Electromagnetic General Relativity: Traveling with Metamaterials to Space

Recently, scientists have been working on materials that are a kind of Harry Potter style invisibility cloaks. The metamaterials are materials that hide objects by optical means. "Meta" is a metaphor for the usual materials we know from everyday life. And in our case, materials whose complex internal structure can guide the light around the bodies, thus masking them from our eyes

The metamaterials are engineered materials that get their unusual properties as a result of an engineering change of their internal structure at a tiny level, and not from their chemistry - as it is in nature. Because of the way these materials are composed, they can interfere with waves - whether these are light waves, water waves or sound waves in the area of ​​the bone they are masking.

To disguise something, for example, rings of metamaterial can be placed around the object that we want to disguise. Tiny loops or cylinders inside these rings deflect the waves around the bone, thus masking it. The deflection prevents both the return and the absorption of the waves, which meet again on the other side and create an illusion as if nothing was there.

While toying with metamaterials, the researchers quickly realized that the field could shed light on the foundations of physics itself. Einstein's theory of general relativity describes how gravity around a large mass body, such as a star, can warp space-time. These are phenomena such as the bending of the light beam around the sun's disk, the perihelion shifts of Mercury's orbit and phenomena such as gravitational lenses.

Scientists started coming and suggested that effects of general relativity could be studied in laboratory experiments here on Earth, and all of this of course if we use metamaterials, those strange materials that make it possible to make objects and light rays disappear and turn them around as if they didn't exist. Initially we built models for black holes. Physicists have realized that the interactions of light and matter with space-time, as predicted by general relativity, can be studied with the help of the new class of artificial optical materials, which have unusual abilities to bend light and also bend other forms of electromagnetic radiation. This equivalence between the curvature of space-time and the propagation of light in optical metamaterials that are engineered in the laboratory is called: "mechanical-optical analogy". The pioneer in the field was Xiang Zhang of Berkeley UniversityY.

After the black holes came the turn of the wormholes. If a mechanical-optical analogy can be built for black holes, why not build such a model for wormholes? A metamaterial wormhole model allows the propagation of electromagnetic waves between two distant points. This is while most of their expansion zone - the channel - remains invisible and hidden by the cloak of maidens of the metamatter. At the unobscured frequency, where the metamaterial is inactive, the resulting structure is a solid cylinder with flared edges. But at the frequencies where the metamaterial is designed and operates as the maiden's cloak, you get the effect of changing the topology of space into a wormhole. Thus, the researchers built a configuration of metamaterials that makes the waves behave as if they were in an invisible channel connected to Euclidean space. Any body within this channel is only visible by waves entering from one of its ends. Whereas electromagnetic waves that propagate from a body inside the wormhole can only leave through the edges - because they are invisible to an outside observer. A magnetic dipole, which is located near one of the ends of the electromagnetic wormhole, will appear to an outside observer as a magnetic monopoly.

An electromagnetic wormhole could have engineering uses for example invisible optical channels, it would be possible to measure electromagnetic fields without disturbing them, these are channels that do not emit radiation except at their ends. Going further with the optical-mechanical analogy, metamaterials can be used to study additional cosmological phenomena.

Igor Smolyaninov of the Department of Chemical and Electrical Engineering at the University of Maryland in College Park likes to play with metamaterials. Less than a year ago he stretched the mechanical-optical analogy to its limit. And he published an article in which he proposed a "toy model" for multiverses. Take the optical space, says Smolyaninov, engineer it so that it plays the landscape of the multidimensional multiverses, which have regions with different topology and different effective dimensions. The view from the metamaterial and the non-linear optics of the metamaterials, he adds, will lead to the toy model. He goes on to show that metamaterials can be used to create multiverses, where different universes have different properties. In fact should be able to create universes where different laws of physics operate. Why is all this good beyond creating an earthly cosmological model for the cosmologists' theories? Because from an engineering point of view, the model is a cadet development for the field of new optical components "in the electromagnetic universe", where the photons behave as if they are massive, massless or charged - all this depends on the topology of space and the laws of space physics. From here it is possible to develop optical components that make use of this type of behavior, On the basis of the optical mechanical analogy.

Smolyaninov is not silent on his guard and three months ago he proposed that the properties of metamaterials could mimic the effects of Alcubierre's hyperspace bubble, which also appeared in the science fiction series "Star Trek".

What is a space bubble? The supercavity or supercavity bubble is an elliptical spherical bubble that separates an inner region that is almost flat. The bubble moves relative to the more or less flat space-time around it at some speed. It moves by a local expansion of space-time behind and an opposite contraction in front. The expansion increases the distance from the starting point while the contraction decreases the distance to the destination. The idea of ​​the space superbubble was first proposed in 1994 by Miguel Alcubierre who was then working at the University of Wales.

Let's say that there is a spaceship standing still inside the bubble, relative to the space-time that is immediately in its vicinity. The spacecraft does not feel any acceleration. After all, it is not possible to move at the speed of light or faster than light from a local point of view. That is, the spaceship cannot move at the speed of light or faster. But the bubble can make space-time move faster relative to an observer outside the bubble. That is, the bubble moves by interacting with the geometry of space-time. The idea is that even though on space-time nothing can move faster than light, space-time itself does not limit the speed at which it or parts of it can be stretched.

In 1895, the young 16-year-old Einstein imagined a wave that propagates at the speed of light. He asked: What will happen if I chase the wave even at the speed of light? Will I be able to get it? According to Newton's laws, Einstein will succeed in obtaining the light wave. He will move with it like a kind of surfer riding the wave. And the result will be a frozen wave that oscillates up and down and does not oscillate forward. But already at the age of 16, Einstein intuitively realized that such a phenomenon had never been observed and he believed that it would never be observed either. And so this thought seemed paradoxical to him. Einstein felt that chasing the light wave, he should measure the same speed of the light wave as the one measured by an observer at rest. Therefore, Einstein will not ride the wave, but the wave will move relative to Einstein at the speed of light. This thought is the first germ for the special theory of relativity.

And here we see the superspace oath allows Einstein to obtain the light wave at the price of an exotic material of course. An exotic substance or negative energy is required to activate the bubble. Therefore, it seems that superspace violates Einstein's special theory of relativity. But special relativity says that a light beam cannot be chased, when both Einstein and the light beam are both being chased in flat space-time. But when space-time is warped, the beam of light can be obtained by taking a shortcut. The spacecraft will reach its destination faster than the light beam. The shortening of the space-time in front and the expansion of the space-time behind create the way of shortening. As mentioned, the price is very heavy. The price is that exotic matter will exist as solutions to Einstein's field equations in general relativity.

What are the energy conditions that violate matter? The conditions are related to the size of the supercavity bubble and the thickness of the bubble's walls. If the exoticism is provided by the quantum nature of the field, which provides "quantum inequalities", then the violations of the energy conditions will be limited to Planck size regions. Therefore the thickness of the bubble will be a consequence of the Planck size.
Quantum theory allows for the existence of the exotic matter or negative energy, but it places a severe limitation on the size of the negative energy and the length of time it is allowed to exist. This means that a structure like the superbubble space has to be limited to a submicroscopic size. And if it is macroscopic in size, then a mechanism needs to be found to limit the huge amounts of negative energy to as thin strips as possible, that is, to a very small volume.

Very thin walls need huge amounts of exotic material. To support a bubble on space traveling at 10 times the speed of light, it would need to have walls no more than 10-23 meters thick. A bubble large enough to contain a spacecraft is 200 meters long and would require a total negative energy equal to 10 billion times the mass of the visible universe. Not practical at all. And so very thin walls need huge amounts of exotic material.
It is possible to improve the construction of the superspace by reducing the surface area of ​​the bubble by the same volume. The total negative energy that would be required to support a spaceman would become quite small. But it must be taken into account that positive energy must be added outside the bubble - a possibly realistic solution for the very, very distant future, and still far from realization.
We will move on to metamaterials. Are they able to be a laboratory model that played the superspace bubble? Smolyaninov says that in the case of the metamaterials the violation of the energy conditions is not a problem. Therefore it is possible to build and realize a space bubble in the laboratory. We need to find the geometry of the metamaterials that can provide the appropriate model and this will help us understand the physics behind the space superbubble. Smolyaninov proposes to build a model of the superspace bubble from magnetoelectric metamaterials built from layers of split ring resonators unique to metamaterials. According to Smolianinov's calculations, with this mechanical-optical analogy to the hyperspace bubble, speeds of up to a quarter of the speed of light can be reached. When will the physicist come who will implement Smolyaninov's idea in the laboratory, concoct, engineer and add a few more elements to Smolyaninov's metamaterials and perhaps demonstrate (in the laboratory of course) faster-than-light travel?

• The scientific article
• Report on the Discovery website
• Discussion in the NASA forum