It from Bit, Bit from It
[Updated 6 February 2026 -MFM]
tldr; If we view the limit where measurement efficiency eta approaches 1 as a boundary condition, then what the Quantum Zeno Effect seems to show is that a quantum-to-classical transition requires an irreversible step that dissipates at least the Landauer bound.
If you have ever felt uneasy reading about quantum mechanics, you are in good company. For nearly a century, the idea that a cat can be both alive and dead — or that an electron exists in a cloud of probability until "looked at" — has struck even world-class physicists as unreasonable. We often try to fix this unease by imagining a "real" hidden state behind the scenes, or by proposing that consciousness somehow collapses the wave function.
But what if quantum mechanics isn't the problem? What if we've been carrying around a mistaken assumption about reality itself?
In 1996, physicist Carlo Rovelli proposed a radical shift called Relational Quantum Mechanics (RQM). His argument parallels Einstein's breakthrough with Special Relativity. Before Einstein, physicists struggled to explain Maxwell's equations because they assumed time was absolute. Einstein solved the problem by accepting that time is relative to the observer. Rovelli suggests we must do the same for quantum states: no "absolute state" of a system exists. A system's state is always relative to another system.
Any System Can Observe
The first step toward clearing up quantum confusion is abandoning the idea that an "observer" must be human, conscious, or even complex. In Rovelli's framework, any physical system can observe another. An electron interacting with a photon observes it. A table lamp interacting with a hand observes it.
Rovelli's "Hypothesis 1" is simple: all systems are equivalent. The laws that describe a single atom also describe you, me, and the entire laboratory. This removes the need for "special systems" — consciousness, gravity, or anything else — to explain wave function collapse. Collapse isn't magical. It's just what happens when two systems exchange information.
"It from Bit" and "Bit from It" are not competing philosophies but two faces of a single principle: information is physical correlation, and physical correlation costs relative entropy — the divergence between two systems' descriptions that must be reconciled for them to share a fact. The lossless limit, in which correlation would be free, is unreachable. That unreachability is not a limitation of our technology. It may be what generates the physical world.
Two Observers, Two Truths
To see how this works, consider what Rovelli calls the "Third Person Problem."
Observer \(O\) measures a system \(S\) — say, an electron. \(O\) interacts with \(S\) and finds the electron is "Spin Up." For \(O\), the wave function has collapsed. Reality is definite: Spin Up.
Now imagine a second observer, \(P\), standing outside the room. \(P\) does not interact with the electron. Instead, she treats \(O\) and \(S\) together as a single quantum system. According to the Schrödinger equation, \(P\) describes them not as "Spin Up," but as an entangled superposition:
$$(\text{Electron Up} + \text{Observer seeing Up}) \text{AND} (\text{Electron Down} + \text{Observer seeing Down})$$
Who is right? Is the electron "really" Up, as \(O\) sees it? Or is it "really" in superposition, as \(P\) describes?
Standard quantum mechanics calls this a paradox. RQM calls it a feature. Both accounts are correct. The divergence between these two accounts — \(O\)'s definite outcome and \(P\)'s entangled superposition — is precisely the relative entropy between the descriptions maintained by two systems that have not yet interacted. That divergence vanishes only when \(P\) enters the room and correlates with \(O\), paying the thermodynamic cost of synchronization.
"Spin Up" is true relative to \(O\). "Superposition" is true relative to \(P\). No contradiction exists because \(O\) and \(P\) describe the system from different frames of reference — just as a moving train looks different to a passenger inside than to a bystander on the platform.
Correlation Keeps Reality Consistent
This might sound like solipsism — each of us living in a private dream world — but Rovelli anchors his framework in physical reality through consistency.
If \(P\) enters the room and asks \(O\) what he saw, a physical interaction takes place. Rovelli proves that quantum mechanics guarantees \(P\) will always find a result consistent with \(O\)'s measurement. If \(O\) saw "Up," \(P\) will measure that \(O\) recorded "Up."
This brings us to RQM's core mechanism: correlation.
For \(P\), the "measurement" that \(O\) performed is not a collapse; it establishes a correlation — an entanglement — between \(O\) and \(S\). The fact that \(O\) has "information" about \(S\) is physically identical to saying \(O\) and \(S\) are correlated. Information is correlation. And correlation is never free — establishing it requires reducing the relative entropy between the correlated systems' descriptions of each other, a reduction that dissipates energy and leaves a thermodynamic record.
The Quantum Zeno Effect
To see this logic at work, consider the Quantum Zeno Effect — specifically the "interaction-free" experiments Kwiat et al. pioneered in 1999.
A photon is repeatedly "checked" to see if an object (call it a "bomb") has absorbed it. If checked frequently enough, the photon freezes in its initial state and never triggers the bomb. If nothing else in the environment around the bomb accidentally triggers it during the experiment, then it's possible with some very high probability to detect whether the bomb is or is not present without triggering it. This is pretty weird stuff if you're not used to the concept of entanglement from quantum mechanics!
How does RQM explain this?
From the bomb's perspective: The photon's quantum state is trying to rotate toward the bomb's path. But the bomb's presence turns each cycle into a measurement — "Has the photon arrived yet?" Each measurement finds almost no amplitude in that path and collapses what little has accumulated. The rotation never completes; the photon stays frozen in its original path.
From the experimenter's perspective: The experimenter sees the photon and bomb interacting through a strong Hamiltonian. This interaction creates a perfect correlation between the photon's path and the bomb's state. No collapse occurs for the experimenter — just a unitary evolution that drags the photon along a frozen path because it is entangled with the bomb.
As Rovelli notes, "The unitary evolution does not break down for mysterious physical quantum jumps... but simply because \(O\) is not giving a full dynamical description of the interaction." \(O\) sees collapse because \(O\) participates in the interaction. \(P\) sees unitary evolution because \(P\) watches the correlation form.
The two descriptions carry different relative entropies with respect to the photon's state. The bomb, coupled to the photon, maintains a low-divergence description — it "knows" whether the photon has arrived. The experimenter, decoupled, maintains a high-divergence description — she models the composite system without resolving it. The Zeno freezing occurs because repeated low-divergence measurements (the bomb checking) prevent the photon's amplitude from accumulating in the bomb's path. Frequent synchronization — frequent payment of the relative entropy tax — keeps the system pinned.[1]
"It from Bit" — or "Bit from It"?
This leads to a profound philosophical implication, often summarized by John Wheeler's phrase "It from Bit" — the physical world ("It") emerges from information ("Bit").
Rovelli dissolves this question. In RQM, "It from Bit" and "Bit from It" collapse into each other because information and physical correlation are the same thing. The deeper question is not which comes first but what it costs to establish the correlation. That cost — the relative entropy two systems produce when they synchronize their descriptions — is the irreducible residue that separates the physical world from the lossless mathematical abstraction we call unitary evolution. Here's Rovelli:
"The fact that the pointer variable in \(O\) has information about \(S\)... is expressed by the existence of a correlation."
"Physics is the theory of the relative information that systems have about each other. This information exhausts everything we can say about the world."
In the lossless limit of the Zeno experiment — where the photon is never absorbed, yet its state freezes — we see this principle in its purest form. The photon is affected physically not by touching the bomb, but by the information that the bomb is present. The "Bit" (the answer "No, not absorbed") is the "It" (the physical freezing of state).
The Lossless Limit Cannot Be Reached
There is a catch. The lossless limit is never achieved in practice — and Bianconi's "Gravity from Entropy" theory suggests it cannot be achieved in principle.
A pure information exchange without energy dissipation is an idealization. To measure the photon, the bomb must couple to it. Even if the photon is not absorbed, the potential for absorption drives the effect. In Kwiat's experiments, efficiency was high but never 100% — always some loss, some decoherence, some thermodynamic cost. But the deeper reason may be structural: Bianconi has shown that gravity itself emerges from the quantum relative entropy between the true spacetime metric and the metric induced by matter fields. If the lossless limit were achievable — if correlation could be established with zero relative entropy — the divergence that generates spacetime curvature would vanish. There would be no gravity. The lossless limit is unreachable not because our instruments are imperfect, but because reaching it would eliminate the structure of spacetime itself.
Even if information is the fundamental currency of reality, every transaction in that currency produces relative entropy. The "Bit" and the "It" are inextricably linked — not as metaphor but as thermodynamic identity. You cannot establish a correlation without producing a divergence between descriptions, and that divergence is what we call physics.
The Synchronization Tax Returns
At this point, the connection to The Synchronization Tax should be clear. Time is the relative entropy two systems produce when they force their descriptions of reality into agreement. Whether you are collapsing a quantum wavefunction, synchronizing a distributed database, or clearing a wire transfer, the mechanism is similar. To have a shared reality, systems must interact. And interaction produces relative entropy.
Rovelli's framework illuminates why. "Collapse" is not a mysterious event; it is the establishment of a correlation between systems. Before the correlation exists, the systems share no timeline — they are concurrent, superposed, each evolving in its own isolated frame. After the correlation, they share a fact. They agree on what happened.
But establishing that correlation requires physical interaction — and physical interaction produces relative entropy. The synchronization tax I described — transaction fees, wire delays, the billable hours of lawyers and accountants — is the macroscopic expression of this quantum principle. These costs do not merely accompany coordination; they constitute it. Without the divergence, there would be no shared fact, no causal order, no time.
In the lossless limit, correlation would be free. But the lossless limit is unreachable — and so we pay. In physics, with relative entropy. In finance, with fees. In every human institution, with the friction of coordinating private knowledge into public fact.
We don't just have information about the world. We are part of the web of correlations that constitutes it. We are not watching reality from outside; we are woven into it, one synchronization at a time — and the tax we pay with every thread is not a toll extracted from us but the very tension that holds the fabric together.
Draft Paper
A draft paper attempting a more formal explanation of what I've described in this essay is available for download here:
The potential social analogues (micromanagement, surveillance) are interesting and may be explored in future essays. From this point of view Goodhart's Law could be understood as analogous to the Quantum Zeno Effect in the high-efficiency regime. North, Wallis, and Weingast suggest that there is an optimal level of synchronization — more frequent than natural states but not so frequent as to be frozen. ↩︎