# counterfactual

```‫פרושים של תורת הקוונטים‬
‫בוהר‪ :‬אסור לשאול איפה החלקיק בין המדידות ‪Duality,‬‬
‫‪Complementarity‬‬
‫לנדאו‪ :‬חייבים עולם הקלסי כדי להגדיר עולם קוונטי‬
‫ספרי לימוד‪ :‬משתנה – אופרטור‪ ,‬משמאות גל רק לאנסמבל‬
‫פון נוימן‪ :‬הכל גל שמשתנה לפי שרדינגר אבל גם קורס במדידה‬
‫בוהם‪ :‬גל (בלי קריסה) הוא ‪ ,pilot wave‬המציאות חלקיקים‬
‫עולמות מרובים‪ :‬הכל גל‪ ,‬אין קריסה‬
‫‪ GRW-Pearle‬הכל גל‪ ,‬יש קריסה ( ‪)Flashes, Density‬‬
‫‪Modal Interpretation‬‬
‫‪Consistent Histories‬‬
‫‪Quantum Logic‬‬
‫‪Information‬‬
Elements of Reality
Counterfactuals
Counterfactuals
If it were that A then it would be that B
If John were to jump out of the window of 10th floor, he would die.
F
If Nixon were to push the nuclear attack button, there would be a nuclear holocaust.
True or False?
B True or False in the CF world with A , closest to the actual world.
Miracles
Time Asymmetry
“closest” is not well defined,
Counterfactuals are vague
F
Counterfactuals in Physics
If it were that A then it would be that B
If it were that A was measured at time t then it would be that A=a
True or False?
B True or False in the CF world with A , closest to the actual world.
SYSTEM
No need for a miracle to have A
In “closest” CF world the system has the same description at time t as in actual world
“closest” is well defined,
Counterfactuals are not vague
Counterfactuals in Classical Physics
If it were that A then it would be that B
If it were that A was measured at time t then it would be that A=a
True or False?
B True or False in the CF world with A , closest to the actual world.
SYSTEM
No need for a miracle to have A
In “closest” CF world the system has the same description at time t as in actual world
“closest” is well defined,
Counterfactuals are not vague
Counterfactuals
=
conditionals
Counterfactuals in Quantum Physics
If it were that A then it would be that B
If it were that A was measured at time t then it would be that A=a
True or False?
B True or False in the CF world with A , closest to the actual world.
SYSTEM
No need for a miracle to have A
In “closest” CF world the system has the same description at time t as in actual world
“closest” is well defined,
Counterfactuals are not vague
Counterfactuals
=
conditionals

Counterfactuals in Quantum Physics
If it were that only A was measured at time t then it would be that A=a
If it were that only B was measured at time t then it would be that B=b
Counterfactuals
= counterfactual conditionals
‫פורמליזם הדו וקטורי‬
The two-state vector
t
P  1
t2

t
t1

P  1


The two-state vector
t
P  1
t2


t

P  1
t1
t2
t
t1


P  1
?

t
P  1

t
t
t
t
t
t
t
The standard (one-state vector) description of a quantum system at time t
H FREE  0
t
t1

P  1
The standard (one-state vector) description of a quantum system at time t
H FREE  0
t
t1

The standard (one-state vector) description of a quantum system at time t
H FREE  0
t
t1

P'  1
 =e
i
t
t1 H FREE dt
'
The standard (one-state vector) description of a quantum system at time t
We assume:
t
t1

P  1
H FREE  0
The standard (one-state vector) description of a quantum system
t
x
x 1
x
x 1
z
z 1
y
y 1
(t )
The time reversal of
t
x
x 1
x
x 1
z
z 1
y
y 1
(t )
The backwards evolving quantum state
x
t
x
x
The time reversal of
x 1
(t )
(t )
x 1
The two-state vector
x
z
z 1
z
y
y
y 1


t2
t
t1

P  1
?

t
P  1

t2
t
z
t1
z 1
z 1
?

z
t
At time t:
Prob( z )  1
Prob( )  cos
zˆ

2
2

ˆ
Prob( z )  1
Prob( )  ?
z 1
t2
z
t
t1
?

z
t

z 1
t1
  1
At time t:
Prob( z )  1
Prob( )  cos
zˆ

2
2

ˆ
Prob( z )  1
Prob( )  0
unknown
t2
t
z
t1
z 1

t1
Prob( )  cos
zˆ

2
2

z
t
At time t:
Prob( z )  1
z 1
ˆ
known
Prob( z )  1
Prob( )  ?
```