Sub-quantum Transformational Relativity is a study of a Unified Theory of both relativity and quantum physics subscribed to by most academic sources within the United Federation of Planets. Although not universally accepted, it is the standard paradigm of StarFleet officers and engineers; used to explain, define, and predict most of the known aspects and properties of the physical multiverse.

Phase study is a secondary discipline within Sub-quantum Transformational Relativity, dealing with how matter and energy exist in various realms of being called parallel quantum realities.

According to the dogma of SqTR existence is divided up into an infinite number of realities, each of which expresses a different timeline of events. All of the matter and energy in any one of these universes is separated from the matter and energy of every other by a distinct characteristic: their quantum resonance frequency.

To discuss concepts of quantum frequency requires an understanding of phase time. Phase time is simply time viewed from an absolute vantage point, not limited to the local timeframes of any one quantum reality. An appropriate analogy can be found in ancient Earth cinema: the time which exists within a movie can be sped up, slowed down, or even paused without the characters within the movie becoming aware of the changes. But an audience (from their absolute vantage point) will take notice of these changes in the time speed. Such is the same for phase time, it is time viewed from a vantage point outside of any one quantum reality.

In phase time, all matter in every universe oscillates between two states: interaction and non-interaction. However, no two universes oscillate at exactly the same frequency; meaning that although the matter in any one particular universe may inhabit the same space as matter in another universe, they are separated by time, or more appropriately, phase time. The quantum resonance signatures (the oscillation periods) of each universe are denoted by integers (1, 2, 3, 4 . . .)

The quantum signature of any piece of matter cannot be shifted from one full integer to another by any known process, because as matter departs from its "original" quantum state, it requires an exponentially increasing amount of energy to push it further, seeking infinity as it approaches the next quantum state.

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Related to the concept of quantum phasing is the concept of sub-quantum phasing. Sub-quantum phasing occurs only between two quantum integers, and is therefore contained to one universe. Instead of changing the resonance of matter from 1 to 2 (which would change the universal orientation of a person or object that is shifted), the frequency is changed by a smaller incremental value, such as 1.0001 or 1.0002. This process, properly called sub-quantum phase transformation, is also known as interphasing.

In interphase mechanics, there are 5 states in which matter and energy can exist:

Asymmetrically phased material (also known as transphasic) is used to describe matter that is not in a steady phasic state. That is to say, the matter in question does not have a normal period of oscillation between an interactive state and a non-interactive state (it's frequency fluctuates randomly). Instead, it shifts randomly between the two states; making it able to pass through virtually any material, regardless of its interphase value.

Phase inverted material refers to matter that has an inverted phase oscillation with respect to another piece of matter. Matter can have no contact or interaction with matter that is phase-inverted to it, and thee two types of matter categorically "do not exist" to each other.

The term "phased" material applies to almost all matter in the multiverse. If two pieces of matter are phased along the same frequency, then they are able to fully interact with and affect each other. The farther out of phase with each other they are (the more distant their interphase values), the less interaction they are able to have. Matter, however, is often referred to as "phased" only when it it oscillates along a different frequency with respect with the observer.

When phased matter interacts (when two pieces of matter not phased 100% along the same frequency and not 100% out of phase comes into contact), massless particles called anyons are produced.

Standing phased (also known as stable) material applies to matter whose phasing state is fixed; that is constant. Such matter would be affected and be able to affect all previous forms of phased matter, as its frequency would effectively be zero. No such matter has been discovered or produced by Federation scientists. Theoretically, creating matter with a standing interactive phased state would be impossible, as it would require an infinite amount of energy. Creating matter with a standing non-interactive phased state would violate the 1st Law of Thermodynamics (conservation of energy; matter cannot be created nor destroyed) as it would be effectively destroying it.

Universally phased material applies to matter whose phasing state has an infinite frequency. That is to say, it occupies all points on a frequency graph at all times. It is simultaneously there and not-there on all points of the interaction/non-interaction barrier at the same time. No such matter has been discovered or produced by Federation scientists. Theoretically, creating matter with a universally phased state would be impossible, as it would require an infinite amount of energy, not to mention violate countless laws of physics that have been considered unshakable throughout the Federation for over two centuries.

The emergence of Sub-quantum Transformational Relativity as a scientific discipline was nothing short of a revolutionary step in Federation physics. It has allowed the development of technologies and schools of thought that would have been unthinkable before its establishment, forever changing how scientists and academics look at existence as we know it.

Sub-quantum Transformational Relativity is only beginning to emerge as a theoretical science within the culture of the Galactic Empire. It's most famous patron is Arthur Sunrider, an ex-Imperial scientist who defected to the Rebel Alliance. His ideas are still largely considered extreme and fanciful, but by far the most impressive proof of his theories was the opening of a quantum gateway to the Alpha Quadrant during an Imperial raid on the rebel stronghold at Sullust in the Lesser Ploroid Sector.