Could quantum decoherence and measurement be deterministic phenomena? eda Nour 1 , co 2 Jean-Marc Sparenberg, R´ Aylin Man¸ Nuclear Physics and Quantum Physics, ´ Ecole polytechnique de Bruxelles, Universit´ e libre de Bruxelles, Belgium October 16th, 2012 The Time Machine Factory 2012, Torino, Italy 1 2nd year undergraduate student 2008 2 2nd year undergraduate student 2012 Jean-Marc Sparenberg (ULB) Deterministic quantum mechanics TM2012 1 / 13
Advocacy for determinism 1 Apparatus hidden variables and Bell’s inequalities 2 A schematic model for deterministic quantum measurement 3 Faster-than-light communication 4 Conclusions and perspectives 5 Jean-Marc Sparenberg (ULB) Deterministic quantum mechanics TM2012 2 / 13
Advocacy for determinism Determinism in quantum mechanics... and beyond! Philosophical motivations for determinism ◮ until recently, science was based on determinism: the same cause always produces the same effect ◮ simpler timeless theories: the present moment “time capsule” [Barbour, 1999] contains both past and future because causally related to it Quantum theory apparently violates this principle ◮ measurement: identical measurements on identical systems in identical states may lead to different results (eigenvalues of an observable, with computable probabilities) ◮ decoherence: linear superposition of states randomly and irreversibly decoheres to a statistical mixture of states (i.e. to a random state with a computable probability) This happens when the quantum system interacts with a macroscopic system (e.g. a readable apparatus) with uncontrollable internal degrees of freedom (“environment”) ◮ could this apparent randomness be actually determined by these degrees of freedom? Jean-Marc Sparenberg (ULB) Deterministic quantum mechanics TM2012 3 / 13
Advocacy for determinism A striking example: α -particle in cloud chamber Spherical- ( s -)wave α emitter 4 ◮ kinetic energy T α = � 2 k 2 / 2 m α ◮ α -particle wave function 2 f ( R ) = e ikR 0 Y R ◮ highly non local: α particle in 2 all directions at the same time [Sigmund, 2006] ◮ but linear local tracks detected 4 4 2 0 2 4 X (wave function reduction) Einstein’s solution: quantum mechanics is incomplete: state of α particle = wave function f ( R ) and hidden variable λ which determines observed result (“God doesn’t play dice”) Problem: existence of λ ⇒ Bell’s inequalities, violated by experiment Present paper: track direction determined instead by microscopic positions of molecules/“droplets to be” in cloud chamber ◮ play the role of apparatus hidden variables Λ ◮ random because of thermal agitation Jean-Marc Sparenberg (ULB) Deterministic quantum mechanics TM2012 4 / 13
Apparatus hidden variables and Bell’s inequalities Advocacy for determinism 1 Apparatus hidden variables and Bell’s inequalities 2 A schematic model for deterministic quantum measurement 3 Faster-than-light communication 4 Conclusions and perspectives 5 Jean-Marc Sparenberg (ULB) Deterministic quantum mechanics TM2012 5 / 13
Apparatus hidden variables and Bell’s inequalities Apparatus hidden variables Λ violate Bell’s inequalities Einstein-Podolsky-Rosen (1935) Bohm-Aharonov experiment Mean correlation between spin 1 and 2 1 2 a and ˆ measured along directions ˆ b � � b ) ≡ 4 a , ˆ a )( s 2 · ˆ E ( ˆ ( s 1 · ˆ b ) � 2 [Bohm-Aharonov, 1957] [Szab´ o, 2008] a , ˆ a · ˆ Quantum mechanics prediction: E Q ( ˆ b ) = − ˆ b � � 1 for entangled state | 00 � = | + � ˆ u 1 |−� ˆ u 2 − |−� ˆ u 1 | + � ˆ √ u 2 2 c ˆ ◮ violates Bell’s inequalities for particular ˆ ˆ a , ˆ b , ˆ c [Bell, 1964] b a a , ˆ c ) | ≤ 1 + E λ ( ˆ ˆ | E λ ( ˆ b ) − E λ ( ˆ a , ˆ b , ˆ c ) ◮ but agrees with experiment (photons) [Aspect et al., 1982] a , ˆ a · ˆ Variables Λ 1 , Λ 2 hidden in apparatuses: E Λ 1 Λ 2 ( ˆ b ) = − ˆ b ⇒ identical to standard quantum mechanics � � � � b ) = � a , ˆ | σ 2 � , ˆ E Λ 1 Λ 2 ( ˆ Λ 1 Λ 2 p (Λ 1 ) p (Λ 2 ) R | σ 1 � , ˆ a , Λ 1 R b , Λ 2 � �� � � � � = 1 a , ˆ a , ˆ Λ 2 p (Λ 2 ) R |−� ˆ b , Λ 2 − R | + � ˆ b , Λ 2 2 Jean-Marc Sparenberg (ULB) Deterministic quantum mechanics TM2012 6 / 13
A schematic model for deterministic quantum measurement Advocacy for determinism 1 Apparatus hidden variables and Bell’s inequalities 2 A schematic model for deterministic quantum measurement 3 Faster-than-light communication 4 Conclusions and perspectives 5 Jean-Marc Sparenberg (ULB) Deterministic quantum mechanics TM2012 7 / 13
A schematic model for deterministic quantum measurement α -particle scattering on single localized obstacle Hypotheses on obstacle α ◮ generic: hydrogen atom [Mott, 1926] , supersaturated vapour alcohol droplet. . . R obstacle ◮ immobile at fixed position a ( T α ≫ T thermal ) r ◮ internal Hamiltonian H and variables r , two levels: a ψ 0 ( r ) , E 0 and ψ 1 ( r ) , E 1 with � ψ 0 | ψ 1 � = 0 α emitter Stationary α -particle + obstacle coupled-channel wave function Ψ( R , r ) = f 0 ( R ) ψ 0 ( r ) + f 1 ( R ) ψ 1 ( r ) ◮ no obstacle excitation ⇒ f 0 ( R ) has energy T α α = T α + E 0 − E 1 ≡ � 2 k ′ 2 ◮ obstacle excitation ⇒ f 1 ( R ) has energy T ′ 2 m α High-energy scattering ⇒ first-order Born expansion Ψ( R , r ) = f (0) ψ 0 ( r ) + f (1) ψ 0 ( r ) + f (1) 0 ( R ) 0 ( R ) 1 ( R ) ψ 1 ( r ) � �� � � �� � � �� � unperturbed elastic inelastic ◮ f (0) 0 ( R ) = spherical wave ◮ f (1) 0 ( R ) , f (1) 1 ( R ) = peaked waves around direction a Jean-Marc Sparenberg (ULB) Deterministic quantum mechanics TM2012 8 / 13
A schematic model for deterministic quantum measurement Wave-function normalization Hypothesis: α -particle (probability) flux F at large distance independent of obstacle presence ◮ without obstacle: f ( R ) = e ikR R F without = 4 π � k ⇒ m α ≡ 4 πv α ◮ with obstacle in a , defining θ ≡ ∠ ( a , R − a ) : | R − a | ψ 0 ( r ) + I 1 ( θ ) e ik ′| R − a | R →∞ C e ikR R ψ 0 ( r ) + I 0 ( θ ) e ik | R − a | Ψ( R , r ) ∼ | R − a | ψ 1 ( r ) � π � π 0 dθ sin θ | I 0 ( θ ) | 2 + 2 πv ′ ⇒ F = 4 π | C | 2 v α 0 dθ sin θ | I 1 ( θ ) | 2 + 2 πv α α � �� � � �� � spherical ≡ 4 πv α (1 −| C | 2 ) > 0 One has thus | C | 2 < 1 , i.e. a flux reduction in spherical wave F spherical = | C | 2 F without ◮ could explain wave-function reduction in a deterministic way ◮ could be exploited for faster-than-light information transfer Jean-Marc Sparenberg (ULB) Deterministic quantum mechanics TM2012 9 / 13
A schematic model for deterministic quantum measurement α -particle scattering on two (and more) localized obstacles Two obstacles ⇒ second-order Born expansion [Mott, Proc. R. Soc. 1926] � � f (0) 00 ( R ) + f (1) 00 ( R ) + f (2) Ψ( R , r a , r b ) = 00 ( R ) ψ 0 ( r a ) ψ 0 ( r b ) f (1) 10 ( R ) ψ 1 ( r a ) ψ 0 ( r b ) + f (1) + 01 ( R ) ψ 0 ( r a ) ψ 1 ( r b ) f (2) + 11 ( R ) ψ 1 ( r a ) ψ 1 ( r b ) b ◮ f (2) 11 ( R ) only significantly different from 0 iff a ∝ b ◮ explains linear tracks from spherical wave a ◮ track direction determined by droplet positions a and b N aligned obstacles ⇒ strong reduction of spherical-wave flux F spherical ≈ | C | 2 N F without ⇒ explains wave-function reduction N randomly-distributed obstacles ◮ direction of best-aligned obstacles singled out as measured track ◮ deterministic explanation to apparently random track detection Jean-Marc Sparenberg (ULB) Deterministic quantum mechanics TM2012 10 / 13
Faster-than-light communication Advocacy for determinism 1 Apparatus hidden variables and Bell’s inequalities 2 A schematic model for deterministic quantum measurement 3 Faster-than-light communication 4 Conclusions and perspectives 5 Jean-Marc Sparenberg (ULB) Deterministic quantum mechanics TM2012 11 / 13
Faster-than-light communication Wave-function reduction ⇒ superluminal information? 4 Presence of obstacle in direction a reduces 2 spherical wave amplitude in all other directions Y 0 ⇒ possible information transfer? 2 ◮ “0”: without obstacle ⇒ no reduction 4 4 2 0 2 4 X ◮ “1”: with obstacle ⇒ reduction without obstacle Spherical wave = highly non-local state 4 2 ⇒ reduction simultaneous in all directions Y 0 ⇒ possible faster-than-light information transfer? 2 4 Practical implementation 4 2 0 2 4 X with obstacle ◮ replace α particle by electric dipole photon ◮ replace droplet by tunable (Zeeman?) two-level single atom ◮ first check: is the photon flux reduced when two-level system tuned? ◮ if yes, second check: is this reduction instantaneous (fibre-optic delay)? Jean-Marc Sparenberg (ULB) Deterministic quantum mechanics TM2012 12 / 13
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