At the beginning of the last century, more exactly in 1905 Albert Einstein developed the relativity. A new era in physics began and with this era some new ideas will emerge. The experimental determination that made Einstein to develop this new theory was the fact that the speed of light is the same in all reference systems. No interaction in this universe, can travel with a greater speed than C (the speed of light) is the main result of this theory.
However, we do have stars, and planets that we want to visit one day, and the result of the Einstein Special relativity was something that was in the way of out dreams. So people have continued to dream after the special relativity.
One day, at the beginning of the 1990 years (in 1994) a mexican physicist (Miguel Alcubierre) has come with the following idea: what if we could make in space something similar to a bubble in the water? It would travel faster than other things in space.
In physical words this bubble is named the Alcubierre me and its like riding a surf board on an ocean wave.
By AllenMcC. (Own work) [CC BY-SA 3.0 (http://creativecommons.org/licenses/by-sa/3.0) or CC BY-SA 2.0 de (http://creativecommons.org/licenses/by-sa/2.0/de/deed.en)], via Wikimedia Commons
Alcubierre presented this theory at many conferences, and people started to believe in it. It was just a theoretical concept at that time (1994) and it had many things against it. Two main things were impossible at that time. As we know it, matter can curve the space in only one way, for the Alcubierre metric to become real, it was necessary to curve the space also the "other" way. This was named the "negative" matter or the "negative" energy. No one knew about it. Instead we knew its equivalent for electrical charges that can have two possible signs (positive and negative)
The second thing was that admitting that we have this negative energy, there were necessary HUGE quantities of it for a travel to the nearby star (a mass equivalent to the mass of planet Jupiter).
Up until 2000 theoretical improvements were made on the alcubierre metric. The shape of the bubble has been redesigned and thus the quantity of negative energy decreased to the equivalent mass of a small star-ship. This was beginning to become believable.
Then around 2000, a 60 year old physicist from the University Of Calfornia has come with the first experimental results, confirming that he obtained negative energy (negative mass) for the first time. Up until this day his results are contested by many physicists, but his explanation was believable. This explanation of the existence of the negative energy started from the Mach principle in physics.
Mach was a philosopher-physicist that around 1900, before Eistein developped the special relativity has said that the mass of an object is not an intrinsic property of that object but something that is given by the action of all other objects in the Universe on that object. In other words, what it counts for your success is not your opinion on you, but the opinion of all other people about you.
Thus when accelerating an object (we give him energy) the mass of that object will fluctuate. It is like in stock-exchange, variations of the market value around an average do occur because of the people sentiment. Thus negative mass fluctuations (a value of the mass smaller than the average) have become possible.
This was great, now we had the possibility of making an Alcubierre drive and travel to the stars. But not so fast! The EM drive is the first "gadget" that some says it employs this principle (it creates negative mass).
The EM drive was proposed in 2001 as an idea by the British scientist Roger Shawyer. It is like a closed unsymmetrical drum, in which we pour EM waves. Imagine you have a small boat on a lake. Start pouting water in that boat and the boat will star to move in a certain direction. This is what happened also with the EM drive: it developed a positive trust in one direction or the other. (about 40%-60%) for each direction.
By David A. Brady, Harold G. White, Paul March, James T. Lawrence, and Frank J. Davies. Eagleworks Laboratories, NASA Lyndon B. Johnson Space Center [Public domain], via Wikimedia Commons
But the drum was closed, and trust obtained from this device was against the physics. Scientist have begun to ask themselves what happened. All were certain that standing waves happened inside the EM drive. Some said that the fluctuations of these standing waves gave the "negative" energy necessary for the trust to happen. Some other said that photons were emerging from this device (although it was closed). Theories continue to come, it is certain that the EM drive has trust!
A good explanation is the following: space is elastic. Energy (from the Einstein theory is equivalent to mass). When a standing wave is made, the antinodes (where the energy is maximum) behave like masses that curve the space-time fabric. Because they fluctuate (the antinodes), also the curvature of the space fluctuates. All elastic things (space also) have a resonance frequency. When the frequency of fluctuations of the space becomes equal the the resonant frequency, the curvature of the space increases greatly with a small input of energy fluctuation. It is a bit like in Star Trek when Klingonians were asking for the resonant frequency of the ship shields.
By Roxanne Ready, license CC BY-SA 3.0 (http://creativecommons.org/licenses/by-sa/3.0) or CC BY-SA 2.0 (Flickr)