by Corey S. Powell
It is the biggest of problems, it is the smallest of problems. At present physicists have two separate rulebooks explaining how nature works. There is general relativity, which beautifully accounts for gravity and all of the things it dominates: orbiting planets, colliding galaxies, the dynamics of the expanding universe as a whole. That’s big. Then there is quantum mechanics, which handles the other three forces – electromagnetism and the two nuclear forces. Quantum theory is extremely adept at describing what happens when a uranium atom decays, or when individual particles of light hit a solar cell. That’s small.
Now for the problem: relativity and quantum mechanics are fundamentally different theories that have different formulations. It is not just a matter of scientific terminology; it is a clash of genuinely incompatible descriptions of reality.
The conflict between the two halves of physics has been brewing for more than a century – sparked by a pair of 1905 papers by Einstein, one outlining relativity and the other introducing the quantum – but recently it has entered an intriguing, unpredictable new phase. Two notable physicists have staked out extreme positions in their camps, conducting experiments that could finally settle which approach is paramount.
Basically you can think of the division between the relativity and quantum systems as “smooth” versus “chunky”. In general relativity, events are continuous and deterministic, meaning that every cause matches up to a specific, local effect. In quantum mechanics, events produced by the interaction of subatomic particles happen in jumps (yes, quantum leaps), with probabilistic rather than definite outcomes. Quantum rules allow connections forbidden by classical physics. This was demonstrated in a much-discussed recent experiment in which Dutch researchers defied the local effect. They showed that two particles – in this case, electrons – could influence each other instantly, even though they were a mile apart. When you try to interpret smooth relativistic laws in a chunky quantum style, or vice versa, things go dreadfully wrong.
Relativity gives nonsensical answers when you try to scale it down to quantum size, eventually descending to infinite values in its description of gravity. Likewise, quantum mechanics runs into serious trouble when you blow it up to cosmic dimensions. Quantum fields carry a certain amount of energy, even in seemingly empty space, and the amount of energy gets bigger as the fields get bigger. According to Einstein, energy and mass are equivalent (that’s the message of E=mc2), so piling up energy is exactly like piling up mass. Go big enough, and the amount of energy in the quantum fields becomes so great that it creates a black hole that causes the universe to fold in on itself. Oops.
Craig Hogan, a theoretical astrophysicist at the University of Chicago and the director of the Center for Particle Astrophysics at Fermilab, is reinterpreting the quantum side with a novel theory in which the quantum units of space itself might be large enough to be studied directly. Meanwhile, Lee Smolin, a founding member of the Perimeter Institute for Theoretical Physics in Waterloo, Canada, is seeking to push physics forward by returning to Einstein’s philosophical roots and extending them in an exciting direction.
To understand what is at stake, look back at the precedents. When Einstein unveiled general relativity, he not only superseded Isaac Newton’s theory of gravity; he also unleashed a new way of looking at physics that led to the modern conception of the Big Bang and black holes, not to mention atomic bombs and the time adjustments essential to your phone’s GPS. Likewise, quantum mechanics did much more than reformulate James Clerk Maxwell’s textbook equations of electricity, magnetism and light. It provided the conceptual tools for the Large Hadron Collider, solar cells, all of modern microelectronics.
What emerges from the dust-up could be nothing less than a third revolution in modern physics, with staggering implications. It could tell us where the laws of nature came from, and whether the cosmos is built on uncertainty or whether it is fundamentally deterministic, with every event linked definitively to a cause.
Small is beautiful
Hogan, champion of the quantum view, is what you might call a lamp-post physicist: rather than groping about in the dark, he prefers to focus his efforts where the light is bright, because that’s where you are most likely to be able to see something interesting. That’s the guiding principle behind his current research. The clash between relativity and quantum mechanics happens when you try to analyse what gravity is doing over extremely short distances, he notes, so he has decided to get a really good look at what is happening right there. “I’m betting there’s an experiment we can do that might be able to see something about what’s going on, about that interface that we still don’t understand,” he says.
A basic assumption in Einstein’s physics – an assumption going all the way back to Aristotle, really – is that space is continuous and infinitely divisible, so that any distance could be chopped up into even smaller distances. But Hogan questions whether that is really true. Just as a pixel is the smallest unit of an image on your screen and a photon is the smallest unit of light, he argues, so there might be an unbreakable smallest unit of distance: a quantum of space.
In Hogan’s scenario, it would be meaningless to ask how gravity behaves at distances smaller than a single chunk of space. There would be no way for gravity to function at the smallest scales because no such scale would exist. Or put another way, general relativity would be forced to make peace with quantum physics, because the space in which physicists measure the effects of relativity would itself be divided into unbreakable quantum units. The theatre of reality in which gravity acts would take place on a quantum stage.
Hogan acknowledges that his concept sounds a bit odd, even to a lot of his colleagues on the quantum side of things. Since the late 1960s, a group of physicists and mathematicians have been developing a framework called string theory to help reconcile general relativity with quantum mechanics; over the years, it has evolved into the default mainstream theory, even as it has failed to deliver on much of its early promise. Like the chunky-space solution, string theory assumes a fundamental structure to space, but from there the two diverge. String theory posits that every object in the universe consists of vibrating strings of energy. Like chunky space, string theory averts gravitational catastrophe by introducing a finite, smallest scale to the universe, although the unit strings are drastically smaller even than the spatial structures Hogan is trying to find.
Chunky space does not neatly align with the ideas in string theory – or in any other proposed physics model, for that matter. “It’s a new idea. It’s not in the textbooks; it’s not a prediction of any standard theory,” Hogan says, sounding not the least bit concerned. “But there isn’t any standard theory, right?”
If he is right about the chunkiness of space, that would knock out a lot of the current formulations of string theory and inspire a fresh approach to reformulating general relativity in quantum terms. It would suggest new ways to understand the inherent nature of space and time. And weirdest of all, perhaps, it would bolster the notion that our seemingly three-dimensional reality is composed of more basic, two-dimensional units. Hogan takes the “pixel” metaphor seriously: just as a TV picture can create the impression of depth from a bunch of flat pixels, he suggests, so space itself might emerge from a collection of elements that act as if they inhabit only two dimensions.
Like many ideas from the far edge of today’s theoretical physics, Hogan’s speculations can sound suspiciously like late-night philosophising in the freshman dorm. What makes them drastically different is that he plans to put them to a hard experimental test. As in, right now.
Starting in 2007, Hogan began thinking about how to build a device that could measure the exceedingly fine graininess of space. As it turns out, his colleagues had plenty of ideas about how to do that, drawing on technology developed to search for gravitational waves. Within two years Hogan had put together a proposal and was working with collaborators at Fermilab, the University of Chicago and other institutions to build a chunk-detecting machine, which he more elegantly calls a “holometer”. (The name is an esoteric pun, referencing both a 17th-century surveying instrument and the theory that 2D space could appear three-dimensional, analogous to a hologram.)
Beneath its layers of conceptual complexity, the holometer is technologically little more than a laser beam, a half-reflective mirror to split the laser into two perpendicular beams, and two other mirrors to bounce those beams back along a pair of 40m-long tunnels. The beams are calibrated to register the precise locations of the mirrors. If space is chunky, the locations of the mirrors would constantly wander about (strictly speaking, space itself is doing the wandering), creating a constant, random variation in their separation. When the two beams are recombined, they’d be slightly out of sync, and the amount of the discrepancy would reveal the scale of the chunks of space.
For the scale of chunkiness that Hogan hopes to find, he needs to measure distances to an accuracy of 10-18m, about 100m times smaller than a hydrogen atom, and collect data at a rate of about 100m readings per second. Amazingly, such an experiment is not only possible, but practical. “We were able to do it pretty cheaply because of advances in photonics, a lot of off-the-shelf parts, fast electronics and things like that,” Hogan says. “It’s a pretty speculative experiment, so you wouldn’t have done it unless it was cheap.” The holometer is currently humming away, collecting data at the target accuracy; he expects to have preliminary readings by the end of the year.
Hogan has his share of fierce sceptics, including many within the theoretical physics community. The reason for the disagreement is easy to appreciate: a success for the holometer would mean failure for a lot of the work being done in string theory. Despite this superficial sparring, though, Hogan and most of his theorist colleagues share a deep core conviction: they broadly agree that general relativity will ultimately prove subordinate to quantum mechanics. The other three laws of physics follow quantum rules, so it makes sense that gravity must as well.
For most of today’s theorists, however, belief in the primacy of quantum mechanics runs deeper still. At a philosophical – epistemological – level, they regard the large-scale reality of classical physics as a kind of illusion, an approximation that emerges from the more “true” aspects of the quantum world operating at an extremely small scale. Chunky space certainly aligns with that worldview.
Hogan likens his project to the landmark Michelson-Morley experiment of the 19th century, which searched for the aether – the hypothetical substance of space that, according to the leading theory of the time, transmitted light waves through a vacuum. The experiment found nothing; that perplexing null result helped inspire Einstein’s special theory of relativity, which in turn spawned the general theory of relativity and eventually turned the entire world of physics upside down. Adding to the historical connection, the Michelson-Morley experiment also measured the structure of space using mirrors and a split beam of light, following a setup remarkably similar to Hogan’s.
“We’re doing the holometer in that kind of spirit. If we don’t see something or we do see something, either way it’s interesting. The reason to do the experiment is just to see whether we can find something to guide the theory,” Hogan says. “You find out what your theorist colleagues are made of by how they react to this idea. There’s a world of very mathematical thinking out there. I’m hoping for an experimental result that forces people to focus the theoretical thinking in a different direction.”
Whether or not he finds his quantum structure of space, Hogan is confident the holometer will help physics address its big-small problem. It will show the right way (or rule out the wrong way) to understand the underlying quantum structure of space and how that affects the relativistic laws of gravity flowing through it.
Part 2 to follow