Transcript The Many-Weirdnesses Interpretation of Quantum Mechanics

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
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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.
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Two Characteristics of (orthodox)
Quantum Mechanics
The outcome of certain
measurements can never
be precisely predicted no
matter how well you
know the initial
conditions. Roll the dice.
non-determinism
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-locality
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Determinism
& Realism
In the orthodox
interpretation of QM,
the idea of non-determinism is
embodied within the more extreme
concept of non-realism.
non-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.
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History of the Worlds
1957 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)]
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)]
The essence of Everett’s many
worlds interpretation is the
same as orthodox QM except
that collapse does not happen.
Superpositions persist.
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“…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
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copies of itself.”
Comparison
Orthodoxy
with Copenhagen
Many Worlds
 ditto
 superposition of states
 ditto
 amplitude squared gives probability
à la Born
 ditto (sort of)
 random collapse to a single answer
 no collapse
Process 1 - deterministic continuous change of
wave function according to wave equation
MW
Orthodoxy
 wave function evolves via a linear
deterministic wave equation
Process 2 - discontinuous change brought about
by ‘observation’
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Consider the measurement of a spin 1/2 particle…
The Difference
Orthodoxy 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.
  E(?)   
measurement
collapse
  E() or   E()
MWI says after you make the measurement, the state still exists
 the experimenter,
 who is herself
in a superposition, along with
described by a more inclusive, entangled superposition.
  E(?)   
measurement
entanglement
  E()  E()
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EntanglementEntanglement
is the natural consequence
of
is Natural
any quantum interaction!
e.g. elastic scattering:
initial:
p f1

pf 2
+
final:

 pi
pi
 p f1

pf 2

+
pf 3

pf 3

pf 4
+
pf 4
+…
entangled state:
  f  p f 1 p f 1 p f 2 p f 2  
p f 3 p f 3  p f 4 p f 4  ...
 f - Bryn
p f 9/21/09
p f
actually a continuous superposition:
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Mawr
 d
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Everett says:
even without collapse, experience of
MWI observer agrees with that of the
orthodox ‘external observer’.
Everett relative states I
Suppose an
experimenter
measures a
spin.
E()

E(,,,,...)
Two possibilities result.
Moreover, repeated measurements of
the same spin will yield identical
results. It looks as if the particle spin
has ‘collapsed’.

E(,,,,...)
E()


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Suppose the
Everett relative states II
E(,,,) 1  2  3  4 Along any branch, the
experimenter
E(,,,) 1  2  3  4 number of ups tends to
measures
E(,,,) 1  2  3  4 equal the number of
many
E(,,,) 1  2  3  4 downs (6 branches out
identically
E(,,,) 1  2  3  4 of 16 with 2 up and 2

prepared
E(,,,) 1  2  3  4 down). As more

E(,,,) 1  2  3  4 measurements are
spins.

E(,,,) 1  2  3  4 done, the branches tend

E(,,,) 1  2  3  4 more and more towards

E(,,,) 1  2  3  4 equal up and down.

E(,,,) 1  2  3  4

E(,,,) 1  2  3  4 The odds for a

Say each
E(,,,) 1  2  3  4 measurement sequence

one is
E(,,,) 1  2  3  4 along any one branch

E(,,,) 1  2  3  4 are the same as
      
E(,,,) 1  2  3  4 predicted by

conventional QM.

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
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Suppose the
amplitudes
for up and
down are not
equal.
Everett relative
states
III
The odds for going down any branch
are given by the amplitude of that
component of the superposition,
a 3bE(,,,) 1  2  3  4

Say each
one is
  a  b 
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.
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Advantage of no collapse
MWI restores:
• locality
• realism
• determinism
• a sensible measurement process
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Orthodoxy isOrthodoxy
…
summary
• non-local
When 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).
measurement
1
 1  2   1  2
e.g.  singlet 

2
collapse


• non-realist
A superposition represents an undefined state.
final   1  2
or
final   1  2
• non-deterministic
 process!
Collapse to a particular final state is a random
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Many Worlds is local!
In the absence of collapse, the remaining
measurement process is entanglement (or
‘entangled splitting’) and is purely local.
MWI is local
Imagine an experiment in
which one spin is measured in
the  basis and the other spin
is measured in the  basis.
  E1(,?)E 2 (?,) 1  2  E1(,?)E 2 (?,) 1 
2
 E1(,?)E 2 (?,) 1  2  E1(,?)E 2 (?,) 1 
2
Into how many pieces has E1 been split, two or four?
 shows E1 has
Factoring
only been split in two by
her local measurement.
  E1(,?) 1 E 2 (?,)  2  E 2 (?,) 
2


 E1(,?) 1 E 2 (?,)  2  E 2 (?,) 
2
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.
  E1(,)E 2 (,) 1  2  E1(,)E 2 (,) 1 
2
 E1(,)E 2 (,) 1  2  E1(,)E 2 (,) 1 
2
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Many Worlds
MWIisis…deterministic,
realist
• local
Splitting along MWI branches is a local process. See previous.
• realist
All 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?)
• deterministic
The 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
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The Measurement Problem I
Shroedinger’s Cat
Until the box is
opened and
examined by the
researcher, the
cat is in a superposition of being
alive and dead.
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with apologies to Berk Breathed
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Wigner’s Friend
The Measurement Problem II
When and how does collapse occur?
Wigner’s
press agent
Wigner’s
friend
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Wigner
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Quantum Suicide
Tests of MWI
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.
[Max Tegmark, “The Interpretation of Quantum
Mechanics: Many Worlds or Many Words?”, Fortsch.
Phys. 46, 855-862 (1998) and arXiv:quant-ph/9709032]
Quantum Immortality
See also:
There’s always some branch that avoids death (debatable).
We should all expect to live forever.
…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]
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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
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