Physics

For the purposes of continuity in the Heisenberg's iteration of the Star Trek universe, we must introduce one or two pieces of quasiscience, which allow us to include elements such as faster-than-light travel which in the real world are impossible or extremely difficult.

Subspace and Multistage Physics

Subspace represents the "extra" normally-unobservable dimensions of spacetime. In these dimensions, effects that are otherwise inexplicable or "impossible" can be performed with relative ease. There is an entire periodic table of elements, the "second-stage" elements, that function in subspace but are also capable of interacting with the first-stage dimensions and elements. There exists a third periodic table of elements beyond these, which are incapable of interacting with what we consider "normal" spacetime. The interactions of these particles with the normal universe of which we are aware and each other are studied as multistage physics. Multistage physics is the core quasiscience around which the fiction stands, the font of all of our necessary space-opera plot devices, the cause of and solution to all of our problems.

Dilithium

Dilithium, chemical symbol ${\overset {2}{Li}}$, is in fact a fairly common element. Not remarkably dense or heavy, it is generally an undetected component of many minerals typical to M-class planets. In fact, to first-stage physics crystalline dilithium and quartz share the same general physical and chemical properties. Under the scrutiny of a subspace scanner, however, dilithium shows numerous luminous 'cracks' pervading into its environment - what seems to traditional physics to be inert, inorganic crystal is in fact generating a small subspace field.

This is very useful - subspace fields invert charge conjugation, so a semi-permeable membrane out of layered sheets of dilithium will convert ordinary hydrogen gas (for the sake of argument, let's say comprising 95% ${}_{1}^{1}\!H$ and 5% ${}_{1}^{2}\!H$) into the antimatter equivalent in equal proportion (in our example, 95% ${}_{1}^{1}\!{\bar {H}}$, 5% ${}_{1}^{2}\!{\bar {H}}$) with an average of 25% "loss" as matter is pushed into higher stages where it is inaccessible from our universe.

Dilithium crystals act as a mediator for the annihilation of matter/antimatter reactions, converting the gamma-ray photons produced into a coherent "warp plasma" composed of the second-stage analogues of protons, neutrons and electrons. In Starfleet M/ARAs the crystals are shaped in such a way that their subspace field lines focus the emissions into a stream which can be carried around the ship and used to power machinery. This mechanism forms the backbone of all primary power sources aboard Starfleet ships.

Other important second-stage elements

Sarium crellide (${\overset {2}{Na}}{\overset {2}{Cl}}$) is a compound of sarium (${\overset {2}{Na}}$) and crellium (${\overset {2}{Cl}}$), used in Federation power cells due to its ability to store nadion charge. It is also used for replicator mass storage in the form of a solid-medium cyclotron, where a magnetic field induces a second-stage energy current which can "dissolve" large quantities of first-stage matter.

Dialuminium (${\overset {2}{Al}}$) is transparent to visual-spectrum light; standard usage on a starship is two layers separated by a forcefield, which allows for information to be overlaid onto the starfield as required. Additional layers can provide for a simple visual effect which simulates the appearance of a three-dimensional object on the two-dimensional surface (so a person moving to one side will see the side of the virtual object).

Ditanium (${\overset {2}{Ti}}$) sees extensive use by Starfleet for the hulls of their starships, often compounded with titanium to produce an alloy which is unfortunately often casually referred to as "tritanium". Where clarity is needed, such as in discussion of theoretical subspace physics, this substance is called "ditanium alloy", while "tritanium" refers to the third-stage element ${\overset {3}{Ti}}$.

Digold (${\overset {2}{Au}}$) is a soft metal, better known by the Ferengi name latinum, whose rarity leads to its natural application, pressed in layers with gold to add bulk, as a currency in the religious commerce system of the Ferengi; a hundred slivers equal one slip, a hundred slips one strip, a hundred strips one bar, a hundred bars one brick, a hundred bricks one block. The First Bank of Ferenginar possesses the six blocks known to exist, while slivers are near-useless; it is rumored that the Grand Nagus possesses his own private block.

Brannon (${\overset {2}{B}}$) is a dense metalloid which impedes dilithium's subspace field and is often a contaminant of dilithium ores. It finds use in starships in inch-thick wires, which are able to project waste heat into subspace, allowing for starships to operate without large, bulky heatsinks.

Warp and Transwarp

Interplanetary government, trade etc. really can't operate if the time between neighbouring stars is measured in decades rather than minutes. This is where the following two concepts enter the quasiscientific arena.

Warp drive

warp factor	speed / c
1	1.0000
1.5	3.4180
2	8.2491
2.5	16.496
3	29.356
3.5	48.317
4	75.276
4.5	112.73
5	164.09
5.5	234.10
6	329.7
6.5	461.37
7	645.87
7.5	911.84
8	1312.7
8.5	1962.3
9	3159.0
9.5	6085
10	∞

Conceived of by Dr. Zefram Cochrane in 2037, completed in 2061, and flight-tested on April 1, 2062, the Continuum Distortion Superimpeller remains Starfleet's method of propelling itself to faster-than-light speeds. How it does this is deceptively simple, and outlined neatly in the device's name.

A CDS drive is capable of maintaining a "bubble" of first-stage space into the second-stage domain of subspace. The physics here are complex, but the main effect is that the speed of light is greater. Cochrane's original vessel could not sustain the degree of power output required to maintain a warp field for a long period of time, instead providing a second-domain boost to his speed to propel him at $1.1c$ (where $c$ is defined as the speed of light with which we are familiar, equal to approximately 300,000 kilometres per second). A modern warp drive deliberately overbalances the warp field to create a low-resistance space in front of the vessel and a high-resistance space behind. As the ship is carried by the low-resistance space in front of it, so is the warp field, propelling the spaceframe like a water wave carrying a boat.

Any speed can theoretically be chosen, but the energy input required to achieve a particular speed varies accordingly. The first warp pioneers measuring energy-efficiency against speed discovered a series of "sweet spots" where the energy output needed dropped; the first occurred at $c$, the second at approximately ${\tfrac {33}{4}}c$. This phenomenon was extremely useful for early reactors, where conserving power was a worthwhile goal, and these were numbered, giving birth to the concept of "warp factor".

Further study revealed that these corresponded to the effective light speed of successive domains of subspace. The relationship between "warp factor" and real-world speed is ${\mathit {speed}}=({\tfrac {\tanh ^{-1}0.1{\mathit {warpfactor}}}{\tanh ^{-1}0.1}})^{3}\times c$ (graphed). A salient point to note (demonstrated in the table to the right) is that the energy theoretically required to attain warp 10 is infinite. In practice most Starfleet vessels as of 2391 are limited to a maximum speed, depending on the power output of the vessel's matter-antimatter reaction core, with a lower "cruising speed" indicating the maximum speed intended by the engineers for normal use. The Galaxy-class is capable of a maximum speed of warp 8.5, cruising at warp 8; the Constitution-class warp 6.5, cruising at warp 5. Due to its unique dual-core design the USS Heisenberg is capable of a maximum speed utilising both warp cores of warp 9 - compare the maximum speed of the original Excelsior-class, warp 7. The Heisenberg's typical cruising speed is warp 7 due to an improved structural integrity system over the original Excelsior-class which was limited to a cruising speed of warp 6.

Transwarp

Spacetime provides a handy way of beating Einstein without resorting to subspace in the form of Einstein-Rosen bridges, colloquially called "wormholes". These are gravitational structures which amount to two black holes stitched together at the event horizon. However, in conventional relativity these structures are effectively unstable - they exist only for an instant before decaying into two black holes, and while a metastable Einstein-Rosen bridge can be stabilised it requires a spherical shell of matter with negative energy density lining the mouth which is gradually depleted as objects pass through. Federation science knows of only one stable wormhole, located in the Bajoran system and linked with a corresponding entity seventy thousand lightyears away in the Idran system in the Gamma Quadrant; this is kept stable by highly advanced noncorporeal beings, worshipped by the Bajoran people as "Prophets", and functions only because it is operated by the Prophets and closed when not in use. The power source and operational principles of this device are unknown, and the Bajoran people have requested that the matter not be investigated as it risks angering their gods.

However, in 2391 the Starfleet Corps of Engineers completed work on the USS Heisenberg, a highly modified Excelsior spaceframe equipped with a brand-new experimental piece of technology based on Borg operating principles (and thus originally based on the combined technologies of many species) called the Metastable Einstein-Rosen Generator Engine, or MERGE. The Heisenberg is equipped with two separate matter-antimatter reaction cores; the primary core is a standard class-10 core from Sovereign-class fabbing facilities, while the second is a class-9 core from the Defiant-class mold. Under normal conditions the primary core performs all the expected functions of the primary warp core on any vessel, providing power to the whole ship while other power systems remain on hot standby. In an emergency both warp cores can have their power outputs channelled into propulsion, allowing the Heisenberg to far exceed the maximum speed of other vessels even of the same class.

When Condition Blue is sounded, the secondary warp core has its power output channelled to the MERGE system, which directs a stream of verterons in front of the ship, forming the precursor field for a wormhole. The speed and direction of the discharged verterons determine the exit point of the wormhole. When a warp field is applied in the vicinity of the verteron field an Einstein-Rosen bridge (referred to as a "transwarp conduit") is opened linking two points in space. This is a perfectly safe environment to travel through at warp, and will carry you to your destination many times faster than even the best warp drive on its own.