Why does a broken egg never reassemble itself? Every law governing the motion of its atoms is perfectly reversible — run the film backward and nothing in the mathematics complains. And yet, in the real world, broken eggs stay broken. This gap between what our equations allow and what nature actually does has haunted physics for over a century. A new paper from the University of Costa Rica proposes an answer that is as philosophically bold as it is mathematically precise.

The Paradox That Won’t Go Away

In the 1870s, the Austrian physicist Josef Loschmidt challenged Ludwig Boltzmann’s statistical explanation of the second law of thermodynamics. His objection was devastatingly simple: if the equations of motion work the same forwards and backwards in time, how can entropy — disorder — only ever increase? This is Loschmidt’s paradox, and it sits at the intersection of thermodynamics, quantum mechanics, and the philosophy of science.

Physicists have proposed many partial answers. Some invoke the statistical improbability of reversal (there are astronomically more disordered states than ordered ones). Others appeal to cosmological boundary conditions — the universe simply started in a very special, low-entropy state. More recent work, cited in this paper, turns to information theory and Landauer’s principle (the idea that erasing information has a minimum physical cost).

But the author — José Mauricio Gómez Julián, writing from the University of Costa Rica — finds all of these solutions insufficient. His central claim is provocative: the paradox is not in nature. It is in our models. We build theories that are fundamentally ahistorical, then act surprised when the real world — which is fundamentally historical — doesn’t obey them. The problem, he argues, is not that reality misbehaves. It is that our theories refuse to remember.

The Philosophical Engine: Dialectical Materialism

The paper is grounded in dialectical materialism — a philosophical tradition rooted in Marx and Engels, developed further by Hegel (in its idealist form) and by Soviet physicists like Blokhintsev and Rosental. If that sounds unusual for a physics paper, the author would say: that’s exactly the point.

Dialectical materialism holds that reality is made of matter in motion, that contradictions are not flaws in our thinking but features of the world, and that quantitative changes eventually produce qualitative leaps. It also insists on a distinction that modern physics has muddled:

• Epistemology — what we can know and measure (our limitations as observers).
• Ontology — what actually exists in the world, regardless of our ability to observe it.

This distinction turns out to be the paper’s sharpest tool. When quantum mechanics says that a particle’s position is “uncertain,” the author asks: is that uncertainty a feature of reality (ontology), or a feature of our knowledge (epistemology)? His answer is nuanced and consequential. The Schrödinger equation itself is fully deterministic — give it an initial state and a Hamiltonian, and it will predict the future wave function with perfect precision. The randomness enters only when we try to measure — when the quantum system meets our macroscopic instruments.

In other words, probability in quantum mechanics is an epistemological resource — a powerful tool for managing complexity and incomplete knowledge — not a statement that reality itself is fundamentally random. This does not mean quantum mechanics is wrong. It means that its probabilistic character tells us about us, not about the universe.

The author is careful, however, to distinguish this from classical Laplacian determinism. Heisenberg’s uncertainty principle, he argues, is ontological — it reflects genuine structural features of reality (the complementarity between position and momentum). So the world is deterministic in a deep sense, but not in the naive clockwork sense. It is deterministic in the way a complex, path-dependent system is deterministic: constrained, structured, lawful — but too intricate for any observer to fully predict.

Path Dependence: History Before Time

Here is where the paper makes its most original conceptual move. The author argues that path dependence is more fundamental than time itself.

What does this mean? In complex systems — economies, ecosystems, living organisms — the current state depends not just on the present conditions but on the entire sequence of events that led there. An economy with the same GDP, population, and technology as another can behave very differently because its institutions, crises, and policy choices followed a different historical path. The paper claims this is not just a feature of complex systems. It is a feature of all physical reality, at every scale.

In this framework, time is reimagined. It is not a background parameter through which things happen (as in Newtonian mechanics), nor a dimension woven into spacetime (as in relativity), but rather a structure that records material transformations — a kind of universal memory. Space and time co-emerge as the necessary fabric for matter to develop and preserve its evolutionary trajectory.

The author traces this insight back to Hegel’s philosophy of nature (published decades before Einstein’s relativity), where place, space, and time are understood as a unity — and where motion (and therefore matter) arises from their contradiction. The passage is striking:

Place is spatial singularity… This perishing and regenerating of space in time and of time in space… is movement. This becoming… is the immediate, identical and existing unity of space and time: it is matter.
— Hegel, Encyclopaedia of the Philosophical Sciences

If path dependence is fundamental, then irreversibility is not something to be explained — it is something to be assumed, just as mathematicians assume the existence of natural numbers rather than proving it. Every broken egg, every aging star, every evolved species is evidence that the universe remembers its own history.

A New Equation for a Remembering Universe

The author doesn’t stop at philosophy. He proposes a concrete mathematical reformulation of the Schrödinger equation — the foundational equation of quantum mechanics — to make path dependence explicit.

Standard quantum mechanics writes:

The paper’s reformulation introduces a history-dependent Hamiltonian:

This is a bold move. It says: the state of a quantum system at any moment is shaped by the entire chain of interactions that brought it there — not just by its instantaneous configuration. The author also defines a metric on this “interaction space,” capturing the distance between interactions in terms of both complexity and energy change, and proves it satisfies the standard properties of a mathematical metric (nonnegativity, symmetry, triangle inequality).

The elegance of this formulation is that it reproduces known physics as special cases:

• Classical regime (low energy, macroscopic): the metric reduces to ordinary Euclidean geometry.
• Relativistic regime (high velocity): it reproduces the Minkowski spacetime interval.
• Quantum regime (entanglement, superposition): the metric captures quantum correlations through entanglement entropy.

Entanglement Without Spookiness

The path-dependent framework also offers a fresh take on quantum entanglement — Einstein’s famous “spooky action at a distance.” In the standard picture, measuring one entangled particle seems to instantaneously affect its partner, no matter how far away. In the author’s framework, entangled particles don’t communicate across space. They share a common interaction history. They are “close” in interaction space even when they are far apart in physical space — much like two points on a folded piece of paper that look distant but are actually adjacent when the paper is unfolded.

Bell’s theorem — which proved that no local realistic theory can reproduce all quantum predictions — is not violated but reinterpreted: the “nonlocality” is real in emergent spacetime but disappears when you consider the deeper interaction space. Locality is preserved at the fundamental level; it only appears broken in the effective spacetime we observe.

Why Does Matter Seek Stability?

The paper’s second major argument is about teleology — the idea that natural processes are directed toward ends or purposes. This is a concept that modern science has largely banished (with some notable exceptions in biology). The author argues it should be restored — but in a materialist, not a mystical, form.

The claim: physical systems universally tend toward maximum achievable stability within their material constraints. This is not an external force or an intelligent design. It is an inherent property of matter itself, arising from the internal contradictions within material systems.

The evidence spans every scale of reality:

• Cosmological: The universe’s laws appear “fine-tuned” for structure and complexity. Cyclic cosmological models suggest a drive to preserve laws conducive to stability.
• Stellar: Stars burn through nuclear fuel, then transform — into white dwarfs, neutron stars, or supernovae — each outcome representing a reorganization toward the next achievable stable state.
• Chemical: The pressure-induced transformation of graphite to diamond. Autocatalytic systems that reorganize when reactants deplete.
• Biological: DNA’s role as a stable transcription template. Gould’s punctuated equilibria — long periods of stasis followed by rapid change. Insect metamorphosis.
• Neural: The brain reorganizing through neuroplasticity after injury or during learning.
• Social: Revolutions occurring when existing structures of production become incompatible with productive forces.

In each case, the pattern is the same: systems seek stability, achieve it temporarily, exhaust the conditions that made it possible, undergo a qualitative transformation, and resume the search in a new configuration. Stability is the attractor; transformation is the mechanism.

Least Action and Ground States

The author connects this teleological perspective to two pillars of physics:

The principle of least action — the mathematical rule that physical systems follow paths that extremize (usually minimize) the “action” functional. This is usually treated as a computational tool. The paper reinterprets it as a teleological law: systems select trajectories in service of their drive toward stability, and the path of least action is the one that best serves this purpose. Sometimes, the system does not take the absolute minimum energy path — because the absolute minimum may not serve the broader goal of sustained stability.

The ground state tendency — quantum systems’ natural inclination to settle into their lowest energy configuration. The author, drawing on Solovej’s work on the stability of matter, argues this is not merely a mechanical outcome but an expression of matter’s fundamental need for stabilization. Electrons don’t “accidentally” fall into lower energy levels. They are driven there by the internal logic of material reality.

The Arrow of Time, Revisited

With path dependence as the foundation, the arrow of time becomes almost trivial to explain. Time flows in one direction because systems are historical. The future depends not only on the present state but on the entire trajectory that led to it. Irreversibility is not a statistical accident or a cosmological boundary condition — it is a structural feature of reality, as basic as the existence of natural numbers in mathematics.

The author draws an analogy to the Cosmic Microwave Background (CMB) — the faint radiation left over from the early universe, which provides a natural “preferred frame” for cosmic observations without violating relativity. Similarly, the paper proposes that a preferred temporal direction can emerge from path dependence without requiring absolute time. Each observer may have their own “proper time,” but the causal structure — the chain of dependencies — is invariant and objective across all reference frames.

This bridges a gap between quantum mechanics and general relativity. Quantum theory works with a notion of time closer to the classical (absolute) picture, while relativity treats time as relative and observer-dependent. The path-dependence framework offers a way to reconcile both: the ordering of interactions is fundamental and observer-independent; the measurement of time is relative.

Testable Predictions

The paper does not remain in the realm of philosophy. It proposes four concrete experimental protocols:

• Decoherence studies: Prepare identical quantum systems, give them different interaction histories, and measure whether their decoherence rates differ. The paper predicts they will.
• Entanglement analysis: Generate entangled photon pairs, expose them to different interaction histories, and check whether entanglement strength decays exponentially with “interaction distance” as the metric predicts.
• Modified double-slit experiment: Introduce controlled interaction histories before particles reach the slits and look for history-dependent deviations in the interference pattern.
• Time emergence clocks: Prepare identical atomic clocks with different interaction histories and compare their temporal evolution rates.

These are technically demanding experiments — requiring millikelvin temperatures, ultra-high vacuum, single-photon detection, and high-fidelity quantum tomography — but they are within reach of current laboratory capabilities. The predictions are specific enough to be falsified, which is exactly what good science requires.

Why This Matters Beyond Physics

If you are an economist, a political scientist, or simply someone who thinks about how societies change, this paper’s conceptual framework should feel familiar — and provocative.

The concept of path dependence is already central to institutional economics (think of Douglass North or Paul David’s QWERTY keyboard). The idea that history matters — that you cannot understand a system’s current state without knowing how it got there — is a staple of comparative politics and historical sociology. What this paper does is argue that path dependence is not just a useful metaphor borrowed from physics. It is a fundamental feature of physical reality itself.

Similarly, the paper’s concept of teleology without intention — systems pursuing stability through the internal logic of their own contradictions — resonates powerfully with Marx’s theory of historical materialism, where modes of production develop, exhaust their potential, and undergo revolutionary transformation. The author draws this connection explicitly, noting that revolutions occur “when existing relations of production become incompatible with developing productive forces.”

And the distinction between epistemology and ontology — between what we can model and what actually exists — is a question every social scientist should take seriously. When our econometric models fail to predict a financial crisis, is the crisis a “black swan” (an anomaly), or is it evidence that our models are too ahistorical to capture reality?

The problem is not that reality “contradicts” theory but that theory is a limited abstraction of reality, creating tension when attempting to make reality fit the model instead of developing models that capture reality’s historical-contextual nature.
— José Mauricio Gómez Julián

A Bridge Between Worlds

This is not a paper that will convince everyone. Its philosophical framework — dialectical materialism — is unfamiliar and, for some, politically charged. Its mathematical proposals, while rigorous, are exploratory and await experimental confirmation. Its claim that teleology is a fundamental feature of matter will strike many physicists as a step backward toward pre-modern thinking.

But that is precisely what makes it worth reading. In a landscape where theoretical physics has fragmented into string theory, loop quantum gravity, and various interpretations of quantum mechanics that all reproduce the same experimental results, a paper that asks “What if we’re starting from the wrong assumptions?” is exactly the kind of provocation that science needs.

The paper’s deepest contribution may be methodological: a demonstration that philosophy and physics can inform each other without either colonizing the other. The philosophical framework provides the conceptual clarity to ask better questions. The physics provides the experimental discipline to test whether those questions have real answers.

Whether or not its specific proposals survive experimental scrutiny, the paper succeeds in something more modest but no less important: it makes you see the broken egg differently. Not as a problem to be explained away, but as evidence of a universe that remembers — and that, in remembering, moves irreversibly forward.