guy blaylock - bryn mawr 9/21/09 1 the many-weirdnesses interpretation of quantum mechanics...

Guy Blaylock - Bryn Mawr 9/21/091

The Many-Weirdnesses Interpretation of

Quantum Mechanics

Weirdness in orthodox quantum mechanics

Weirdness in the ‘Many-Worlds’ interpretation

A comparison of weirdnesses

MWI may be less weird than what you already believe



Characteristics of a Garden Variety Classical

Scientific Theory(scientific) realism – characteristics

or qualities of a system exist and are well defined, independent of any outside influence or observation.

determinism – complete knowledge of the current state of a physical system is sufficient to determine the future state of the system.

locality – actions at one location do not immediately have any effect at a separate location.


Two Characteristics of (orthodox)

Quantum MechanicsThe outcome of certain measurements can never be precisely predicted no matter how well you know the initial conditions. Roll the dice.

What happens in one part of the universe can instantaneously affect the behavior of a distant part of the universe. The effects of these actions are not localized to one region, but rather, they permeate all space.

non-determinism non-locality


Determinism & Realism

Non-realism implies that when an object is out of sight and isolated from its surroundings, its location becomes not only unknown, but undefined. In order for it to acquire a well-defined location, somebody must see it, or it must interact in some other way with the environment around it.

In the orthodox interpretation of QM, the idea of non-determinism is embodied within the more extreme concept of non-realism.

non-realismnon-realism


History of the Worlds1957 Hugh Everett writes a thesis on the “relative state” interpretation of QM [Hugh Everett III, “Relative State’ Formulation of Quantum Mechanics”, Rev. Mod. Phys. 29, 454-462 (1957)]

The essence of Everett’s many worlds interpretation is the same as orthodox QM except that collapse does not happen. Superpositions persist.

Bryce DeWitt popularizes, embellishes and somewhat misrepresents the concept in the “many worlds” interpretation[Bryce S. DeWitt , “Quantum mechanics and Reality”, Physics Today 23, 30-35. (1970)] “…every quantum

transition taking place on every star, in every galaxy, in every remote corner of the universe is splitting our local world on earth in myriads of copies of itself.”


Comparison with Copenhagen

wave function evolves via a linear deterministic wave equation

superposition of states

amplitude squared gives probability à la Born

random collapse to a single answer

ditto

ditto

ditto (sort of)

no collapse

Orthodoxy

Many Worlds

Process 1 - deterministic continuous change of wave function according to wave equation

Process 2 - discontinuous change brought about by ‘observation’

Orthodoxy M

W


The DifferenceOrthodoxy says before you make the measurement, the state may exist in a superposition. After a non-deterministic collapse, the system (experimenter & particle) is in one of two definite states.

MWI says after you make the measurement, the state still exists in a superposition, along with the experimenter, who is herself described by a more inclusive, entangled superposition.

€

ψ =E(?) ↑ + ↓[ ]

€

ψ =E(↑)↑

€

ψ =E(↓)↓measuremen

t

collapse

measurement

entanglement

€

ψ =E(?) ↑ + ↓[ ]

€

ψ =E(↑)↑ + E(↓)↓

or

Consider the measurement of a spin 1/2 particle…


Entanglement is NaturalEntanglement is the natural consequence of any quantum interaction!

e.g. elastic scattering:

€

rp i

initial:

final: + + + + …

€

− rp i

€

rp f1

€

− rp f1

€

rp f 2

€

− rp f 2

€

rp f 3

€

− rp f 3

€

rp f 4

€

− rp f 4

€

ψ f =r p f 1 −

r p f 1 +

r p f 2 −

r p f 2 +

r p f 3 −

r p f 3 +

r p f 4 −

r p f 4 + ...

entangled state:

€

ψ f = dΩ r p f∫ −

r p factually a continuous

superposition:


Everett relative states IEverett says: even without collapse, experience of MWI observer agrees with that of the orthodox ‘external observer’.

Everett says: even without collapse, experience of MWI observer agrees with that of the orthodox ‘external observer’.Suppose an

experimenter measures a spin.

Moreover, repeated measurements of the same spin will yield identical results. It looks as if the particle spin has ‘collapsed’.

Two possibilities result.

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E(↑)↑

€

E(↓)↓

€

E(↑,↑,↑,↑,...)↑

€

E(↓,↓,↓,↓,...)↓


Everett relative states II

€

E(↑,↑,↑,↑)↑ 1 ↑ 2 ↑ 3 ↑ 4

Suppose the experimenter measures many identically prepared spins.

€

E(↑,↑,↑,↓)↑ 1 ↑ 2 ↑ 3 ↓ 4

€

E(↑,↑,↓,↑)↑ 1 ↑ 2 ↓ 3 ↑ 4

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E(↑,↑,↓,↓)↑ 1 ↑ 2 ↓ 3 ↓ 4

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E(↑,↓,↑,↑)↑ 1 ↓ 2 ↑ 3 ↑ 4

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E(↑,↓,↑,↓)↑ 1 ↓ 2 ↑ 3 ↓ 4

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E(↑,↓,↓,↑)↑ 1 ↓ 2 ↓ 3 ↑ 4

€

E(↑,↓,↓,↓)↑ 1 ↓ 2 ↓ 3 ↓ 4

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E(↓,↑,↑,↑)↓ 1 ↑ 2 ↑ 3 ↑ 4

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E(↓,↑,↑,↓)↓ 1 ↑ 2 ↑ 3 ↓ 4

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E(↓,↑,↓,↑)↓ 1 ↑ 2 ↓ 3 ↑ 4

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E(↓,↑,↓,↓)↓ 1 ↑ 2 ↓ 3 ↓ 4

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E(↓,↓,↑,↑)↓ 1 ↓ 2 ↑ 3 ↑ 4

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E(↓,↓,↑,↓)↓ 1 ↓ 2 ↑ 3 ↓ 4

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E(↓,↓,↓,↑)↓ 1 ↓ 2 ↓ 3 ↑ 4

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E(↓,↓,↓,↓)↓ 1 ↓ 2 ↓ 3 ↓ 4

€

ψ = ↑+↓[ ]

Say each one is

Along any branch, the number of ups tends to equal the number of downs (6 branches out of 16 with 2 up and 2 down). As more measurements are done, the branches tend more and more towards equal up and down.

The odds for a measurement sequence along any one branch are the same as predicted by conventional QM.


Everett relative states IIISuppose the amplitudes for up and down are not equal.

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a3bE(↑,↓,↑,↑)↑ 1 ↓ 2 ↑ 3 ↑ 4

€

ψ = a↑ +b↓[ ]

Say each one is

The odds for going down any branch are given by the amplitude of that component of the superposition,

just like the odds of collapsing to that particular result are given by the same amplitude in conventional QM.

In this way, MWI reproduces the Born probabilities of conventional QM.

In this way, MWI reproduces the Born probabilities of conventional QM.


Advantage of no collapseMWI restores:

•locality

•realism

•determinism

•a sensible measurement process


Orthodoxy summaryOrthodoxy is …•non-localWhen an entangled state is collapsed by interacting with one of the two entangled partners, the other partner is collapsed via a non-local process (see EPR).

e.g.

•non-realistA superposition represents an undefined state.

•non-deterministicCollapse to a particular final state is a random process!

€

ψsinglet =1

2↑

1↓

2− ↓

1↑

2( )measurement

collapse

€

ψfinal = ↑1↓

2

€

ψfinal = ↓1↑

2

or


MWI is local

€

ψ =E1(↑,?)E2(?,→)↑1

→2

+ E1(↓,?)E2(?,←)↓1

←2

+ E1(↓,?)E2(?,→)↓1

→2

+ E1(↑,?)E2(?,←)↑1

←2

€

ψ =E1(↑,?)↑1

E2(?,→) →2

+ E2(?,←) ←2( )

+ E1(↓,?)↓1

E2(?,→) →2

+ E2(?,←) ←2( )

Many Worlds is local!In the absence of collapse, the remaining measurement

process is entanglement (or ‘entangled splitting’) and is

purely local.

Many Worlds is local!In the absence of collapse, the remaining measurement

process is entanglement (or ‘entangled splitting’) and is

purely local.

Imagine an experiment in which one spin is measured in the basis and the other spin is measured in the basis.

Factoring shows E1 has only been split in two by her local measurement.When the two experimenters communicate their results to each other, each experimenter is split again, but this occurs only via a chain of local interactions at sublight speed.

€

ψ =E1(↑,→)E2(↑,→)↑1

→2

+ E1(↓,←)E2(↓,←)↓1←

2

+ E1(↓,→)E2(↓,→)↓1

→2

+ E1(↑,←)E2(↑,←)↑1←

2

Into how many pieces has E1 been split, two or four?


MWI is deterministic, realist

Many Worlds is …

•localSplitting along MWI branches is a local process. See previous.

•realistAll possibilities do in fact exist in one branch or another. Instead of one reality in an ill-defined state, there are multiple definite realities. (a little too much realism?)

•deterministicThe wave functions evolve according to a deterministic wave equation and every possible results of a measurement is realized in its own world. Although an experimenter may still end up wondering how she ended up with a particular measurement result. (not usefully predictive?)

“it is quite likely that at some future time we may get an improved quantum mechanics in which there will be a return to determinism” - P.A.M. Dirac

“it is quite likely that at some future time we may get an improved quantum mechanics in which there will be a return to determinism” - P.A.M. Dirac


Shroedinger’s Cat

Until the box is opened and examined by the researcher, the cat is in a super-position of being alive and dead. with apologies to Berk

Breathed

The Measurement Problem I


Wigner’s Friend

When and how does collapse occur?

WignerWigner’s friend

Wigner’s press agent

The Measurement Problem II


Tests of MWI

Tests of MWI

[Max Tegmark, “The Interpretation of Quantum Mechanics: Many Worlds or Many Words?”, Fortsch. Phys. 46, 855-862 (1998) and arXiv:quant-ph/9709032]

A daring proponent of MWI presses an almost fully loaded gun to his head and pulls the trigger. If MWI is correct, he will have the experience of always surviving the suicide attempt. His consciousness continues only in those worlds where he lives.

Quantum Suicide

There’s always some branch that avoids death (debatable). We should all expect to live forever.

Quantum Immortality

…and on a grand scale…Observation within a model of the universe that predicts low probability of life could be evidence of MWI.[Don N. Page, “Observational Consequences of Many-Worlds Quantum Theory”, arXiv:quant-ph/9904004]

See also:


multiple cats

Advantages and Disadvantages restores realism, determinism,

locality

offers an answer for the measurement problem

science fiction terminology (though Fred Hoyle would approve)

risky testing

popular among cosmologists

too many cats

guy blaylock - bryn mawr 9/21/09 1 the many-weirdnesses interpretation of quantum mechanics...

Documents

guy blaylock bryn mawr

nonrealism slide

worlds interpretation

nondeterministic collapse

orthodox interpretation

quantum transition

orthodox qm

current state