The assumption that a complete description of an early state of the universe does not privilege any position or direction in space leads to a unified account of probability in cosmology, macroscopic physics, and quantum mechanics. Such a description has a statistical character. Deterministic laws link it to statistical descriptions of the cosmic medium at later times, and because these laws do not privilege any position or direction in space, the same must be true of these descriptions. If the universe is infinite, we can identify the probability that the energy density at a particular instant and a particular point in space (relative to a system of spacetime coordinates in which the postulated spatial symmetries are manifest) lies in a given range with the fractional volume occupied by points where the energy density lies in this range; and similarly with all other probabilities that figure in the statistical description. The probabilities that figure in a complete description of the cosmic medium at any given moment thus have an exact and objective physical interpretation. The statistical entropy and the information associated with each cosmological probability distribution are likewise objective properties of the universe, defined in terms of relative frequencies or spatial averages.
The assumption that a complete description of an early state of the universe does not privilege any position or direction in space leads to a unified account of probability in cosmology, macroscopic physics, and quantum mechanics. Such a description has a statistical character. Deterministic laws link it to statistical descriptions of the cosmic medium at later times, and because these laws do not privilege any position or direction in space, the same must be true of these descriptions. If the universe is infinite, we can identify the probability that the energy density at a particular instant and a particular point in space (relative to a system of spacetime coordinates in which the postulated spatial symmetries are manifest) lies in a given range with the fractional volume occupied by points where the energy density lies in this range; and similarly with all other probabilities that figure in the statistical description. The probabilities that figure in a complete description of the cosmic medium at any given moment thus have an exact and objective physical interpretation. The statistical entropy and the information associated with each cosmological probability distribution are likewise objective properties of the universe, defined in terms of relative frequencies or spatial averages.
Quantum cosmology is the quantum theory of the entire universe. Although strange at first sight, it is appropriate because (1) our world appears to be fundamentally quantum, (2) the classical description of gravity breaks down at singularities it would give at the beginning of the universe, and (3) our universe has many properties that cannot be explained by a classical description of them. A quantum state of the universe should obey certain constraints, such as the Wheeler-DeWitt equations. One approach to interpreting such a state is {\it Sensible Quantum Mechanics} (SQM), in which nothing is probabilistic, except, in a certain frequency sense, conscious perceptions. Sets of these perceptions can be deterministically realized with measures given by expectation values of positive-operator-valued {\it awareness operators}. These may be defined even when the quantum state itself is not normalizable, though there still seem to be problems of divergences when one has an infinite amount of inflation, producing infinitely large spatial volumes with presumably infinite measures of perceptions. Ratios of the measures for sets of perceptions (if finite) can be interpreted as frequency-type probabilities for many actually existing sets rather than as propensities for potentialities to be actualized, so there is nothing indeterministic in a specific SQM. One can do a Bayesian analysis to test between different specific SQMs. One can also make statistical predictions of what one might perceive within a specific SQM by invoking the {\it Conditional Aesthemic Principle}: among the set of all conscious perceptions, our perceptions are likely to be typical.
Every vertex of the magic cube of physics discussed so far introduced a major element in the development of physics and the whole of science. Mechanics introduced the basic concept of equations of motion, or time-evolution of a physical system given certain initial condition and the associated idea of determinism, even with its generalization in the form of chaos, the dependence of the outcomes of the temporal evolution on the initial conditions. These concepts taken for many particles, or elements of a physical system, led to the probabilistic description of many particle systems, in the realm of statistical physics and thermodynamics, whereby the averages over time of various observable quantities were related to the ensemble averages, that involve classical, so-called Kolmogorov, probability measures, at least for certain “equilibrium” situations. The second law of thermodynamics introduced the concept of entropy and its probabilistic increase, the first truly emergent, probabilistic law in physics (temperature and pressure, being other emergent quantities, apart from entropy, the measure of disorder of a statistical system). In the context of Newtonian gravity, one gets, at least in retrospect the geometric description of gravity in non-relativistic, Galilean spacetime. Galilean relativity, based on the asymmetric mixing of space and time, with the absolute, universal time, true for all observers, gets generalized in special theory of relativity to observer dependent space and observer dependent time, viewed as “slices” of a new concept of spacetime, with the new concept of causal structure, that distinguish timelike, null and spacelike events. This in turn is made into a full dynamical geometric structure of spacetime with a relativistic description of gravity stemming from curvature of spacetime, and a dynamical causal structure, tied to gravity. In our next story, the story of quantum theory, we will encounter fundamental, intrinsic probabilities, that can interfere, unlike the classical probabilities of statistical thermodynamics, and which are consistent with equations of motion of individual elements, and not, as in statistical thermodynamics, with temporal averages over the time evolution of many elements. This is the big new lesson of quantum theory, that transcends the lessons of classical spacetime physics.
In a deterministic theory, one can deduce the state of the universe at any one time from the dynamical laws that govern its evolution and its state at any other time.In particular, one can deduce from the conditions that obtained at some early boundary condition for the universe, its state at all subsequent times.It is a piece of well-received philosophical common sense that there is no room in a deterministic theory for objective probabilities.Arguments will be given below that this piece of philosophical common sense is mistaken, and that a probability measure over the space of physically possible trajectories is an indispensable component of any theory -deterministic or otherwise -that can be used as a basis for prediction or receive confirmation from the evidence.Phase space is the central representational space in physics.It is the space within which all of the states pertaining to a system are represented, and it encodes all of the general information that we have about those states.To take an obvious example (less obvious examples will be given below) the fact that a pair of quantities are represented by different dimensions in phase space encodes the fact that they represent separate degrees of freedom.Physically possible histories are represented by trajectories through phase space and in a deterministic theory, when dealing with a closed system, there is (no more than) one trajectory through each point.Since the universe as a whole is the only truly closed system, this means there is one trajectory through each point in the phase space of the universe.Probabilities may be invoked in applications of theory, when the state of a system or the values of external variables are not known with full precision, but they are eliminable given complete knowledge.And they don't appear in the statement of the laws.The laws serve simply to identify the physically allowable trajectories.About Newtonian dynamics, Laplace famously said "given for one instant an intelligence which could comprehend all the forces by which nature is animated and the respective situation of the beings who compose it -an intelligence sufficiently vast to submit these data to analysis -it would embrace in the same formula the movements of the greatest bodies of the universe and those of the lightest atom; for it, nothing would be uncertain and the future, and the past, would be present to its eyes."ii It is a short step from this to the idea that probabilities invoked in classical contexts are subjective rather than objective.If they represent anything, it is facts about our epistemic states, not facts about the world.iii Popper, and Lewis, and other influential figures have endorsed this view, categorically rejecting any role for objective probabilities indeterministic contexts.In Popper's words:
We reconsider the problem of the interpretation of the Quantum Theory (QT) in the perspective of the entire universe and of Bphr idea that the classical language is the language of our experience and QT acquires a meaning only with a reference to it. We distinguish a classical or macroscopic level, and a quantum or microscopic one that is perceived only through the modifications that it induces in the first. The macroscopic state of the universe is assumed to be specified by a set of variables, a classical energy momentum tensor and some conserved currents, which are supposed to have a well defined value across the entire space-time. To the energy-momentum tensor a classical metric is related by the Einstein equation. The quantum state and dynamics are expressed by the usual QT formalism in terms of a density operator and the ordinary quantum operators in Heisenberg picture. For the macroscopic variables a basic distribution of probability is postulated in terms of a density and the corresponding quantum operators, so in some way their evolution is driven by the underlying QT. Such postulate essentially replaces the usual elfadjoint operators correspondence. For the Universe we adopt a variance of the ΛCDM model with Omega=1, one single inflaton with an Higgs type potential, the initial time at t=minus infinite. The expectation values of all fundamental fields are supposed to vanish for time going to minus infinite. In the framework the scalar fluctuation in the Cosmic Microwave Background are correctly explained giving appropriate calue to the parameters in the potential. As in more conventional models the absence of the tensor fluctuations remains not understood, if even a quantum metric is introduced. This seems to suggest that Gravity is a pure classical phenomenon, what could be consistently accommodated in our formalism by an appropriate even if somewhat ad hoc assumption
Theory of Relational Dimensional Coexistence: An Ontological Model of Observation, Light, and the Multiverse Giuseppe Trizzino Abstract This work outlines a theoretical framework of Relational Dimensional Coexistence, proposing that spatial dimensions and physical reality do not possess absolute, independent existence. Existence is modeled as an emergent property generated through observation. By integrating principles of relational quantum mechanics with an asymmetric causal model of perception, it is postulated that energy exists as a static, primordial stock, but that observation via electromagnetic propagation (light) acts as the fundamental tool and medium for its activation: observing implies being observable, thus giving rise to an infinite network of universes in which the primordial energy stock takes on dimensional form through specular relation. 1. Introduction: The Problem of Ontological Independence Traditional physics treats space, time, and energy as pre-existing background metrics within which observers subsequently evolve. However, quantum mechanics—particularly in relational interpretations (Rovelli) and the principle of complementarity (Bohr)—suggests that physical properties materialize only through interaction. This work introduces a radical inversion: the act of observation precedes and conditions the existence of the dimension itself. Without an active observational bridge, energy, light, and spatial dimensions collapse into nothingness. 2. The Principle of Observability and Openness to the Multiverse A fundamental pillar of this model is the ontological reflexivity of observation: Whoever observes, exists and is observable: Observation is never a one-way street or an isolated privilege. The moment a universe (or dimension) A observes a universe B, A activates its own energy field and demonstrates its existence precisely by virtue of the fact that the observer can itself be observed. The probability of infinite universes: Because every act of observation generates space for the observed and legitimizes the existence of the observer within the energy circuit of light, the system is not confined to a single pair of realities. Probabilistically, this opens up an unlimited multiverse: an infinite network of dimensions that watch each other, move reciprocally, and keep each other alive. 3. The Three Hypotheses of Relational Dynamics Within this system of universes, the interaction between two dimensions (e.g., A and B) is articulated in three distinct configurations: First Hypothesis (A observes B): Universe A observes B in an energetically passive manner via light (without exerting mechanical force or violently altering the other). A can only observe without acting, or interact; only B (the observed) can change its reality and dimension. This act allows B to exist and have the freedom to move and mutate its own dimension. At the same time, A lives and justifies its own existence precisely through its act of observing (since observing implies being inserted into the network of observability). Second Hypothesis (If B also observes A): If Universe B begins to observe A, and if A is simultaneously inserted into the visual field of a third element (C), the network expands. This is not a simple sum of isolated gazes, but an ontological chain reaction that expands the multiverse. Third Hypothesis (Reciprocal and Symbiotic Observation): By law, by chance, or by causality, observation becomes perfectly reciprocal and simultaneous. In this state, A observes B and B observes A in the same instant. Observation becomes symbiotic: the two dimensions coexist as a dimension and an anti-dimension (positive and negative), relating in such a way as to allow the coexistence and life of both, without ever being able to "touch" or mechanically destroy the other. 4. Light and Energy as Ontological Consequences The model redefines the causal chain of the universe: {Observation / Observability} — {Medium (Light)} — {Energy} — {Dimensional Existence} Light as a Non-invasive Bridge: Observation occurs via light, which acts as a medium of informative and specular connection, devoid of violence or mechanical force, but an absolute potential. Energy as a Product of Relation: We live in a universe made of energy, but energy, as a static primordial stock, acts as a vehicle for dimension and reality. Without the act of observation and the condition of observability, the medium does not "turn on," energy does not manifest, and there can be no dimension. Observation as Tool and Medium: Spatial reality exists and is maintained in life solely by the energy flow triggered by the gaze. The primordial stock is inherently static. It is the act of observation that acts as the tool and medium to unlock that energy, turning on light as an informative vector. 5. Conclusion The Relational Dimensional Coexistence model demonstrates that cosmic loneliness is a physical and logical impossibility. Reality is an immense fabric of mirrors: dimensions exist because they watch one another, reciprocally authorize each other to be, move through the freedom of the observed, and sustain themselves as a single, infinite energy system based on light and reciprocity. How can a dimension or reality be born from an observation? If we state that the energy stock is already there (static and primordial), how does the simple "act of looking" (the gaze) materially bring about a dimension or reality that did not exist before? The answer lies in moving beyond the idea that space is an "empty container" that exists regardless. In our model, a dimension is not a block of matter, but the geometric and relational space that opens up when energy is directed. The vacuum has no coordinates without a relation: Before observation, the primordial energy stock is a "zero-dimensional" entity, an unformed potential, infinite but immobile. It has no "up," "down," "inside," or "outside" because there is no distance to measure. Geometric space (dimension) arises only the moment there is a point of view pointing toward another point. The distance traveled by light traces the inaugural line of space. Light as the "Pencil" of Space: Light is not just information traveling; physically, it is energy in motion. The moment the gaze (via light) departs from A to reach B, that energy beam establishes a coordinate. It creates a living Cartesian axis between the two. Without that beam, the two are in an unformed non-place. With the beam, distance is traced, and tracing a distance means creating dimension. Actualization of Potential: Taking the principle of quantum indeterminacy: a particle is a "cloud of probability" until a measuring instrument forces it to "choose" a defined position. Extending this to a cosmic scale: the primordial energy stock is the infinite probability cloud. Observation is the act of universal measurement that "collapses" potential into a precise geometric reality. Static energy becomes spatiality precisely because the gaze forces it to focus on an axis of relation. Why is everything, nothing, and everything possible? In traditional quantum physics, as long as a system is isolated and unobserved, it exists in a superposition of states (the wave function). It is only interaction with the outside—the act of measurement—that forces the wave function to "collapse," extracting from the chaos of probabilities a unique event. Applying this to our theory: The Chaos of Potential: Without observation, the primordial energy stock fluctuates in a state of pure acausal potential. Everything is in potential and nothing is in act. Observation as "Cosmic Collapse": The act of observing acts as the ultimate measurement tool of reality, forcing primordial energy to exit probabilistic superposition. The Birth of Dimension: The moment the gaze sets the limit and traces the coordinate between universes, the "everything is possible" crystallizes into a precise geometric form. Spatial dimension arises exactly from this collapse: space is nothing more than the distance established and rendered real by the interruption of probability.
We present a unified framework in which the universe is described by a single global quantum probability distribution that is continuously refined by universe observer events — physical correlations that act as objective Bayesian informational updates. While the framework builds upon QBism (Bayesian view of measurement) and holographic dark energy (future-horizon cutoff), it introduces several original elements: a precise, objective definition of a Universe Observer Event (UOE) as the minimal process generating at least one bit of mutual information; a convergence theorem showing that, in the limit of infinite sampling, local descriptions converge to the true global distribution; an informational-pressure interpretation of dark energy arising from the expansion needed to accommodate increasing samples; and a dynamical selection mechanism in which the Standard Model parameters emerge as stable fixed points of the global Bayesian update superoperator. This minimal postulate resolves the measurement problem without ad-hoc collapse, derives emergent spacetime and gravity from holographic sampling of entanglement, explains dark sectors as unobserved probability regions, and naturally accounts for the small cosmological constant and the ``why now?'' coincidence. The framework predicts a mildly phantom and time-varying equation of state wDE(z) distinguishable from ΛCDM, testable with near-future data from DESI, Euclid, and LISA. It offers a concrete, observer-centric path toward a Theory of Everything in which all physical laws and the emergence of life and consciousness arise from the universe's continuous self-description through informational updates.