Research
The program, in order.
PRQT did not arrive as a single paper, and it has not stopped. Over roughly five decades it has grown from a relativistic quantum mechanics of one particle to fields, many-body systems, statistical mechanics, neutrinos, nonlocality, curved spacetime and quantum cosmology. What follows is a curated walk from the 1977 dissertation to the current book manuscript — the foundation from which scientific and technical exploration proceeds.
A curated selection, not a complete bibliography. Each entry records where the work appeared — dissertation, journal, book or current manuscript. That is provenance, not a ranking.
§ R.1A reader’s key
How to read a claim.
Ideas should be examinable on their arguments, mathematical structure, predictions and contact with evidence. Serious readers distinguish what a framework proposes from what it has shown. We try to do the same.
Neither publication nor recency settles a claim. Published work preserves the historical derivations and the record; current work shows where the framework is now.
- Proposes
- What PRQT puts forward: its postulates, formal structure, and interpretation.
- Reproduces
- Where the framework recovers an accepted result or limit. Compatibility — necessary, but not by itself evidence for PRQT over alternatives.
- Discriminates
- Where PRQT predicts something different from standard treatments, so that observation could in principle tell them apart.
- Open
- What remains unresolved, model-dependent, or speculative — named as such, not smoothed over.
§ R.2Chronology
Five decades, one thread.
1977
I
First comprehensive foundation
Quantum Mechanics of Relativistic Spinless Particles
John R. Fanchi · Ph.D. dissertation, University of Houston
The first comprehensive formulation of what became the Four-Space program and, later, PRQT: a positive probability density over spacetime, an invariant evolution parameter, mass as an observable and dynamical quantity, superpositions of mass states, particle decay, and early calculations of where the theory’s predictions part from conventional ones. Like other early work, it sometimes describes the evolution parameter in proper-time language; the explicit historical-time framing comes later.
- Relativistic quantum foundations
- Mass as a dynamical quantity
- Particle decay
1978
II
Canonical early formulation
Quantum Mechanics of Relativistic Spinless Particles
Fanchi & Collins · Foundations of Physics
A canonical early published statement of the Four-Space formulation.
- Relativistic quantum foundations
1979
III
Field theory
A Generalized Quantum Field Theory
Physical Review D
Extends the invariant-parameter framework into quantum field theory, and introduces an additional generator interpreted as a mass operator.
- Generalized quantum field theory
- Mass as a dynamical quantity
1983
IV
Many-body systems
Relativistic Many-Body Systems: Evolution-Parameter Formalism
Carries the evolution-parameter formalism from single particles to interacting N-body systems.
- Many-body systems
1986
V
Historical time
Parametrizing Relativistic Quantum Mechanics
Physical Review A
A pivotal step. The paper explicitly distinguishes coordinate time from an invariant historical time, and presents an operational construction of a clock for it. The two-temporal-variable framing of the mature program grows from here.
- Historical time
1987
VI
The arrow of time
Entropy and Time(s)
Connects historical time to thermodynamic irreversibility, under explicitly stated assumptions.
- Historical time
- Relativistic statistical mechanics
1988
VII
Statistical mechanics & cosmology
Cosmological Implications of the Gibbs Ensemble in Parametrized Relativistic Classical Mechanics
Takes a parametrized Gibbs ensemble to cosmological questions. Its ultrarelativistic limit gives 2NkBT where the conventional treatment gives 3NkBT — a difference the program later revisits in accelerator and quark–gluon-plasma contexts.
- Relativistic statistical mechanics
Book · Anchor work
1993 — Parametrized Relativistic Quantum Theory
A major book-length synthesis of the program’s first decades, and a defining milestone in its published record.
1998
VIII
Neutrino physics
The Mass Operator and Neutrino Oscillations
Brings the mass operator to neutrino oscillations. In the simplified treatment the oscillation phase differs materially from the standard result — which makes neutrino data one of the program’s strongest routes to a test against observation.
- Neutrino physics
- Mass as a dynamical quantity
2000–2001
IX
Nonlocality
A relativistic quantum potential
Work develops a relativistic quantum potential and, with it, an interpretation of nonlocal correlations within the framework.
- Nonlocality & the quantum potential
2011
X
Mature synthesis
Manifestly Covariant Quantum Theory with Invariant Evolution Parameter in Relativistic Dynamics
A concise, peer-reviewed overview of the program in its mature form, written before the current book.
- Historical time
- Relativistic quantum foundations
2017–2019
XI
Neutrinos & statistical mechanics, revisited
Back to testable ground
Research re-engages relativistic statistical mechanics — including what the 2NkBT result would mean for accelerator and quark–gluon-plasma physics — and develops three-state and four-state neutrino treatments.
- Relativistic statistical mechanics
- Neutrino physics
Book · Anchor work
2023 — Confronting the Enigma of Time
A book-length treatment of the problem of time — the question at the center of the program.
2023
XII
Curved spacetime · neutrino mass
Into curved spacetime
The same year, research extends PRQT into curved spacetime and takes up three-flavor neutrino mass comparisons.
- Curved spacetime
- Neutrino physics
2025–2026
XIII
Active research
Many bodies, curved spacetime, an expanding universe
Recent work develops many-body and multicomponent PRQT in curved spacetime and applies it to quantum-cosmological, expanding-universe settings. Exploratory tachyon and cosmology work continues alongside it, and is explicitly model-dependent.
- Curved spacetime
- Quantum cosmology
- Tachyon models (model-dependent)
2026
XIV
Current synthesis · The work continues
PRQT – An Arena for Competing Paradigms
Current book manuscript, 2026
The program’s current synthesis, and the clearest present statement of PRQT’s framing and terminology. Where the published record preserves the historical derivations and applications, this manuscript shows where the framework is now — and where the research is going next, including later chapters on applications that are being prepared for Paraqyt.
- Historical time
- Relativistic quantum foundations
§ R.3From foundations to implications
Where it can be tested next.
PRQT makes concrete claims that can be examined against theory and data. These are the directions under active work — each growing out of milestones in the chronology above.
Open questions and research directions — not results already in hand.
- Neutrinos, head to head
- Modern analyses that confront the standard and the PRQT evolution laws with the same neutrino data.
- Builds on 1998 · 2017–2019
- 2NkBT or 3NkBT
- Translating the parametrized ultrarelativistic result into accelerator and quark–gluon-plasma terms.
- Builds on 1988 · 2017–2019
- Is historical time measurable?
- Whether historical time can be measured independently, or is only a relational reparametrization.
- Builds on 1986
- Interference in time
- Temporal-interference effects the framework predicts, and what it would take to observe them.
- Builds on the temporal-interference theme
- Curvature and consistency
- Benchmarking PRQT in curved spacetime against the consistency demands of any quantum-gravity framing.
- Builds on 2023 · 2025–2026
§ R.4Onward
The research is the foundation for what comes next.
Research
Here is where the framework came from.
Five decades of derivations, results and open questions — read in order, with provenance.
Applications
Here is how we can explore where it might go.
Implications for physical systems, experimental approaches and technology — explored from the framework outward, and tested against it in Paraqyt.
Explore applications§ R.5Fields of inquiry
Where the work goes.
Not every branch is developed equally, and not every branch is equally settled. This is an index, not a ranking.
- §01
Historical time
An invariant evolution parameter, distinct from coordinate time, that orders how physical systems evolve — made explicit in 1986 and central to the mature framing.
- §02
Relativistic quantum foundations
Quantum mechanics formulated in four-dimensional spacetime, with a probability density over spacetime and an invariant evolution parameter.
- §03
Mass as a dynamical quantity
Mass treated as an observable, dynamical quantity — with superpositions of mass states — rather than a fixed input.
- §04
Generalized quantum field theory
Field theory extended to an invariant evolution parameter, with an additional generator interpreted as a mass operator.
- §05
Many-body systems
Interacting N-body systems in the evolution-parameter formalism, and more recently in curved spacetime.
- §06
Relativistic statistical mechanics
Parametrized ensembles, including the ultrarelativistic 2NkBT-versus-3NkBT difference and its accelerator and quark–gluon-plasma implications.
- §07
Neutrino physics
Oscillations through the mass operator, from the 1998 phase result to three- and four-state treatments and three-flavor mass comparisons.
- §08
Nonlocality & the quantum potential
A relativistic quantum potential and an interpretation of nonlocal correlations within the framework.
- §09
Particle decay
Decay described within the parametrized framework, from the earliest work onward.
- §10
Interference in time
Temporal-interference effects the framework predicts — a candidate route to distinguishing it experimentally.
- §11
Curved spacetime
PRQT formulated in curved spacetime, including many-body and multicomponent systems.
- §12
Quantum cosmology
Applications to expanding-universe and quantum-cosmological settings.
- §13
Tachyon models (model-dependent)
An exploratory, model-dependent branch, including tachyon–cosmology work. One strand of a much larger program, and labelled as such.
§ R.6The Library
A catalogue is being assembled.
A full bibliography of the published work — with verified details, and links to where each work can be legitimately read or purchased — will live here. Until then, the chronology above lists the key works, and Paraqyt is how authorized scientists, engineers and technical teams work with the corpus directly, from the published record to current synthesis.