(Image: Claudia Marcelloni/CERN)
A RATHER glib distinction is often made between the two pillars of modern physics. Quantum mechanics is the physics of the very small, while general relativity is the physics of the very large. That’s not quite accurate – for example, quantum-mechanical effects have been observed spanning hundreds of kilometres. And at some scale, surely these two supremely accurate theories must come together.
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Yet wherever they do cross paths, the two theories fail to play nicely together – such as around black holes (see “General relativity at 100: The paradox of black holes“). Efforts to establish a quantum theory of gravity have stumped many physicists over the past century. Einstein himself became extremely unproductive in his later years as he sought such a “theory of everything“.
To understand why, we must start with a fundamental tenet of quantum physics. Heisenberg’s uncertainty principle embodies the fuzziness of the quantum world. It allows particles, such as electrons or photons of light, the equivalent of an interest-free loan: they may borrow energy from empty space and use it to make mass, according to Einstein’s famous equation E = mc2. This mass takes the form of short-lived “virtual” particles. The only caveat is they must pay this energy back – the particles must disappear once again – before anyone asks any questions. The more energy they borrow, the quicker this must happen.
Given such freedom, one can imagine an electron, photon or any other particle going to town, taking out many zero-interest loans in succession. As a result, calculating even a prosaic quantum process – an electron travelling from left to right, say –becomes enormously complex. In the words of physicist Richard Feynman, we must “sum over all possible histories”, taking into account the infinite variety of ways virtual particles can be produced (see diagram).
The history of applying quantum theory to nature’s forces is a history of getting to grips with these unruly infinities. One huge success story is electroweak theory, the theory that combines the electromagnetic and weak nuclear forces to explain how electrons and photons work. Its predictions, of everything from particle masses to their decay rates, are accurate up to 10 decimal places.
The winding way to electroweak theory is marked by at least nine Nobel prizes. The eventually successful variant, a bedrock of today’s “standard model” of particle physics, tamed the mathematics using a bunch of undiscovered massive particles, the W, Z and Higgs bosons.
Fortune eventually favoured this brave conjecture: the W and Z bosons were discovered at CERN in 1983, with the Higgs following in 2012. The first of those successes, in particular, led many physicists to believe this strategy was something like a general prescription for developing quantum theories: if your model produced infinities, just add in extra particles of large mass to solve the problem.
Suppose, then, gravity is made of quantum particles called gravitons, much as light is made of photons. Following the uncertainty principle, gravitons borrow energy to make other, virtual gravitons. As we sum over all possible histories, the calculations rapidly spiral as expected into a chaos of infinities.
But this time, the fix doesn’t work. Eliminating these infinities requires inventing a second particle with a mass 10 billion billion times that of a proton. As ever, the larger the amount of energy borrowed, the more quickly it must be paid back, so these fixer particles are very short-lived. This means they can’t get very far, and so occupy only a minute amount of space.
But general relativity says that mass bends space-time. Concentrate enough mass into a small area, and a black hole will form, a point of infinite curvature in space-time. And this is exactly the guise our new particle takes. Nature plays a cruel joke on us: our scheme to eliminate one sort of infinity creates another.
Changing the game
Attempts to get round this fundamental roadblock have led us to destinations such as string theory, which assumes all particles are manifestations of more fundamental vibrating strings. When we start summing over all possible histories of these “fluffier” objects, the hard infinities produced by virtual particles drop away almost by magic. Another commonly considered idea is loop quantum gravity, which suggests that space-time itself is chopped up into discrete blocks. This pixelation imposes an upper limit on the amount of energy any particle can borrow, again rendering calculations finite.
Despite their seemingly radical assumptions, these two candidate unified theories are in many ways the most conservative extensions of current models: both attempt to preserve as much of the theoretical underpinnings of quantum mechanics and general relativity as possible.
“Few people want to believe reality has no single consistent underpinning”
What about more esoteric ideas, such as changing the rules of the existing game? For instance, if general relativity were to treat space and time separately again, rather than lumping them into one combined space-time, that might provide some wiggle room. But relativity and quantum mechanics both tally so well with reality in their respective spheres that it is devilishly difficult to formulate such tweaks. Few physicists would care to consider an even more radical possibility: that quantum mechanics and general relativity cannot be unified, and reality has no single, consistent logical underpinning.
In the first century of general relativity, all these considerations have been theoretical. But now technology is finally catching up. Despite liberal use of gravitons for calculations, we have yet to detect their existence directly. Gravitational-wave experiments such as Advanced LIGO in Louisiana and Washington state and the proposed eLISA spacecraft will hopefully close that gap (see “General relativity at 100: The missing piece of the jigsaw“) – and so perhaps lead us to a deeper understanding of how gravity really works.
Read more: “General relativity at 100: Einstein’s unfinished masterpiece”
This article appeared in print under the headline “General relativity at 100: Still no theory of everything”
