Planar Space

Planar Space is a term referring to a universe through which ships travel from star system to star system. It is the current means for interstellar travel for the Humankind Empire of Abh and the four Nations Alliance to control and travel the Milkyway Galaxy.

Normal Space
Normal Space is a term referring to the four dimensional space-time with it's Einsteinian Relativity. For a centuries travel trough normal space has been a dangerous, tedious, and long term adventure for humans.

Plane Space
Normal Space is a term referring to an alternate universe with two spatial dimensions and one time dimension. It has different laws of physics than normal space. It connects vast distances in Normal Space within reachable distances. Natural access to Plane Space is possible through Sords or Gates or Portal (J-Novel Club translation). Matter that enter a Sord from Normal Space is transformed into Space-Time particle (Supflasath). Traveling ships need a space-time generator to create artificial normal space encasing the ship to protect it. This space is called a space-time bubble (Flasath). Space-Time particle that exit a Sord from Plane Space are released as visible energy. The stream of matter or space time particles is determine by the vacuum pressure within Normal Space. A Sord that is close to a star will be under the solar pressure of the star and receive more matter from the solar wind. Sords that are near the galactic center receive the high pressure of young stars and the galactic pressure waves leading to a constant stream from those Sords. These 'volcano' Sords are known as Kiigaf. Because of the high streams of these Sords the galactic center is near impossible to navigate. The streams of space-time particle act as a fluid in plane space and create friction to traveling ships. Therefore, these streams are displayed as density gradients which make Sords look like hills or valleys just like high or low pressure zones on a weather map. The gradients also indicate the direction of flow. A ship traveling through plane space 'displaces' or disturbs the space-time particle sea which send out mass waves (Sesuwas) detectable by sensors. Mass waves travel indefinitely through Plane Space. The frequencies and wavelengths of mass waves are fixed in Plane Space; they overlapped and created unavoidable interference. Sending Space-Time particle is the only effective means of communication. However, transmission speed is slow and has very limited range. For distance communication, communication boats or ships are necessary.

The common measurement for distances is the Imperial nautical mile Cédlairh and the Imperial knot Dirgh. One Cédlairh is defined as the distance a space-time bubble with a mass of 100 tons travels in perfect motion in one second of plane-space time. One Dirgh is the velocity at which it is possible to travel one Cédlairh in one hour of plane-space time.

A Pelia can travel six thousand Cédlairh in about five hours. A slow supply vessel (Isath) could cover that distance in about seventy hours.

History
The theoretical work for plane space was first published by Nadia Houdini (ナディア・フーディニ) for a mathematical lecture. Through trade during the Wandering Age the Abh gain access to the Houdini theory. Bibo Suryumune, a specialized scientist in stellar evolution, became aware of the theory, and discovered the possibility of plane-space navigation, including its research. Through long research the Abh were finally able to create a space-time generator which allowed travel through plane space. Independently, human people from Midgrat (now Dakufo) in the Sumei system developed their own plane space technology shortly before the Abh. The Midgratian happily sold their technology for a price to various human colonies.

Yuanon particle
After a long time of sending ships into space, a research vessel named the Oort Cloud discovered a mysterious particle approximately three-tenths of a lightyear from the sun. It was only about a thousand times the mass of a proton, but radiated nearly five hundred megawatts of energy. It was hypothized as a "white hole" or "null space" or "hyperspace." Scientists named them Yuanons. Then for a long time these rare and precious particles were used as the heart of interstellar ships to explore distant system ad colonized them. It was only later that they were discovered to be the state of a "closed Sord" (Sord Loeza). As a closed Sord the yuanon particle is a low energy state of a Sord.

Space-Time particle
A space-time particle is the state of matter within plane-space. As plane-space does not support the third dimension, all matter entering plane-space is reduced to this state. Technically it is not a particle. (It does have a mass, though.) When it leaves plane space and come into normal space, it is transformed to a four-dimensional space-time particles about the size of an electron.

Space-time particle roam plane-space from a high density area to a lower density area. In practice this means from a spewing geyser Sord to a sinkhole Sord.

A stream or current of space-time particle causes resistance to ships moving in reverse direction, while imparting some relative velocity in the other direction.

Sord
A Sord is the second form of the yuanon particle. It is also called an "open Sord" (Sord Gulark). As a Sord allow ships to transit into plane-space it also referred as a gate. It has the appearance of a phosphorescent, and spherical singularity space with a size of one SeDagh(1000 km) in diameter. Left alone a Sord can loose enough energy to become a closed Sord. The half-life (the period for the phenomenon to occur with a 50% probability) is 12 years. This means after 12 years the probability of it becoming a closed gate is 50%.

A transit through a Sord is dangerous in that the difference of dimensions causes ships to appear at a random position around the Sord on the other side. As the sole access point to plane-space or normal space a Sord is a military asset of high value. As communication and sensors are limited a transit can be a dangerous task for military ships.

Sord Rings
There are approximately thirty billion Sords all existed in the Milky Way Galaxy (Elukufa). However, their position in normal space do not relate normally to the plane-space sides of the Sord. At times it somewhat appears random.

In normal space, the Sord are scattered in a ripple-like formation: a central cluster surrounded by numerous rings (Speish) that increased in size away from the center. The gap between the central cluster and the first ring (Speish Kasna) was slightly smaller than the gap between the first and second ring (Speish Mata). Gaps and rings alternated, making up the basic structure of the Milky Way Sord Group (Sordlash Elukufar).

The number of gates in each ring was the same, so the Sord are farther apart in the outer rings than they are in the inner rings.

Most of the Sords that humanity used existed in the relatively crowded Central Territory (Sorl Bandak), which form seven of the rings. Many of these Sord led to central plane-space locations, enabling explorers to exit plane-space through different Sord and come out in completely different ripples of the Milky Way galaxy.

From the eighth to the eleventh ring, the Sords were scattered far from each other, such that they are regarded as Unexplored Territory (Sorl Geiraza).

Of the eight Imperial Kingdom, seven lay in the central territory. Only Sord Ilysr led to the outer reaches, where Sord were harder to come by.

The Abh viewed their single-frontier Sord as an opportunity, using it to take control of the twelfth ring (Speish Lomata) and establish military bases to prevent others from using Speish Lomata's Sord.

The Ilysr Kingdom was also known as "Arms of the Abh" as it surrounds the Milky Way Sord Group.

At the outer edge of the twelfth ring there was an anomalistic cluster of Sord which, it was widely believed, led to an entirely different galaxy. As long as the Empire had Ilysr Kingdom, no other nations could access those gates, and so only the Empire would be able to reach the other galaxy.

Space-Time Generator
A space-time generator is essential for a ship to travel and survive within plane space. A space-time generator creates a three dimensional space-time bubble around the ship which protects as well as serves as a means of propulsion and communication.

Space-time generator technology is currently the only known technology for faster than light interstellar travel. There are two distinct lines of technology:
 * Abh
 * Sumei

The technology revolutionized interstellar travel for humans for the past thousand years. Until then humans traveled for a long time in generation ships through normal space under Einstein relativity. The space-time generator technology is still one of the most guarded secrets of their owners and operators.

Space-Time Bubble
A space-time bubble is the artificial three-dimensional space created by a space-time generator. It is a safe haven for ships.

As the space-time bubble is fixed due to the generator within the ship so is the space it represents. Non-moving objects within the bubble will not change their relative position to the ship.

As mass is a direct transdimensional property it plays an important role for a space-time bubble. The bubble's "size" in plane-space is fixed by the mass within the bubble. This affects the resistance and velocity within plane-space.

The space-time bubble is always in constant rotation. If its axis of rotation was perpendicular to the floor, then it would remain stationary, but if the bubble rotated around an axis parallel to the floor, then it would roll. A rolling bubble was called Noktaf, and a stationary bubble was called Skobrotaf.

Any adjustments to travel speed had to come from adjusting the angle of the axis of rotation. Similarly changing direction can be achieved by turning the ship.

When two space-time bubble meet in order to occupy the same space, this is called merging. When two or more ships gather in one and the same bubble, only one ship is needed to maintain the bubble. This allows a group of ships to save fuel. The merging causes a visible illuminating effect. Due to the nature of plane-space ships emerge at random altitude when merging.

When ships within a group generate their own bubble and disperse, the separation is simply called separating. The mode by which ships travel by themselves is termed as moving in single bubbles.

By emitting space-time particles a space-time bubble can serve as a means of limited communication within plane-space.

Facts

 * Fact 1


 * Fact 2


 * Fact 4


 * Fact 5


 * Fact 6


 * Fact 7


 * Fact 8


 * Fact 9

Analysis
Despite all the facts given we don't know anything about how to derive to speed or the size of the space-time bubbles. It appears things were developed over time and novel books, hence, the facts are not quite consistent. It also appears Morioka isn't well versed in math or physics, hence, the facts are also messed up. There is a possibility of faulty Tokyopop translation, not to mention that it's abridged, but these facts mostly agree with fan translations.

Communication
Fact 2 says mass waves travel very far. Fan translation actually say there's no limit to distance. Practical communication distance is limited by the quality of the transmission. As the waves interact with other waves, the longer the distance the more broken up is the original wave e.g. noise. Therefore, communication distance is further in less sord active or calm areas. Fact 2 & Fact 8 states raging battle cause chaos with Supflasath, hence, communication with Supflasath between Flasath becomes less effective.

Speed of ships
Fact 1 & Fact 2 support each other by saying mass is the deciding factor in a ship's speed, and that it's proportional. We don't know whether it's linear or exponential or inverted proportional.

Fact 4 says that Supflasath are the resistance acting factor.

Fact 7 established the measurement system.

Fact 5 is supposed to tell the reader two things. However, it's an utterly mess if both point of views are combined.
 * a rough distance measure of a part of the galaxy in plane space
 * a comparison of ships and speeds
 * The Pelia Lafiel and Jinto used needed two days (Keishu to Febdash) to traverse what appears to be 20 degrees of circumference on the 12th Sord ring. Yet it says what appears to be 80 degrees of circumference is 6000 Kedlairl/Gedolel(K) and can be traversed in 5 hours.
 * Here, it seems there is a mess of distance and time. It is reasonable to believe it would take a day for every 10 degrees of cicumferance otherwise a Pelia could travel around the galaxy in just 22.5 hours. The speeds given would become false.
 * It's also reasonable to believe a Pelia does indeed travel 6000 Kedlairl in 5 hours. Fact 5 & Fact 7 Here a mine would be comparable to a missile (3600K/h) while a Pelia would equal a fighter jet (1200K/h). However, the distance given for Sugfugnoff and Ilysr Sord would be false.


 * If speed and mass are linear proportional then supposedly a mine is 100 tons, a Pelia 300 tons, and a transport ship is 4200 tons.
 * No matter how this is viewed it can't right. A Pelia by best estimate is around 100 tons, perhaps a bit on the light side, but 300 tons e.g. comparable to the space shuttle is off. Likewise a transport with just 4200 tons is utterly worthless compared to the expenditure and investment. It also means a million tons ship is so slow it takes forever to get anywhere. There would be no difference to travel in normal space.
 * If speed and mass are inverted exponential proportional then supposedly a mine is 100 tons, a Pelia 900 tons, and a transport 2469600 tons. This looks more reasonable, but the Pelia is still way off.
 * Fact 9 supports an inverted exponential proportional function. Jadbayr Usem Futune consists of 45 patrol ships and like-massed transports.
 * speed-factor$$= (mass2/mass1)^b=1/(v2/v1).$$
 * solving $$(1/45)^b=1.73$$ gives $$b = (\log(1.73) / \log(1/45)) = -0.14399002012462608463430663139281$$
 * solving for the Pelia $$(x/100)^b=1/3$$ gives $$x = \sqrt[b]{(100^b)/3} = 205859.8$$ tons.

Size of space-time bubble
Fact 1 says the rotation is constant, hence, size doesn't matter either for speed. It may matter regarding resistance as in Fact 4.

The space-time bubble is a spatial field, and like any field its strength wanes/decreases with distance. Like any kind of energy field its strength-gradient is inverse to distance following the inverse square law. We don't know how quickly the energy dissipates over a certain distance, though. Yet, the bubbles are said to have a wall while they are shown to have gradient lines in the animation. It can be surmised there's a threshold strength beyond which a bubble becomes reality.

As far as energy to power it is concerned, we can surmised that it follows the power law, meaning the difference is cubed. A two unit radius sized bubble would require 8 times the energy of a one unit radius sized bubble. Size matters! Therefore, to conserve fuel a fleet or group of ships often bunch together to use a single bubble from a single ship. Needless to say, the disadvantage is decreased speed. If speed and mass are inverted exponential proportional this is very advantageous.