many worlds - many minds a view of our universe ingvar lindgren
TRANSCRIPT
Many Worlds - Many Minds
A view of our universe
Ingvar Lindgren
Einstein
Dispute about the interpretation of QM
Bohr
”God plays dice” ”God does NOT play dice”
...modern experiments and the discovery of decoherence have shifted the prevailing quantum interpretations away from wave function collapse towards unitary physics,....
Copenhagen school
Bohr, Heisenberg, Pauli
Result
i
Wave function
ci i
M
Measuring process acc. to Cop. interpret.
A measurement is performed by a macroscopic apparatus System is instantaneously and randomly transformed to an eigenstate of the observable.
Wave function collapse
The probability for a certain result is |ci|2 ”God plays dice”
Max Born’s probalitity interpretation
EPR paradoxEinstein-Podolsky-Rosen 1935
Hidden variables? Bell’s inequality
Two-photon decay
J=0
J=0
Photons of opposite polarization. Acc. to Cop. interpret. the photons have no specific polarization, before the pol. has been measured. Superposition of states.
ci i i
The measurement of photon 1 gives it a specific polarization. Then also the polarization of photon 2 will be given.
Schrödinger’s cat
Radiation from a radioactive material initiates a buttet that kills the cat.
Before the observation, the cat is acc. to Copenhagen interpret. in a superposition of dead and alive.
Superposition -- entanglement
ci i
Mathematically a state can be expanded in any complete basis set.
Entanglement: Coupling of physical states (eigenstates of an observable)
Collapse of wave function: Abrupt destruction of entanglement
ci i i
Problems with the Copenhagen interpretation
• The measurement process requires an macroscopic observer.
• The collapse of the wave function does not follow any known laws of physics.
• Born’s statistical interpretation is an additional assumption that does not follow from the model.
• Artificial border between micro and macro systems.
H u g h E ve r e tt
J o h n W h e e le r
H u g h E v erett ’s in terp reta t io nR e v. M o d . P h y s ic s 2 9 , 4 5 4 ( 1 9 5 7 )
Entire world evolves accord. to time-dependent Schrödinger eq.
• Also measuring device treated quantum mechanically (von Neumann)
• Dropping collapse of wf
ci |
Si
0>No interaction between system and meas. device
Measuring device affected by interaction with the system under study
ci |S
i
i>
No interaction between system and meas. device
Interaction between system and meas. device
S M
S M
Everett termed this ”relative-state model”
DeWitt introduced around 1970 the term ”Many-worlds interpretation”
Observer connected to ONE branch, sees only that branch
S M
S1M1
S2M2
S M
S1M1O1
S2M2O1
The Everett original model is incomplete.
Does not explain the emergence of stable,non-interfering brances
Does not explain the emergence of classicality
Decoherence has to be considered
Why no interference between the branches?
Dynamical dislocation of
quantum-mechanical entanglements,
destruction of quantum coherence
Decoherens (W.H. Zurek, H.D. Zeh ~1980)
Zurek, Rev. Mod. Phys. 75, 715 (2003)
Purely quantum-mechanical phenomenon
Caused by interaction by the environment
Wojciech Hubert Zurek
Dieter Zeh
Left alone, strong coherences between the branches
Complete entanglement
S M
S1M1
S2M2
S M
S1M1
S2M2
Interaction with environment
S M
S1M1
S2M2
Entanglement with environmentreduces entanglement between branches
S M
S1M1
S2M2
Further entanglement with environmentreduces further entanglement between branches
Eventually development of stable pointer states Not further affected by environment Branches completely decoupled
Emergence of classicality
S M
S1M1
S2M2
pointer statesstable, decoupled
classicality
classicality
S M
S1M1
S2M2
Zurek: Einselectionenvironment-induced superselection
Preferred states: Independent of initial conditions
pointer statesstable, decoupled
classicality
classicality
S M
S1M1
S2M2
This is the measurement process in MWI
Different “worlds” - different “minds”Observer in one branch not aware of the other branches
No macroscopic observerNo collapse
Continuous transition to classicality – No cat!
pointer statesstable, decoupled
classicality
classicality
S M
S1M1
S2M2
Compare Darwin's theory:Origin of the spicies
Survival of the fittest
”Quantum Darvinism”
pointer statesstable, decoupled
classicality
classicality
S M
S2M2
classicality
Copenhagen interpretation:
Nature selects randomly ONE branch
”God plays dice”
Extra detektor
Extra detektor
Stern-Gerlach magnet to measure spin orientation
Extra detector will destroy interference
System (spin) – detector (magnet) – environment (extra detektor)
System (spin) – detector (magnet):
= s+d+ e+ > + s-d- e- >
|s+d+><s+d+| +s+d+><s-d-|+s-d-><s+d+| +|s-d-> <s-d-|
Density matrix = | > < | =
Interference terms
= s+d+>+ s-
d->
Reduced density matrix for sd system (<ei|ej> = ij):
r= e <e| > < |e> = |s+d+> <s+d+| + |s-d-> <s-
d-| No interference
H. D. Zeh:The importance of decoherence was overlooked for
the first 60 years of quantum theory precisely
because entanglement was misunderstood ....
Quantum-mechanical decoherence has been verified experimentally
Zeilinger et al., Nature 401, 680 (1999)
Haroche et al, PRL 77, 4887 (1996)
Serge Haroche Anton Zeilinger
Advantages with Everett-DeWitt model(with decoherence)
Schrödinger equation strictly valid.
No collapse of wave function.
No classical observer needed. No artificial border between micro and macro systems.
Decoherence leads to emergence of classicality – No cat states
Born’s statistical interpretation follows from the model (Zurek 2005)
Many experts consider this to be the most – or even the only -- consistent interpretation of mechanics quantum presented so far.
Dieter Zeh 2000:
The multi-universe interpretation (which should rather be called multi-consciousness interpretation) seems to be the only interpretation of a universal quantum theory (with an exact Schrödinger equation) that is compatible with the way the world is perceived. However, because of quantum non-locality it requires an appropriate modification of the traditional epistemological postulate of psycho-physical parallelism.
In this interpretation, the physical world is completely described by Everett's wave function that evolves deterministically (Laplacean). This global quantum state then defines an inde-terministic (hence "branching") succession of states for all observers. Therefore, the world itself appears indeterministic subjective in principle, but largely objective through quantumcorrelations (entanglement).
Dieter Zeh 2000:
... the Heisenberg-Bohr picture of quantum mechanics is dead.
Neither classical concepts, nor any uncertainty relations, complementarity, observables, quantum logic, quantum statistics, or quantum jumps have to be introduced on a fundamental level.
The decoherence leads to disentanglement of entangled states. The branches still exist but are not aware of each other.
Personal view
Universe – a bifurcations tree
Universe – a bifurcations tree
Universe – a bifurcations tree
Universe – a bifurcations tree
Universe – a bifurcations tree
Life
.......
Universe – a bifurcations tree
Life
..............
Homosapiens
Universe – a bifurcations tree
Life
..............
. . . . . .
Homosapiens
I.L.
Universe – a bifurcations tree
Life
..............
Homosapiens
..............
Probability for Life Hom.sap. I.L extremely small.
. . . . . . I.L.
Universe – a bifurcations tree
Tage Danielssons statistik
”Jag menar, före Harrisburg så var det ju ytterst osannolikt att det som hände i Harrisburg skulle hända, men så fort det hade hänt, rakade ju sannolikheten upp till inte mindre än 100 procent, så det var nästan sant att det hade hänt.”
Life
..............
Homosapiens
..............
Probability for Life Hom.sap. I.L extremely small.
. . . . . .
”Men när det väl har hänt, är sannolikheten 100 %, och det är nästan sant att det har hänt.”
I.L.
Universe – a bifurcations tree
Life
..............
Homosapiens
..............
. . . . . .
All branches remain – no collapse of wave function
I.L.
Universe – a bifurcations tree
My universe
..............
. . . . . . I.L.
LifeHomosapiens
But each observer can see only one branch –
”Many minds”
All branches remain – no collapse of wave function
..............
. . . . . .
LifeHomosapiens
”Anthropic principle”
Looks like a collapse of wave function for each observer
I.L.
All branches remain – no collapse of wave function
My universe
But each observer can see only one branch –
”Many minds”
Anthropic principle
Anthropic principle
No coincidence that the universe has the properties it has
Acc. to anthropic principle universe must have exactly these properties
in order for humans to be created and to develop
If not, we would not exist and could not worry about it.
(Dicke 1961, Brandon Carter, 1973)
Barrow and Frank, Oxford 1988
Brandon Carter
A Brief History of Time (1988) (9 . )mill copies
Stephen Hawking
Universe in a nutshell (2001)
Hugh Ross: Fingerprint of God Creator and the Cosmos
Martin Rees: Before the beginning
Barrow-Silk: The left hand of creation
The direction of time (5.ed.)
Knowledge and the world
H. Dieter Zeh
Max Tegmark
Commentary
Natu re 448 , 2 3- 2 4 (5 J u ly 2 0 0 7 )
Many lives in m any w orlds
Max Tegm ark1 1. I n this Universe , Max Tegm ark is a physicist a t the Massa chusetts I nstitute o f Techno logy , C am bridge,
Massachusetts, US A . Top o f page
Abstract
Accepting quantum physics to be universally true, argues Max Tegmark, means that you should also believe in parallel universes.
M I R A G E EN TER PR I S ES / R G A
I s it only in fiction that we can experience parallel lives? I f atom s can be in two places at once, so can you.
I.L. Interpretation of Quantum Mechanics, http://fy.chalmers.se/~f3ail/
Peter Byrne: The Many Worlds of Hugh Everett, Sci. Amer. Nov. 2007
Stanford Encyclopedia of Philosophy
Zurek, Rev. Mod. Phys. 75, 715 (2003)
Further reading
D. H. Zeh, arXiv:quant-ph
Tegmark and Wheeler: 100 years of the Quantum, arXiv:quant-ph/0101077v1
Zurek, Physics Today 44, 36 (1991)