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Spooky action at distance
also for neutral kaons?
What has CP violation to do with nonlocality?
by
Beatrix C. Hiesmayr
Faculty of Physics
University of Vienna
Austria
Physics   Particle Physics   Quantum Theory
Discrete 2008, Beatrix C. Hiesmayr
What does Particle Physics teach us about QM?
... a lot!!
Is there nonlocality also in high energy
systems? Are Bell inequalities violated?
Particle physics?
photons, atoms,
single neutrons,
...
Spooky action at distance
also for neutral kaons?
Discrete 2008, Beatrix C. Hiesmayr
The EPR scenario
Antisymmetric Bell state:
   12  l  


1
2

1
2

1
2



1
2
1
2
0
H


K
B
I
l
 1
0
l
0
l
l
 
l
 1 l 0
r
 V
l
 
r
r
 K
 V
0
0
 
r

... photon
 B
 II
0
 B0
l
l
 
r

 ... kaon
 ... B-meson
r
l
r
r
... spin 1/2
 K0
r
 B

... qubit
 H
l
 K
0

r
r
r
... single neutron in
interferometer
Discrete 2008, Beatrix C. Hiesmayr
The EPR scenario
1935: Einstein-Podolsky-Rosen-PARADOX
Completeness of the theory: “Every
element of the physical reality must
have a counterpart in the theory”
 Quantum theory is not complete!
Discrete 2008, Beatrix C. Hiesmayr
What are Bell inequalities?
No spooky action
at distance!
realism
locality
free will
Local realistic theories:
Quantum Mechanics:
P (a , b)  P (a , c )  P (c , b)
inequalities for probabilities
 always satisfied!
quantum mechanical
probabilities may violate
the inequalities!
Experiment has to decide!
Discrete 2008, Beatrix C. Hiesmayr
Generalized Bell inequality for kaons
Bertlmann, Hiesmayr, PRA 63 (2001)
What can Alice & Bob measure?
Are you in a certain
quasispin kn or not?
measurement device
ta
kn 
1
 n  n
2
2

 n K 0  n K
0

quasispin
local realistic theories
SCHSH (kn , km , kn' , km ' ; ta , tb , tc , td )
 E ( kn , t a ; km , t b )  E ( kn , t a ; km ' , t c )  E ( k n ' , t d ; k m , t b )  E ( k n ' , t d ; k m ' , t c )  2
• vary in times
• vary in quasi-spin
• or both
QM:
S Photon  2 2  2.8
Discrete 2008, Beatrix C. Hiesmayr
!?Nonlocality related to a symmetry violation?!
Bell inequalities
CP violation
world
anti-world
Discrete 2008, Beatrix C. Hiesmayr
CP violation
K0 , K
0

2
 ,
CP  1
3

CP  1
Experiment: 1964 Christensen, Cronin, Fitch and Turlay
KS 
KL 
1
2 (1 | |2 )
1
2 (1 | |2 )
{ K1   K 2 }
  103
{ K 2   K1 }
CP violation
Leptonic charge asymmetry:
( K L   l  l )  ( K L   l  l )
3


(
3
.
27

0
.
12
)

10
( K L   l  l )  ( K L   l  l )
Discrete 2008, Beatrix C. Hiesmayr
Generalized Bell inequality for kaons (I)
SCHSH (kn , km , kn' , km ' ; ta , tb , tc , td )
 E ( kn , t a ; km , t b )  E ( kn , t a ; km ' , t c )  E ( k n ' , t d ; k m , t b )  E ( k n ' , t d ; k m ' , t c )  2
I. Vary in quasi-spin:
kn  K S , km  K
k n'  k m '  K 1
0
 0
?! CP violation
related to nonlocality
!?
•Bertlmann, Grimus, Hiesmayr,PRA (2001)
•Hiesmayr, Found. of Phys. Lett (2001)
  0
 0
  0
Leptonic charge asymmetry:
( K L   l  l )  ( K L   l  l )

 (3.27  0.12) 103
 
 
( K L   l  l )  ( K L   l  l )
Discrete 2008, Beatrix C. Hiesmayr
Generalized Bell inequality for kaons (II)
SCHSH (kn , km , kn' , km ' ; ta , tb , tc , td )
 E ( kn , t a ; km , t b )  E ( kn , t a ; km ' , t c )  E ( k n ' , t d ; k m , t b )  E ( k n ' , t d ; k m ' , t c )  2
II. Vary in time:
kn  km 
k n'  k m '  K
0
0
0
E ( K , ta ; K , tb )  cos m(ta  tb )  e ( ta  tb )
S Photon  2 2  2.8 Violation!
Kaons?
•Bertlmann, Bramon, Garbarino, Hiesmayr,
Phys. Lett. A (2004)
•Bertlmann, Hiesmayr, Phys. Rev. A (2001)
S Kaon ( t a , t b , t c , t d )  2 NO violation!
Strangeness oscillation/decay:
x 
m
2m

1

S
PROPOSITION:
The CHSH-inequality is violated iff x>2
for kaons or for other mesons x>2.6.
B-mesons: x=0.77
D-meson: x<0.03
Bs-mesons: x>20.6
Discrete 2008, Beatrix C. Hiesmayr
Bell-CHSH
forkaons
kaons
Bell-CHSHtype
type inequality
inequality for
Bertlmann, Hiesmayr, PRA 63 (2001)
0
0
0
0
SCHSH ( K , K , K , K ; t a , t b , t c , t d )
0
0
0
0
0
0
0
0
 E ( K , ta ; K , tb )  E ( K , ta ; K , tc )  E ( K , t d ; K , t b )  E ( K , t d ; K , t c )  2
Is it really not possible to distinguish
E ( K , t ; K , t )  cos m(t  t )  e
between local realistic theories and
quantum mechanics for neutral kaons in
Photons:
S
 2 2 a2.8direct
Violation! experiment?
0
0
a
 ( ta  tb )
b
a
b
Photon
Kaons?
S
Kaon
You have to be
•Bertlmann, Bramon, Garbarino, Hiesmayr,
( t a , t b , t c , t d )  2 NO violation!
Phys. Lett. A (2004)
more tricky!
•Bertlmann, Hiesmayr, Phys. Rev. A (2001)
Strangeness oscillation/decay:
x 
m
2m

1

S
PROPOSITION:
The CHSH-inequality is violated iff x>2
for kaons or for other mesons x>2.6.
B-mesons: x=0.77
D-meson: x<0.03
Bs-mesons: x>20.6
Discrete 2008, Beatrix C. Hiesmayr
Bell inequality sensitive to strangeness violated?
Hiesmayr, Eur. Phys. J. C (2007)
0
0
0
0
local realistic theories
SCHSH ( K , K , K , K ; t a , t b , t c , t d )
0
0
0
0
0
0
0
0
 E ( K , ta ; K , tb )  E ( K , ta ; K , tc )  E ( K , t d ; K , t b )  E ( K , t d ; K , t c )  2
Can we violate the BI for a certain initial
state and if, what is the maximum value?
Arbitrary initial state:
  r1e i K S K S  r2e i K S K L  r3e i K L K S  r4e i K L K L
1
Expectation value:
2
3
4
Discrete 2008, Beatrix C. Hiesmayr
Bell inequality sensitive to strangeness violated?
Can we violate the BI for a certain initial
state and if, what is the maximum value?
Hiesmayr, Eur. Phys. J. C (2007)
YES!!
The maximal violation is obtained
for a non-maximal entangled state Smax  2.15
A. DiDomenico
A. Go
Discrete 2008, Beatrix C. Hiesmayr
Different view on CP violation (1)
Hiesmayr, Huber Phys. Lett. A (2007)
Bohr’s principle of complementarity:
Quantum systems possess properties
that are equally real but mutually exclusive!
wave-particle duality
Interferometric duality:
The observation of an interference pattern and
the adquisition of which-way information are
mutually exclusive!
predictability=
a priori which-way knowledge
P
pure state: equality
2
21
V0
Greenberger,Yasin (1988);
Englert (1996)
fringe visibility
Discrete 2008, Beatrix C. Hiesmayr
Different view on CP violation (2)
Hiesmayr, Huber Phys. Lett. A (2007)
predictability=
a priori which-way knowledge
pure state: equality
2
2
P V  1
fringe visibility=interference1 contrast
Kaon in time:
K (t ) 
0
short-lived state
N
2p

e

S
2
t  imS t
KS  e
long-lived state

L
t  imL
2
t
KL

Bramon,Garbarino, Hiesmayr, Phys. Rev. (2004)
P ( K S (t ) ) 
V ( K S (t ) ) 
1 
2
1 
2
e S t K S
2
eS t K S
2
2
1 
„A kaon is a kind of
double slit“
CP violation shifts
obtainable information
to different aspects of
reality!
Discrete 2008, Beatrix C. Hiesmayr
Summary/Outlook:
• CP violation implies nonlocality
• CP violation shifts obtainable information to different
aspects of reality
• kaons provide a ``dynamical´´ nonlocality
• nonlocality and entanglement are different quantum
features
for quantum particles with more
degrees of freedom
Hiesmayr, Huber, Spengler; in preparation
direct experimental test of BI are highly desired!
(open: if non—maximal entangled states can be produced in experiment)
Outlook:
BI with regenerators:
A. DiDomenico A. Go
Testable BI for DAPHNE (Frascati,Rom)?