GU 2007 Quantum Illusions and Time 1 Quantum Illusions and Time Joan Vaccaro KK.

1GU 2007 Quantum Illusions and Time

Quantum Illusions and TimeQuantum Illusions and TimeJoan Vaccaro

K K


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



• 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



• 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



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



…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)



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)



radioactive atom + Geiger detector12

6

39

00:00

Schrödinger’s Cat



radioactive atom + Geiger detector

hammer trips and breaks vial of poison

cat dies


12

6

9

09:30




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



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.)



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



The cat that may (or may not) be fed

12

6

9

00:00

3




12

6

9

09:30

3




12

6

9 3

00:15

Why don’t we see this superposition?



This is what happens when we look…here kitty-kitty…



This is what happens when we look…there you are

you’re so hungry you’ve over eaten

…so how do we see superpositions



The dropped cat experiment (with catchers) - how to “see” a superposition

interference

probability




interference

probability




probability

d

xL

interference

Parameters d = 0.1mx = 1m m = 10 kg L = 1067 m t = 1026 y



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

$ $$$



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



• 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



• 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



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



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



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!



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)



(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



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!!!



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

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GU 2007 Quantum Illusions and Time 1 Quantum Illusions and Time Joan Vaccaro KK.

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