Inconsistent Histories Revealed
by Quantum Measurement
A New Class of Paradoxes and their
Implications
Avshalom Elitzur and Shahar Dolev
Bar-Ilan University
Overview:
• The Rationale
• The three views concerning time
• The issue of time-asymmetry and
indeterminism
• Two types of QM experiments: Spatial and
temporal paradoxes
• Our strategy
• Inconsistent histories?
• Back to time
The Rationale:
• QM challenges our basic notions of space and
•
•
time.
Therefore, a better understanding of the
quantum riddles will come from a deeper
account of spacetime.
Conversely, a better understanding of spacetime
might emerge from investigating into quantum
riddles
Three Views of Time:
• “Block Universe”
• “Extreme
Presentism”
• “Becoming”
The Issue Of Time-Asymmetry
And Indeterminism
Run Simulation!
The Issue Of Time-Asymmetry
And Indeterminism
The Issue Of Time-Asymmetry
And Indeterminism
Two Types Of QM Experiments:
• Experiments presenting spatial
peculiarities:
EPR Experiment
E-V Experiment
Two Types Of QM Experiments:
• Experiments presenting temporal
peculiarities:
HBT Experiment
Delayed Choice
Schrödinger’s cat
Aharonov’s and Cramer’s proposal
• Aharonov’s and Cramer’s unifying theories:
x
x
x
?
x
1. Offer
2. Confirmation
3. Negotiation
4. Handshake
• All type-A experiments are in fact type-B
•
experiments.
The problem: Block Universe again.
?
Our Strategy:
• Postpone the Quantum-classical Interaction.
• Pursue the bomb idea
• This was first taken up by Hardy.
Results:
• The first result (Hardy, 1992): EPR formed by a single
particle in an MZI:
1. Particles in superpositions
(but not entangled)
2. “Silent” Detector clicks
3. The particles become entangled


 
1
x 
xx11  x2 x1  x1x
2  2 x2 
2
2
Results:
• Second result (Hardy, 1992): a quantum
mechanical bomb more intriguing than EV
1. Particle in a superposition
2. “Silent” Detector clicks
3. The particle must have “collapsed”
into the crossing box
4. The photon must have gone
through the opposite path!
Inconsistent Histories?
• A new class of paradoxes: When the
measurement measures not only a state
but an entire evolution, then
– indeed sometimes an entire evolution seems
to be formed;
– sometimes that evolution looks like a
Schrödinger cat with a history of a dead cat
but traces of a live one.
Inconsistent Histories?
• Non sequential behavior of the wave function:
1. Particles in superposition
(but not entangled)
2. “Silent” Detector clicks
3. The middle particle was measured
and found to have “collapsed” into
the intersecting box
4. All other particles returned to their
original superposition!
Inverse EPR…
(Elitzur, Dolev, Zeilinger 2001)
… or better call it: RPE
Inverse EPR
1. Particles in superposition
(but not entangled)
2. “Silent” Detector clicks
3. The particles become entangled


 
1 1
x1 x x2x1x1 x2 
x2 
 x2 
22 1
Inverse EPR
• With an inconsistent history?
1. To test non-locality, test for Bell
Inequality
2. Use Spin measurement in 3
directions: x, y, and z
3. Spin x (“which box”)
measurement allows only one
history for the photon

1
x1  x2 x1  x21  x2 
2

4. Consequently, the entanglement
disappears
Inconsistent Histories?
THIS SENTENCE HAS NEVER
BEEN WRITTEN
:-)
Back To Time
• Could there be a transactional model in
which spacetime itself is subject to
dynamics?