Why did the chicken cross the road?

To test the vehicular analogy of her new spacetime cloak, that's why.


Text and figures by Paul Kinsler, Imperial College London (p.kinsler@imperial.ac.uk)


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This is a simple analogy of how the new space-time "event" cloak operates. This device was proposed by Martin McCall, Alberto Favaro, and Paul Kinsler of Imperial College London, along with Alan Boardman of the University of Salford; and has been published in Journal of Optics 13, 024003 (2011). Here the array of cars represent photons or data packets, and the chicken-crossing-the-road is the event we are aiming to cloak from view.

Diagram of the chicken crossing the road

Here a chicken is attempting to cross the road, while remaining hidden from the watchful Traffic Observatory, which accurately collects and analyses the information from the passing traffic flow -- just as the eye can only register information from photons that hit the retina, as they hit the retina. If the chicken crossed normally at a pedestrian crossing, or simply (and dangerously) attempted to dodge the cars, the resulting pauses or disturbances in the behaviour of the cars would make the attempt easily detectable to the Observatory. How then, might the chicken cross the road without being detected?

An ordinary spatial cloak

In spatial cloaking, the illuminating light is diverted around an object, creating a dark spot in space where the object cannot be seen. Next, the diverted illumination is seamlessly rediverted back into what it would have been had the cloak not intervened. Thus the object cannot be seen, and the illumination seems normal and undisturbed.

In such a setup, we can make the chicken invisible to the Traffic Observatory if it remains on a traffic island. Here the traffic can part to travel either side of the traffic island, and smoothly merge back together afterwards. When it remains on the traffic island, the chicken leaves the traffic undisturbed; but if it ventures off it will cause disruption detectable at the Traffic Observatory.

The standard (or minimal) spacetime cloak

The standard spacetime cloak achieves its end by doing the bare minimum, it slows down and speeds up the illuminating photons to create a dark interval in which events can happen undetected. The, by reversing the procedure, the dark gap can be closed up before the illumination is detetected, leaving no visible trace of the cloaked event. In the proof of principle experimental scheme that we proposed in our article, we used light signals travelling down optical fibres. Because light travelling down an optical fibre travels with a speed that depends on the total light intensity in the fibre, we can use an intense control beam to speed or slow our illumination in the way required by our spacetime cloak concept.

In this first animation, where the field of view moves in step with the average velocity of the cars, we can see how the feat can be achieved. The cloaked region is the temporary gap that opens up when the leading cars briefly speed up, and the trailing ones briefly slow, creating a gap in the traffic. These speed changes might be induced by the electronic speed limit signs you sometimes see on major motorways, or perhaps the weather - traffic often slows when it rains, for example.

Once the gap in the traffic is created, the speedy chicken then takes the opportunity to cross through it from the side road (at the bottom of the frame) to another further on (at the top of the frame). Here, the chicken needs to be speedy, because she must travel forward along the road as well as across it, in order to keep pace with the gap in traffic. However, if the gap in the traffic was wider, the road narrower, or the chicken even faster, the chicken could cross the road more directly.

Standard cloaking for the chicken crossing the road (animation)

After the chicken has crossed, the leading cars briefly slow, and the trailing ones briefly speed up; so that they seamlessly return to the positions they would have had without the interruption. Throughout this process the cars can never exceed some specified maximum speed limit (the vehicular "speed of light"), so that their average speed must be less than that.

The Cornell experimental spacetime cloak

Cornell-style cloaking for the chicken crossing the road (animation)

Recently (arxiv:1107.2062) a group at Cornell has not only improved on our suggestion for an experiment, but they've actually made one, using devices called "time lenses" to achieve the necessary speed changes. This enables much larger time intervals to be cloaked, but has to do more work on the illumination to achieve this. The Cornell time lenses act on the illuminating light by giving it a small, time-dependent spread of colours. Then, the modified light is sent through an optical fibre where the different colours travel at different speeds, thus creating the cloaked time interval. As usual, the process is then reversed, closing the gap and converting the modified multicolour illumination back into its original state.

In the traffic analogy, we mimic the colour separation by sorting the cars into different lanes. We start by using only one lane of the motorway, that is, the medium speed centre lane; then the cars sort themselves into the correct faster or slower lanes, as appropriate. As you can see on the second animation, the different lane speeds again create a car-free gap, in which the chicken can cross.

As before, the slow cars now speed up, and the fast cars slow down in order to close the gap. To keep the animation simple, the cars do not follow the lane speeds in this phase, although that could be done.

Because of all the "lane-changing", this spacetime cloak is a little bit more restricted than our original conception, but it has the considerable advantage of being much easier to achieve.

Summary

In either spacetime cloak analogy given above, the cars never interact with the chicken, and they stay on their intended paths without hesitation, deviation (or repetition); and only slow down or speed up in accordance with their predetermined speed changes. One might even imagine the chicken choreographs this performance by using the computer systems controlling the electronic speed limit signs on the highway.

Consequently, when the cars pass the Traffic Observatory further down the road, there is no evidence that a chicken crossed the road, or that anything at all altered the traffic flow -- their average speed is just as expected, as is their current speed, and none have unexpectedly swerved into another lane.

So why did the chicken cross the road? Not only will we never know for sure, but a sufficiently clever chicken will never leave any evidence of how.

Text and figures by Paul Kinsler, Imperial College London (p.kinsler@ic.ac.uk)

KEY PHASES: spacetime chicken event, space time chicken event