Cosmology from Transactional Entropic Gravity: A Concise Review

This paper provides a concise review of a cosmological model based on transactional entropic gravity, originally presented at the 2025 Lake Como School and detailed in a 2023 publication by Schlatter and Kastner, which addresses dark matter, dark energy, and cosmological tensions.

The Gist

The Big Idea: The Universe is a Conversation, Not a Container

Imagine you walk into a room and see a table. You assume the table exists because it's sitting there in the empty space.

This paper says: No, that's wrong.

According to the authors (Kastner and Schlächer), space and time aren't a pre-existing "container" where things happen. Instead, space and time are created by things talking to each other.

Think of the universe not as a stage, but as a giant, cosmic phone call.

• The "Call": In quantum physics, particles (like electrons) don't just sit there. They constantly send out "offers" (offer waves) and receive "confirmations" (confirmation waves). When a sender and a receiver agree, a "transaction" happens.
• The Result: This transaction is what creates a "moment" in time and a "point" in space. Without these transactions, there is no space or time. The universe is literally "growing" as these conversations happen.

1. Gravity is Just "Information Pressure" (The Entropic Force)

Why do apples fall? Why do planets orbit? Usually, we say gravity is a mysterious force pulling things together.

The Paper's View: Gravity is actually a result of information and heat.

• The Analogy: Imagine you are standing in a crowded room (the universe). If you try to move, people bump into you. It feels like a force pushing you back.
• The Science: In this theory, the "crowd" is made of all the possible places a particle could be. When a particle actually "transacts" (shows up at a specific spot), it reduces the uncertainty (entropy) of the universe.
• The Result: The universe "wants" to maximize its information. To do this, it pushes matter together. This push feels exactly like gravity. It's not a magical pull; it's a thermodynamic pressure, like air pushing on a balloon.

2. The "Cosmological Constant" (Dark Energy) is a Repulsive Push

You've heard of Dark Energy, the mysterious force making the universe expand faster and faster.

The Paper's View: This isn't a mysterious new energy. It's just the recoil of the cosmic phone calls.

• The Analogy: Imagine two people shaking hands. When they shake, they push against each other. If billions of particles are constantly "shaking hands" (transacting) across the universe, the momentum of these exchanges creates a tiny, constant pressure pushing everything apart.
• The Result: This pressure is what we call the Cosmological Constant ($\Lambda$). The paper argues that this pressure is directly linked to how many transactions are happening per second.
• The Twist: Because the universe is getting bigger, the "density" of these transactions changes. This suggests that the expansion of the universe might actually be slowing down slightly over cosmic time, rather than speeding up forever.

3. Dark Matter is an Illusion (The MOND Connection)

This is the most famous part of the paper. Astronomers see galaxies spinning so fast that they should fly apart. They assume there is invisible "Dark Matter" holding them together.

The Paper's View: There is no Dark Matter. The math of gravity just changes at very large distances.

• The Analogy: Imagine you are listening to a radio.
  • Close up: The signal is clear and strong (Newtonian gravity).
  • Far away: The signal gets weak, but the universe has a "background hum" (the expansion of space) that interferes with the signal.
• The Science: The authors use "Thermal Clocks." Every object in the universe has a temperature based on its motion. They show that if you sync these clocks across the universe, the rules of gravity change at the edges of galaxies.
• The Result: At the edges of galaxies, gravity doesn't get weak as fast as Newton predicted. It stays stronger. This explains why stars spin fast without needing invisible Dark Matter. This matches a theory called MOND (Modified Newtonian Dynamics), but the authors derive it from their "Transactional" theory instead of just guessing the math.

Summary: The "Growing Universe"

The paper paints a picture of a universe that is:

1. Discrete: It's made of individual "events" (transactions), not smooth space.
2. Relational: Space and time only exist because particles are interacting.
3. Self-Regulating: The "Dark Energy" pushing us apart and the "Gravity" pulling us together are two sides of the same coin: the exchange of information and momentum between particles.

In a nutshell:
The universe isn't a static box where things happen. It is a dynamic, growing network of conversations. Gravity is the pressure of those conversations, and the "Dark" stuff (Dark Energy and Dark Matter) is just the background noise of the universe expanding as those conversations get more spread out. We don't need invisible ghosts to explain the cosmos; we just need to understand how the universe talks to itself.

Technical Summary

Based on the provided text, here is a detailed technical summary of the paper "Cosmology from Transactional Entropic Gravity: A Concise Review" by R. E. Kastner and Andreas Schläfer.

1. Problem Statement

The paper addresses two major unsolved problems in modern cosmology and astrophysics:

• Dark Energy and the Cosmological Constant ($\Lambda$): The origin and magnitude of the accelerated expansion of the universe remain unexplained within standard General Relativity (GR).
• Dark Matter and Galaxy Rotation Curves: The discrepancy between observed galactic rotation velocities and predictions based on visible mass (Newtonian gravity) usually necessitates the hypothesis of Dark Matter. Alternatively, Modified Newtonian Dynamics (MOND) proposes a modification of gravity but lacks a fundamental derivation from first principles.

The authors propose that both phenomena are not caused by unknown substances (Dark Matter/Energy) but are natural consequences of Transactional Entropic Gravity, a theory where spacetime and gravity emerge from quantum mechanical transactions.

2. Methodology and Theoretical Framework

The authors utilize the Relativistic Transactional Interpretation (RTI) of quantum mechanics as the foundational ontology. The methodology proceeds through the following logical steps:

• Ontological Shift: Spacetime is not a primary structure but "supervenes" on quantum interactions called transactions. A transaction involves an emitter, an absorber, and a real (on-shell) photon, creating an invariant null interval.
• Emergence of Spacetime: Spacetime events are the actualization of these transactions. The metric structure is constituted by these events and their connections.
• Entropic Gravity Derivation:
  • The authors apply the thermodynamic equivalence principle ($E = S \cdot T$) to transactions.
  • They define entropy based on the information bits on a sphere surrounding an emitter, utilizing the holographic principle and the Planck length ($l_P$).
  • They associate a Davies-Unruh temperature ($T = \hbar a / 2\pi c k_B$) with the acceleration of the transaction.
  • By calculating the change in entropy when a test mass enters a transaction, they derive an entropic force that reproduces Newton's law of gravitation ($F = GMm/R^2$).
• Cosmological Constant Derivation:
  • The exchange of photon momenta in transactions exerts a repulsive pressure.
  • This pressure is modeled as a stress-energy term derived from the density of transactional events ($\delta$).
  • Using a Poisson distribution for the stochastic occurrence of transactions in spacetime, they derive a global term that enters the Einstein field equations as the Cosmological Constant $\Lambda$.
• Galaxy Rotation Derivation:
  • The authors analyze the Schwarzschild-de Sitter spacetime (a central mass in an expanding universe).
  • They introduce "thermal clocks" (based on Unruh temperature) and "light clocks" (based on the speed of light $c$).
  • By enforcing the syncronization (syncalibration) of these clocks between a stationary observer and a co-moving observer, they derive an interpolation formula for acceleration that transitions from Newtonian to MOND-like behavior.

3. Key Contributions

A. Derivation of the Cosmological Constant ($\Lambda$)

The paper provides a microscopic derivation of $\Lambda$ from the density of quantum transactions.

• Mechanism: The repulsive effect of photon three-momenta exchanged in transactions creates a pressure term.
• Result: The cosmological constant is defined as $\Lambda \equiv 8\pi^2 l_P^2 \varrho_A$, where $\varrho_A$ is the average rate of transaction density.
• Scaling: The authors show that $\Lambda$ is inversely proportional to the square of the universe's radius ($R_{universe}^2$). This implies $\Lambda$ is not a true constant but decreases over cosmic time scales as the universe expands, potentially explaining the "Hubble Tension" or future deceleration of expansion.

B. Derivation of MOND from First Principles

The paper derives the Modified Newtonian Dynamics (MOND) acceleration scale ($a_0$) without ad-hoc assumptions.

• Mechanism: The derivation relies on the interplay between the entropy of the de Sitter horizon (associated with $\Lambda$) and the entropy reduction caused by a central mass $M$.
• Result: An interpolation formula for acceleration $a(r)$ is derived:
  $$a(r) \approx \sqrt{M G a_0} / r$$
  where $a_0 \approx c H_0$ (the Hubble acceleration).
• Significance: This recovers the Tully-Fisher relation ($v^4 \propto M$) naturally, suggesting that "Dark Matter" effects are actually entropic corrections arising from the transactional nature of gravity in an expanding universe.

C. Unification of Quantum Mechanics and Gravity

The work bridges the gap between the quantum substratum (Hilbert space states) and the emergent spacetime manifold. It posits that gravity is an entropic force resulting from the "coming-into-being" of spacetime events via transactions.

4. Key Results

1. Newtonian Gravity: Recovered as an entropic force arising from the entropy gradient of transactional possibilities on a sphere.
2. Einstein's Equations: Derived with a cosmological constant term ($\Lambda g_{\mu\nu}$) appearing on the left-hand side, originating from the global transaction density rather than local matter distribution.
3. Cosmological Scaling: $\Lambda \propto 1/R_{universe}^2$. This predicts that the acceleration of the universe's expansion is not constant but will eventually decrease as the universe grows larger.
4. Galactic Dynamics: The effective acceleration at large distances matches the MOND prediction ($a \propto 1/r$), explaining flat rotation curves without invoking particle dark matter.
5. Critical Radius: A transition radius $r_0 = \sqrt{GM/a_0}$ is identified, below which Newtonian gravity dominates and above which the MOND/entropic correction takes over.

5. Significance

• Elimination of Dark Components: The model suggests that neither Dark Matter nor Dark Energy are required as distinct physical entities. Instead, they are emergent phenomena resulting from the thermodynamic and quantum properties of spacetime transactions.
• Resolution of Tensions: By linking $\Lambda$ to the size of the universe, the model offers a potential resolution to the discrepancy between local and early-universe measurements of the Hubble constant (Hubble Tension).
• Fundamental Mechanism for MOND: It provides a rigorous theoretical underpinning for MOND, which has historically been a phenomenological fit lacking a relativistic or quantum foundation.
• New View of Spacetime: It reinforces the "growing universe" concept where spacetime is a secondary structure emerging from quantum interactions, challenging the standard view of spacetime as a fixed background.

In conclusion, Kastner and Schläfer present a cohesive framework where the large-scale structure of the universe (accelerated expansion) and the dynamics of galaxies (rotation curves) are unified under a single principle: Transactional Entropic Gravity.