Honoring Epimenides of Crete \(±Δx\): From Quantum Paradoxes, through Weak Measurements, to the Nature of Time

---

 

Honoring Epimenides of Crete (

±Δx): From Quantum 

Paradoxes, through Weak Measurements, to the Nature of 

Time 

Eliahu Cohen

1a

, Avshalom C. Elitzur

2 

1 

School of Physics and Astronomy, Tel Aviv University, Tel-Aviv 69978, Israel 

                                                   

2 

IYAR, The Israeli Institute for Advanced Research, Rehovot, Israel

 

Abstract.

 Quantum temporal peculiarities, involving ordinary and weak measurements, 

are explored. We introduce the foundations of weak measurement and outline some novel 

theoretical and experimental predictions derived from it. We then show how weak values, 

which explicitly depend on both forward and backward evolving state-vectors, can serve 

as  important tools for gaining new insights into the nature of time.  

1 Introduction 

Thankful for this invitation to present our work in the stunning island of Crete, we take the 

liberty of indulging in some historical reflections as an introduction.  

Crete was the birthplace of Epimenides (7

th

/6

th

 Century BC), author of the famous paradox 

based on the self-contradicting statement "all Cretans are liars." The Quantum Liar Paradox 

[1] described below is a physical manifestation of that ancient millstone, suggesting that 

Nature herself is capable of creating self-contradictions.     

Second, not far from this place is the village Milatos, which in ancient times gave its name to 

the more famous town Miletus, birthplace of the first scientist known to history. Thales 

(624–546 BC) was the discoverer of electricity and magnetism, and it so happened that 

another work of ours presented in this conference [2,3] deals with the very nature of the 

electric and magnetic fields.  

And of course there were many other giants in the neighboring islands and shores during that 

golden age. Archimedes (287–212 BC), long before the advent of calculus, recognized the 

importance of infinitesimals. The "slope of a line segment as short as a point" sounds just as 

absurd as Epimenides' "this statement is false," yet it eventually turned out to be one of 

mathematics' most powerful tools. Archimedes was inspired by the earlier legendary dispute 

between Parmenides (5th century BC) and Heraclitus (535–475 BC), about the nature of 

time. For Parmenides, change was an illusion of the senses, reality being eternal and 

                                                 

a

 [e-mail] 

DOI: 10.1051

/

C

Owned by the authors, published by EDP Sciences, 2014

,

/

0 002       

(2014)

2 01

epjconf

EPJ Web of Conferences

4 710002

71

8

This is an Open Access article distributed under the terms of the Creative Commons Attribution License 2.0, which permits 

unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. 

8

Article available at

http://www.epj-conferences.org

or

http://dx.doi.org/10.1051/epjconf/20147100028

---

immutable. Heraclitus, in contrast, held change to be reality's main attribute. Parmenides' 

disciple, Zeno (490–430 BC), has derived one of the most famous paradoxes concerning the 

alleged atomicity of time, a challenge that provoked not only Archimedes' infinitesimals but 

also, in 20

th

 Century, the quantum-mechanical realization [4].  

All these thinkers belonged to the small genius nation of which Crete was part, whose 

scholars have first raised the great questions of science and philosophy with utmost clarity 

and acuity. Our research aspires to resolve quantum paradoxes as well as problems about the 

nature of space-time, guided by the intuition that these two realms are closely related.

Presenting this work in this ancient cradle of science is therefore another source of awe and 

inspiration. 

2 Quantum Temporal Paradoxes  

The most paradoxical effects displayed by quantum measurements involve spatial and 

temporal anomalies, e.g., respectively, the EPR [5] and the delayed-choice [6] experiments. 

Because time is the most elusive and unique dimension of space-time, we shall focus on 

some novel quantum effects that strongly strain common-sense intuitions about time.  

2.1 Motivation 

Several years ago, during a class on quantum mechanics, one of us (AE) was presented with 

a question from an inquisitive student. Why, she asked, should one think that Schrodinger's 

cat was superposed before the box’s opening? This possibility can be ruled out by allowing a 

certain time interval, say, three days, pass between the potentially lethal event and the 

opening. Then, if the cat is found to be dead, it would be also decomposed, whereas if it is 

alive it would be also lean and starved. In both cases, it should be clear that it has never been 

superposed!    

It takes some reflection in order to realize why this clever reasoning does not rule out that 

superposition has prevailed within the box all along: Quantum observation determines not 

only the cat’s state at that moment, but also its entire history since the lethal event’s 

(non)occurrence! 

This example indicates that some kind of retrocausality is inherent in nearly all quantum-

mechanical paradoxes, thereby giving additional credence to models that take this peculiarity 

as their cornerstone. The most daring attempt of this kind is Aharonov’s two state-vector 

formalism [7,8], which furthermore derives many surprising predictions, some of which are 

being verified nowadays. Cramer’s [9] transactional interpretation also invokes this kind of 

peculiar causality, yielding an interpretation which is elegant and parsimonious. Novel 

elaborations of this model, attempting to accommodate it to recently-discovered quantum 

phenomena, merit further interest [10-15]. 

 

 

EPJ Web of Conferences

00028-p.2

---