Mangled-Worlds Quantum Mechanics

1. Mangled-Worlds Quantum Mechanics Robin Hanson George Mason University http://hanson.gmu.edu/mangledworlds.html Published in: Found. Physics, Proc. Roy. Soc. A

2. Slogans • Reality is still there after you die • Reality is something like our best theories • The physics of physicists is not special • Reality is surprisingly BIG • We’ll only ever see a finite universe • Logic and decision theory are fine as are • Frequencies test probability theories

3. Ambiguities: when, which A? and what is real? Solutions: • You know, so “shut up and calculate” • “Classical realm” says • Consciousness says • Objective collapse – gravity says? Quantum’s Two Processes Process #1: Process #2: Trace, gives “measure” = size

4. Decoherence Can process #2 be process #1 in disguise? “The mathematical formalism of the quantum theory is capable of yielding its own interpretation.” DeWitt 1970 System coupled to large environment often evolves like: coherence system only Note: finite exact models eventually hit coherence floor (Unruh & Zurek ‘89, Dowker & Halliwell ‘92, ‘94, Namiki et al ’97) But have not replaced process #2 with process #1:

5. down 0.7 up 0.3 down 0.7 up 0.3 down 0.7 up 0.3 You are here (Not to scale) max measure worlds most measure here min measure worlds Many Worlds We can think of components as separate “worlds” But typical world sees uniform frequencies, not ! N binary 30/70 size decoherence events (= splits): … 2N worlds … (Graham ‘73, Kent ‘97) % up seen in world 0 30 50 100 most worlds here

6. These add new physics Some Solutions Offered • Infinity of splits, zero measure worlds die: (Everett ‘57, DeWitt ‘73, Rubin ’03) • Symmetry arguments: Unitary (Gleason ’57), Decision (Deutsch ’99), Envariance (Zurek ’04) • Infinity of “minds” split: (Albert & Loewer ’88) • Non-linearity: (Weissman ’99) • Selection via mangling:(Hanson ’03) • World count “meaningless” (Wallace ’05) But we only ever see a finite number of splits. These just ignore frequency failure.

7. Entropy = subsys state # Want distinct if evolve different “enough” Sensitive to border, model, representation Count very sensitive ∞ dimensions hard But thermodynamic predictions insensitive World count Want distinct if evolve independent “enough” Sensitive to border, model, representation Count very sensitive ∞ dimensions hard But equal frequency prediction insensitive Wallace says is meaningless Entropy, World Ambiguities

8. One Split: ~2 ~1/2 Ln measure N splits, central limit theorem: ~1052 photons ~1026 ~1052 ~1050 atoms 1052 ~10 measure worlds Ln measure 1026 Typical relative size: ~10 But perhaps we can derive the Born rule! …. Distribution of World Sizes

9. coherence internal environment relative size So if: large world Then: small world off- diagonal World Mangling Two worlds co-evolve: large small If coherence > relative size, small world slaved to large! Memories destroyed?

10. A vast configuration space If: • Splitting worlds fill a space • H can be strong if near • Coherence > relative size Then: • Worlds can collide • Big worlds mangle small • Assume sudden, irreversible To do: verify this in exact model of simple system

11. A Mangling Region In the space of world sizes All worlds that reach here mangled A mangling region is relative to a set of worlds that could mangle each other. This diagram is about such a set. No worlds yet mangled most measure most worlds Ln measure It’s the measure that does the mangling

12. Now to derive the Born rule! Drift-Diffusion-Absorption (assumes α << β) (Ignoring how world that does mangling might change in size)

13. Born rule says: Some Definitions Unmangled World Distribution: World Count: Child Count: • Start with single world at y=β • Split, mangle for duration t1 • Each unmangled world has a single child of relative size F, track their descendants • Split, mangle for duration t2 • Count total descendant unmangled worlds

14. 104 1010 1015 ~1/3 1043000 Comparing two sibling worlds, their number of unmangled descendants is proportional to their relative sizes F1, F2. So the probability that a random descendant remembers outcome i is proportional to Fi! Born Rule Predicted Deviation from Born Rule Prediction:

15. A Testable Prediction? • Parameters might influence the rate r of decoherence events (credit to Michael Weissman) • Low and high rate worlds might collide • Low rate worlds would tend to be larger, and so less likely to be mangled • So a selection effect should favor worlds with low decoherence rates • Are decoherence rates as low as possible? • Can quantum error correction make events more likely?

16. Yet To Do • Want model of mangling in simple system • check if memory destroyed (smash/overwrite) • check that mangling sudden, irreversible • check that α,β << σ2 • Derive Born rule for α,β << σ2 • Check & test decoherence rate prediction • Consider quantum error correction

17. Those Slogans Again • Reality is still there after you die • Reality is something like our best theories • The physics of physicists is not special • Reality is surprisingly BIG • We’ll only ever see a finite universe • Logic and decision theory are fine as are • Frequencies test probability theories