For Francophones, I have a piece in the February issue of La Recherche on spacetime cloaking, part of a special feature on invisibility. For some reason it’s not included in the online material. But here in any case is how it began in my mother tongue.
We all have experiences that we’d rather never happened – or perhaps that we just wish no one else had seen. Now researchers have shown how to carry out this kind of editing of history. They use the principles behind invisibility cloaks, which have already been shown to hide objects from light. But instead of hiding objects, we can hide events. In other words, we can apparently carve out a hole in spacetime so that no one on the outside can tell that whatever goes on inside it has ever taken place.
“Such speculations are not fantasy”, insist physicist Martin McCall of Imperial College in London and his colleagues, who came up with the idea last July . They imagine a safe-cracker casting a spacetime cloak over the scene of the crime, so that he can open the safe and remove the contents while a security camera would see just a continuously empty room.
Suppose the cloak was used to conceal someone’s journey from one place to another. Because the device splices together the spacetime on either side of the ‘hole’, it would look as though the person vanished from the starting point and, in the blink of an eye, appeared at her destination. This would then create “the illusion of a Star Trek transporter”, the researchers say.
“It’s definitely a cool idea”, says Ulf Leonhardt, a specialist in invisibility cloaking at the University of St Andrews in Scotland. “Altering the history has been the metier of undemocratic politicians”, he adds, pointing to the way Soviet leaders would doctor photographs to remove individuals who had fallen from favour. “Now altering history has become a subject of physics.”
Lost in spacetime
Conventional invisibility cloaks hide objects by bending light rays around them and then bringing the rays back onto their original trajectory on the far side. That way, it looks to an observer as though the light has passed through an empty space where the hidden object resides. In contrast, the spacetime cloak would manipulate not the path of the rays but their speed. It would be made of materials that slow down light or speed it up. This means that some of the light that would have been scattered by the hidden event is ushered forward to pass before it happened, while the rest was held back until after the event.
These slowed and accelerated rays are then rejoined seamlessly so that there seems to be no gap in spacetime. It’s like bending rays in invisibility cloaks, except that they are bent not in space but in spacetime.
How do you slow down or speed up light? Both have been demonstrated already in some exotic substances such as ultracold gases of alkali metals: light has been both brought to a standstill and speeded up by a factor of 300, so that, bizarrely, a pulse seems to exit the system before it has even arrived. But the spacetime cloak needs to manipulate light in ways that are both simpler and more profound. Light is slowed down in any medium relative to its speed in a vacuum – that is precisely why it bends when it enters water or gas from air, causing the phenomenon of refraction. The amount of slowing down is measured by the refractive index: the bigger this value, the slower the speed relative to a vacuum.
In a spacetime cloak, the light must simply be slowed or speeded up relative to its speed before it entered the cloak. If the cloak itself is surrounded by some cladding material, then the light must be speeded up or retarded only relative to this – there’s no need for fancy tricks that seem to make light travel faster than its speed in a vacuum.
But to obtain perfect and versatile cloaking demands some sophisticated manipulation of the light, for which you need more that just any old transparent materials. For one thing, you need to alter both the electric and the magnetic components of the electromagnetic wave. Most materials (such as glass), being non-magnetic, don’t affect the latter. What’s more, the effects on the electric and magnetic components must be the same, since otherwise some light will be reflected as it enters the material – in this case, making the cloak itself visible. When the electric and magnetic effects are equalized, the material is said to be “impedance matched”. “For a perfect device, we need to modulate the refractive index while also keeping it impedance matched”, explains Paul Kinsler, McCall’s colleague at Imperial.
There aren’t really any ordinary materials that would satisfy all these requirements. But they can be met using the same substances that have been used already to make invisibility shields: so-called metamaterials. These are materials made from individual components that interact with electromagnetic radiation in unusual ways. Invisibility cloaks for microwaves have been built in which the metamaterial ‘atoms’ are little electrical circuits etched into copper film, which can pick up the electromagnetic waves like antennae, resonate with them, and re-radiate the energy. Because the precise response of these circuits can be tailored by altering their size and shape, metamaterials can be designed with a range of curious behaviours. For example, they can be given a negative refractive index, so that light rays are bent the wrong way. “Metamaterials that work by resonance offer a large range of strong responses that allow more design freedom”, says Kinsler. “They are also usually designed to have both electric and magnetic responses, which will in general be different from one another.”
Using a combination of these materials, McCall and colleagues offer a prescription for how to put together a spacetime cloak. It’s a tricky business: to divert light around the spacetime hole, one needs to change the optical properties of the cloaking material over time in a particular sequence, switching each layer of material by the right amount at the right moment. “The exact theory requires a perfectly matched and perfectly timed set of changes to both the electric and magnetic properties of the cloak”, says Kinsler.
The result, however, is a sleight of hand more profound than any that normal invisibility shields can offer. “If you turn an ordinary invisibility cloak on and off, you will see a cloaked object disappear and reappear”, explains Kinsler. “With our concept, you never see anything change at all.” At least, not from one side. The spacetime hole opened up by the cloak is not symmetrical – it operates from one side but not the other (although the cloak itself would be invisible from both directions). So an observer on one side might see an event that an observer on the other side will swear never took place.
Could such a device really be used to hide events in the macroscopic world? Physicist John Pendry, also at Imperial (but not part of McCall’s group) and one of the pioneers of invisibility cloaks, considers that unlikely. But he agrees with McCall and colleagues that there might well be more immediate and more practical applications for the technique. “Possible uses might be in a telecommunications switching station, where several packets of information might be competing for the same channel”, he says. “The time cloak could engineer a seamless flow in all channels” – by cloaking interruptions of one signal by another, it would seem as though all had simultaneously flowed unbroken down the same channel.
There could be some more fundamental implications of the work too. This manipulation of spacetime is analogous to what happens at a black hole. Here, light coming from the region near the hole is effectively brought to a standstill at the event horizon, so that time itself seems to be arrested there: an object falling into the hole seems, to an outside observer, to be stopped forever at the event horizon. The parallel between transformation optics and black-hole physics has been pointed out by Leonhardt and his coworkers, who in 2008 revealed an optical analogue of a black hole made from optical fibres. Leonhardt says that the analogy exists for spacetime cloaks also, and that therefore these systems might be used to create the analogue of Hawking radiation: the radiation predicted by Stephen Hawking to be emitted from black holes as a result of the quantum effects of the distortion of spacetime. Such radiation has never been detected yet in astronomical observations of real black holes, but its production at the edge of a spacetime ‘hole’ made by cloaking would provide strong support for Hawking’s idea.
Unlike black holes, however, a spacetime cloak doesn’t really distort spacetime – it just looks as though it does. “I can certainly imagine a transformation device that gives the illusion that causal relationships are distorted or even reversed – a causality editor, rather than our history editor”, says Kinsler. “But the effects generated are only an illusion.”
In the pipeline
In order to manipulate visible light, the component ‘atoms’ of a metamaterial have to be about the same size as the wavelength of the light – less than a micrometre. This means that, while microwave invisibility cloaks have been put together from macroscale components, optical metamaterials are much harder to make.
There’s an easier way, however. Some researchers have realised that another way to perform the necessary light gymnastics is to use transparent substances with unusual optical properties, such as birefringent minerals in which light travels at different speeds in different directions. Objects have been cloaked from visible light in this way using carefully shaped blocks of the mineral calcite (Iceland spar).
In the same spirit, McCall and colleagues realised that sandwiches of existing materials with ‘tunable’ refractive indices might be used to make ‘approximate’ spacetime cloaks. For example, one could use optical fibres whose refractive indices depend on the intensity of the light passing through them. A control beam would manipulate these properties, opening and closing a spacetime cloak for a second beam.
However, as with the ‘simple’ invisibility cloaks made from calcite, the result is that although the object or event can be fully hidden, the cloak itself is not: light is still reflected from it. “Although the event itself can in principle be undetectable, the cloaking process itself isn't”, Kinsler says.
This idea of manipulating the optical properties of optical fibres for spacetime cloaking has already been demonstrated by Moti Fridman and colleagues at Cornell University . Stimulated by the Imperial team’s proposal, they figured out how to put the idea into practice. They use so-called ‘time lenses’ which modify how a light wave propagates not in space, like an ordinary lens, but in time. Just as an ordinary lens can separate different light frequencies in space, and can thus be used to spread out or focus a beam, so a time lens uses the phenomenon of dispersion (the frequency dependence of the speed at which light travels through a medium) to separate frequencies in time, slowing some of them down relative to others.
Because of this equivalence of space and time in the two types of lens, a two-part ‘split time-lens’ can bend a probe beam around a spacetime hole in the same way as two ordinary lenses could bend a light beam around either side of an object to cloak it in space. In the Cornell experiment, a second split time-lens then restored the probe to its original state. In this way, the researchers could temporarily hide the interaction between the probe beam and a second short light pulse, which would otherwise cause the probe signal to be amplified. Fridman and colleagues presented their findings at a Californian meeting of the Optical Society of America in October. “It's a nice experiment, and achieved results remarkably quickly”, says Kinsler. “We were surprised to see it – we were expecting it might take years to do.”
But the spacetime cloaking in this experiment lasts only for a fleeting moment – about 15 picoseconds (trillionths of a second). And Fridman and colleagues admit that the material properties of the optical fibres themselves will make it impossible to extend the gap beyond a little over one millionth of a second. So there’s much work to be done to create a more perfect and more long-lasting cloak. In the meantime, McCall and Kinsler have their eye on other possibilities. Perhaps, they say, we could also edit sound this way by applying the same principles to acoustic waves. As well as hiding things you wish you’d never done, might you be able to literally take back things you wish you’d never said?
1. M. W. McCall, A. Favaro, P. Kinsler & A. Boardman, Journal of Optics 13, 024003 (2011).
2. M. Fridman, A. Farsi, Y. Okawachi & A. L. Gaeta, Nature 481, 62-65 (2012).