Causal Loops

Context Recap

• Previously in the course we have already examined:
  • David Lewis’s analysis of what counts as time travel.
  • His solution to classic grandfather-type paradoxes (e.g.": killing one’s own grandfather before conception").
  • Lewis’s argument that a time-traveller can still causally affect the past without contradiction.
• Today’s focus: a different (non-paradoxical yet puzzling) phenomenon raised by backward time travel – causal loops.

What Is a Causal Loop?

• General idea: a closed chain of events that “loops” back so that an event ends up being (part of) its own cause.
• Formally:
  \text{Event }E1 \to E2 \to \dots \to En \to E1
  with no external causal “entry point.”
• Key intuitive tension: Where does the information (or causal efficacy) originate?
  • Seems to violate the ordinary expectation that every new piece of information is produced by some earlier, independent process.

Fictional Illustration 1 – The Shakespeare Case

• Setup:
  • You travel from 2012 (carrying a 2012 printing of The Complete Works of Shakespeare) back to 1588.
  • You meet young “Will Shaxbert,” hand him his future plays.
  • He copies them, they get performed/printed, become canonical, are ultimately re-printed in 2012—the very copy you brought.
• Puzzle:
  • Shakespeare “copies” Hamlet but doesn’t actually create it.
  • The 2012 edition exists because of Shakespeare’s copying.
  • Yet the content seems to appear from nowhere. Who composed “What a piece of work is a man”?
  • Answer (per the loop): no one; the text “merely exists.”

Fictional Illustration 2 – The Telephone/Time-Machine Blueprint

• Sequence summarised:
  1. Present-you receives a phone call from an oddly familiar voice: “Don’t say a word—write these instructions down and follow them.”
  2. Instructions allow you to build and operate a time machine.
  3. You travel slightly into the past.
  4. You phone your own earlier self, utter exactly the same words, giving exactly the same instructions.
• The knowledge of how to build the machine exists in the loop, with no external origin.
• Again, no contradiction (no grandfather paradox), yet profoundly counterintuitive.

The Core Philosophical Challenge

• People instinctively follow the Principle of Sufficient Reason (PSR): every fact, entity, or state of affairs must have an explanation.
• In a causal loop, PSR appears violated at the level of the whole loop:
  • Each individual step is causally explained by an earlier step inside the loop.
  • But the entire closed chain seems to have no external justification.
  • Where does the information originate?

Lewis’s Response – Three Kinds of Causal Histories

Lewis argues that all causal chains face a similar “ultimate-origin” problem; loops are not uniquely mysterious.

1. Infinite Linear Chain

• Picture: \dots \to E{-2} \to E{-1} \to E0 \to E1 \to \dots (extending without beginning).
• Every event has a prior cause, but there is no first event.
• Therefore, there is still no global answer to “Where does the whole chain come from?”—it has no starting point.

2. Finite Linear Chain

• Example drawn from modern physics: Big-Bang cosmology.
  • The Big Bang is not merely the first event in time; it is the boundary of time itself.
  • Famous analogy (Stephen Hawking): asking “What’s before the Big Bang?” is like asking “What’s north of the North Pole?”
• Quantum mechanics also allows uncaused spontaneous events (e.g., vacuum fluctuations).
• In such a finite chain, there are earlier-events explanations up to a finite limit, but nothing preceding that limit. Again, PSR stops.

3. Finite Non-Linear Chain (Causal Loop)

• The Shakespeare and telephone examples.
• Closed, self-sustaining structure with no external start.
• Contrary to intuition, but not more epistemically problematic than the two linear options.

Comparative Moral

• Whether causal history is:
  • \text{Infinite Linear}
  • \text{Finite Linear (Big Bang / quantum event)}
  • \text{Finite Non-Linear (Loop)}
    the ultimate-origin question lacks an answer.
• Therefore causal loops are equally (not uniquely) mysterious.

Key Take-Aways

• Causal loops do not generate logical contradictions; they merely defy everyday causal intuitions about information origination.
• Lewis’s stance: accepting time travel plus the metaphysical possibility of loops commits us to no worse mystery than we already face in cosmology or infinite regress scenarios.
• Result: Backwards time travel remains conceptually coherent even in the presence of causal loops.

Connections & Broader Implications

• Cosmology: Big Bang as a finite linear “boundary”; causal loops mirror cosmology’s unanswered origin question.
• Quantum physics: spontaneous, acausal events legitimize finite ungrounded chains.
• Philosophy of Science: undermines a universal PSR; suggests explanations can bottom out or cycle.
• Metaphysics of Information: raises the prospect of information that is ontologically recycled rather than produced.
• Ethical/Practical: If causal loops are possible, intellectual property notions (“authorship,” “invention”) become complicated—e.g., Who owns Hamlet if no one authored it?
• Further Inquiry: Whether laws of nature permit stable closed timelike curves (CTCs); current general-relativity solutions (Gödel universe, Tipler cylinders) show theoretical space for loops.

Study Pointers

• Be able to define a causal loop and contrast it with linear causal chains.
• Memorise the Shakespeare and telephone examples as standard illustrations.
• Understand Lewis’s three-option schema and why each faces the same origin-question threat.
• Reflect on whether the Principle of Sufficient Reason must hold absolutely or can be limited.
• Consider practical ramifications (IP law, ethics) if causal-loop scenarios were real.