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From my project, will take much more editing:

The only true source of power awesome enough to create the energy required for this new technology is antimatter. By the time faster than light concepts were truly starting to be realized, antimatter had been a common concept, starting as early as the 1880s. In this time, scientists believed that no space could be completely devoid of matter, even sub-atomically, and so all space was filled with a medium called aether (also known as æther or ether). Eventually, the properties and effects of aether were used to explain many problems in physics, many of which were more correctly described by Einstein’s theories of Relativity.

            In the late 1880s, Karl Pearson developed a theory in which aether would flow in and out of normal space into and out of a fourth dimension. In this theory, the flow into normal space was essentially normal matter, however the flow out of normal space was called negative matter. Pearson is credited with coining the term, and the concept of antimatter becomes common among theorists thereafter.

            The term “antimatter” came later, first used by Arthur Schuster in 1898. Schuster believed that there was an entire anti-universe complete with anti-solar systems as well as anti-particles. Schuster also hit on an important truth; he believed that matter and antimatter would annihilate each other. The problem with these ideas at this time was that they were only ideas; Schuster never made a serious hypothetical proposal to the scientific community, nor did he present any real evidence to support his speculation.

            The first modern proposal of antimatter came in 1928 by Paul Dirac. Dirac realized that his version of the Schrödinger Wave Equation was predicting the possibility of anti-electrons. Though Dirac did not actually use the term antimatter, his predictions of anti-electrons were proven in 1932 by Carl Anderson. Anderson called these anti-electrons “positrons,” meaning positive electron, since a anti-electron is essentially an electron with a positive charge.

            Although antimatter was believed to exist by this time, humanity could not seem to find it anywhere in the universe. This concept of a higher propagation of matter over antimatter is known as baryon asymmetry, and it is still not known why this imbalance exists. It is believed that there would have to be only one more matter particle per billion matter/antimatter particle pairs to create an imbalance in the universe, and it is difficult to determine if antimatter might exist in large quantities outside of the galaxy. Although many antiparticles are created inside the galaxy, they are quickly annihilated when they come into contact with matter. The exact natural existence of antimatter as a whole still remains a mystery.

            Since its discovery, antimatter has been studied in as much detail as possible. It was discovered that the main requirement to naturally create antimatter was a significantly high temperature, and in 1995 CERN announced that it had successfully created nine antihydrogen atoms using an early particle collider. These particles were highly energetic from the collisions that created them, and analysts were not able to adequately study them before they annihilated. However, in 2002, the ATHENA project announced that they were able to successfully create “cold” antihydrogen (antihydrogen that was less energetic). ATHENA was able to slow the particles down in a particle decelerator, then passed them through foil, and then captured them in a penning trap. Although this process was effective in slowing down the particles enough to study, the process was highly inefficient. During the process of “cooling,” most of the particles are lost, only approximately .04% of the particles make it to the penning trap.

In 2004, ATHENA released a new method of cooling the antihydrogen more efficiently. The process was similar only cooled electrons were injected into the penning trap, this time filled with only antiprotons. Since antiprotons and electrons both have a negative charge they do not react with each other to annihilate, they do however create Coulomb collisions, which describes the interaction of the negative electric charge of both particles to reverse the excitement of the particles. The Coulomb reactions that occur as a result of the mix essentially cool the antiprotons while simultaneously warming the electrons, creating equilibrium. While the temperature in the first trap is being adjusted a second trap is prepared by first collecting positrons from radioactive sodium and then injecting them into the trap. Once the temperatures of the two traps are at their desired range, the antiprotons are mixed into the second trap with the positrons; the Coulomb reaction in this case is the attraction of the opposing charges together to form antihydrogen.

Though this process was far more effective it was also extremely expensive, estimated at 25 billion dollars in United States money per gram of positrons, and 62.5 trillion United States dollars per gram of antihydrogen. 

From my paper on the development of warp drive:

Why is this barrier so daunting to astrophysicists? This question can best be answered by Albert Einstein. In 1905, he published the Special Relativity Theory, which describes the physical conditions of objects in motion. Einstein theorized that in a vacuum (also known as free space) where there are no particles of matter, gravity and other universal forces were constant and the speed of light would also be constant to any outside observer, regardless of the observers’ motion in relation to the light source. This provided the constant in Einstein’s famous formula for Special Relativity: , where c is the speed of light, a constant in free space.

The theory of Special Relativity goes on explain that as an object moves faster and faster, approaching the speed of light, the physical properties exerted on it change dramatically. Specifically, perception of time changes and mass begins to take on properties of energy rather than of typical massive matter. As such it was theorized that an object could not be accelerated to the speed of light without changing the nature of the object in some way. Once this happens, the object becomes the same energy as light when it travels at this speed, and thus cannot naturally travel faster.

So how then, if an object cannot even move at the speed of light in normal spacetime, does an object move faster than light? In 1915, Einstein published the General Relativity Theory, which mainly describes his concept of how gravity actually works in relation to Special Relativity. In this theory, Einstein explained that gravity is one of many dominant forces playing on the universe. These forces affect both space and time as a single dimension that exists around us, known as spacetime. In this model, spacetime is altered by gravitational pull, as well as the pull of the other forces expelled on the universe. These forces play dramatic roles on our understanding of physics and the how the universe works. It alters our perception of time, space geometry, dimensional space, light, and many other oddities that exist in our universe.

Spacetime, Einstein believed, could be viewed as a sort of fabric that stretches across the universe. Gravity, created by a mass, would be like placing a weight on the fabric, which would sink where the weight had been placed. If you were to put a ball bearing on the cloth and let it roll freely, it would become attracted to the weight’s impression on the material. This is how gravity is believed to work, and subsequently, gives light to the nature of normal spacetime; it provides the idea that spacetime can be and is curved.

This concept allows for the possibility of an object travelling faster than the speed of light if spacetime is curved around the object. Einstein himself offered his thoughts on the subject with the equation =   , where  is the Einstein Curvature Tensor (which describes the curvature of space), and G is the gravitational constant. In this model, the object is not technically exceeding the speed of light, it simply appears that way to an outside observer. The question then becomes how to create a curvature of space and how can that curvature be used to accelerate an object past the speed of light (and what would happen to that object when it reaches those speeds).

Hadeon Eon

            The Hadeon Eon, sometimes considered part of the Archean Eon, marked the formation of Earth. Little was known about this time because the evidence on Earth from this Eon had not been preserved due to the planets ever changing geology and climate. At this time, earth would be considered a Class E planetoid, after it had grown to around 10,000 km in diameter. The surface would have been either completely or partially molten, and temperatures would have been extremely high. There would be little to no solid rock on the surface, until the planet could cool down.

            Due to accretion, the surface was under a constant bombardment of meteorites, and volcanism was extensive. As the crust began to cool into solid rock, the surface would crack to allow for heat of the molten rock below to escape. This was due to a high geothermal gradient, causing a decreased heat flow from the surface to outer space than we see today. Also, the bombardment of meteorites impacting the earth tore holes into the surface allowing even more molten rock to poor through. This process would go on for hundreds of thousands of years, and was known as the late heavy bombardment, which ended approximately 3.8 billion years ago.

            Although surface temperatures were extremely high, sporadic detrital zircon crystals dated as far back as 4.3 Billion Years Ago indicate that at least by this time earth had some oceans or seas. During this time it is believed that Earth went through a rapid cooling phase where the crust began to solidify, allowing for water to condense on the surface. The crust would still be partially molten, however temperatures on the more solid and rocky continents would have been cool enough for shallow seas to form. This period most likely came to an end when the Late Heavy Bombardment began around 4.1 Billion Years Ago, causing breaks in the solid surface allowing for molten rock to once again cover most of the surface.

Before I start going into utter craziness about how warp drive works on star trek, first I should probebly explain what warp drive is and how it affects space.

On that note, you must first understand how SPACE works before you can understand how to warp it. Albert Einstein thought up the modern concept of space when he developed his theories on how physics worked when dealing with strange concepts like gravity or light. Einstein believed that space could be looked at like a fabric that has been pulled taught and so it was uniform in nature, a flat surface. Obviously, the universe is not flat, it is 3-dimentional, but Einstein felt that this idea was the best way to explain the dimention of space that we inhabit (in Star Trek, this is referred to as the space-time continuum). He felt that gravity could be explained by the way it affects the “fabric” of space rather than how gravity affects individual objects.

Gravity, in the idea of the fabric, would be like placing a weight on the fabric. Invariably, the weight would sink. This sinking into the fabric is how massive objects affect the spacetime continuum. If you were to roll a ball bearing across the fabric in the general direction of the weight, the sinking affect will catch the ball as it rolls, this would be like being caught in the massive objects gravity well. As the ball rolls around the weight, it is orbiting the weight. Eventually, it will stop against the object, and occupy the same relative space. This is known to scientists as “accretion,” and an example can be anything from a black hole sucking in another star to two planets crashing into each other to form a larger one or asteroids coming together to form planetoids or an asteroid striking a planets surface.

As objects become more massive (either by increasing mass and/or density), they sink deeper into the spacetime fabric, causing more gravitational pull. Einstein felt that this is how our dimention of space worked. The reason it is called “spacetime” is because it didn’t take scientists long to figure out that time is also affected by gravity when they put Einstein’s theories to the test.

Time, though it is linear and travels only in one direction (that we know of), does move in different speeds relative to gravity. For example, if you were to place a clock on a satellite, and match it with a clock on the surface of Earth, the clock orbiting would move faster than the one on Earth. Time itself does not change, for example you could not measure a space minute and call it 45 earth seconds, but simply our perception of time changing as a result of gravity when we observe it from outside. If you were on the spaceship, it would be more like the clock on earth would be moving slower, rather than yours moving faster. Either way, a minute is still a minute. 
If it confuses the hell out of you (like it does me), don’t worry, it’s not important. Scientists, with all their calculations, experiements, and theories, don’t really get it either. The question they are attempting to answer is whether it is actually gravity that causes “time-dilation” (the changes in perceptive speed), or if it is gravities affect on the spacetime fabric. And if so, how can we understand why this happens?

Very crazy stuff if you ask me!