Quantum Gravity With and Without the Math

Part I: Without the Math

This is Part 2 of a three-part series. Part 1 introduced the projection framework for quantum mechanics. Part 3 connects dimensional apertures to time dilation.

Dimension glossary (used throughout this series):

• D (Hilbert/state dimension): size of the full state space
• d (spacetime dimension): 3+1 in our classical description
• k (aperture): effective degrees of freedom accessible to a given observer+interface

TL;DR: Quantum gravity looks paradoxical if you demand a single classical spacetime before measurement. In a unitary + decoherence picture, "classical spacetime" is an emergent description, not the fundamental substrate. So gravity needn't "wait for collapse"—because the thing that "collapses" is our low-dimensional description, not reality. The hard problem shifts from "how does gravity pick A or B?" to "how does classical geometry emerge so robustly from quantum correlations?"

The problem everyone agrees on

Here's the puzzle that's haunted physics for 90 years:

1. Quantum mechanics says a particle can be in a superposition of two locations
2. General relativity says mass curves spacetime
3. So what happens when a mass is in superposition?

Does spacetime curve toward location A? Location B? Both? Neither until someone looks?

The options all seem bad:

• Spacetime superposes too — but we've never observed macroscopically distinct superpositions of geometry, and it's unclear what that would even mean
• Gravity sees the expectation value — useful as an approximation, but not obviously consistent in all regimes
• Gravity causes collapse — Penrose's proposal, but requires new physics we haven't found
• Something else entirely — maybe gravity isn't quantum?

This tension has driven decades of competing proposals. Maybe the question is wrong.

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The projection move (recap)

In the previous post, we reframed quantum mechanics:

The quantum state is a high-dimensional object. Classical outcomes are low-dimensional projections. "Collapse" is what projection looks like from inside.

Measurement doesn't reveal a pre-existing fact. It creates one by projecting the quantum state onto a basis. The question "which slit did it go through?" is not answered by reality—it's imposed by measurement.

Now apply this to gravity.

Framing note: I'm not proposing a completed theory of quantum gravity here. I'm arguing that many "paradox" statements arise from mixing levels of description—demanding a classical spacetime story in regimes where only a quantum description is well-defined. The goal is conceptual hygiene: identify what a consistent theory would treat as fundamental vs emergent.

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What if gravity doesn't need to choose?

The puzzle assumes gravity must couple to something classical: a definite position, a definite mass distribution. Then asks: what happens before collapse gives us that?

But in the projection picture, there is no "before collapse" classical state. The classical description isn't waiting in the wings—it's generated by measurement.

What does gravity couple to, then?

The quantum state itself.

If collapse is an artifact of subsystem description (as in unitary-only interpretations + decoherence), gravity doesn't need to wait for it—because there's nothing to wait for. The wavefunction—the high-dimensional object—is what's physically real. Classical spacetime is what we extract when we observe at our scale.

(By "projection," I mean the emergence of a stable classical description after entanglement with many environmental degrees of freedom selects an effectively classical basis. The global state can remain unitary while local descriptions become classical. This post assumes a broadly unitary + decoherence picture, where "collapse" is not a fundamental dynamical event.)

The quantum state is the territory. Classical spacetime is the map.

When we ask "does spacetime curve toward A or B?", we're demanding gravity respect a classical distinction that only exists after projection. That's a category error.

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The split planet

Imagine a planet in superposition of two orbits.

In the Paradox View, you demand a single classical metric sourced by a definite position—but that classical description isn't available prior to decoherence/projection. There's no single classical geometry. Penrose suggested this tension causes collapse; nature can't tolerate the ambiguity.

In the Substrate View, gravity couples to the quantum mass-energy distribution. The well doesn't flicker. It forms a stable, smooth curve shaped by the energy distribution—which happens to have two lobes. To gravity, that's no stranger than a dumbbell.

(A complete story likely requires the gravitational field itself to participate quantum-mechanically. The point here is that the conceptual demand for a single classical metric is what generates the paradox.)

Three versions of "gravity sees the quantum state":

1. Semiclassical approximation: Keep geometry classical, source it with ⟨T̂⟩. Useful but breaks down when fluctuations matter.
2. Branch-relative classicality: After decoherence, each quasi-classical branch has its own effective geometry. No single global classical metric, but local classical descriptions within branches.
3. Fully quantum gravity: The gravitational field becomes entangled with matter. Geometry is not classical at the fundamental level.

I'm not picking one here. The point is that all three dissolve the paradox by rejecting the demand for a pre-decoherence classical metric.

The superposition isn't a problem in principle—it's a well-defined quantum stress-energy distribution.

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Gravity doesn't wait for you

We think of "collapse" as a physical event where the universe decides what to be.

But as we argued with the coffee mug: collapse is an artifact of projection. It's what happens when you force a 3D object through a 2D aperture.

Gravity doesn't force the object through an aperture. Gravity is the shape of the container.

If this is right:

1. An effective spacetime description can remain smooth. It curves around the quantum state |ψ⟩ without needing to "pick" a classical outcome
2. Measurement is local. When we measure, we update our description
3. No paradox. The gravity well was always determined by the wave, not the classical outcome we later extract

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Why this dissolves the usual conflicts

Several research programs converge on this picture:

Emergent spacetime. Classical geometry appears as a coarse-grained projection of deeper quantum structure—just like classical position.

ER = EPR. Maldacena and Susskind proposed that entanglement and wormholes are the same thing. Entangled particles aren't connected through spacetime—their entanglement is spacetime geometry at some level. This makes correlations prior to geometry.

Holography. The information content of a region scales with surface area, not volume. Bizarre if spacetime is fundamental. Natural if spacetime is a projection of lower-dimensional quantum degrees of freedom.

Relational QM. Facts are relative to interactions. There's no observer-independent classical history—just correlations between subsystems.

These are different programs with different formalisms. I'm not claiming equivalence—only that they all demote classical spacetime from "fundamental stage" to "emergent description." That shared intuition is what matters here.

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Who collapses the universe?

In textbook collapse language, measurement is often described as requiring an external observer. But in cosmology, there is no outside—the universe includes all possible observers.

So who collapses the universal wavefunction?

Nobody. In unitary-only approaches, the universal quantum state evolves unitarily, forever. "Collapse" is what happens when a subsystem (us) extracts information about another subsystem (the rest) through physical interaction.

We're inside the wavefunction, not outside it. Our experience of definite outcomes is a feature of our position as entangled subsystems—not evidence that the universe has collapsed into a classical state.

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Time without time

In canonical approaches to quantum gravity, one encounters the Wheeler-DeWitt equation—which has a notorious feature: no explicit time parameter.

The universe, described this way, is frozen.

Where does our experience of time come from?

The projection answer: time emerges from records.

When we measure, we create records. Records establish before/after. The entropic arrow—the sense of flow—arises from information asymmetry: we remember the past (records exist) but not the future (records don't exist yet).

Records require irreversible entanglement with many degrees of freedom (decoherence), which is what makes a direction of time robust for subsystems like us.

Time isn't built into the universe's quantum state. It's built into how finite observers create and correlate records within that state.

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The real mistake

The deepest error isn't technical. It's conceptual.

We keep asking: "How does gravity behave when a particle hasn't yet chosen a position?"

But position isn't something the particle has prior to measurement. It's something we extract by forcing a projection.

Quantum gravity becomes paradoxical only if we insist that spacetime must be built from the same low-dimensional narratives we use to describe lab outcomes.

Once we stop making that demand, gravity no longer needs to collapse anything.

It only needs to respond to what is already there.

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What this doesn't solve

Let's be honest about limits:

We don't have a full theory of quantum gravity. The projection framing is conceptual clarification, not a computational framework. It suggests where to look, not what we'll find.

We don't have the emergence dynamics. Saying "gravity couples to the quantum state" doesn't derive how classical geometry emerges from entanglement structure. The projection framing identifies the conceptual target—but we still need the dynamics that recovers Einstein's equations as a coarse-grained limit.

We can't test the deepest regime directly (yet). Planck scales, black hole interiors, the early universe remain out of reach. But there may be nearer-term experimental windows—tabletop tests of gravity-mediated entanglement, for instance—on whether gravity preserves high-dimensional correlations or collapses them.

"Emergent spacetime" is a slogan, not a derivation. Active research, not settled science.

It doesn't tell you what replaces a classical metric. In deep superposition regimes, demanding a classical metric is the wrong starting point—but this framing doesn't say what the right description is.

Steelman objection: Even if collapse is epistemic, gravity still has to respond to quantum fluctuations, not just expectation values. A consistent theory likely needs a fully quantum gravitational field, not a classical metric sourced by ⟨T̂⟩. The projection framing clarifies the conceptual target—but the dynamical details require real quantum gravity.

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Optional coda: why this matters for the mind

This section is an analogy, not a physics claim. Skip it if you want physics only.

I'm pushing this framing hard because it's a general mistake: confusing a measurement interface for the underlying dynamics. Gravity is one case; minds may be another.

Why is a website about biological coherence writing about quantum gravity? Because the error physicists make with gravity is the same error neuroscientists make with the brain.

(I'm not claiming brains are quantum computers. I'm claiming the mistake—confusing readout variables for the underlying dynamics—generalizes across domains.)

We look for the "neural correlate of consciousness" in the firing of specific neurons (the particles). We ask: "When does the brain decide? When does the thought collapse into a definite state?"

But the mind, like gravity, likely operates on the coherent high-dimensional manifold—the "wave"—not the discrete spikes we measure with electrodes. Spikes are a sparse, low-dimensional readout of richer dynamics (oscillatory coherence, population states, phase-locking). The coherence is the object.

If gravity can handle a superposition without breaking, maybe the brain can too. Same geometry. Different substrate.

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The computational limit is dimensional

Digital computers aren't too slow—they're too flat.

Digital computers represent high-dimensional structure, but their native state is a discrete register configuration. High-dimensional dynamics are emulated, not lived. Matrix multiplication is still low-dimensional linear algebra applied sequentially. When we simulate quantum systems, costs explode exponentially (2^N amplitudes for N qubits). When we simulate brains, we discretize oscillatory manifolds into spike counts and wonder why the model feels hollow.

The problem isn't processing power. It's dimensional mismatch.

We don't need new physics. We need substrates that natively represent dimensionality.

How this differs from string theory, loop quantum gravity, etc.: Those programs still seek tractable structures—10 dimensions, 11 dimensions, discrete spin foams. They're looking for something we can calculate.

The proposal here is more radical: the substrate dimensionality scales with degrees of freedom. A system of n coupled oscillators is an n-dimensional dynamical system. A brain has 86 billion neurons. A mole of gas has 10²³ particles. The dimensionality isn't exotic—it's just big.

For any macroscopic system, the state space is effectively unbounded. And crucially: you can't simulate it. That's not a bug—it's a prediction.

The computational intractability of quantum gravity isn't a problem to be solved. It's evidence that we're projecting from a substrate whose dimensionality exceeds any finite representation.

The quantum gravity "paradox" and the hard problem of consciousness share the same root: we're projecting high-dimensional dynamics onto low-dimensional representations, then wondering why the projection looks strange.

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Is spacetime the bottleneck?

Everything above is a reframing of existing unitary + decoherence intuitions. What follows is more speculative.

Here's a more radical possibility: what if 3+1D spacetime isn't where physics happens, but the aperture through which high-dimensional dynamics get squeezed?

The analogy comes from neural dynamics. Cortical activity routinely gets pinned through low-dimensional constrictions—synchronized oscillatory states where effective dimensionality collapses. Then it diffracts back out into high-dimensional desynchronized states. The constriction isn't where the interesting dynamics live; it's where they become temporarily visible to coarse observation. (See the cortical oscillations paper for the formal treatment.)

If this picture is right:

• Before the bottleneck: The quantum state lives in high-D Hilbert space. Full superposition, full entanglement.
• At the bottleneck: Classical spacetime. Decoherence pins the state to a low-D projection. This is where we observe.
• After the bottleneck: Entanglement with the environment spreads correlations into effectively infinite dimensions. Information isn't lost—it's diffracted.

The fact that we observe three large spatial dimensions might not be fundamental. It might be the width of the aperture through which we're forced to look.

The proposal in one sentence: A high-dimensional substrate flows through a dimensional aperture (k=3), and the physics of our world emerges from this flow.

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The aperture isn't fixed

But k=3 isn't universal. The dimensional aperture can vary:

In spacetime:

• Far from mass: k=3 (normal spatial geometry)
• Black hole horizon (external observer): k=2 (holographic surface—the Bekenstein-Hawking entropy scales with area, not volume)
• Black hole horizon (infalling observer): k=3 (smooth space, nothing special at the crossing)
• Singularity: k→1? k→0? (dimensional collapse, breakdown of classical description)

Notice that k is observer-relative. The external observer sees a 2D bottleneck; the infalling observer sees continuous 3D space. Same physics, different effective dimensionality depending on your embedding. This is black hole complementarity—and it's exactly what the projection framing predicts.

And here's the connection to time: the external observer also sees time freeze at the horizon. The infalling observer experiences normal time flow. The dimensional collapse and the time dilation are the same phenomenon. When k drops, you lose access to degrees of freedom you could previously correlate with—and time emerges from correlations (the Wheeler-DeWitt point). At k=2, the external observer can only see the surface; the interior dynamics are frozen for them, not frozen in themselves.

The same happens at high velocity: length contracts in the direction of travel (that spatial dimension gets squashed), and time dilates proportionally. Lorentz contraction and gravitational time dilation are both cases of the same relationship—reduce the accessible dimensional aperture, and time slows. Whether it's a black hole or a spaceship, squashing k dilates time.

In minds:

• Normal waking: k = moderate (balanced attention bandwidth)
• Focused attention: k contracts (tunnel vision, flow states, reduced peripheral awareness)
• Psychedelics: k expands (increased neural dimensionality)
• Slow-wave sleep: k pinches down (the cortical oscillation bottleneck)
• Anesthesia/coma: k→minimal

The mind isn't passively receiving a fixed-k projection. It's actively modulating its aperture width—expanding and contracting the dimensional bandwidth of experience.

Both gravity and consciousness might be stories about variable-k flows through dimensional bottlenecks.

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Thermodynamic emergence: horizons as computational bottlenecks

Here's where this connects to something deeper.

Ted Jacobson showed in 1995 that if you assume:

1. Local thermodynamic equilibrium at causal horizons
2. The Bekenstein-Hawking entropy-area relation
3. Energy conservation

...then Einstein's field equations follow. Gravity isn't a force that needs quantizing—it's an equation of state, like the ideal gas law. It describes how thermodynamic consistency constrains the geometry of horizons.

In our language: a horizon is a computational bottleneck.

When you squeeze an aperture—when you reduce k—you're not just limiting what an observer can see. You're erasing information. The degrees of freedom that become inaccessible don't vanish; they get traced out, compressed, forgotten by that observer's description.

This erasure has a thermodynamic cost. Landauer's principle: erasing one bit costs at least $k_B T \ln 2$ of heat. Shrinking your aperture means compressing your description of the world, and compression is irreversible.

So the thermodynamic story becomes:

• Aperture squeeze = coarse-graining = information erasure
• Information erasure has minimum thermodynamic cost (Landauer)
• Horizons are surfaces where aperture → minimal (k→2)
• Jacobson's derivation says: thermodynamic consistency at horizons → Einstein equations

The implication: spacetime geometry is the shape of the compression gradients induced by dimensional apertures.

This isn't claiming to derive GR. It's pointing at why the thermodynamic connection exists. When you ask "how must geometry behave if observers at different apertures are to have consistent thermodynamics?"—you get Einstein.

The black hole horizon isn't just a geometric surface. It's where the computational cost of maintaining a decohered, low-dimensional description becomes extreme. Time freezes because correlation rate → 0. Entropy is proportional to area because that's the channel capacity of the bottleneck. The holographic principle is a statement about compression limits.

Gravity might be what thermodynamically consistent dimensional compression looks like from the inside.

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Part II: With the Math

Everything above can be stated precisely. The math just formalizes the same projection logic.

The universal state

The state of the universe is:

$|\Psi\rangle \in \mathcal{H}_{\text{universe}}$

This state is the complete physical description. It does not contain definite classical facts—it contains amplitudes for correlations.

Subsystem descriptions

A subsystem $S$ is described by the reduced density matrix:

$\rho_S = \text{Tr}_E(|\Psi\rangle\langle\Psi|)$

where we trace out (ignore) the environment $E$.

This reduced state generically looks mixed and decohered—diagonal in some basis—even if the global state is pure. "Collapse" is not a physical process. It's what happens when you compute $\rho_S$: you select a subsystem and discard correlations with the rest.

Semi-classical gravity

The standard semi-classical approximation:

$G_{\mu\nu} = 8\pi G \langle \hat{T}_{\mu\nu} \rangle$

This is not a full quantum-gravity theory, and it can't be the final word in regimes where stress-energy fluctuations matter. But it captures a key conceptual move: gravity should respond to the quantum description of matter—not to the classical outcomes we extract after decoherence. The projection framing identifies why this is the right direction, even if the full dynamics require going beyond expectation values.

The Wheeler-DeWitt equation

In canonical approaches to quantum gravity, the universe satisfies:

$\hat{H}|\Psi\rangle = 0$

The Hamiltonian annihilates the state. No time evolution. The universe is "frozen."

(This "timelessness" depends on the canonical quantization context and choice of variables—it's not the settled interpretation across all quantum gravity approaches. But it illustrates the general puzzle.)

Time reappears relationally: when a subsystem $S$ is entangled with a "clock" subsystem $C$, the correlations between $S$ and $C$ look like time evolution from $S$'s perspective.

$|\Psi\rangle = \sum_t |t\rangle_C \otimes |\psi(t)\rangle_S$

Time is not fundamental. It's a feature of how subsystems correlate.

Entanglement as geometry (Ryu-Takayanagi)

In holographic theories:

$S_A = \frac{\text{Area}(\gamma_A)}{4G_N}$

The entanglement entropy of a boundary region $A$ equals the area of the minimal surface $\gamma_A$ in the bulk (divided by Newton's constant).

In holographic setups, geometry is entanglement, quantitatively. The spatial structure we call "spacetime" may literally be built from the pattern of quantum correlations.

Tensor networks

Tensor network models (MERA, etc.) construct spacetime-like structures from patterns of quantum entanglement. The "extra dimension" in holography emerges from the entanglement structure of the boundary theory.

This is active research, not settled physics. But it points toward the same conclusion: spacetime is derived, not fundamental.

Thermodynamic emergence

Jacobson (1995) showed that Einstein's field equations can be derived from thermodynamic assumptions applied to local causal horizons. If you assume the Clausius relation (δQ = TdS) holds at horizons and that entropy scales with area, general relativity emerges as an equation of state.

This suggests gravity isn't a fundamental force—it's what thermodynamics looks like when you coarse-grain over microscopic degrees of freedom.

The connection to information geometry and dimensional thermodynamics is less well understood but potentially deep. If the "cost" of maintaining correlations across a dimensional projection has thermodynamic structure, then:

• Bekenstein-Hawking entropy (area scaling) reflects the dimensional bottleneck at horizons
• The Landauer bound on computation connects to the cost of dimensional reduction
• Spacetime geometry might literally be the shape of thermodynamic gradients in a high-D state space

This is speculative territory—but it's where the projection framing naturally leads.

Some of our own work explores these connections:

• The Dimensional Landauer Bound (in preparation): Erasing degrees of freedom has thermodynamic cost. Dimensional reduction isn't free—it dissipates.
• Minimal Embedding Dimension: What's the minimum dimensionality needed to faithfully represent a system's dynamics? This is the aperture width question formalized.
• Projection Discontinuities (under review): When you project high-D dynamics onto low-D observables, discontinuities can emerge—apparent singularities that don't exist in the full space.
• Limits of Falsifiability: What's knowable is observer-relative. The projection determines the epistemic horizon.

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The Punchline

Quantum gravity seems paradoxical because we keep asking: "When does the classical spacetime appear?"

But that question assumes classical spacetime is the destination, and the quantum state is a waystation. We said it earlier, and it bears repeating:

The quantum state is the territory. Classical spacetime is the map.

Maps are useful precisely because they leave things out. Classical spacetime—smooth, definite, geometric—is useful because it captures what matters for creatures like us: slow, big, constantly decohering into our environment.

But no one asks a map to explain the territory.

The territory doesn't need to wait for the map to be drawn.

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One-sentence synthesis:

Quantum gravity becomes paradoxical when you ask gravity to see classical outcomes that exist only after projection. Let gravity see the quantum state, and the paradox dissolves.

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This post is speculative. I'm not claiming to have solved quantum gravity. But the conceptual reframing matters: the hard part might not be "quantizing gravity" but understanding why classicality emerges so robustly that we ever thought gravity was classical in the first place.

This is Part 2 of a series. See Part 1: Quantum Mechanics Without the Math for the projection picture applied to standard QM. Part 3: Time From Dimensions explores the connection between dimensional apertures and time dilation.

For the mathematical framework on observation limits, see our paper on the limits of falsifiability.