Defining relational persistence
Persistence here denotes the capacity of an organisation to retain a recognisable identity over a given duration. That identity may correspond to a quantum state, a bound structure or a sustained functioning. It depends on the constituents present, on their configuration, on the interaction regime and on the conditions of the medium. The term « relational » underlines this coupling without attributing the same mechanism to every level of matter.
Changes in temperature, density or energy availability modify the organisations that are accessible. The fields of quantum chromodynamics can take part in a very hot plasma, then in confined hadrons as the thermodynamic regime evolves. Protons and neutrons can form certain nuclei depending on their number and their binding energy. Atoms produce different molecules according to their electronic structure and the chemical conditions. In a cell, functional continuity persists across the renewal of some of its components.
These examples rest on distinct kinds of evidence. The properties of the strong interaction, the masses of the hadrons and the QCD crossover are established by theory, lattice calculations and experiment. Extending the notion of relational persistence across several scales is an analytical proposal. It remains plausible when it distinguishes the mechanisms proper to each domain, and becomes hypothetical as soon as it claims to describe a common law independent of those mechanisms.
Hadronisation, a documented passage
At high energy and over very short distances, the coupling of the strong interaction decreases. This asymptotic freedom allows perturbative calculations in the appropriate domain [1, 2]. At lower energies the coupling increases and the dynamics becomes strongly non-perturbative. Confinement then describes the absence of isolated quarks and gluons among ordinary observable states [3].
In the primordial Universe, expansion reduced the temperature and the energy density of the quark–gluon plasma. At low baryon chemical potential, lattice QCD calculations describe the passage toward hadronic matter as a crossover. Several observables evolve within a common temperature range, without a single temporal boundary between two perfectly separated phases [4]. One determination of the pseudo-critical temperature gives 156.5 ± 1.5 MeV [5].
Cooling transforms the collective regime and the effective states of matter. Quarks, antiquarks and gluons remain the internal degrees of freedom of the hadrons, while colour-singlet states become the observable units at low energy. The individual number of quarks and gluons varies over this evolution, since pairs appear, annihilate and exchange energy. Continuity bears on the fields, the symmetries and the conserved quantities.
Heavy-ion collision experiments temporarily produce a hot, dense medium, then measure the hadrons issuing from its evolution. Abundances, correlations and kinematic distributions constrain statistical models, recombination descriptions and fragmentation models. Real-time microscopic reconstruction remains partial, because the medium evolves out of equilibrium while expanding and cooling.
From plasma to proton
The notation « uud » indicates the valence quarks of the proton and makes it possible to recover several quantum numbers. It summarises one component of its structure. The proton also comprises gluons as well as quark–antiquark pairs whose contribution depends on the scale of observation. Its mass comes principally from the collective dynamics of QCD, far more than from the sum of the intrinsic masses of its valence quarks. Ab initio lattice calculations reproduce the masses of the light hadrons with a precision that ties this property to the fundamental theory [6].
The proton persists as a confined quantum state despite continuous internal activity. Its experimental stability contrasts with the short lifetime of many hadrons and with the decay of the free neutron. Confinement makes bound structures possible; quantum numbers, accessible final states and conservation laws then determine their transformation channels. A composite unit can thus retain an identity without immobility of its internal constituents.
Hadronisation also shows that a change of descriptive level can be physically justified. Quark and gluon degrees of freedom dominate the description of the hot plasma. Hadrons become the effective units in the low-energy regime. This passage supports the idea of relational persistence in this precise case, because the durable state depends jointly on the constituents, their correlations, the dynamics of QCD and the medium.
A four-dimensional grid
Comparison between levels gains in precision when four dimensions are kept separate. Composition delimits the possible states. Configuration describes the arrangement or the correlations actually realised. The interaction regime specifies the mechanisms that produce or sustain that organisation. The environment defines the conditions under which it can appear and last.
| Level | Composition | Configuration and interaction | Conditions of persistence |
|---|---|---|---|
| Hadron | Quarks, antiquarks and gluons | Colour-singlet state governed by QCD | Low-energy regime compatible with hadronic states |
| Nucleus | Protons and neutrons | Binding energy, proton-to-neutron ratio, shell effects | Configuration located within a domain of nuclear stability |
| Molecule | Atoms and electrons | Geometry, electronic states and chemical bonds | Compatible temperature, pressure, solvent, radiation and reaction kinetics |
| Cell | Molecules, ions and compartments | Metabolism, catalysis, regulation and selective exchanges | Supply of energy and matter within a domain compatible with viability |
The boundary that individuates an organisation changes with the level. A hadron is distinguished by its confined state, a molecule by its electronic and geometric architecture, a cell by a membrane associated with regulated exchanges. The word « boundary » here denotes the condition of individuation relevant to the system studied. It presupposes no universal material wall.
Duration also depends on timescales. One configuration may form and then disappear before becoming a measurable unit. Another may be produced rapidly and keep its properties for a long time. Comparing the times of formation, relaxation, collision, repair and decay makes it possible to connect persistence to observable processes.
From particles to the living
Mechanisms diversify as the levels rise. Some particles last because the accessible transformations are limited by their quantum numbers and by conservation laws. Hadrons add confinement. Nuclei depend on residual nuclear interactions, on binding energy and on shell effects. Atoms and molecules rest on electromagnetic states whose stability varies with the medium and with reaction kinetics.
The living introduces active maintenance. A cell renews molecules, preserves gradients, repairs certain structures and regulates its exchanges by consuming energy. Its continuity bears on a functional organisation able to survive the replacement of many components. That organisation remains physical and obeys thermodynamics. Local maintenance is accompanied by exchanges of matter and energy with the environment and by an overall dissipation.
Reproduction shifts the scale of continuity once more. An organism has a limited duration, whereas a lineage can transmit structures and variations across generations. Populations, ecosystems and societies also preserve certain relations by means of cycles, memories and collective coordination. Bringing them alongside the physical levels remains analogical as long as no common measurable mechanism is specified.
Scope, limits and counter-tests
Relational persistence provides a reading grid, not a completed universal theory. Confinement, chemical bonding and metabolism belong to different domains. A rigorous application must define the unit studied, the relevant duration, the relations measured, the variables of the medium and the mechanism of maintenance. Without this translation, the notion remains descriptive.
The mode of proof depends on the scale. In hadron physics, the predictions of QCD can be confronted with lattice calculations, spectra and collisions. In chemistry, structures of identical composition can be compared while controlling their geometry and their environment. In biology, perturbations of gradients, metabolic pathways or repair mechanisms make it possible to measure their contribution to viability. These methods support local relations and do not by themselves demonstrate a transdisciplinary invariant.
A counter-test must be formulated for each use. The grid loses its interest if composition and initial conditions already predict the duration with the same precision, or if the relational variables chosen improve neither explanation nor prediction after controlling for known factors. It also fails when one and the same set of variables receives incompatible definitions from one level to another. Its value thus depends on controlled comparisons and on criteria announced before interpretation.
In its present state, the proposal is strongly supported for the particular cases in which structure, interactions and medium are measured. Its general extension remains plausible as a comparative method and hypothetical as a single principle of material history. This distinction preserves what the framework contributes without confusing a convergence of explanations with a demonstrated law.
Principal references
[1] Gross, D. J. and Wilczek, F. (1973). « Ultraviolet Behavior of Non-Abelian Gauge Theories ». Physical Review Letters, 30, 1343. DOI
[2] Politzer, H. D. (1973). « Reliable Perturbative Results for Strong Interactions? ». Physical Review Letters, 30, 1346. DOI
[3] Wilson, K. G. (1974). « Confinement of Quarks ». Physical Review D, 10, 2445. DOI
[4] Aoki, Y. et al. (2006). « The Order of the Quantum Chromodynamics Transition Predicted by the Standard Model of Particle Physics ». Nature, 443, 675-678. DOI
[5] Bazavov, A. et al. (2019). « Chiral Crossover in QCD at Zero and Non-zero Chemical Potentials ». Physics Letters B, 795, 15-21. DOI
[6] Dürr, S. et al. (2008). « Ab Initio Determination of Light Hadron Masses ». Science, 322, 1224-1227. DOI