Download 6 GU 2007 Quantum Illusions and Time

Quantum Illusions
and Time
Joan Vaccaro
K
K
GU 2007 Quantum Illusions and Time
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Contents
Quantum States
Many Worlds
Many Times
Quantum States
Photons (particles

j
of light)

i
• polarisation of E (electric field):
two orthogonal directions
y
V
x
E
z
y
x E
z
GU 2007 Quantum Illusions and Time
H
V
H
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Contents
Quantum States
Many Worlds
x
E
V
z

i
H
state  H  V
• superpositions
placement of “one thing on top
of another”
y
• measurement
y
 
ij

j
• arbitrary polarisation
y
Many Times
V
E
x
50%
z
E
H
x
PBS
z
GU 2007 Quantum Illusions and Time
y
x
E
z
50%
H
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Contents
Quantum States
Many Worlds
Many Times
• superposition of two positions
y
x
opaque absorber with 2 slits
U upper
E
d
z
state  U  L
L lower
• verifying the superposition
y
interference
pattern
x
E
photons pile up here
one at a time
1

d
z
but NOT here
need many photons for verification
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Contents
Quantum States
Many Worlds
Many Times
Experiments
Young
photons
electrons
& Thomson
atoms
neutrons
bucky balls
virus?
bacteria?
flea?
cat?
people?
1802 Young
1926 Davisson, Germer
Thomson
1930 Estermann & Stern
1945 Wollan & Shull
2002 Zeilinger
Shull
Zeilinger
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Contents
Quantum States
Many Worlds
Many Times
Many Worlds
…first a bit of history…
• 1920’s: treatment of radioactive decay
radioactive
atom

possible tracks Tr() &
paths Pa() of single particle
cloud chamber
Tr(1), Pa(1)
Tr(2), Pa(2)
Tr(3), Pa(3)
k
GU 2007 Quantum Illusions and Time
Tr(4), Pa(4)
but only one track per
particle is seen
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Contents
Quantum States
Many Worlds
Many Times
Copenhagen Interpretation:
• 1927: Bohr and Heisenberg in Copenhagen
when experimenter
looks at cloud chamber
its state collapses

Tr(1), Pa(1)
Tr(2), Pa(2)
Tr(3), Pa(3)
3
GU 2007 Quantum Illusions and Time
Tr(4), Pa(4)
see only one track
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Contents
Quantum States
Schrödinger’s Cat
00:00
12
9
Many Worlds
Many Times
radioactive
atom + Geiger
detector
3
6
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Contents
Quantum States
Schrödinger’s Cat
09:30
12
Many Worlds
Many Times
radioactive
atom + Geiger
detector
9
6
cat dies
GU 2007 Quantum Illusions and Time
hammer trips
and breaks vial
of poison
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Contents
Quantum States
Many Worlds
Schrödinger’s Cat
radioactive
atom + Geiger
detector
00:15
12
9
Many Times
3
hammer trips
and breaks vial
of poison
6
cat dies
Partial decay leads to superposition state
until experimenter looks inside box and state collapses
oh no…
hi kitty
50%
chance
GU 2007 Quantum Illusions and Time
OR
50%
chance
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Contents
Quantum States
Many Worlds
Many Times
I don’t like it and I’m sorry I
ever had anything to do
with it.
collapse is not described by
any dynamical process
(with forces, potentials etc.)
Schrödinger
oh no…
hi kitty
50%
chance
GU 2007 Quantum Illusions and Time
OR
50%
chance
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Contents
Quantum States
Everett 1957 (50
th
Many Worlds
Many Times
anniversary year)
• applying quantum mechanics to universe (cosmology)
• no external observers (experimenters) to collapse state
We need new toy example
• don’t know how to treat “no life process” (dead) and
“life process” (alive) as physical states
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Contents
Quantum States
Many Worlds
Many Times
The cat that may (or may not) be fed
00:00
12
9
3
6
GU 2007 Quantum Illusions and Time
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Contents
Quantum States
Many Worlds
Many Times
The cat that may (or may not) be fed
09:30
12
9
3
6
GU 2007 Quantum Illusions and Time
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Contents
Quantum States
Many Worlds
Many Times
The cat that may (or may not) be fed
00:15
12
9
3
6
Why don’t we see this superposition?
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Contents
Quantum States
Many Worlds
Many Times
This is what happens when we look…
here kitty-kitty…
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Quantum States
Many Worlds
Many Times
This is what happens when we look…
there you are
you’re so hungry
you’ve over eaten
…so how do we see superpositions
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Contents
Quantum States
Many Worlds
Many Times
The dropped cat experiment (with catchers)
- how to “see” a superposition
interference
probability
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Contents
Quantum States
Many Worlds
Many Times
The dropped cat experiment (with catchers)
- how to “see” a superposition
interference
probability
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Contents
Quantum States
Many Worlds
Many Times
The dropped cat experiment (with catchers)
- how to “see” a superposition
Parameters
d = 0.1m
x = 1m
m = 10 kg
L = 1067 m
probability
t = 1026 y
interference
d
x
GU 2007 Quantum Illusions and Time
L
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Contents
Quantum States
Many Worlds
Many Times
we never even try to do this kind of experiment
- need control (& disentangle atom… from cat etc.)
- but, importantly, need to repeat it many times to build up
interference pattern
separate “worlds” evolve…
you’ve fat!
here’s food
$
$$$
the poor but happy world
the rich but sad world
the perception of
“one single world” is an illusion
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Contents
Quantum States
Many Worlds
Many Times
Many Times
David Pegg’s quantum theory of time
• canonical approach to quantising gravity
• Wheeler-deWitt - equation:
- universe is in a stationary state
Pegg, J.Phys. A 24,
- no motion – frozen dynamics
3031 (1991).
- energy is well known (zero)
prob.
X
prob.
P
• Heisenberg uncertainty principle
X
if you know position X well, momentum P is uncertain
“
“
energy E “
time T
“
“
P
 time in the universe must be uncertain
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Contents
Quantum States
Many Worlds
Many Times
• use new set of axes – each axis represents a different
time

axes chosen to make
projections all equal
state of the universe
3
2
1
1
2
3
4
5
History vector
– totality of reality – state at all times
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Contents
Quantum States
Many Worlds
Many Times
• divide universe into 2 parts: Clock + Rest
clock must have equally spaced energy levels
R
C
orthogonal clock states
1
M
M+1
P
find interval where Clock and Rest
are separate and non-interacting
• rewrite interval in terms of orthogonal clock states
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Contents
Quantum States
M
M+1
R1
C
Many Worlds
Many Times
P
R2
R3
RP
R
• the dynamics of Rest can be written in terms of the time
parameter t defined by Clock: t =

Rn+1
Rn
t
Schrödinger’s equation
for dynamics
GU 2007 Quantum Illusions and Time
i ˆ
 H

 Rn
t
Rn
i ˆ
 H

Rn
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Contents
R1
Quantum States
R2
Many Worlds
Many Times
R3
RP
C
R
we live at these different times
the perception of
“one present” is an illusion
this illusion is on par with the
single world illusion
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Contents
Quantum States
Many Worlds
Many Times
Puzzle: how does our perception of travelling in
time arise?
R1
R2
these states of Rest are
non-orthogonal
Rm-1
R
R3
RP
so can’t be sure which
one we are in
Rm
Rm+1
• this gives a connection
between different states of Rest
• but the connection is the same
in both directions!
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Contents
Quantum States
Many Worlds
Many Times
Puzzle: why do we travel in one direction in time?
• anti-particles are the time reversed versions of particles
time
gamma ray
photons
electron
e
antielectron
e+
electron
e
electron
e
antielectron
e+
space
• all anti-particle and particle pairs are time symmetric
except for Kaons (K mesons)
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Contents
Quantum States
Many Worlds
Many Times
Neutral kaons K0 have a lifetime of less than 106 s.
Decay paths:
positron
antimatter 
e+
pion
neutrino

K0  e+ +  + 
K0  e +  + +  (more likely)
electron
pion
antineutrino
• equal number of K0 and K0 are found
to yield different numbers of e+ and e
• violation of CP &  T symmetry
(CERN 1998)
R1
K0
matter
R2
antimatter
K0
R3

+
e
matter
RP
t
K0
short lifetime
K0
long lifetime
time asymmetric
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Contents
Quantum States
R1
t
Many Worlds
R2
RP
K0
long lifetime
K0
short lifetime
Rm-1
R3
Many Times
only unsure of which
state in the “future” we
are in
Rm
Rm+1
Kaons appear to be responsible for us
travelling through time!!!
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Contents
Quantum States
Many Worlds
Many Times
Conclusion
Many worlds: we exist in many worlds but have
the illusion (and pleasures) of only one
- but somewhere we are having a really good time
Many times: we exist at many times but have the
illusion of only one present which marches steadily
toward to our demise! - but consoled by knowing
we still exist at earlier times
RIP
Free will: even our perception of free will is an illusion
– we cant change the future because we already exist
there (hopefully)
- but we can enjoy the illusion
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