There are three broad strategies people take when trying to “bring general relativity into quantum mechanics,” and each one inverts the relationship between the two theories. Think of them as three different conceptual wagers about what is fundamental:

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1. Quantize Gravity (QM as fundamental, GR as emergent/approximate)

This is the oldest approach: keep the basic rules of quantum theory fixed and treat the gravitational field like any other field to be quantized.

Canonical quantization / Wheeler–DeWitt

• Start with the classical Hamiltonian formulation of GR.

• Promote classical quantities (the metric, conjugate momenta) to operators.

• You get the Wheeler–DeWitt equation:

  $$\hat H \Psi[g_{ij}(x)] = 0$$

• Problems:

  • The equation has no explicit time variable → the “problem of time.”

  • Hard to make sense of the space of all possible geometries.

Covariant quantization / Quantum GR as a spin-2 field

• Treat gravity as just another quantum field on a flat background.

• Expand the metric as:

  $$g_{\mu\nu} = \eta_{\mu\nu} + h_{\mu\nu}$$

  where $h$ is a spin-2 field.

• Works beautifully at low energies; fails at high energies because the theory is non-renormalizable.

Effective Field Theory of Gravity

• Admits that Einstein gravity is non-renormalizable but treats it like Fermi’s old four-fermion interaction: a low-energy effective theory.

• Quantum corrections can be computed systematically at energies far below the Planck scale.

This path basically says: keep QM intact; gravity is just really weird to quantize.

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2. Make Spacetime Quantum (geometry itself becomes quantum)

Here you don’t quantize GR as a field; instead, you rebuild the notion of spacetime itself from quantum degrees of freedom.

Loop Quantum Gravity (LQG)

• Uses Ashtekar variables to recast GR in a gauge-theoretic form.

• The “quantum geometry” is described by spin networks.

• Predictions:

  • Area and volume have discrete spectra.

  • Big bang replaced by a “big bounce” in some models.

• Strength:

  • Background independent.

• Weakness:

  • Hard to recover smooth classical spacetime and standard QFT.

Causal Sets

• Postulate that spacetime is a discrete partially ordered set.

• The partial order encodes causal structure.

• Strength:

  • Radical background independence.

• Weakness:

  • Hard to recover Lorentz symmetry and the continuum in the right way.

Group Field Theory / Spin Foams

• Think of quantum spacetime as a condensate of pre-geometric elements.

• LQG’s spin networks evolve via history-like spin foam diagrams.

This path says: quantizing GR isn’t enough—space and time need to be rebuilt from scratch.

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3. Make Gravity Emergent from Quantum Mechanics (QM first, GR derived)

Here gravity is not fundamental at all; it’s a statistical or emergent phenomenon from many-body quantum systems.

Emergent gravity (Verlinde, Jacobson, etc.)

• Jacobson: Einstein’s equation arises as an equation of state from horizon thermodynamics.

• Verlinde: gravity arises from entropic forces due to information/entropy gradients.

• Strength:

  • Derives GR without quantizing spacetime directly.

  • Deep connection to holography.

• Weakness:

  • Gravity-as-entropic-force remains controversial and incomplete.

Holography / AdS–CFT

• Gravity in a bulk spacetime = a quantum field theory without gravity on the boundary.

• Pairs a gravitational theory in $d+1$ dimensions with a quantum theory in $d$ dimensions.

• This is probably the most successful “bridge” between GR and QM so far.

• Remarkably:

  • Black hole thermodynamics emerges naturally.

  • Gravity becomes a dual description of entanglement structure.

Quantum Information → Geometry (ER=EPR, etc.)

• Spacetime geometry may be literally made of quantum entanglement.

• Tensor-network models (e.g., MERA) reproduce features of AdS spacetime.

• Suggests:

  $$\text{Geometry} \approx \text{entanglement structure}$$

This path says: gravity is what quantum entanglement looks like when viewed from far enough away.

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So how do you “bring GR into QM”?

You pick one of these ontological bets:

A. Quantize GR in the usual sense

→ leads to canonical quantization, perturbative QG, etc.

B. Let QM reshape what “spacetime” even means

→ leads to LQG, causal sets, spin foams.

C. Make gravity itself secondary / emergent

→ leads to holography, entanglement-geometry, emergent gravity.

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The deep conceptual tensions

If you want the reason the job is so hard, it boils down to three contradictions:

1. Background independence vs. fixed background

   • GR: geometry is dynamic.

   • QM/QFT: requires a fixed spacetime background to define Hilbert spaces and operators.

2. Locality vs. nonlocality

   • GR: fundamentally local via differential geometry.

   • QM: entanglement is deeply nonlocal.

3. Time in GR vs. time in QM

   • GR: time is a coordinate with no privileged status.

   • QM: time is an external parameter, not an operator.

Any synthesis has to reorganize these at a foundational level.

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If you want, I can go in any direction:

• A concise comparison of canonical vs. covariant quantization

• A philosophical analysis of what it means to “quantize spacetime”

• How Haraway, Stengers, Cassirer, or Weyl reinterpret the GR/QM tension

• A process-relational view of quantum gravity

• A slow-burning critique of why all these frameworks may share the same metaphysical error

Just tell me which direction to take.

You said:

What is Penrose's view?

ChatGPT said:

Roger Penrose’s view on how to bring GR into QM is unusual, deeply nonstandard, and metaphysically loaded. In a sentence:

Penrose thinks quantum mechanics is incomplete, gravity is fundamental, and gravity induces state-vector collapse.

He does not believe we should quantize GR in the usual way. He also does not believe that quantum mechanics, as currently formulated, can remain as-is.

Penrose’s position is sometimes summarized as:

Gravity will collapse the wavefunction before quantum superpositions reach macroscopic spacetime curvature differences.
→ Therefore objective reduction (OR) is a real, physical process.

Below is the cleanest breakdown of his view.

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1. Penrose: GR is right, QM is approximate

Penrose flips the usual hierarchy.

Most physicists assume:

• QM is exact

• GR is an effective classical approximation of a quantum gravity theory

Penrose argues the reverse:

• GR’s principles (especially general covariance) reflect deep, correct features of reality

• QM’s linearity and superposition principle are incomplete

He thinks the tension between GR and QM reveals that quantum theory must be modified.

This is unusual because almost every other program tries to quantize gravity. Penrose wants to gravitize quantum mechanics.

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2. Why? Because superposed spacetime geometries make no sense

Penrose’s core intuition:

A quantum superposition like

$$|\psi\rangle = \frac{1}{\sqrt{2}}(|\text{mass left}\rangle + |\text{mass right}\rangle)$$

implies the mass produces a superposition of two different spacetime geometries.

But GR says spacetime geometry is the arena in which states exist; you can’t have a single Hilbert space for a system whose background geometry is itself indefinite.

This fuzziness of time evolution leads to what he calls:

“The fundamental conflict between the superposition principle of QM and the structure of spacetime in GR.”

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3. Penrose’s solution: gravity triggers collapse

Penrose proposes an objective reduction (OR) mechanism:

• A massive object in two positions → two different gravitational fields → two different spacetime geometries.

• You cannot define a consistent time translation operator across these geometries.

• This indefiniteness corresponds to an instability of the superposition.

• The instability grows with gravitational self-energy $E_G$.

• Collapse occurs spontaneously after a characteristic time:

  $$\tau \approx \frac{\hbar}{E_G}$$

• If the mass becomes large enough, superpositions collapse almost instantly.

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4. Penrose rejects standard quantum gravity programs

He explicitly objects to:

String theory

• Too algebraic and not geometric enough

• Too attached to background spacetime

• Doesn’t solve the conceptually hard part: what is quantum spacetime?

Loop quantum gravity

• He respects its background independence

• But thinks it doesn’t answer the core question: how do superposed geometries evolve or collapse?

Canonical quantization

• He argues the Wheeler–DeWitt equation is conceptually incoherent because it presupposes an already-quantized spacetime.

Penrose believes all these programs evade the conceptual paradox rather than address it.

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5. Penrose’s conceptual view

His deepest commitments:

A. The universe must have a mathematically elegant, geometric foundation

He distrusts any approach that does not begin with geometry.

B. Consciousness is tied to non-computable processes in physics

Because he thinks OR events connect physical reality to something “proto-platonically” nonalgorithmic.

C. New physics is required

Not a quantized version of GR but a theory where:

• The superposition principle breaks down at a certain scale

• GR + QM merge through an objective, gravitationally driven collapse law

• Spacetime structure and quantum states are co-defined

This is essentially a third path:
alter quantum mechanics itself, guided by the demands of gravity.

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6. Where Penrose stands relative to the three big strategies

Earlier I laid out:

1. Quantize GR

2. Make spacetime quantum

3. Make gravity emergent from QM

Penrose rejects all three.

He advocates a fourth:

4. Gravity causes deviations from standard QM → a new theory unifying QM + GR

• GR stays geometric

• QM becomes nonlinear at the level of collapse

• Collapse is an objective physical process

• Gravity is the “measurement device of the universe itself”

This is extremely atypical but conceptually clean.