麻豆传媒

IF PHYSICISTS went in for commandments, the first would surely be: thou shalt not get something from nothing. Also known as the principle of energy conservation, this universal accounting law makes it impossible for energy to be magicked either into or out of existence.

Whenever a suspicious transaction seems to take place in physics, a careful audit with the principle of energy conservation usually reveals the source of the error 鈥� some overlooked entry in the ledger that, once taken into account, helps balance the books.

This time-honoured technique has allowed us to predict planets and discover particles. But now it appears to be under attack. Look out into the depths of the universe today, and you see a vast quantity of energy. It is so vast, in fact, that it accounts for over two-thirds of all the energy there is. And this mysterious stash is growing continuously 鈥� energy laundering on the grandest of cosmic scales.

Working out where this so-called dark energy comes from is probably the biggest problem in physics. We have long been frustrated in finding a solution, but now two groups of physicists think they have it. If they are right, we may have found dark energy鈥檚 source in the imperfect joins of the universe where different theories of reality meet. Follow the trail back, and we could even arrive at a better theory of reality.

We鈥檝e known about the invisible elephant in the universe for some time. In 1998, astronomers observing distant supernovae noticed that they were even dimmer than expected. We expected their light to fade as it travelled towards us across an expanding universe, but these new results suggested there was a foot on the accelerator.

Dark energy is the mysterious substance conjured up to explain what is pushing the universe apart ever faster. And as the latest data from sources like the Planck space telescope reveal, it is spread evenly throughout the universe at a density equivalent to around half a dozen protons in every cubic metre of space.

The simplest way to explain this all-pervasive energy is to think of empty space as not being empty after all. On very small scales, quantum mechanics says that any vacuum is filled with the wriggling of quantum fields. But calculations following that approach give us a dark energy density that is 120 orders of magnitude larger than the one astronomers measure from the accelerating expansion of the universe. Almost laughably wrong.

鈥淒ark energy may be a cosmic accounting error, rather than an unknown substance鈥�

Some researchers, however, haven鈥檛 given up on making these two numbers square. According to a new paper by Qingdi Wang, a student of theoretical physicist Bill Unruh at the University of British Columbia in Canada, these jiggling fields would tend to cancel each other out on larger scales, drastically deflating the prediction.

But frustration at the inability to make progress has now led some to suggest that it鈥檚 all down to a cosmic accounting error. The idea is that dark energy is not actually a substance held in the universe鈥檚 vaults 鈥� it鈥檚 something that appears on the books purely because there鈥檚 something else we鈥檝e overlooked.

Energy conservation is such a basic principle that any apparent violation should give pause for thought. The seminal work of mathematician Emmy Noether in the early 20th century showed that energy conservation was an expression of something even more fundamental: the idea that the laws of physics are immutable over time. And indeed, it is a principle that has paved the way for centuries of discovery (鈥�What has conservation of energy ever done for us?鈥�).

When it comes to dark energy, cosmologists already had a vague idea where the accounting error might lie. According to Einstein鈥檚 equations of general relativity, energy is absorbed and released all the time by the bending and stretching of the fabric of space-time. When photons seem to lose energy as they travel across an expanding universe, for example, that energy is all assumed to go into the universe鈥檚 geometry. On the scale of the cosmos as a whole, energy is always appearing to be either created or destroyed.

Similarly, dark energy isn鈥檛 adding or subtracting anything from the universe鈥檚 overall budget. From afar, cosmologists are confident that everything balances out between the universe鈥檚 stuff and the warped space-time holding it. But up close, the exact nature of the transaction bestowing space with extra energy remains mysterious. 鈥淭he question is 鈥榃here is it coming from?'鈥� says Spiros Michalakis at the California Institute of Technology in Pasadena.

Secret source

For Thibaut Josset of Aix-Marseille University in France, the processes responsible for that transaction lie in the jagged edges where quantum mechanics and general relativity meet. For decades, we have been looking for a unified theory of quantum gravity, one capable of explaining microscopic quantum processes alongside the large-scale workings of gravity. Thus far, no such theory exists.

One key difference between general relativity and quantum mechanics lies in the way they see the universe鈥檚 fundamental structure. In Einstein鈥檚 view, which works perfectly for objects on the scale of planets, stars and galaxies, the four dimensions of space and time are smooth and continuous. But quantum mechanics, which seems to govern reality at small scales, implies that deep down, space, like everything else, must be made up of discrete units that we still don鈥檛 know how to describe.

Such a grainy structure would have repercussions for the objects that inhabit it. Relativity dictates that particles with mass bloat or compress the space around them depending on how much mass they have. The process is often equated to a taut sheet bending under the influence of a bowling ball rolling around on top of it. But what if up close, the sheet鈥檚 surface was stippled?

In such a situation, Josset and his colleagues argue, particles are likely to feel that graininess as a form of friction, shedding energy into the stitching of space.

If their model holds, the matter in the universe has been losing energy continuously since a fraction of a second after the big bang.

Adding up the little losses of energy between then and now gives an estimate for dark energy鈥檚 strength closer to reality than the 120 orders of magnitude overestimate, although still quite a way off. 鈥淲e are only seven orders of magnitude away,鈥� says Josset鈥檚 colleague Alejandro Perez of Aix-Marseille University in France, noting that they plan to keep refining their estimate.

鈥淭iny violations of energy conservation build up during the universe鈥檚 history鈥�

鈥淭he magic of this thing is that very tiny violations of energy conservation, that are very, very hard to detect in normal, local experiments, build up during the very long history of the universe,鈥� says Perez. Add them all up, and you could have enough to explain away dark energy. In other words, it is the tiniest drip-drip of energy 鈥� the smallest of leaks in space-time 鈥� that is causing this biggest of problems to accumulate.

The leak would have to be so small as to have gone unnoticed so far. At the Large Hadron Collider and elsewhere, experimental physicists are on the lookout for apparent violations of conservation of energy, as spotting one might indicate the existence of new particles. So far they haven鈥檛 found any good leads, and the chances are they won鈥檛 with current particle colliders. But the amount of energy non-conservation these experiments allow is still enough to hide the observed strength of dark energy, Perez says, something like the mass of a proton going missing every year from a cube of water 10 kilometres across.

While physicists have long known about general relativity鈥檚 ability to transfer energy in and out of the space-time curvature on a grand scale, they have struggled to make it work on the scales Josset describes. What has stood in their way, says Sabine Hossenfelder, a theoretical physicist at the Frankfurt Institute for Advanced Studies in Germany, is that Einstein鈥檚 equations are ruthless about energy conservation when you zoom in on small regions of space. Any quantum jiggery-pokery would invalidate the mathematics.

That is, until Josset鈥檚 colleagues suggested using a less restricted view that Einstein himself had worked on. This workaround allowing Josset to relax its restrictions on energy conservation.

鈥淚鈥檓 annoyed I didn鈥檛 think of it earlier,鈥� says Hossenfelder.

But one of Josset鈥檚 assumptions remains contentious. The idea that space-time is ultimately made up of grains, while popular, is far from proven. Identifying the source of dark energy in the interplay between quantum theory and general relativity may require a different approach. Natacha Altamirano of the Perimeter Institute in Waterloo, Canada, and her colleagues have come at the problem from a different angle. Or rather from the largest possible scale, to examine how quantum mechanics and general relativity play off each other across the entirety of the universe.

Altamirano鈥檚 work considers what would happen to a particle traversing the smooth hills and valleys described by Einstein鈥檚 theory, but within a universe itself following the fuzzy rules of quantum mechanics.

Considering a quantum universe is a familiar gambit in theories of quantum cosmology, which try to explain the universe鈥檚 earliest instants back when it was still tiny and ruled by wild fluctuations. If the whole universe was quantum, then, much like an electron orbiting an atom, the cosmos could theoretically exist as a superposition of many different possible sizes and states at once.

In practice, the universe鈥檚 choices are a lot more limited. The reason lies in Heisenberg鈥檚 uncertainty principle, which governs the precision with which we can know the value of any quantum variable. Measure the position of a particle very accurately, for example, and you can鈥檛 closely measure its momentum, and vice versa. As photons travel from one galaxy to another, they lose energy. And in the language of the uncertainty principle, that鈥檚 a lot like taking a cosmological measurement.

All those unintentional measurements of the universe force the quantum uncertainty to go somewhere else. And one of the ways that can manifest itself is in the form of information loss elsewhere: a little more uncertainty in the rate the universe is accelerating, for example. That change, in turn, would have consequences for all other variables that depend on that rate, further changing the acceleration of the universe in a perpetual feedback loop.

鈥淔inding dark energy may involve treating the universe as a quantum object鈥�

Unless you accounted for it, all that noise would add up to a mysterious dark energy-like term popping out of the void. 鈥淚f I decide to describe my universe with a theory of general relativity that conserves energy, I would see this extra fluid,鈥� says Altamirano. As to whether the dark energy density that emerges from such a model might turn out to match reality in a way that rivals Josset鈥檚, Altamirano is still working on generating such a figure. 鈥淚 can鈥檛 tell how possible that is,鈥� she says.

Josset鈥檚 and Altamirano鈥檚 approaches come at a time when dark energy has repeatedly foiled theorists鈥� attempts to nail it down. Not everyone is convinced the pair are barking up the right tree, though. For Antonio Padilla at the University of Nottingham, UK, the sheer difference in scales makes it unlikely that quantum gravity effects on the smallest imaginable sizes can explain dark energy, which is manifest across billions of light years.

They can鈥檛 both be right, either. Because the two approaches use different mathematical language to discuss how gravity and the quantum world interact, they produce different answers for what happens to cosmology. Altamirano鈥檚 model produces something like dark energy, but it鈥檚 a kinder, gentler version. As the universe expands, it dilutes in space, whereas the dark energy density predicted by Josset鈥檚 model remains a constant, in keeping with observations.

Ironing out such wrinkles to everyone鈥檚 satisfaction would probably need a fully formed theory of quantum gravity 鈥� or at least some as-yet unimagined experimental test that would allow us to look at the universe鈥檚 very earliest moments. Until then, dark energy will continue to accumulate interest in the distant reaches of the cosmos 鈥� a silent rebuke to the idea that we have our cosmic accounting practices in hand.

This article appeared in print under the headline 鈥淥ur leaking universe鈥�