthest you can see in each direction is the horizon, which is at a distance determined by the speed that light can travel from this point to you over the entire lifetime of the universe—about 15 billion light years. From the position at the north, the radiation at the south comes from a point that is twice this distance: double the age of the universe. Yet the temperature of the background radiation is incredibly uniform, with deviations of only one part in ten thousand. How can these completely disconnected parts of the universe be essentially identical in temperature? To answer this question, Magueijo and Albrecht argued that the speed limit for light in the early universe was raised, opening up the horizons and allowing everything to communicate much faster and have the same temperature. "The idea is so simple I can’t believe no one proposed it before," says Magueijo. "Well in fact the idea had been around, but what matters is what you do with it."

The flatness problem arises because of how the expansion of the universe is precisely balanced by the gravitational attraction of its matter, which is just sufficient to halt the expansion—preventing an open universe that accelerates into sterile emptiness—but not sufficient to curve it into a closed universe that ends in a cosmic crunch. This balancing act requires an unacceptably precise critical density within a fraction of a second of the Big Bang, hence the problem. This issue is resolved in the VSL model because the early universe is actually pushed back towards the critical density if it veers off into either scenario. This is because the curvature of spacetime is proportional to the energy density, but—unlike in the standard cosmological model—with a varying speed of light, energy is not conserved, allowing mass to be created or destroyed as the curvature veers towards an open or closed universe respectively.

Despite its success at explaining both the horizon and flatness problems, the VSL model initially appeared a bit too radical for many physicists. In part, that was because both these problems could be solved by a less controversial theory that did not throw out the sacred constancy of light’s speed: Inflation. Developed by FQXi member and cosmologist Alan Guth at MIT, in the late 1970s, inflation is the idea that the universe rapidly expanded for a brief period soon after the Big Bang. Now accepted as the textbook explanation for early universe cosmology, it addressed the horizon problem because, prior to inflation, far flung reaches of the universe would have been in contact, evening out their temperature. The process of inflation also naturally leads to the finely-balanced curvature of the cosmos that is observed, without requiring a precisely-tuned critical density soon after the Big Bang.

Magueijo acknowledges the success of the inflationary paradigm, but adds that until VSL theory came along, there were no serious alternatives to inflation. "I think it’s very bad in science when you only have one theory and no competitors to measure it against," he says. Magueijo also notes that VSL theory had another immediate advantage over inflation: While solving the flatness problem, Magueijo and Albrecht were surprised and excited to find that because VSL theory allowed matter to be created and destroyed as the universe’s curvature changed, they had stumbled on an explanation for where all the matter of the universe had come from.

VSL theory was eventually published in 1999, the culmination of a two-year battle with the editor, risking scientific isolation and loss of job. Then on the cusp of publication there was disappointment: John Moffat, a physicist now at the Perimeter Institute (PI) in Waterloo, Ontario, contacted them to claim prior discovery, notifying them that his work on VSL had been published in a minor journal and had gone unnoticed since 1992. Interestingly, he had faced the same fight for publication with the same major journal, and conceded.

Magueijo has documented the struggle to get VSL accepted for publication in gory detail in his book Faster Than the Speed of Light. The reaction to the book, particularly with various institutions, was "a huge mess" he says. He is candid about the aftermath: "My book created a lot of problems. I don’t like bureaucracy and I portray the process of administrators taking over scientific institutions. The whole refereeing process is awful…the problem is with the institutions."

It took tenacity and guts to stick by the theory during the fraught period before its first publication. Magueijo traces his boldness to his upbringing in Portugal, among a population recovering from the restrictions of fascism. "You could be tortured, it was a horrible situation and people actually fought against it and paid a big price," he says. He grew up on these stories of resilience: fascism fell when he was 7 years old. He was particularly inspired by his tutor of musical composition, Lopes Graca, who had spoken out against the regime and was jailed and his music banned as a result. "Lopes Graca was a good role model for me because of his attitude and bravery. The threat we face for standing by our ideas is a lot softer now, yet we are so easily cowed by the establishment," says Magueijo.

Cosmic Challenger

FQXi member Lee Smolin, a physicist at PI, recalls the skepticism surrounding the publication of the theory and the reasons behind it: "It challenged accepted ideas about fundamental physics and accepted ideas about cosmology that many cosmologists believe in," says Smolin. However, he emphasizes that his friend Magueijo, is "no crank"; rather he is "extremely insightful, deeply imaginative, ambitious, and provocative, both intellectually and as a person."

The next few years were telling for VSL theory. Magueijo and Albrecht had found interesting results, but not enough to inspire a large following. But then, in 2007, the team had another exciting breakthrough: explaining structure in the universe. This marked VSL’s graduation into a true alternative to inflation. "That’s the proof of the pudding in any theory—if you produce the structure," says Magueijo. Suddenly there was an explosion of people working on VSL.

A successful cosmological model can’t just produce any old structure, it has to produce structure that matches what we observe. When we look at the universe, we can see that the clumps of matter—on whatever scale you look—gather into the same honeycomb pattern. "Scale by scale by scale, the structure is invariant," says Magueijo. He found that VSL predicts this scale invariance if you use what is called a bimetric approach: a theory of two frames or metrics, one for gravity and one for matter. In this approach, the speed of light is proportional to the density of the universe. The key is in considering the timing at which quantum fluctuations in the early universe—which could be the seeds for galaxies—leave the horizon. With the speed of light shrinking, the horizon shrinks and different scales leave the horizon. "This is the whole game, it’s like cookery, and it’s about the dynamics and timing of these fluctuations leaving the horizon," says Magueijo.

Strings, Loops, and Potholes

Beyond these successes with structure formation, in recent years, independent researchers from string theory—which posits that elementary particles are comprised from tiny, vibrating loops of energy—have also added a new dimension to the VSL program. Magueijo has been encouraged to find that VSL cosmology can be independently realized using string theory, if you consider not just strings—linear, one-dimensional objects—but also membranes—planar, two-dimensional objects. Welcome to M-theory. When modeling a discretized geometry of spacetime in M-Theory, FQXi member Stephon Alexander, now at Haverford College, Pennsylvania, found that for very high frequencies light photons have to "leapfrog over the potholes" in spacetime, which increases their speed, says Magueijo. In effect, the speed of light becomes color-dependent, increasing the most for the highest frequencies. The further you go back in time towards the Big Bang, the hotter the cosmic plasma, and the higher the speed of light in the early universe.

Another attraction of VSL is that it can act as a bridge between quantum gravity theories and observations. Quantum gravity theories aim to unite relativity and quantum gravity, to achieve a theory of everything. One of the most developed approaches is Loop Quantum Gravity, which rules out special relativity as proposed by Einstein. Special relativity is based on two pillars: the notion that there are no special places—or reference frames—in the universe, and the constancy of the speed of light in a vacuum. Loop Quantum Gravity proposes either that the first pillar of special relativity is wrong, and there is a preferred reference frame—a radical suggestion—or that you can preserve the universality of quantum spacetime, and instead, embrace VSL and sacrifice the second pillar, making light’s speed energy-dependent. "This isn’t such a big deal," says Magueijo.

Saying that the speed of light depends on energy is equivalent to saying that the spacetime geometry depends on energy: constructing the universe in radio or X-rays produces different spacetime geometries, says Smolin. This work, which goes by the name of deformed special relativity, underlies his recently published ideas on relative locality in collaboration with Giovanni Amelino-Camelia, at Sapienza University of Rome, Italy, Laurent Freidel, also at PI, and Jerzy Kowalski-Glikman, at the University of Wrocław, Poland; Amelino-Camelia was partially supported by FQXi funding. "In relative locality you give up the idea that there’s a universal notion of spacetime," Smolin says. The theory can be constrained by experiments to measure the possible energy dependence of the speed of light at very high energies, for example, from gamma ray bursts, which could observe a speed-dependence in the arrival times of photons. "The fact we haven’t seen it yet puts constraints on what you can do in quantum gravity," says Magueijo.

Signs of Speediness

Magueijo hopes that observational evidence will one day distinguish between the competing cosmological models of VSL and inflation. In his opinion, VSL goes one better than inflation, because small variations in the speed of light could be observed nowadays, making it testable: "Mainstream cosmology these days is inflation, but there’s no proof of it. It could be completely wrong. What I like so much about VSL was that it could be tested here and now." For instance, if primordial gravity waves—ripples in spacetime set off in the early universe—are detected, that would rule out VSL completely. That’s because the speed of such ripples in VSL is smaller than the speed of photons, so primordial gravity waves remain within the horizon, hence we can’t see them.

Finding positive evidence for VSL is not quite as easy. Astronomers have been hunting for variations in the fine-structure constant, a measure of the strength of the electromagnetic interaction, which depends on the speed of light. (See also, "Testing Times for Nature’s Constants.") There have been tantalizing suggestions from quasar absorption spectra, which depend on the value of the fine-structure constant, that the speed of light varies. Those studies looked at quasars at increasingly large distances—and hence further back in time—to see if the fine-structure constant changed in value and seemed to find a slight change. However, astronomers now think that the initial results point to a possible spatial variation in the speed of light, rather than a variation in time (arXiv:1202.4758v1). According to Michael Murphy of the Swinburne University of Technology in Australia, who has been involved in making such quasar observations, the statistical significance of a spatial variation is not yet sufficient to pass judgment on a variation in the physical constants.

Magueijo emphasizes that all cosmological models are "speculative" to varying degrees, even though the hallowed inflationary theory has now become mainstream. Moffat argues that inflation’s popularity over VSL "is a sociological problem" and it is crucial to get more data to help choose between the rival models. Most likely, evidence to differentiate VSL from inflation could come from the shape of the distribution of patterns in the cosmic background radiation data collected by the Planck satellite, Moffat adds.

That’s something that Magueijo is currently looking into, though he admits that it will not be easy to rule out inflation because there are so many different versions of it that can produce any fluctuation you can think of. "In a way it’s the victim of its own success; it has become a theory of anything," says Magueijo.

"These are very hard experiments to do on the edge of knowledge," agrees Smolin. He continues to welcome VSL: Theory is concentrated on too few ideas these days, he says. "Magueijo has been very challenging to us—in terms of having ideas that challenge our confidence that we know the right direction for fundamental physics. This is a good thing."