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Quantum Illusions and Time. Joan Vaccaro. K. K. y. E. x. z. y. x. E. z. Quantum States. Photons (particles of light). polarisation of E (electric field): two orthogonal directions. E. y. x. z. y. E. x. z. E. y. x. y. x. z. E. z. arbitrary polarisation. - PowerPoint PPT Presentation
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1GU 2007 Quantum Illusions and Time
Quantum Illusions and TimeQuantum Illusions and TimeJoan Vaccaro
K K
2GU 2007 Quantum Illusions and Time
Contents Quantum States Many Worlds Many Times
Quantum StatesQuantum StatesPhotons (particles of light)• polarisation of E (electric field):
two orthogonal directions
V
H
V
H
xy
z
E
xy
z
E
j
i
3GU 2007 Quantum Illusions and Time
Contents Quantum States Many Worlds Many Times
• arbitrary polarisation
• superpositionsplacement of “one thing on topof another”
V
H
xy
z
E
xy
z
E
xy
z
E
xy
z
E
PBS
50%
50%
V
H
H
• measurement
VHstate
j
i
ji
4GU 2007 Quantum Illusions and Time
Contents Quantum States Many Worlds Many Times
• superposition of two positions
xy
z
E
• verifying the superposition
xy
z
E
opaque absorber with 2 slits
LUstate
U
L
upper
lower
interferencepattern
photons pile up hereone at a time
but NOT here
need many photons for verification
d
d
1
5GU 2007 Quantum Illusions and Time
Contents Quantum States Many Worlds Many Times
Experiments
photons 1802 Youngelectrons 1926 Davisson, Germer
& Thomsonatoms 1930 Estermann & Sternneutrons 1945 Wollan & Shullbucky balls 2002 Zeilingervirus?bacteria?flea?cat?people?
Thomson
Young
Shull
Zeilinger
6GU 2007 Quantum Illusions and Time
Contents Quantum States Many Worlds Many Times
…first a bit of history…• 1920’s: treatment of radioactive decay
paths Pa() of single particlecloud chamber
radioactive atom
possible tracks Tr() &
k but only one track per particle is seen
Many WorldsMany Worlds
Tr(1), Pa(1) Tr(2), Pa(2)
Tr(3), Pa(3) Tr(4), Pa(4)
7GU 2007 Quantum Illusions and Time
Contents Quantum States Many Worlds Many Times
3
Copenhagen Interpretation:• 1927: Bohr and Heisenberg in Copenhagen
when experimenter looks at cloud chamber its state collapses
see only one track
Tr(3), Pa(3) Tr(4), Pa(4)
Tr(1), Pa(1) Tr(2), Pa(2)
8GU 2007 Quantum Illusions and Time
Contents Quantum States Many Worlds Many Times
radioactive atom + Geiger detector12
6
39
00:00
Schrödinger’s Cat
9GU 2007 Quantum Illusions and Time
Contents Quantum States Many Worlds Many Times
radioactive atom + Geiger detector
hammer trips and breaks vial of poison
cat dies
Schrödinger’s Cat
12
6
9
09:30
10GU 2007 Quantum Illusions and Time
Contents Quantum States Many Worlds Many Times
Schrödinger’s Cat
Partial decay leads to superposition state
radioactive atom + Geiger detector
hammer trips and breaks vial of poison
12
6
9 3
00:15
cat dies
until experimenter looks inside box and state collapseshi kitty oh no…
OR50% chance
50% chance
11GU 2007 Quantum Illusions and Time
Contents Quantum States Many Worlds Many Times
hi kitty oh no…
OR50% chance
50% chance
I don’t like it and I’m sorry I ever had anything to do with it.
Schrödinger
collapse is not described by any dynamical process(with forces, potentials etc.)
12GU 2007 Quantum Illusions and Time
Contents Quantum States Many Worlds Many Times
Everett 1957 (50th 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
13GU 2007 Quantum Illusions and Time
Contents Quantum States Many Worlds Many Times
The cat that may (or may not) be fed
12
6
9
00:00
3
14GU 2007 Quantum Illusions and Time
Contents Quantum States Many Worlds Many Times
The cat that may (or may not) be fed
12
6
9
09:30
3
15GU 2007 Quantum Illusions and Time
Contents Quantum States Many Worlds Many Times
The cat that may (or may not) be fed
12
6
9 3
00:15
Why don’t we see this superposition?
16GU 2007 Quantum Illusions and Time
Contents Quantum States Many Worlds Many Times
This is what happens when we look…here kitty-kitty…
17GU 2007 Quantum Illusions and Time
Contents 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
18GU 2007 Quantum Illusions and Time
Contents Quantum States Many Worlds Many Times
The dropped cat experiment (with catchers) - how to “see” a superposition
interference
probability
19GU 2007 Quantum Illusions and Time
Contents Quantum States Many Worlds Many Times
The dropped cat experiment (with catchers) - how to “see” a superposition
interference
probability
20GU 2007 Quantum Illusions and Time
Contents Quantum States Many Worlds Many Times
The dropped cat experiment (with catchers) - how to “see” a superposition
probability
d
xL
interference
Parameters d = 0.1mx = 1m m = 10 kg L = 1067 m t = 1026 y
21GU 2007 Quantum Illusions and Time
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…here’s food you’ve fat!
the poor but happy world the rich but sad world
the perception of “one single world” is an illusion
$ $$$
22GU 2007 Quantum Illusions and Time
Contents Quantum States Many Worlds Many Times
Many TimesMany Times
Pegg, J.Phys. A 24, 3031 (1991).
David Pegg’s quantum theory of time• canonical approach to quantising gravity• Wheeler-deWitt - equation:
- universe is in a stationary state - no motion – frozen dynamics - energy is well known (zero)
• Heisenberg uncertainty principleif you know position X well, momentum P is uncertain
“ “ energy E “ time T “ “
time in the universe must be uncertain
X P
prob.prob.X
P
23GU 2007 Quantum Illusions and Time
Contents Quantum States Many Worlds Many Times
• use new set of axes – each axis represents a different timeaxes chosen to make projections all equal
state of the universe
1 2 3 4 5
1
2
3
History vector – totality of reality – state at all times
24GU 2007 Quantum Illusions and Time
Contents Quantum States Many Worlds Many Times
• divide universe into 2 parts: Clock + Restclock must have equally spaced energy levels
C R
orthogonal clock states
find interval where Clock and Rest are separate and non-interacting
• rewrite interval in terms of orthogonal clock states
1 M M+1 P
25GU 2007 Quantum Illusions and Time
Contents Quantum States Many Worlds Many Times
C
R1 R2 R3 RP
• the dynamics of Rest can be written in terms of the time parameter t defined by Clock: t =
Schrödinger’s equationfor dynamics
M M+1 P
R
Rn+1 Rn
tH
i ˆ
Rn
Rn
tH
i ˆ
Rn
26GU 2007 Quantum Illusions and Time
Contents Quantum States Many Worlds Many Times
C
R
R1 R2 R3 RP
we live at these different times
the perception of “one present” is an illusion
this illusion is on par with the single world illusion
27GU 2007 Quantum Illusions and Time
Contents Quantum States Many Worlds Many Times
Puzzle: how does our perception of travelling in time arise?
R1 R2 R3 RP
Rm-1 Rm
Rm+1
R
these states of Rest arenon-orthogonal so can’t be sure which
one we are in
• this gives a connection between different states of Rest
• but the connection is the same in both directions!
28GU 2007 Quantum Illusions and Time
Contents Quantum States Many Worlds Many Times
space
timegamma ray photons
electron e
anti- electron e+
anti- electron e+
electron e
electron e
Puzzle: why do we travel in one direction in time?
• anti-particles are the time reversed versions of particles
• all anti-particle and particle pairs are time symmetric except for Kaons (K mesons)
29GU 2007 Quantum Illusions and Time
Contents Quantum States Many Worlds Many Times
(more likely)
• equal number of K0 and are found to yield different numbers of e+ and e
• violation of CP & T symmetry (CERN 1998)
K0
matterK0
e+
K0
+
e
antimatter
matter
antimatter
positron pion neutrino
electron pion antineutrino
Neutral kaons K0 have a lifetime of less than 106 s.
Decay paths:
K0 e+ + + e + + +
R1 R2 R3 RP
K0
K0
long lifetime
time asymmetric
K0
short lifetime
t
30GU 2007 Quantum Illusions and Time
Contents Quantum States Many Worlds Many Times
R1 R2 R3 RP
Rm-1
Rm
Rm+1
only unsure of which state in the “future” we are in
K0tK0
long lifetimeshort lifetime
Kaons appear to be responsible for us travelling through time!!!
31GU 2007 Quantum Illusions and Time
Contents Quantum States Many Worlds Many Times
Many worlds: we exist in many worlds but havethe 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
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
ConclusionConclusion
RIP