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Too Beautiful Not to be True: The Hidden Logic of Quantum Mechanics Avshalom C. Elitzur Copyleft Permission is granted to everyone to copy and/or use this work or any part of it.
Too Beautiful Not to be True:The Hidden Logic of Quantum Mechanics
Avshalom C. Elitzur
Copyleft Permission is granted to everyone to copy and/or use this work or any part of it.
Abandon hope all ye who enter hereAbandon hope all ye who enter here
Dante
© Jie Qi
Schrödinger
Determinism
Locality
Objectivity
trough
crest
trough
crest
trough
crest
trough
crest
“in phase”
“out of phase”
constructive interference
destructive interference
The Double-Slit Experiment (Courtesy of Tel-Aviv Municipality)
Constructive interference
Destructive
Constructive
Proof: Light=Waves
Interference of water waves
Interference of light waves
The Mach-Zehnder Interferometer:
• Photon is emitted and split into two
• Reflected back (notice phase shift upon reflection!)
• One half split again
• Second half split again (at the same time)
• Destructive Interference on detector D
• Constructive Interference on detector C
• All light reaches detector C.
D C
solid mirrors
half-silvered mirrors
light source
detectors
0% 100%
Interference
50%
Confused? Don’t worry: It will soon get much worse.
Interference occurs with single 1. Photons2. Electrons3. Neutrons4. Atoms5. Molecules6. …
Can we outsmart the “which path” uncertainty?
110 0
0% 100%
Interference
50%
Can we outsmart the “which path” uncertainty?
50% 50%
50%
Can we outsmart the “which path” uncertainty?
50% 50%
50%
Can we outsmart the “which path” uncertainty?
0% 100%
Interference
Can we outsmart the “which path” uncertainty?
0% 100%
Interference
Meet the Uncertainty Principle: 2
hpx
position unknown
? ?
momen
tum co
nserved
momen
tum co
nserved
Heisenberg
0% 100%
Interference
position known
momen
tum co
nserved
momen
tum co
nserved
momentum lost
Meet the Uncertainty Principle: 2
hpx
Heisenberg
Potestas Est* Nam et Ipsa IgnorantiaScientia
Can we outsmart the “which path” uncertainty? No, but
Interaction-Free Measurement:The Elitzur-Vaidman (1993) Bomb-Testing Experiment
1. Photon emitted
2. Split
3. No Boom
4. Remaining wave splits
5. “Forbidden” detector D clicks
D C
A New Monster is Born
What was I thinking…
© Ted Dawson
The Einstein-Podolsky-Rosen ExperimentClassical analogue: Two coins
? ?
The Einstein-Podolsky-Rosen ExperimentQuantum version: Two particles
The Einstein-Podolsky-Rosen ExperimentQuantum version: Two particles
Or
1. Is your spin “up” in the α direction?
2. Is your spin “up” in the β direction?
3. Is your spin “up” in the γ direction?
50% “Yes” , 50% “No”
Bell’s Test for Particle Telepathy: 3 Possible Questions, 2 Possible Answers
50% “Yes” , 50% “No”
50% “Yes” , 50% “No”
Overall: 100% correlations for same-question pairsbut 50% correlations for different-question pairs!
pre-established agreement would give higher correlations!
“Telepathy” between particles proved
A quantum dynasty
Bohm
Aharonov
Vaidman Elitzur Dolev
3. Is your spin “up” in the γ direction?
The Elitzur-Dolev Quantum Liar Paradox:Replacing Bell’s Third Question
50% “No”
Bell’s Test for Particle Telepathy: 3 Possible Questions, 2 Possible Answers
3. Are you entangled with the other particle? 50% “Yes” ,
1. Is your spin “up” in the α direction?
2. Is your spin “up” in the β direction?
50% “Yes” , 50% “No”
50% “Yes” , 50% “No”
The Quantum Liar Paradox
• Two excited atoms A1 and A2 reside in cavities facing a beam-splitter
• One detector clicks, source of the photon uncertain
• Thereby entangling the two atoms
• An orthogonal measurement to excited/ground is introduced
• EPR
• Bell-inequality violated
• The liar paradox all over again
*212*12
1AAAA
The Quantum Liar Paradox
– One atom is found to be excited, which seems to indicate that it emitted no photon.
– Hence, it could not interact with the other atom and should not be entangled with it.
– But, by violating Bell’s inequality, its “having preserved its photon” is due to entanglement with the other atom!
THIS SENTENCE HAS NEVER
BEEN WRITTEN
(-:
Which is equivalent to saying
Lavrentiy Beria
Большая Советская Энциклопедия
History, The Soviet Encyclopedia’s Version
When the “hero of the people” former KGB head is shot as a traitor, you take back old volumes of the encyclopedia, take out the pages of the entry “Beria” and replace them with “Bering.”
Could Nature be similarly reiterating a process’s evolution at the quantum level?
Our Relativistic Quantum Model
References
Dolev, S., & Elitzur, A.C. (2001) Non-sequential behavior of the wave-function. http://arxiv.org/PS_cache/quant-ph/pdf/0102/0102109v1.pdf
Elitzur, A.C., & Dolev, S (2006) Multiple interaction-free measurement as a challenge to the transactional interpretation of quantum mechanics. In Sheehan, D. [Ed.] Frontiers of Time: Retrocausation – Experiment and Theory. AIP Conference Proceedings, 863, 27-44.
Elitzur, A.C., & Dolev, S (2007) The inexhaustible source of insights revealed by every photon. Proceedings of SPIE Volume 6664: The Nature of Light: What Are Photons?, C. Roychoudhuri, A.F. Kracklauer, & K. Creath, Eds, 666402-666413.http://a-c-elitzur.co.il/uploads/articlesdocs/photon5(2).pdf
(Herman Minkowski, 1909)
What a pity to die at the dawn of relativity!
