What the Universe preserves
Physical traces, information and the limits of historical reconstruction
Didier Daloze · ori-c.be · ORI-C
Introduction
The past does not always disappear without remainder
The past leaves durable differences in the present: craters, strata, spectra, gravitational waves. These traces do not restore the event, but they preserve effects of it which, correctly interpreted, constrain historical inferences.
This essay proposes an operational vocabulary: trace, memory, learning, then encoding, accessibility, detectability, identifiability and inference. It applies it to cosmological archives, multimessenger astronomy and black holes in order to specify what remains physically encoded and what an observer can reasonably reconstruct.
This proposal presupposes no cosmic memory. Physical traces have neither intention nor adaptive function. The text addresses an educated scientific or semi-professional readership. The necessary technical notions are introduced within the thread of the argument, while the formal tools are gathered in a methodological appendix.
1. When a transformation leaves a difference
The trace as a relation between two states
A trace is not the past itself. It is a present property whose existence or value depends on an earlier event.
A crater does not contain the impact. Its form nevertheless depends on the energy, the angle, the velocity and the matter involved in the collision. A stellar spectrum does not directly contain the complete history of a star, but its lines inform us about its composition, its temperature and its motion. The abundances of heavy elements in a galaxy depend on the generations of stars and the explosions that preceded it.
The trace may be defined here as a persistent difference produced by a past transformation and liable, under certain conditions, to constrain an inference about that transformation.
This definition carries three cautions.
First, not every transformation leaves a durable trace. Differences may dissipate, mix or become indiscernible.
Second, a trace never necessarily preserves the whole history. Several different events may produce similar present states.
Third, the existence of a trace does not guarantee its legibility. It may lie outside our causal horizon, below the instrumental threshold, or in a form our models cannot interpret.
Structural, sustained and functional traces
It is useful to distinguish three modes of persistence.
A structural trace persists mainly in the material configuration produced by an event: crater, stratum, crystalline deformation, scar or distribution of chemical elements.
A sustained trace depends on a continuous activity of stabilisation, repair or renewal. Many biological states belong to this category, since their maintenance requires flows of matter and energy.
A functional trace intervenes in a subsequent dynamic and contributes to modifying an operation or a response of the system.
These categories can overlap. A scar is structural, but it may also modify the future mechanical response of a tissue. A synaptic modification can be sustained and functional. A crater remains a structural trace without thereby becoming a memory of the planet.
Non-equilibrium plays a major role in the formation of many traces and in the active maintenance of the living. It is not, however, a universal condition of their persistence. A structure can preserve the effect of an event after the flows that produced it have ceased.
2. To persist does not mean to memorise
From support to function
A physical trace results from a past transformation. A memory requires more: the trace must be able to be read, reactivated or mobilised within a subsequent dynamic.
A memory may thus be defined as a material organisation in which a persistent trace can contribute to modifying a future operation, decision or response.
Mobilisation may be automatic, physiological, computational or conscious. A population of immune cells can modify a later response without conscious representation. A database becomes functionally a memory when a reading system uses its recorded states. A conscious recollection mobilises other architectures, but it too remains physically embodied.
Learning adds a further condition. It appears when the use of traces issuing from experience durably transforms a future response, a threshold, a strategy or a capacity.
We shall therefore distinguish:
Trace: persistent difference produced by a past transformation.
Memory: legible or reactivatable trace that takes part in a subsequent dynamic.
Learning: durable modification of a future response on the basis of traces of experience.
This distinction prevents us from projecting onto non-living matter the properties proper to regulated, adaptive or cognitive systems. The Universe produces traces. Some organised systems use them. A few become able to interpret them.
Borderline cases: status depends on function
The categories are carved out not only by the nature of the support, but by the role it plays within a defined organisation. An epigenetic mark may be described as a structural trace when one considers its molecular persistence, and as a functional memory when a cellular mechanism reads it and it durably modifies a response. It is therefore not the molecule alone that fixes the status, but the relation between support, reading mechanism and later effect.
Conversely, a gravitational wave coming from a past event remains a propagated physical trace. Its detection does not retroactively transform it into a memory of the system that produced it. The stabilised record in an instrument, a database or a scientific practice may, on the other hand, become a support of memory for the system that uses it.
3. The physical archives of the Universe
Fossil light
To observe far is to observe old. Light has a finite speed. The photons reaching our instruments today left their source in the past. A distant galaxy is therefore visible not in its supposed present state, but in the state it was in when the radiation was emitted.
The cosmic microwave background constitutes a major case. It does not show the absolute origin of the Universe. It preserves radiation released when the primordial plasma became transparent, about 380,000 years after the beginning of the cosmic expansion described by the standard model. Before that recombination, ionised matter continually scattered photons and made the Universe opaque to the electromagnetic radiation now observable. Its anisotropies carry information about the density fluctuations from which the large-scale structures developed.
This radiation is a physical archive, but a partial one. Through the photons that compose it, it does not give direct access to epochs earlier than its release. Those periods can nevertheless be constrained indirectly by their later effects and sought, in principle, by means of other messengers. The background therefore does not necessarily erase all earlier information: it marks above all a limit to direct electromagnetic observation.
Different messengers, different histories
Light, neutrinos, cosmic rays and gravitational waves do not interact with matter in the same way. They therefore do not carry the same fragments of history.
Gravitational waves from a compact merger encode the orbital dynamics, the masses, certain rotation parameters and the properties of the final object. Electromagnetic signals inform us more about matter, magnetic fields and environment. A multimessenger observation does not merely juxtapose several instruments. It combines several physical modes of persistence and transmission of traces.
This plurality reminds us that no cosmic archive is total. Each messenger selects, transforms and blurs certain information.
GW170817: crossing traces without confusing them
The merger of two neutron stars, GW170817, detected in 2017 at about 40 megaparsecs, shows concretely what a multimessenger observation produces. The gravitational signal constrained the masses, the orbital dynamics and the tidal deformabilities. The gamma-ray burst, the kilonova and the later emissions informed us about matter ejection, nucleosynthesis and the structure of the jet.
Gravitational waves allow a luminosity distance to be estimated, but that estimate is strongly correlated with the inclination of the system. A more distant source seen almost face-on can produce an amplitude comparable to that of a nearer source observed at another angle. Identifying the host galaxy and the electromagnetic observations help reduce this degeneracy. The reconstruction therefore gains in precision not because one channel would be complete, but because different channels jointly constrain the same parameters.
The searches conducted by ANTARES, IceCube and the Pierre Auger Observatory detected no high-energy neutrino in coincidence with GW170817. This non-detection does not mean that no neutrino was produced. It makes it possible to constrain certain emission models within the energy range and for the directions to which the instruments were sensitive. It does not by itself determine the geometry of the jet and must not be confused with the search for low-energy thermal neutrinos from a possible hot remnant.
An absence of signal becomes informative only relative to a sensitivity, a time window, a direction and an emission model. It then reduces the space of compatible scenarios without turning instrumental silence into proof of physical absence. In a probabilistic analysis, a non-detection can thus modify the likelihood and the relative weight of scenarios as soon as the probability of detecting nothing differs between them.
4. Black holes and traces
What the exterior lets us see
Having distinguished trace from memory, this vocabulary must be tested in a case where the persistence of information itself becomes problematic. Black holes constitute its most demanding limit.
In classical general relativity, a stationary, isolated black hole is described externally by a small number of global parameters, chiefly its mass, its electric charge and its angular momentum. The theorems grouped under the expression « no hair » formalise this strong reduction of the external description under determinate assumptions.
Very different formation histories can therefore lead to black holes possessing the same macroscopic parameters. There is here a degeneracy: several earlier configurations correspond to one and the same stationary external state.
This does not demonstrate that all the initial information has been destroyed. It means only that it is not legible in the macroscopic parameters alone of the final external geometry.
One must distinguish:
information absent from the external macroscopic observables
and
information fundamentally destroyed.
The first proposition belongs to the classical stationary description. The second engages the compatibility between gravitation and quantum mechanics.
The environment as archive
An astrophysical black hole never appears without a history or an environment. Its formation and its activity can leave traces in gravitational waves, the motion of nearby objects, the accretion disc, the jets, the cavities carved in gas and the evolution of the host galaxy.
During a merger, the gravitational signal comprises several phases. The orbital inspiral informs us about the progenitor objects. The merger explores a strongly non-linear regime. The ringdown phase corresponds to the relaxation of the final object, which radiates its residual deformations as gravitational waves. The frequencies and damping times of the quasi-normal modes depend notably on the mass and the rotation of the final black hole.
The stationary black hole may thus present a very impoverished external description while its environment and the radiation emitted during its formation preserve a richer history.
Macroscopic reduction, dispersion or loss
Three situations must remain distinct.
Macroscopic reduction means that many microstates or many histories lead to the same global observable quantities.
Dispersed information means that it survives in global correlations or in the environment, but in a form extremely difficult to recover. In a unitary evaporation scenario, « dispersed » does not designate a mere spatial spreading: the information could be encoded in high-order multipartite correlations, distributed within the radiation and, depending on the framework considered, in other degrees of freedom. The difficulty is then no longer merely causal or instrumental; it may become a problem of quantum control and of decoding complexity.
Fundamental loss means that distinct initial states really do lead to the same final quantum state, with no possibility of reconstruction even in principle.
The no-hair theorem establishes a macroscopic reduction. It does not by itself decide between dispersion and fundamental loss.
One must also avoid identifying the absence of hair with the claim that all the missing information would simply be « stored behind the horizon ». The theorem bears on the poverty of the stationary external description under determinate assumptions. The question of where and how the microscopic distinctions are encoded belongs to a complete quantum theory of gravitation.
A complementary proposal concerns « soft hair ». Hawking, Perry and Strominger argued that asymptotic symmetries of BMS type and the associated very-low-energy modes could carry additional charges at the horizon. This line qualifies the image of an object entirely described by three numbers, without directly contradicting the classical no-hair theorems. Its role in the restitution of hard information nevertheless remains debated: the existence of soft charges does not, by itself, establish a complete mechanism for recovering the initial state.1
5. The information paradox
The tension between Hawking and unitarity
Quantum field theory on a curved space-time leads to the prediction that black holes emit thermal radiation. A black hole may thus progressively lose mass and, over immense durations, evaporate.
If a pure quantum state forms a black hole and if evaporation leaves only exactly thermal radiation lacking the necessary correlations, the final state appears mixed. Such an evolution would come into tension with the unitarity of quantum mechanics, according to which the information contained in the initial state must remain encoded in the global evolution.
The paradox therefore does not come from a mere instrumental difficulty. It signals an incompatibility between several principles when they are combined in a semi-classical description. If unitarity is preserved, the late radiation must therefore carry correlations that depart from the exact thermality of the semi-classical description. If it is not, one of the usual principles of quantum mechanics, or the framework in which they are applied, must be modified. It is this alternative that gives the paradox its fundamental reach.
Page curve and islands
If evaporation is unitary, the entanglement entropy of the radiation must not increase indefinitely. It should grow during a first phase, reach a maximum, then decrease when the correlations needed to purify the state become accessible within the radiation. This evolution is represented by the Page curve.
Work using quantum extremal surfaces, gravitational replicas and « islands » has made it possible to reproduce a curve compatible with unitarity in several models. The best-controlled results rest notably on two-dimensional models of dilaton gravity or on black holes coupled to an absorbing bath, within a semi-classical approximation. The prescription is obtained from gravitational path integrals and depends on the choice of state, the boundary conditions and the split between black hole and radiation.
These calculations profoundly reformulate the entropy of the radiation. Islands intervene in the prescription for computing the fine-grained entropy, by way of the generalised entropy, the quantum extremal surfaces and the relevant saddles of the gravitational path integral; they do not describe the dynamic, unitary trajectory of each emitted quantum. Nor do they demonstrate, by themselves, how the information is microscopically encoded, transferred and then recovered in a four-dimensional astrophysical black hole, nor how to locate it simply within determinate correlations.
Reproducing the Page curve is an important condition of coherence. It is not, by itself, a complete demonstration of how each detail of the initial state becomes recoverable.
Hayden–Preskill type models illustrate another distinction. Under assumptions of unitary dynamics and fast scrambling, information added to an already strongly entangled black hole can rapidly become present in the radiation. This does not mean it is easily decodable. Complexity arguments, associated notably with Harlow and Hayden, indicate that some decoding tasks may be prohibitive for a realistic observer. Presence within correlations, physical accessibility and computational recoverability must therefore remain distinct.
For known astrophysical black holes, Hawking radiation is far too weak to allow direct verification. Current observations test above all general relativity, black-hole populations and the traces of their formation, not the complete quantum mechanism of information restitution.
6. From trace to reconstruction
The case of black holes shows that information may be absent from macroscopic observables without its fundamental destruction being demonstrated. We must now distinguish what remains encoded from what an observer can effectively reconstruct.
A chain in which every link can give way
The past does not become knowledge in a single step. It passes through a chain:
event → physical trace → observable → detection → data → model → historical inference.
Each transition can fail.
An event may leave no durable difference. A trace may persist in a causally inaccessible region. An observable may remain below instrumental noise. Precise data may be compatible with several histories. A model may omit a decisive mechanism. An inference procedure may finally select a mistaken explanation.
We must therefore distinguish:
• encoding: what remains physically correlated with the history;
• accessibility: what can reach the observation apparatus;
• detectability: what can be distinguished from noise;
• identifiability: what makes it possible to tell several possible histories apart;
• inference: the conclusion produced from the data and the model.
Encoded information is not necessarily accessible. Accessible information is not necessarily detectable. A detected trace does not necessarily identify a unique history. An identifiable history may still be badly reconstructed.
Reading scheme — the five filters of reconstruction
| 1. ENCODING → | 2. ACCESSIBILITY → | 3. DETECTABILITY → | 4. IDENTIFIABILITY → | 5. INFERENCE |
|---|---|---|---|---|
| What remains correlated with the past? | What can reach the observation apparatus? | What can be distinguished from noise? | Which histories do the data allow us to tell apart? | What can the model conclude, and with what uncertainties? |
Each filter conditions the next; several complementary channels can nevertheless be combined.
A functional, not a law
The reconstructibility of a historical parameter may be represented conceptually by:
R_q(t)= F_q(I_enc(t),A_causal(t),D_obs(t),M_inf(t)),
where the index q designates the historical question posed.
I_enc represents the information bearing on that question still encoded in the present physical state considered. A_causal describes the physical channel through which part of that information becomes accessible. D_obs summarises detectability, noise, resolution and data quality. M_inf gathers the hypotheses, the likelihood and the procedures by which identifiability is tested and the inference produced.
This writing is neither a fundamental equation nor an already measurable score. It constitutes a grammar of research. It represents reconstruction as a problem of inference across several physical and instrumental channels that select, transform and add noise to the information without being reducible to a single channel. To become operational, it must be applied to a precise question and translated into defined quantities: mutual information, divergence between distributions, Fisher matrix, reconstruction error or Bayesian model comparison. Its structure is conditional and not additive: one bottleneck may limit the whole reconstruction relative to a given question and channel, without another physical route being necessarily excluded. It is therefore often more accurate to speak of a network of coupled chains than of a universal product of factors.
The question would not be « can the history of the black hole be reconstructed? », but for example:
Can a formation by isolated binary evolution be distinguished from a dynamical formation in a cluster on the basis of the observed distributions of masses, spins and eccentricities?
Reconstructibility is always relative to a variable, a data set, a family of models and an accepted level of uncertainty.
Four examples for reading the chain
The same vocabulary takes on a different sense according to the object studied:
1. Impact crater. The event is encoded in a shape, fractures and transformed materials. Access is direct, but erosion reduces detectability and several projectiles can produce similar morphologies.
2. Cosmic microwave background. The anisotropies encode properties of the primordial plasma. The photons are accessible, but recombination forms a screen for earlier epochs and the inference depends on a cosmological model.
3. GW170817. The gravitational waves, the kilonova and the gamma-ray burst encode complementary aspects of the merger. Their combination reduces certain degeneracies without reconstituting a single narrative of every mechanism.
4. Evaporating black hole. The very question of encoding remains theoretically open. A globally unitary evolution could preserve the information in high-order multipartite correlations, widely dispersed within the radiation, without making it decodable by a finite observer with limited physical and computational resources.
The relevance of a model cannot be decreed
The inference model cannot be validated by direct access to the past. Its relevance is tested by its capacity to explain independent data, to produce new predictions and to withstand changes of method, instrument or auxiliary assumptions.
Validation is therefore indirect, comparative and fallibilist: predictive tests on data not used for fitting, coherence between distinct observables, sensitivity analyses to priors and auxiliary assumptions, coverage checks and the search for systematic failures. A model does not gain credibility because it retrospectively tells the data, but because it passes tests it was not built to reproduce automatically.
Convergence between several messengers strengthens a reconstruction but does not make it infallible. Distinct channels may depend on the same theoretical assumption, the same catalogue or correlated selection biases. Useful redundancy is therefore not the mere repetition of a result. It requires measurement routes independent enough that their errors do not reproduce themselves automatically.
GW170817 illustrates a physical complementarity rather than an absolute independence. Gravitational waves are chiefly related to the relativistic dynamics of the compact system, whereas interpreting the kilonova also mobilises numerical relativity, hydrodynamics, radiative transport, opacities and nucleosynthesis. Crossing them can therefore reduce certain degeneracies along different directions in parameter space. But these analyses also share astrophysical assumptions and may inherit correlated biases: the « orthogonality » of the constraints must remain a local approximation, not a guarantee against circularity.
An artefact is a recorded difference whose principal source belongs to the instrument, the processing or the environment rather than to the phenomenon studied. It is sought through calibration, noise characterisation, injection of simulated signals, comparison between detectors and robustness under several methods of analysis. No « raw trace » imposes itself without mediation, but not every interpretation is equivalent. Some explain more data, predict better and better withstand independent checks.
7. Time transforms the legibility of the past
Erasing, transporting, revealing
Time is not only what destroys traces. It acts in several ways.
It can erase them through dissipation, mixing or decoherence. It can stabilise them within a structure. It can transport them, as radiation does. It can also make them accessible late: the light of a distant event becomes observable only after travelling the distance that separates us from it.
A trace may therefore be ancient in its origin and new for the observer.
Time also modifies the conditions of observation. Cosmic expansion shifts wavelengths. Horizons can render certain regions definitively inaccessible. Stars go out, archives disperse and signals sink beneath diffuse backgrounds. Conversely, new instruments can render legible traces long present.
Knowledge of the past thus has its own temporality. What is physically preserved, what reaches the observer and what becomes interpretable do not necessarily coincide.
There is, however, no universal ranking of archives by lifetime. The persistence of a signal depends on its coupling to the environment, its frequency, the backgrounds that mask it, cosmic expansion and the question posed. A weakly perturbed messenger may preserve certain correlations over very long durations while becoming practically undetectable; conversely, a local trace may remain legible if it is stabilised within a structure. Physical durability and epistemic legibility are not the same quantity.
8. Which observer?
Detecting is not understanding
A physical detector changes state under the effect of a phenomenon. A photographic plate, a sensor or an interferometer can produce a record without consciousness or interpretation.
A recording system stabilises that change in an exploitable form: image, spectrum, time series or digital signal.
An epistemic observer then uses a model to relate these data to properties not directly present in the record. It compares hypotheses, estimates parameters and quantifies uncertainties.
We shall therefore reserve the term epistemic observer here for a system taking part in a procedure of inference. It is defined not by membership of the human species, but by its function in the reconstruction. The detector produces a difference. The record preserves it. The epistemic observer relates that datum to hypotheses and attempts to attribute a historical meaning to it.
This distinction does not make reality dependent on the human mind. The event and the trace can exist without us. What depends on the observer is the reconstruction formulated from a situated access, finite data and a revisable model.
9. When the trace becomes functional
From the physical to the living without confusing the levels
The living belongs entirely to the physical world, but it adds particular organisations. It does not merely carry the effects of its history. Certain traces are stabilised, read and used to modify future responses.
In a non-living physical system, a perturbation can produce a persistent difference. In certain biological organisations, that difference can take part in a regulation, become a memory or transform a later response. In certain cognitive and social systems, traces can further be represented, compared, discussed and transmitted.
This material continuity does not abolish the functional differences.
The physical world produces traces.
The living can render certain traces functional.
Cognition can reconstruct a meaning from them.
Science organises collective procedures to test that reconstruction.
The Universe therefore does not progressively become conscious by necessity. It has only produced, in at least some regions, material systems capable of interrogating the traces from which they themselves issue.
10. Two perspectives on physical information
Wheeler and « it from bit »
With the formula « it from bit », John Archibald Wheeler explored the idea that the description of physical reality is deeply bound up with the distinctions made possible by acts of measurement. This proposal admits several readings. It must not be reduced to the claim that matter is literally composed of information, nor that the human observer alone creates reality.
The framework developed here remains more limited. Traces are physical differences that can persist independently of our observation. The observer intervenes in their detection, their selection and their interpretation, not in the necessity of their past existence.
Rovelli and relational information
On a relational conception, information does not constitute an autonomous substance. It characterises correlations between the states of physical systems. This perspective converges with the importance granted here to access and interaction, while requiring a further distinction.
A trace can persist materially without any actual interaction with an observer. What it allows one to infer, on the other hand, depends on the interactions through which another system accesses it. The physical existence of the trace and the information available to an observer must therefore not be confused.
This position avoids two excesses. It does not turn information into a primary substance, nor does it suppose that a trace spontaneously delivers its history. The real carries differences. Knowledge depends on the experimental and theoretical relations that render some of those differences interpretable.
11. Open lines of research
Quantifying parametric degeneracies
Reconstruction always remains relative to a determinate variable. For GW170817, for instance, the luminosity distance is strongly correlated with the inclination of the system. Other parameters, such as masses, spins and tidal deformabilities, may likewise display correlations or depend on the assumptions chosen for the waveforms and the equation of state.
A first programme would consist in measuring how the addition of an electromagnetic counterpart reduces the parameter space compatible with the gravitational data. The functional R_q could be translated, in a local approximation, into a Fisher matrix. If Γ denotes that matrix, the local uncertainty volume varies approximately as:
V_q ∝ 1 / √det(Γ_q).
The gain brought by crossing messengers could then be represented by the ratio between the volume obtained with gravitational waves alone and the volume obtained after adding the electromagnetic data.
This approximation nevertheless becomes fragile when the distributions are asymmetric, multimodal or limited by physical constraints. A full Bayesian analysis then remains necessary. The information gain can notably be estimated by a Kullback–Leibler divergence between the initial distribution and the distribution obtained after observation. It is therefore preferable to speak of a reduction of the uncertainty volume or of information gain rather than of « compressibility » of information.
There is therefore no single, model-independent figure for the « exact reduction » brought by the electromagnetic counterpart of GW170817. The gain depends on the variable chosen, the priors, the jet or kilonova models, the waveforms and the data sets included. The aim of the protocol is not to announce a universal percentage, but to publish, for each configuration, posterior distributions, information gains and reproducible coverage tests.
Extending island physics to rotating black holes
The no-hair theorems describe a macroscopic reduction of the history accessible from outside. Island calculations concern another question: the compatibility of the computation of the radiation's entropy with a unitary quantum evolution.
A major theoretical extension would consist in extending these calculations to rotating black holes closer to real astrophysical objects. A Kerr black hole introduces superradiance, the angular dependence of the modes, the transmission factors of the gravitational barrier and a joint evolution of mass and angular momentum. The absence of spherical symmetry also complicates the search for quantum extremal surfaces.
It is not simply a matter of computing a spectral correction produced by the islands. These intervene first in the generalised-entropy prescription and in the computation of the entanglement entropy of the radiation. The programme must therefore distinguish the instantaneous Hawking spectrum, the evolution of mass and rotation, and then the global computation of the entropy.
This line remains chiefly theoretical. Even a coherent four-dimensional formulation would not immediately supply an astrophysical test, since the Hawking radiation of known black holes remains far too weak to be observed directly.
Separating energy transported from information reconstructed
Photons, neutrinos and gravitational waves have radically different modes of propagation and interaction. Each therefore selects a particular part of the event.
Two quantities must be separated. The energy fraction of a messenger m may be written:
f_E^(m) = E_m / E_tot.
The information gain it brings about a historical variable θ_q rather falls under a quantity such as:
ΔI_q^(m) = I(θ_q ; D_m),
where D_m designates the data of the messenger considered.
A channel may transport relatively little energy while strongly constraining a parameter. Conversely, an energetically dominant emission may remain poor for the historical question under study.
The non-detection of high-energy neutrinos associated with GW170817 therefore does not prove that no neutrino was produced. Referred to the sensitivity of the instruments, the direction of the source and the emission models, it constrains certain hypotheses about hadronic acceleration and neutrino production in the jet.
Higher-order quasi-normal modes do not constitute an energy external to the gravitational channel. They belong to the ringdown phase, but their low amplitude makes them hard to distinguish. Their detection could nevertheless supply important information about the mass, the rotation and the compatibility of the final object with the Kerr geometry.
The question then becomes: how much energy and how much information about a determinate variable are transported by each messenger, and how does their combination reduce the degeneracies between scenarios?
Extending observation beyond recombination
The cosmic microwave background marks a limit to direct electromagnetic observation of the periods preceding recombination. It does not represent an absolute limit to their study.
Relic cosmological neutrinos are thought to have decoupled about one second after the beginning of the hot expansion. Their detection would give access to a far older epoch than the one revealed by the background. It would not, however, supply direct access to inflation, presumed to be much earlier.
Primordial gravitational waves could also carry traces of very ancient processes. They could come from inflation, but also from phase transitions, topological defects or other mechanisms of the primordial Universe. Detecting a stochastic background would therefore not suffice to demonstrate a particular inflationary scenario. Its spectrum would have to be measured and several production mechanisms compared.
LISA will explore a low-frequency band inaccessible to ground-based observatories and will be able to search for certain primordial gravitational backgrounds. Its sensitivity will nevertheless be limited to a determinate frequency range and will have to be separated from the astrophysical backgrounds produced by numerous compact sources. Future neutrino detectors will pursue another part of this opening, without guaranteeing detection of the relic cosmological background.
The operational formulation is therefore not « gaining direct access to inflation », but determining which future observables will be able to constrain the periods preceding recombination and, depending on their origin, certain scenarios of the primordial Universe.
A first demonstrable protocol
Among these lines, the reduction of parametric degeneracies constitutes the most accessible pilot case. A protocol could follow seven steps:
1. choose a precise historical variable, such as inclination, a tidal-deformability parameter or an equation-of-state parameter;
2. define one and the same set of initial assumptions;
3. carry out an inference with gravitational data alone;
4. repeat the analysis with the relevant electromagnetic data alone;
5. carry out a joint inference;
6. measure the gain through the posterior volume, the Kullback–Leibler divergence and the coverage error;
7. test the robustness to waveform models, astrophysical assumptions and correlated biases.
GW170817 already provides a partial realisation of this. The gravitational data imposed an upper bound on certain combinations of tidal deformability, while the interpretation of the kilonova, coupled with numerical-relativity simulations, proposed a complementary bound. The gain therefore does not come from a mere stacking of data: it depends on assumptions about the ejecta, the opacity, the remnant and the equation of state. This case illustrates both the power and the model-dependence of multimessenger inference.
Other multimessenger events observed by a network of gravitational detectors with increased sensitivity and endowed with electromagnetic counterparts will make it possible to test this grid on a population rather than on a single case.
The functional R_q would thus become a grid of conditional reconstructibility applied to a falsifiable question, rather than a general and abstract measure of the recoverable past.
Conclusion
Assessment, questions and methods
Not every transformation leaves a durable trace. Not every durable trace is accessible. Not every accessible trace is detectable. Not every detected trace makes its history identifiable. And not every identifiable history is necessarily correctly reconstructed.
Conceptual assessment. Knowledge of the past depends on a chain of conservation, transmission, detection and inference, each link of which has its limits.
Black holes make this difficulty extreme. Their stationary external state reduces a complex history to a few macroscopic parameters. Their environment and the radiation emitted during their formation may preserve more detail. Quantum theory suggests that the disappearance of macroscopic distinctions must not be too quickly confused with a fundamental destruction of information. But the exact way in which that information remains encoded and might be restored remains one of the great open problems of physics.
Open questions. Our incomprehensions prove neither the absence of structure nor the complete conservation of every history. The priority problems concern the quantity of information still encoded, its accessibility according to the messengers, the identifiability of competing histories, and the dependence of results on models.
Gravitational decoherence makes the boundary between effective loss and fundamental loss particularly delicate. In a reduced description, where certain degrees of freedom are ignored, it can produce a loss of coherence and render the information locally unusable. If the global evolution remains unitary, that information is nevertheless not destroyed: it is redistributed into correlations with the environment. A fundamental loss would require a non-unitary dynamic or a deeper modification of the quantum framework, a distinct and unestablished hypothesis.
Other possible archives finally deserve to be tested. The large-scale distribution of galaxies, cosmic voids or cosmological magnetic fields could preserve constraints on primordial asymmetries and mechanisms. Their reconstructive value nevertheless depends on the capacity to separate an initial signature from later non-linear and astrophysical transformations.
The Universe does not remember in the sense in which an organism uses a memory. But its transformations produce persistent differences, correlations and modifications of structure. Some render part of the past accessible. Others disappear, disperse or cross causal limits.
Promising methods. Multimessenger astronomy, Bayesian analysis, the study of correlations, inter-instrumental robustness tests and future detectors offer the most concrete routes for turning this grid into a research programme.
The past is therefore neither entirely present nor entirely lost. It survives selectively in what the transformations have preserved and in what our position as observers still allows us to read.
The Universe does not remember. It preserves differences. Science begins when some of those differences become legible traces, and then hypotheses about a history we can never observe directly in its entirety.
Methodological appendix
Mutual information
Within a defined generative model, the mutual information I(Q;X) can quantify the statistical dependence between a historical variable Q and a present physical state X. In the quantum regime, for a joint state ρ_QX, the mutual information is written I(Q:X) = S(Q) + S(X) − S(QX), where S denotes the von Neumann entropy. This quantity operationalises encoding relative to the choice of variables, of partition and of model; it is not an absolute measure of what the real preserves.
If I(Q;X) = 0 for the complete state and the genuinely relevant partition, no procedure founded on X can reconstruct Q. In practice, a zero obtained within a reduced description can only signal that the correlation is absent from the degrees of freedom retained; it does not by itself demonstrate a fundamental destruction of information.
Chain of channels and bottlenecks
A simplified scheme may be written Q → X → O → D → Q_est, where X is the present state carrying any correlations with Q, O the physically accessible part, D the data produced by the detector and Q_est the final estimate. If each stage is represented by a stochastic or quantum channel, processing cannot by itself create information about Q.
I(Q;D) ≤ I(Q;O) ≤ I(Q;X).
This data-processing inequality formalises the idea of successive losses or bottlenecks, while leaving open the combination of several complementary channels. It does not turn the chain into a universal law: the variables, channels and partitions must be defined for each problem.
Causal accessibility
Accessibility may be represented by a classical or quantum channel E_q that transforms the encoded state X into a set of accessible observables O:
O = E_q(X).
The quantity I(Q;O) then measures what remains correlated with Q after that channel. A ratio I(Q;O) / I(Q;X) may sometimes serve as an indicator of transmission when the denominator is non-zero, but it does not define a universal coefficient of accessibility. The channel may depend on frequency, geometry, time, messenger and the causal structure of the model. In frameworks where the notion of horizon is dynamic, observer-dependent or non-classical, E_q must be defined from the observables and the theory considered; it does not necessarily reduce to a binary projection.
Fisher and Cramér–Rao
For a signal model h(θ) and a defined noise model, the Fisher matrix is written locally:
Γ_ij = (∂h/∂θ_i | ∂h/∂θ_j).
Under regularity assumptions and at a sufficiently high signal-to-noise ratio, the inverse of this matrix supplies a local approximation of the minimal covariance. This method does not replace a Bayesian inference when the distributions are asymmetric or multimodal. A singular or ill-conditioned matrix signals locally poorly identifiable directions, but Fisher information remains a local measure: it does not necessarily detect global degeneracies, separated posterior modes or non-regular boundaries.
Bayesian evidence
For a model M_q, the evidence is:
P(D | M_q) = ∫ P(D | θ, M_q) P(θ | M_q) dθ.
The Bayes factor compares the evidences of two models:
B_12 = P(D | M_1) / P(D | M_2).
The evidence depends on the priors. It does not constitute an automatic Occam's razor independent of the initial assumptions. It compares the integrated predictive plausibility of defined models, but does not by itself summarise the identifiability of the parameters. That also depends on the structure of the likelihood, on the map relating parameters to observables, and on the geometry of the posterior distribution.
Non-detection and likelihood
A non-detection is itself a result of observation. It becomes informative when P(non-detection | M_1) differs from P(non-detection | M_2) for the models compared. It can then shift the likelihood ratios and the posterior distributions without implying that the physical phenomenon sought is absent.
Bibliographic markers
Cosmological traces and the microwave background
NASA, Cosmic Background Explorer (COBE), mission overview and maps of the cosmic microwave background.
NASA/WMAP, A Universe of Surprise: About the Cosmic Microwave Background.
Gravitational waves and black holes
Abbott, B. P. et al. (LIGO Scientific Collaboration and Virgo Collaboration) (2016). Observation of Gravitational Waves from a Binary Black Hole Merger. Physical Review Letters, 116, 061102.
LIGO Scientific Collaboration, scientific glossary: merger, ringdown phase and black-hole modes.
Thermodynamics and information of black holes
Hawking, S. W. (1975). Particle Creation by Black Holes. Communications in Mathematical Physics, 43, 199–220.
Page, D. N. (1993). Information in Black Hole Radiation. Physical Review Letters, 71, 3743–3746.
Almheiri, A., Hartman, T., Maldacena, J., Shaghoulian, E. & Tajdini, A. (2021). The Entropy of Hawking Radiation. Reviews of Modern Physics, 93, 035002.
Hawking, S. W., Perry, M. J. & Strominger, A. (2016). Soft Hair on Black Holes. Physical Review Letters, 116, 231301.
Mirbabayi, M. & Porrati, M. (2016). Shaving off Black Hole Soft Hair. Physical Review Letters, 117, 211301.
Hayden, P. & Preskill, J. (2007). Black Holes as Mirrors: Quantum Information in Random Subsystems. Journal of High Energy Physics, 2007(09), 120.
Harlow, D. & Hayden, P. (2013). Quantum Computation vs. Firewalls. Journal of High Energy Physics, 2013(06), 085.
Inference and reconstructibility
Cover, T. M. & Thomas, J. A. (2006). Elements of Information Theory (2nd ed.). Wiley.
MacKay, D. J. C. (2003). Information Theory, Inference, and Learning Algorithms. Cambridge University Press.
Multimessenger astronomy
Abbott, B. P. et al. (2017). Multi-messenger Observations of a Binary Neutron Star Merger. The Astrophysical Journal Letters, 848, L12.
Radice, D., Perego, A., Zappa, F. & Bernuzzi, S. (2018). GW170817: Joint Constraint on the Neutron Star Equation of State from Multimessenger Observations. The Astrophysical Journal Letters, 852, L29.
Albert, A. et al. (2017). Search for High-energy Neutrinos from Binary Neutron Star Merger GW170817 with ANTARES, IceCube, and the Pierre Auger Observatory. The Astrophysical Journal Letters, 850, L35.
Perspectives on information
Wheeler, J. A. (1990). Information, Physics, Quantum: The Search for Links. In W. H. Zurek (ed.), Complexity, Entropy and the Physics of Information. Addison-Wesley.
Rovelli, C. (1996). Relational Quantum Mechanics. International Journal of Theoretical Physics, 35, 1637–1678.
Instruments and prospects
European Space Agency (ESA). LISA mission and science objectives. Mission documentation.
LIGO Scientific Collaboration. Methodological work on degeneracies between luminosity distance and inclination of compact sources.
Status of the text
This essay distinguishes established results, open problems and a methodological proposal by the author. The descriptions of the cosmic microwave background, gravitational waves, the external parameters of black holes and the information paradox draw on the scientific literature. The chain « transformation → persistence → accessibility → detectability → identifiability → reconstruction », the functional R_q and their conditional translation in terms of channels, mutual information and inference constitute a heuristic grid. They are not presented as a new physical law, but as a framework meant to specify what must be measured, which assumptions make a reconstruction possible and what could refute it.