Barandes + Verlinde: On the Stochastic Emergence of Gravity

Sequel to Reconstructing Spacetime

Characters

  • Jacob Barandes – Theoretical physicist proposing indivisible stochastic processes as the foundation of quantum mechanics.
  • Erik Verlinde – Physicist known for entropic gravity, arguing that spacetime and gravity emerge from information-theoretic principles.

Scene

A quiet, sunlit room at the Institute for Fundamental Questions. Two chalkboards are covered with equations and diagrams. Jacob is sketching a non‑Markovian transition graph; Erik is reviewing holographic entropy bounds.

Jacob

You know, Erik, if you really think gravity is emergent, then you shouldn’t be surprised that spacetime itself might just be an artifact — a projection of deeper statistical processes.

Erik

I’d agree with that. In fact, I argue spacetime is emergent — from entropy gradients driven by information flow. But I admit, I still take states and entropies as defined on space. What are you offering instead?

Jacob

Something even more elemental. I say: forget Hilbert space, forget even space. Reality is indivisible transition — not being, but becoming. Every “state” we observe is just a cut through an underlying non‑Markovian, history‑dependent stochastic process.

Erik (smiling)

A kind of Heraclitean physics?

Jacob

Exactly. No wavefunction, no collapse — just probabilities evolving irreducibly. What you call “non‑locality” in quantum mechanics is just a misreading of the non‑Markovian fabric of this unfolding.

Erik

So you’re embedding entanglement in time?

Jacob

Yes — entanglement is not spooky action across space, but joint memory embedded in the process. The correlations are historical, not spatial.

Erik

That’s fascinating. Because in my view, gravity emerges from a system’s statistical tendency to maximize entropy—a core idea of entropic or emergent gravity. And the geometry of space encodes the information content. But if what you’re saying is true, maybe that geometry isn’t primary — it’s statistical scaffolding over your process fabric.

Jacob

Exactly. Your entropy gradients could arise from asymmetries in transition histories. In my language, when processes become locally divisible—say, due to decoherence—they reset, forming the micro‑foundations of causal horizons.

Erik (pausing)

And those horizons are where I derive Newton’s laws. So perhaps gravity is just the macroscopic thermodynamic curvature of your indivisible flow—a concept explored also by Ted Jacobson, who derived Einstein’s equations from horizon thermodynamics.

Jacob

Yes! The curvature isn’t “baked into” spacetime — it’s the aggregate signature of underlying stochastic causality, resisting division. You interpret it as entropic force. I see it as process rigidity—the path‑dependence resisting shortcuts.

Erik

Then maybe Einstein’s equations are a thermodynamic constraint on your histories. That would mean we’re both describing the same underlying tapestry—I from the outside in, you from the inside out.

Jacob (softly)

A tapestry woven not of space and time… but of irreducible transitions.

Erik

Then entropy is how we see those threads. And gravity is how they pull.

They pause, both staring at the same chalkboard now—Jacob’s process diagrams blurring into Erik’s entropic surfaces. The boundaries dissolve, and so do the frameworks. Only patterns remain.

Appendix A: Indivisible Processes and Emergent Gravity

For Undergraduate Physics Students

A1. Motivation

This model proposes a new way to understand both quantum mechanics and gravity by focusing not on particles or fields, but on the irreducible processes that link events over time. Rather than building physics from static “states,” it builds it from dynamic, history-dependent transitions — like flipping a coin whose outcome depends on all previous flips.

A2. Key Ideas

A2.1. Indivisible Stochastic Processes (Jacob Barandes)

  • Think of a quantum system not as a particle in a state, but as a process unfolding over time, where you can’t slice it into independent steps.
  • These processes are non-Markovian: their future depends not just on the present, but on the whole history.
  • What we usually call the “wavefunction” is a bookkeeping tool, not a physical object. The real “stuff” is the flow of probabilities between configurations.

A2.2. Emergent Gravity (Erik Verlinde)

  • Gravity is not a fundamental force like electromagnetism. Instead, it arises from changes in entropy—a statistical push toward disorder.
  • As particles move, they rearrange information in space, and this reorganization creates what we interpret as a gravitational pull.
  • Space and time themselves may emerge from underlying information or entanglement — not as a fixed stage, but as a dynamic outcome.

A3. Joint Model Synthesis

  1. Reality = Irreducible Transitions
  • The basic unit of physics is a transition — not a particle or wave, but a causal connection between configurations.
  1. Quantum Behavior = Statistical Memory
  • Quantum phenomena like interference and entanglement arise from the non-local memory built into these processes.
  1. Gravity = Large-Scale Statistical Signature
  • At macroscopic scales, the collective effect of these indivisible processes behaves like entropy gradients, producing what we call gravity.
  1. Spacetime = Emergent from Process
  • Both space and time are emergent frameworks that help describe the patterns in the process network, not ingredients of reality itself.

A4. Why It Matters

  • Unification Potential: This model could unite quantum mechanics and gravity, not by modifying either, but by rethinking both from the ground up.
  • Interpretive Clarity: It avoids paradoxes like wavefunction collapse or action-at-a-distance by treating quantum mechanics as a statistical theory of processes.
  • Conceptual Elegance: Instead of two incompatible languages (quantum and relativistic), this offers one processual language to describe all of physics.

A5. Analogy: Physics as a Film

  • In standard physics, we look at each frame of the film (a snapshot of the universe) and try to predict the next one.
  • In this model, we focus on the cuts between frames — the editing, the pacing, the transition — as the real thing.
  • The geometry of spacetime (what you see on screen) is just the visual shadow of the deeper story told by the transitions.

A6. Further Exploration

  • Pre-requisites: Familiarity with basic quantum mechanics (Hilbert space, wavefunctions), classical thermodynamics (entropy), and statistical mechanics.
  • Topics to Explore:
  • Markov vs. non-Markov processes
  • Path integrals and quantum histories
  • Holographic principle and black hole entropy
  • Decoherence and quantum measurement theory

In short: This is physics not of particles or fields, but of memory, flow, and emergence.

Appendix B: Key Challenges for the Indivisible–Emergent Model

Despite its conceptual appeal and unifying potential, the joint model of indivisible stochastic processes and emergent gravity faces several important theoretical, empirical, and philosophical challenges. These need to be addressed to elevate the model from an interpretive framework to a robust physical theory.

B1. Theoretical Challenges

  • Lack of a unified formalism
  • No single mathematical structure yet unites stochastic processes and spacetime emergence.
  • Standard tools like Lagrangians, Hilbert spaces, and tensor fields are not obviously derivable.
  • Bell’s theorem and apparent locality
  • Reproducing quantum correlations requires non-local memory or history.
  • The model must clarify how it avoids violating relativistic causality while maintaining realism.
  • Compatibility with relativity
  • Needs to recover Lorentz invariance, causal structure, and general covariance from a pre-geometric substrate.
  • How do stochastic histories manifest as smooth, local spacetime?

B2. Empirical Challenges

  • Lack of novel predictions
  • The model currently mirrors quantum mechanics and thermodynamic gravity but offers no testable differences.
  • Without experimental consequences, it risks remaining purely interpretive.
  • Conservation laws
  • It’s unclear how energy, momentum, and angular momentum conservation arise in a fundamentally non-field-based, process-centric model.
  • Quantum field theory compatibility
  • No clear route yet to recovering gauge symmetry, renormalization, and Standard Model particle content.
  • Fermionic degrees of freedom and spin-statistics need explanation within the framework.

B3. Philosophical and Interpretive Challenges

  • Ontological ambiguity
  • Are stochastic processes real, or just modeling tools?
  • If the wavefunction is secondary, what is the primary stuff of reality?
  • Observer role and measurement
  • What defines a “division” in an indivisible process — is it objective, relational, or informational?
  • How does the model handle outcome definiteness without collapse?
  • Time and causality
  • If time emerges from process, what defines the sequence or ordering of those processes?
  • Is there a hidden meta-time, or does causality arise relationally?

B4. Developmental and Community Obstacles

  • Lack of mainstream traction
  • The model is not yet widely cited or debated in leading quantum gravity or QFT communities.
  • Interdisciplinary complexity
  • Bridging quantum foundations, statistical mechanics, and emergent spacetime theories requires a rare blend of expertise.
  • Need for working models
  • Toy models or simulations are needed to demonstrate how stochastic processes generate spacetime or reproduce Einstein’s equations.

B5. Summary of Core Challenge Areas

  • Theoretical: No complete mathematical framework.
  • Empirical: No falsifiable predictions or experimental tests.
  • Philosophical: Unclear ontology, observer role, and temporal structure.

Despite these open issues, the model’s unifying vision offers a rich arena for future theoretical development and cross-disciplinary dialogue.

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