How to become invisible(?)
Perfect invisibility or “cloaking” is an intriguing idea, but it is easy to show it is impossible.
If a light pulse cannot propagate through a volume, but must in some fashion propagate round the outside, then the information to recreate it on the far side cannot arrive soon enough to do so. Therefore, by causality, perfect cloaking or invisibility to light pulses is impossible.
Suppose we have a volume that is to be perfectly invisible. Then light must appear to propagate as if the volume was not there. If light cannot propagate directly through the volume (and if we do not allow any alternate path directly through the volume for information to flow at the velocity of light from one side to the other), then we cannot possibly recreate some unknown pulse on the other side. The information cannot get there fast enough to recreate it. So perfect cloaking or invisibility to pulses is then impossible. We could always tell that the original pulse does not get there on time.
It is possible to make a volume perfectly invisible if we allow the information to flow through the volume fast enough. This perfect invisibility would be possible in principle, for example, for acoustic waves if we detected the incident acoustic wave and propagated the information quickly enough – for example, as electromagnetic waves or signals – through the volume. There is an appropriate formula for calculating the necessary sources from the measured wave at the surface. Implementing that in a simulation does indeed show that such effective cloaking is then possible.
If an appropriate set of “microphones” and “loudspeakers” is placed round a volume, then, with appropriate rapid calculations and with information flowing through the volume faster than the wave velocity, it is possible to obtain perfect cloaking or invisibility in principle, as illustrated in this simulation.
If we examine that problem closely enough, we conclude that the necessary process would require that the amplitude of the “sources” (e.g., loudspeakers) at each point on the surface would in general depend on the measured incoming wave at all points on the surface. So, the necessary response is “non-local”, and therefore also can never be emulated just by some special material on the surface (presuming the material has essentially “local” response).
D. A. B. Miller, “On perfect cloaking,” Opt. Express 14, 12457-12466 (2006) https://doi.org/10.1364/OE.14.012457