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Where Are All The Tourists From 3025?

Andrew Jackson

TL;DR

This paper tackles why no time-travellers are observed despite theoretical permission for backward time travel. It proposes a formal framework where possible worlds are coarse-grained into macrostates identified by construction numbers, and transitions between macrostates follow a continuous-time Markov process with rates $\alpha_j = \beta \frac{j}{2(j+1)}$. The key analytic result is that, as orthogonal time $t$ tends to infinity, the probability concentrates on the macrostate with construction number $0$, i.e., $P_0^t \to 1$, while all other $P_j^t \to 0$, implying time travel is self-suppressing and timelines converge to a no-time-machine regime. Numerical simulations across varying state counts and initial conditions corroborate the asymptotic outcome, reinforcing the claim that the asymptotic limit is observable to non-travellers and that the parameter $\beta$ does not affect the long-run behavior. The work situates this dynamic instability as an alternative to physics-based prohibitions, offering a novel lens on the absence of observed time-travellers and connecting to ideas like Niven's Law.

Abstract

This paper examines the distinct lack of clear examples of time-travellers and proposes an explanation for their absence without assuming technical barriers to constructing time machines. Instead, it develops and then analyses a model of the consequences of time-travellers; finding that time travel is self-suppressing.

Where Are All The Tourists From 3025?

TL;DR

This paper tackles why no time-travellers are observed despite theoretical permission for backward time travel. It proposes a formal framework where possible worlds are coarse-grained into macrostates identified by construction numbers, and transitions between macrostates follow a continuous-time Markov process with rates . The key analytic result is that, as orthogonal time tends to infinity, the probability concentrates on the macrostate with construction number , i.e., , while all other , implying time travel is self-suppressing and timelines converge to a no-time-machine regime. Numerical simulations across varying state counts and initial conditions corroborate the asymptotic outcome, reinforcing the claim that the asymptotic limit is observable to non-travellers and that the parameter does not affect the long-run behavior. The work situates this dynamic instability as an alternative to physics-based prohibitions, offering a novel lens on the absence of observed time-travellers and connecting to ideas like Niven's Law.

Abstract

This paper examines the distinct lack of clear examples of time-travellers and proposes an explanation for their absence without assuming technical barriers to constructing time machines. Instead, it develops and then analyses a model of the consequences of time-travellers; finding that time travel is self-suppressing.

Paper Structure

This paper contains 27 sections, 1 theorem, 14 equations, 10 figures.

Table of Contents

  1. Introduction
  2. Preliminary Analysis and Model Setup
  3. Ontology of the Model: Timelines, Construction Numbers, and Macrostates
  4. Grouping Microstates into Macrostates
  5. Grouping Microstates into Macrostates
  6. Dynamics of the Model: Symmetries and State Transitions
  7. A Formal Statistical Model
  8. Dynamics of Timelines and Stable Timelines
  9. A Comparison to Special Relativity
  10. Perceptions of the Effects of Time Travel for Non-Travellers
  11. Analytic Analysis of the Model
  12. Reformulation as a System of Differential Equations
  13. Asymptotic Behavior of the Model
  14. Numerical Analysis of the Model
  15. System with 5 Macrostates, Starting in Macrostate 3
  16. ...and 12 more sections

Key Result

Lemma 1

The probabilities of being in each macrostate, $P_j^t$, of the Markov chain model presented in Sec. sec:ModelStatement, are governed by the differential equations: and $\alpha_j$ is as in Def. def:transitionDef.

Figures (10)

  • Figure 1: A depiction of a subset of nodes in the Markov chain and the transition probabilities (exclusively) between them. Note that there are, in general, more nodes in this chain that are not shown but do have arrows to and from the nodes $\mathbb{M}_{j+1}$ and/or $\mathbb{M}_{j-1}$.
  • Figure 2: Occupancy probabilities as the Markov chain evolves of a five state Markov chain model, with the initial state being the one with a construction number of three.
  • Figure 3: Occupancy probabilities as the Markov chain evolves of a 500 state Markov chain model, with the initial state being the one with a construction number of 3.
  • Figure 4: Occupancy probabilities as the Markov chain evolves of a 500 state Markov chain model, with the initial state being the one with a construction number of 100.
  • Figure 5: Occupancy probabilities as the Markov chain evolves of a 1000 state Markov chain model, with the initial state being the one with a construction number of 50.
  • ...and 5 more figures

Theorems & Definitions (2)

  • Lemma 1
  • proof