Could quantum decoherence and measurement be deterministic [PDF]

SLIDE 1

Could quantum decoherence and measurement be deterministic phenomena?

Jean-Marc Sparenberg, R´ eda Nour1, Aylin Man¸ co2

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

12nd year undergraduate student 2008 22nd year undergraduate student 2012 Jean-Marc Sparenberg (ULB) Deterministic quantum mechanics TM2012 1 / 13

SLIDE 2

1

Advocacy for determinism

2

Apparatus hidden variables and Bell’s inequalities

3

A schematic model for deterministic quantum measurement

4

Faster-than-light communication

5

Conclusions and perspectives

Jean-Marc Sparenberg (ULB) Deterministic quantum mechanics TM2012 2 / 13

SLIDE 3

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

SLIDE 4

Advocacy for determinism

A striking example: α-particle in cloud chamber

Spherical- (s-)wave α emitter

◮ kinetic energy Tα = 2k2/2mα ◮ α-particle wave function

f(R) = eikR

R

◮ highly non local: α particle in

all directions at the same time

◮ but linear local tracks detected

(wave function reduction)

4 2 2 4 X 4 2 2 4 Y

[Sigmund, 2006]

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

SLIDE 5

Apparatus hidden variables and Bell’s inequalities

1

Advocacy for determinism

2

Apparatus hidden variables and Bell’s inequalities

3

A schematic model for deterministic quantum measurement

4

Faster-than-light communication

5

Conclusions and perspectives

Jean-Marc Sparenberg (ULB) Deterministic quantum mechanics TM2012 5 / 13

SLIDE 6

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 measured along directions ˆ a and ˆ b E(ˆ a,ˆ b) ≡ 4

2

(s1 · ˆ

a)(s2 · ˆ b)

1

2 [Bohm-Aharonov, 1957] [Szab´

, 2008]

Quantum mechanics prediction: EQ(ˆ a,ˆ b) = −ˆ a · ˆ b for entangled state |00 =

1 √ 2

|+ˆ

u1|−ˆ u2 − |−ˆ u1|+ˆ u2

◮ violates Bell’s inequalities for particular ˆ

a,ˆ b, ˆ c [Bell, 1964] |Eλ(ˆ a,ˆ b) − Eλ(ˆ a, ˆ c)| ≤ 1 + Eλ(ˆ b, ˆ c)

◮ but agrees with experiment (photons) [Aspect et al., 1982]

ˆ a ˆ b ˆ c Variables Λ1, Λ2 hidden in apparatuses: EΛ1Λ2(ˆ a,ˆ b) = −ˆ a · ˆ b ⇒ identical to standard quantum mechanics EΛ1Λ2(ˆ a,ˆ b) =

Λ1Λ2 p(Λ1)p(Λ2)R

|σ1, ˆ

a, Λ1

R
|σ2,ˆ

b, Λ2

= 1

2

Λ2 p(Λ2)
R
|−ˆ

a,ˆ

b, Λ2

− R
|+ˆ

a,ˆ

b, Λ2

Jean-Marc Sparenberg (ULB)

Deterministic quantum mechanics TM2012 6 / 13

SLIDE 7

A schematic model for deterministic quantum measurement

1

Advocacy for determinism

2

Apparatus hidden variables and Bell’s inequalities

3

A schematic model for deterministic quantum measurement

4

Faster-than-light communication

5

Conclusions and perspectives

Jean-Marc Sparenberg (ULB) Deterministic quantum mechanics TM2012 7 / 13

SLIDE 8

A schematic model for deterministic quantum measurement

α-particle scattering on single localized obstacle

Hypotheses on obstacle

◮ generic: hydrogen atom [Mott, 1926],

supersaturated vapour alcohol droplet. . .

◮ immobile at fixed position a

(Tα ≫ Tthermal)

◮ internal Hamiltonian H and variables r, two levels:

ψ0(r), E0 and ψ1(r), E1 with ψ0|ψ1 = 0

α emitter α

bstacle

R a r

Stationary α-particle + obstacle coupled-channel wave function Ψ(R, r) = f0(R)ψ0(r) + f1(R)ψ1(r)

◮ no obstacle excitation ⇒ f0(R) has energy Tα ◮ obstacle excitation ⇒ f1(R) has energy T ′

α = Tα + E0 − E1 ≡ 2k′2 2mα

High-energy scattering ⇒ first-order Born expansion Ψ(R, r) = f(0)

0 (R) unperturbed

ψ0(r) + f(1)

0 (R) elastic

ψ0(r) + f(1)

1 (R) inelastic

ψ1(r)

◮ 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

SLIDE 9

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) = eikR

R

⇒ Fwithout = 4π k

mα ≡ 4πvα

◮ with obstacle in a, defining θ ≡ ∠(a, R − a):

Ψ(R, r) ∼

R→∞ C eikR R ψ0(r) + I0(θ) eik|R−a| |R−a| ψ0(r) + I1(θ) eik′|R−a| |R−a| ψ1(r)

⇒ F = 4π|C|2vα

spherical

+ 2πvα π

0 dθ sin θ|I0(θ)|2 + 2πv′ α

π

0 dθ sin θ|I1(θ)|2

≡ 4πvα(1−|C|2)

>0

One has thus |C|2 < 1, i.e. a flux reduction in spherical wave Fspherical = |C|2Fwithout

◮ 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

SLIDE 10

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] Ψ(R, ra, rb) =

f(0)

00 (R) + f(1) 00 (R) + f(2) 00 (R)

ψ0(ra)ψ0(rb)

+ f(1)

10 (R)ψ1(ra)ψ0(rb) + f(1) 01 (R)ψ0(ra)ψ1(rb)

+ f(2)

11 (R)ψ1(ra)ψ1(rb)

◮ f (2)

11 (R) only significantly different from 0 iff a ∝ b

◮ explains linear tracks from spherical wave ◮ track direction determined by droplet positions a and b

a b

N aligned obstacles ⇒ strong reduction of spherical-wave flux Fspherical ≈ |C|2NFwithout ⇒ 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

SLIDE 11

Faster-than-light communication

1

Advocacy for determinism

2

Apparatus hidden variables and Bell’s inequalities

3

A schematic model for deterministic quantum measurement

4

Faster-than-light communication

5

Conclusions and perspectives

Jean-Marc Sparenberg (ULB) Deterministic quantum mechanics TM2012 11 / 13

SLIDE 12

Faster-than-light communication

Wave-function reduction ⇒ superluminal information?

Presence of obstacle in direction a reduces spherical wave amplitude in all other directions ⇒ possible information transfer?

◮ “0”: without obstacle ⇒ no reduction ◮ “1”: with obstacle ⇒ reduction

Spherical wave = highly non-local state ⇒ reduction simultaneous in all directions ⇒ possible faster-than-light information transfer?

4 2 2 4 X 4 2 2 4 Y

without obstacle

4 2 2 4 X 4 2 2 4 Y

with obstacle

Practical implementation

◮ 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

SLIDE 13

Conclusions and perspectives

Schematic model for deterministic quantum measurement

◮ spherical-wave alpha-particle detection in cloud chamber ◮ direction of linear trajectory determined by best aligned droplets ◮ “wave mechanics unaided” [Mott, 1926]

Hidden variables Λ = microscopic state of apparatus/environment

◮ violate Bell’s inequalities, agree with standard quantum mechanics

Wave-function non-locality ⇒ instantaneous information transfer

◮ presence of droplet in one direction

immediately affects normalization of spherical wave in all directions

◮ practical implementation: photons, Zeeman tunable atoms, fiber optics

Possible mistakes in present results

◮ validity of coupled-channel and Born expansions? ◮ validity of stationary scattering state formalism and flux interpretation?

Theoretical developments

◮ wave packets and time-dependent approach (1D, 3D) ◮ microscopic description of (cold) polarisers

⇒ use of Bell-pair non-locality with polarized photons?

Jean-Marc Sparenberg (ULB) Deterministic quantum mechanics TM2012 13 / 13