Dear explorers,
When we concluded the previous leg of our voyage across the Dirac Sea, we stood before the Big Ring – that impossible cosmic structure, perhaps an echo from a previous eon. We asked: if time is emergent, if spacetime is not fundamental, then what is? And how can we experimentally test this radical idea?
Today we dive deeper than ever. From atomic interferometers in laboratory basements to the wave function of the entire Universe – from an equation that contains no time to the mechanism that gives birth to it. This is a post about time, about collapse, and about how one experimental confirmation of a cubic phase dependence can change everything we know about reality.
🧭 Penrose and Dunajski: A Phase Difference Growing with the Cube of Time
In 2023, Roger Penrose and Maciej Dunajski published a paper titled “Quantum state reduction, and Newtonian twistor theory”. In it, they analyzed the equivalence principle in quantum mechanics – the relationship between superposition and gravity in the Newtonian limit. What they derived was not just another theoretical prediction. It was a mathematical bombshell.
Their key result: the phase difference between the wave function of a particle at rest (exposed to gravity) and the same particle in free fall is proportional to the cube of time, T3.
This is not arbitrary. Standard quantum mechanics knows linear phase evolutions () or, in cases of acceleration, quadratic dependencies (). The cubic dependence is a signal that something deeply non-trivial happens when gravity and quantum superposition meet. It directly follows from the integral of the gravitational potential along a path involving acceleration – it encodes information about the curvature of spacetime directly into the phase of the wave function.
Penrose and Dunajski also employed a twistor approach (Newton–Cartan geometry and non-relativistic twistor theory), seeking a deeper geometric framework to explain wave function collapse. Interestingly, Penrose admitted in a recent interview that he is no longer so convinced of the correctness of twistor theory in its original form – because it requires zero spatial curvature, while observations increasingly point to a positive cosmological constant. Yet this does not diminish the significance of their derivation of the phase difference. On the contrary, it became experimentally testable.
🔬 Folman’s Experiment: When Atoms Dance the T3 Waltz
Ron Folman of Ben-Gurion University and his team constructed a Stern-Gerlach atom interferometer that, for the first time, realized the phase dependence. Their paper, published in Physical Review Letters, bears the simple title: “T³ Stern-Gerlach Matter-Wave Interferometer”.
In the experiment, rubidium-87 atoms, cooled to temperatures just above absolute zero (in a Bose-Einstein condensate), were split into a superposition of two spin states. One state remained at rest in the laboratory reference frame (exposed to gravity), while the other fell freely. By measuring the relative phase between the two “parts” of the wave function, they confirmed what Penrose and Dunajski had predicted: the phase grows with the cube of time, T3.
Later, in 2025, the same team published “Observation of the quantum equivalence principle for matter-waves”, directly confirming that the equivalence principle holds even in the quantum domain. This is what some authors call the Quantum Equivalence Principle (QEP).
What does this mean? In classical physics, the equivalence principle states that gravity and acceleration are locally indistinguishable. Folman showed that this holds even when a particle can be in a superposition of “being accelerated” and “not being accelerated”. It is a fundamental test of the interface between quantum theory and gravity.
⏳ What T3 Tells Us About the Nature of Time
The appearance of a cubic time dependence in such a fundamental equation truly suggests that we are not dealing with the ordinary “ticking” of uniform, Newtonian time.
is not an arbitrary mathematical curiosity. It directly emerges from integrating the gravitational potential along a path that includes acceleration – it encodes the curvature of spacetime into the phase of the wave function. When a superposition “experiences” curvature through different paths, time begins to behave in this non-trivial way.
From the perspective of contemporary debates on the emergence of time, the dependence is a precious clue. At the heart of quantum mechanics lies linear evolution (the Schrödinger equation), while gravity is inherently nonlinear (due to its interaction with all forms of energy, including its own). When these two worlds collide in Folman’s interferometer, the nonlinearity manifests through this unusual time dependence. It is a direct window into the domain where the quantum and the classical separate – where time itself perhaps comes into being.
🌌 The Wheeler-DeWitt Equation: A Wave Function Without Time
And now we arrive at perhaps the deepest insight into the nature of reality. The Wheeler-DeWitt equation – an attempt to write down the wave function of the entire Universe – has a shocking property:
It contains no time as a variable. H^Ψ=0.
This is not a technical error. It is a direct consequence of applying canonical quantization to General Relativity. The Hamiltonian of the whole Universe equals zero – the Universe as a whole does not evolve in time because there is nothing “outside” it with respect to which it could evolve. Time, in this fundamental equation, is simply not needed.
This is known as the “problem of time” in quantum gravity. If the most basic equation is timeless, how then do we explain our undeniable experience of time, change, and causal sequence?
The answer increasingly gaining ground in modern physics is: time is not fundamental. Time is emergent. It arises as a result of some deeper process – and that process is precisely the mechanism of wave function collapse. As long as the Universe remains in a coherent superposition (as in its early state), time does not flow. It begins to “flow” only with the first reduction, the first breaking of symmetry, the first foaming on the surface of the Dirac Sea.
💥 The Problem of the First Collapse: The Early Universe and Gravitational Reduction
It is logical to assume that the Universe, when it was on the order of the Planck length (), possessed a wave function. In that regime, energy and self-gravity were unimaginably enormous. A key question arises: how could a state of coherence be maintained at the very beginning of the Universe?
According to Penrose, it could not – at least not for long. The immense gravity must have caused an almost instantaneous collapse of the wave function. That would be the first objective reduction (OR) – the first transition from quantum to classical, the first emergence of time as we know it.
This also resolves the question of parallel universes. Although some authors link the early superposition of the Universe to Everett’s “many-worlds” interpretation, excessive gravity would have prevented such branching. Each separate universe would have collapsed under its own gravity. Penrose would agree here: gravity is a natural censor that prevents “many worlds”.
The question, however, is: when did time emerge from that timeless state? According to General Relativity, under conditions of extreme energy and spacetime curvature – just as in the center of a black hole – the flow of time ceases. The early Universe was exactly such a state. Yet we are witnesses that this stalemate was resolved: the Universe expands, galaxies recede, we write these lines.
🌀 CCC versus Inflation: Two Paths to Resolution
How was that early stalemate resolved? The standard answer is inflation – a brief period of exponential expansion proposed by Alan Guth. Inflation explains many features of our universe: homogeneity, isotropy, and the absence of magnetic monopoles.
Penrose, however, offers a radically different vision. His Conformal Cyclic Cosmology (CCC) claims that inflation was not needed – because what we call the Big Bang is not a beginning, but merely a transition (crossover) from a previous eon. Inflation is, in fact, the exponential expansion of the previous eon, mapped by conformal geometry into our beginning.
In this picture, the early superposition of the Universe did not have to be resolved “all at once”. It was already resolved in the previous eon, and what entered our eon was only information about that resolution – in the form of gravitational waves and structures like the Big Ring. CCC thus avoids the problem of the “first collapse”: it occurred in an infinitely distant past, through an infinite chain of eons.
⚖️ Penrose-Fuentes: A Billion Atoms – The Experiment That Will Decide
We return to Earth. Is Penrose’s collapse mechanism real? How can we test it?
Penrose and Ivette Fuentes have calculated the threshold: on the order of a billion atoms in coherent superposition are needed to experimentally confirm or refute the mechanism of objective reduction. Folman’s experiments with individual atoms are below this threshold – they test QEP, but not OR. Their atoms are too “light” to feel the gravitational wind strongly enough to collapse them.
An experiment with a billion atoms would be the first direct test of the boundary between the quantum and classical worlds. If confirmed, it would mean that gravity truly plays the role Penrose ascribes to it – not as a force to be quantized, but as the mechanism that translates quantum into actual.
📜 Quantum Archaeology: Reading the Past from the Dirac Sea
And now we come to the concept that ties everything together. Quantum archaeology – the idea that the past is not lost, but that all information about it is preserved in the current state of the Universe – rests on a fundamental principle of quantum mechanics: unitarity. The evolution of the wave function is reversible. Information is not destroyed. With sufficient knowledge and computational power, the past can be reconstructed – not as a story, but as an exact quantum configuration.
The Wheeler-DeWitt equation gives this a cosmic dimension: there exists something like the wave function of the entire Universe, which contains within it the superposition of all possible histories. Our reality is only one of them – the one that gravitational collapse “chose” and made classical.
Quantum archaeology thus becomes a bridge between the physical and the metaphysical: it suggests that all of history – every battle, every thought, every breath – is inscribed in the Dirac Sea, waiting to be read.
🌊 Synthesis: The Dirac Sea, the Gravitational Wind, and Emergent Time
We can now weave all threads into a single, magnificent picture:
- The Dirac Sea – the infinite ocean of quantum fields – has its internal dynamics described by SU(3) × SU(2) × U(1). Electrons, photons, gluons – all are excitations of fields, waves on the surface of the sea.
- The gravitational wind is an external influence. It is not part of the sea, not a gauge field, has no carrier particle. It is a manifestation of spacetime curvature and the mechanism of objective reduction.
- Folman’s experiment showed that this wind already alters the phase of the waves (through the dependence), but is still not strong enough to break them – for that we need a billion atoms.
- The Wheeler-DeWitt equation reveals that the sea, in its deepest state, is timeless. Time is not fundamental; it arises only with the first collapse, with the first foaming of a wave that becomes classical.
- The Big Ring and CCC suggest that this process is not a one-time event. Eons succeed one another, and information – inscribed in gravitational waves – is transmitted through conformal crossings.
- Quantum archaeology is the logical consequence: if information is indestructible and time is emergent, then the past – in all its details – is preserved in the current configuration of the sea.
🎬 Epilogue: Water from the Dirac Sea
In the final scene of Andrei Tarkovsky’s Solaris, the protagonist arrives at his father’s house. It looks like Earth, but something is profoundly different. Water drips on the figures, runs through the rooms – yet it is not rain from the sky. It is something else, something deeper, more mysterious.
It is water from the Dirac Sea.
That scene has, without warning, surfaced in my mind as the perfect illustration for this post. The boundary between the quantum and the classical is permeable. The sea seeps through. And just as the hero of Solaris cannot be sure whether he is on Earth or on the ocean-planet, we cannot say with certainty where the quantum sea ends and our classical world begins.
Perhaps the dripping water is not a sign of leakage, but of connection. A reminder that we are, always and forever, afloat on the infinite ocean.
This post continues the series begun with “⚛️ Quantum Archaeology: Reading the Past from the Dirac Sea” and continued through “🌊Ψ Dirac and the Idea of Discrete Spacetime”, “🌊🌀 Symphony of the Sea: SU(3) × SU(2) × U(1) and Gravity as Wind over the Dirac Ocean” and “🌌🔄 The Big Ring and the Echo from a Previous Eon”.
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