72nd icrea colloquium "laws, chance and quantum randomness" by carl hoefer

Objective chance and quantum randomness

Carl Hoefer ICREA - U. Barcelona

Sept. 27, 2016

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Philosophers of science:

1. Try to understand the notion of law of nature or physical law.

2. Try to understand the notions of objective or intrinsic randomness, and objective chance.

Physicists are often curious about these topics too!

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Goals of [the long version of ] this talk:

1. Explore the notion of an (irreducible, fundamental) probabilistic law of nature, and argue that we don’t have a good grasp of what it means to postulate such a thing.

Valerio Scarani: “What does it mean, a physical law that has statistical character?”

A. Einstein: “Der Gott würfelt nicht.”

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Goals of this talk:

1. Explore the notion of an (irreducible, fundamental) probabilistic law of nature, and argue that we don’t have a good grasp of what it would mean to postulate such a thing.

2. Show that, by contrast, a probabilistic law that is grounded on underlying determinism can be grasped easily - and we have many good examples of such laws.

3. Offer some comments on how the randomness found in quantum mechanics could be of this variety.

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Objective probabilities or ‘chances’

• Pr(Heads) = 0.5, flipping a ‘fair’ coin

• Pr(00) in throw of 38-slot roulette wheel = 1/38

• Pr(Pu241 decay in 1 year) = 0.05

• Pr(spin-z up | spin-x up earlier) = 0.5

–...whatkindoffactsarethese?–Canwemakesenseofthemasobjec*veandground-leveltruths?

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De Finetti on ‘probability’:

“My thesis, paradoxically, and a little provocatively, but nonetheless genuinely, is simply this:

PROBABILITY DOES NOT EXIST The abandonment of superstitious beliefs about the existence of the Phlogiston, the Cosmic Ether, Absolute Space and Time, . . . or Fairies and Witches was an essential step along the road to scientific thinking. Probability, too, if regarded as something endowed with some kind of objective existence, is no less a misleading misconception, an illusory attempt to exteriorize or materialize our true probabilistic beliefs.”

• (But we must leave this topic to one side for now.)

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Distinctions and notations

• indeterminism = ¬ determinism

• indeterminism vs random behavior

• indeterminism vs probabilistic (or ‘stochastic’) laws

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Non-random indeterminisms• Classical Mechanics (CM):

–Space Invaders (5-particle system in t-reverse) –Norton’s Dome (& other symmetry-breaking situations)

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Non-random indeterminisms• General Relativity (GR):

–Naked singularities (e.g. “white holes”) –Other types of ‘hole’ –models with no Cauchy surface

• What all these CM and GR cases have in common:

• No involvement of probability; indeterminism = simple breakdown of determinism.

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• indeterminism vs probabilistic laws

• randomness in general vs probabilistic-law-randomness

–examples:cancerincidence,vsradioacCvedecayrate

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• product randomness vs process randomness

–[apparentrandomnessvsintrinsicrandomness]

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• product randomness vs process randomness

–[apparentrandomnessvsintrinsicrandomness]

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Outline:

I. The dialectics of primitive chance laws.

II. Chances from underlying determinism

III. QM & intrinsic randomness

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Outline:



III. QM & intrinsic randomness

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Chance from Determinism

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Diaconis’ coin-flip analysis

VerCcal:rateofrotaConHorizontal:iniCalupwardvelocity


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Galton board

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Galton board & IC distributions

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AnyoftheseICdistribuConsleadstothesamesta*s*caloutcomepaNern.

Galton board & IC distributions

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SomepossibleICdistribuConshoweverdonotgive‘right’results

⇍

Outline:



III. QM& intrinsic randomness: the heterodox view

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Bohmian Mechanics

• De Broglie 1927;

• David Bohm 1952

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Bohmian Mechanics

• QM represents physical systems with a ‘wavefunction’, Ψ.

• Basic idea of BM: In addition to Ψ, there are in fact point-like particles with well-defined positions at all times, moving on continuous paths. Ψ acts on the particles like a ‘pilot wave’, determining their velocities at every moment.

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Standard two-slit experiment of QM allegedly shows wave-like behavior of things like photons, electrons:

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Bohmian particles passing through double slit

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A theory with some appeal …

“Is it not clear from the smallness of the scintillation on the screen that we have to do with a particle? And is it not clear, from the diffraction and interference patterns, that the motion of the particle is directed by a wave? De Broglie showed in detail how the motion of a particle, passing through just one of two holes in screen, could be influenced by waves propagating through both holes. And so influenced that the particle does not go where the waves cancel out, but is attracted to where they cooperate. This idea seems to me so natural and simple, to resolve the wave-particle dilemma in such a clear and ordinary way, that it is a great mystery to me that it was so generally ignored.” (J. Bell 1986)

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Bohmian mechanics: spin-measurement

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Norsen(2013):howBohmianparCclesgetdistributed(unequalweightstate)

Bohmian mechanics

1. Characterization of state: (Ψ, X)

2. Schrödinger’s evolution:

3. The guidance equation (GE):

– IfthewavefuncConiswriNeninpolarform,theguidanceequaCon

simplyreads.

4. The statistical postulate:

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≡ … ∈

Ψ … ∈

! ! !"

! ! !"

31 2 N

31 2

X (X , X , , X )

( , x , , ; )

N

NNx x t

t∂Ψ

= Ψ∂

Hih

∇ Ψ= =

Ψ

!""" #v Im kkk

k

dxdt m

ρ = Ψ2

0 0( , ) (x, )x t t

Ψ = !/iSRe

= ∇!""

m v Skk k

Bohmian mechanics

• The Bohmian particles follow trajectories in 3d-space according to the so-called Guidance equation:

(GE)

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∇ Ψ= =

Ψ

!""" #v Im kkk

k

dxdt m

Bohmian mechanics

• BM makes probabilistic predictions because of the ‘Quantum Equilibrium’ or Statistical Postulate:

(SP)

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ρ = Ψ2

0 0( , ) (x, )x t t

QM & intrinsic randomness. . . What about Bohmian Mechanics??

• In order to say we have certified randomness from quantum phenomena, we have to rule out BM and similar Det hidden variable theories. . . How?

• Usual complaints made against BM:

• BMrequiresconspiratorialiniCalcondiCons• BMdoesnotallow‘freechoice’ofA,B• BMallowsfaster-than-lightsignalling

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QM & intrinsic randomness. . . What about Bohmian Mechanics?

• But these complaints are misguided:

• BMinvolvesnoconspiratorialsuper-determinism• BMallowsfreechoiceofmeasurementse[ngsinBellexperiments

• BMisano-signallingtheory– ...sothestandardreasonsforexcluding‘hiddenvariable’theories,likeBM,seemineffecCve.

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QM & intrinsic randomness. . . What about Bohmian Mechanics??• BMallowsfreechoiceofmeasurementse[ngsinBell

experiments

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Causal structure (assumed) of EPR-type experiments

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• A, B: settings for measurement device

• X, Y: spin/polarization measurements (spacelike separation between A, X and B, Y).

• Z: pre-existing states able to causally influence A, X, B and Y.

A B

X Y

Z

E F

Causal structure of EPR experiments (for Bohmians)

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• Determination of A, B partly or fully affected by external factors E, F.

• Red arrows: non-local causal influence, a feature of Bohmian mechanics.

A B

X Y

Z

E F

Causal structure of EPRB experiments (for Bohmians)

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• Determination of A, B can be by human agents’ free choices;

• Or from photons from opposite sides of the galaxy if you like.

• No ‘conspiratorial conditions’ needed for deterministic story.

A B

X Y

Z

E F

QM & intrinsic randomness. . . What about Bohmian Mechanics??

• Conspiracy (in the sense commonly invoked in the Bell Test field) not needed. Non-local action at a distance is all that is required to explain violation of Bell inequality.

• Experimenter ‘free choice’ perfectly OK (unless you think determinism rules out free choice tout court)

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. . . and what about signalling?

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• BM is a “parameter dependent” theory.

• Parameter dependence ≠ effective signalling

• Statistical postulate ensures no effective signalling possible

• SP ≠ conspiratorial initial conditions in the “superdeterminism” sense.

A B

X Y

Z

E F

Important note: I am not endorsing Bohm’s theory

• There are reasons to be skeptical that BM is on the right track.

• But - violation of no-signalling (at the surface level, where we have reason to trust N-S), or of free choice, are not among those reasons

• Plus: where there’s one theory, there may be more out there waiting to be discovered.

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Contrast: properties of standard QM

• Non-local

• Contextual

• Parameter-dependence [Copenhagen]

• [arguable] causation at spacelike separation

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Summing up1. I argued that it’s difficult to spell out what we mean when we postulate

intrinsic randomness of the propensity or chance-law variety.

2. By contrast, I argued, we can understand objective probability claims if they arise from determinism + nicely-distributed initial conditions.

– Quantum“randomness”inBohmianMechanicsisofexactlythissort.

3. I noted that while Bohmian QM has no intrinsic randomness (being deterministic), it satisfies no-signalling in a pragmatic or effective sense. At the surface, it’s a counterexample to randomness-certification arguments; but at the deep level one could say it is a “signalling” theory. But in this deep-level sense, we have no way to rule out that nature herself is signalling.

4. Distinction: certified [intrinsic] randomness vs certified [effective] randomness. BM is counterexample to former, but not the latter.

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72nd icrea colloquium "laws, chance and quantum randomness" by carl hoefer

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