blaylock p424class30oct09
TRANSCRIPT
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8/9/2019 Blaylock P424Class30Oct09
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Blaylock - P424 Seminar 10/30/09
! hair balls, litter boxes, decapitated birds
! Schroedingers Cat & Wigners Friend
! altering the past & Wheelers Delayed Choice
! interference and choice! the remaining options
! hair balls, litter boxes, decapitated birds
! Schroedingers Cat & Wigners Friend
! altering the past & Wheelers Delayed Choice
! interference and choice! the remaining options
The problem with catslessons in quantum collapse
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ShroedingersCat
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
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Wigners Friend
When and how does collapse occur?
WignerWigners
friend
Wigners
press agent
The Measurement Problem II
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A Question of Consciousness?
Would the collapse
take place if the
researcher were in
the box?
Would the collapse
take place if it were
recorded by
computer?
Would the collapse
take place if an
amoeba were in the
box?
(I dont think so)
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Electron doubleslit experiment
Each single electron by itself follows the
rules of the interference pattern.
The interference pattern shows
contributions from both slits.
Each electron must in some sense go
through both slits.
Buildup of electron
interference pattern in
Jnssons experiment.
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Wheelers delayed choice
BS1
BS2
M2
M1
D2
D1
In a Mach-Zender
interferometer, each
photon travels both
paths and interferes,
destructively at D1 andconstructively at D2.
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If the second beam
splitter is removed, the
detection of the photon
at D1 or D2 collapses
the trajectory to one orthe other path.
Wheelers delayed choice
BS1
M2
M1
D2
D1
If the decision to use or remove BS2 is made at the
last instant, then it seems the collapse to one path or
both paths occurs after the photon has passed BS1!!!
Vincent Jacques et al.,
Experimental
Realization of
Wheeler's Delayed-
Choice Gedanken
Experiment, Science315 966 - 968 (2007).
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Gravitational Lenses
Light from a distant source can travel more than one patharound a source of gravity to get to an observer on Earth.
There appears to be more than one source, or the source is distorted.
View without
gravity.View with gravity.
If the source, mass and Earth areall exactly in line the source will
appear to be spread into a ring.
Big Mass
Distant
Source
Big Mass
Distant
Source
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Big Mass
Distant
Source
10 billion light years
The choice about whether to
collapse the photons to a
single path or to both paths
occurs 10 billion years afterthe photons left the source.
Distant
Source
Does our choice of measurement affect the past?
cosmic delayed choice
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8/9/2019 Blaylock P424Class30Oct09
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Blaylock - P424 Seminar 10/30/09
Collapse is nonlocal
This is a very special, very restricted form of
nonlocality. We still cant make anything travelfaster than the speed of light, or send a signal
faster than the speed of light. Collapse is no use
for intergalactic telephone calls.
Collapse changes a wave that is spread out over a region to a
wave that is localized at one spot. This is a case of action-at-a-
distance!
Rather like voodoo.
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Collapse is not relativistically invariant
"twin
=
1
2VV + HH( )
Consider two photons
produced in an entangled state:
Copenhagen says when Alice
measures one photon, both
collapse simultaneously.
From Bobs perspective
in his relativistic space
ship, Alices photon
collapses afterthe other.
I what reference
frame is the
collapse
simultaneous, and
why that frame?
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Not Even Wrong
Wolfgang Pauli, when
shown the paper of a
colleague, once said:
Not only is that not right,
its not even wrong!
Copenhagen: An isolated
cat is in a superposition of
two possibilities until he isobserved. Then suddenly,
The idea of collapse was an ill-defined ad hoc addition to the (very
well defined) evolution described by the Schroedinger equation.
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two parts to collapse
Disappearance of interference (a.k.a. decoherence)
recognized as a change in the rules of probability from
those of a superposition to those of a mixture
can be understood in terms of interaction with an
environment
Choice of a single outcome (a.k.a. projection)
who knows how to understand it
is this a deterministic, reversible process or not?
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Combining Probabilities
mixtures add:
superpositions interfere:
+ =
or+ = or or
Superposition is distinguished
from the more common type
of combination, which is
described as a mixture.
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which path collapse
In the electrondouble slit
experiment, the
interference pattern
implies the electron
is in a superposition
of going throughboth slits.
If we shine a lighton the mask, the
superposition
collapses to one
path and the
interference pattern
disappears.
Superposition:add amplitudes then
square to get probability
Mixture:add probabilities
directly
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Double slitIn an undisturbed electron double slit experiment two electron waves
combine constructively in the center of the screen, giving maximumprobability of detecting an electron at that location.
minimum*destructively*
*Electrons (fermions) have an extra minus sign in the combination rules.
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Scattering shift
If the wave has shifted by as much as half a wavelength, there will be
zero probability of detecting an electron in the center of the screen, and
maximum probability somewhere else.
What if a photon scatters off the electron on its way to the screen.
Scattering will change the direction and the momentum(wavelength) of the electron.
original
new
n.b.
If the wavelength/frequency
has changed, the interference
pattern will change as a
function of time.
minimum
high
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Scattering uncertaintyBut the location and the momentum transfer of interaction is uncertain!There are many possibilities for where the scattering takes place, and how muchmomentum is transferred. Many possibilities for interaction form manysuperposing interference patterns.
If the photon is low energy and doesnt disturb the electron too
much, the interference pattern gets smeared out just a bit.
original
new
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DecoherenceWith many small interactions, or several high-momentuminteractions, the disturbance is big enough to completely
smear out the interference.
The pattern smears out to the appearanceof a mixture.
If interactions are strong enough and energetic enough
to resolve the slits, the pattern is completely smeared.
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potential solutions
Specify the collapse
dynamical collapse
Get rid of the collapse
multiple realities: Many Worlds
one reality: (nonlocal) Hidden Variable Theory
Sweep it under the rug
shut up and calculate
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John Wheeler
What part of
quantum theory
do you not
understand?