Zeno of Elea Shines a New Light on Quantum Weirdness

María Esther Burgos

doi:10.4236/jmp.2017.88087

Abstract

After a brief reference to the quantum Zeno effect, a quantum Zeno paradox is formulated. Our starting point is the usual version of Time Dependent Perturbation Theory. Although this theory is supposed to account for transitions between stationary states, we are led to conclude that such transitions cannot occur. Paraphrasing Zeno, they are nothing but illusions. Two solutions to the paradox are introduced. The first as a straightforward application of the postulates of Orthodox Quantum Mechanics; the other is derived from a Spontaneous Projection Approach to quantum mechanics previously formulated. Similarities and differences between both solutions are highlighted. A comparison between the two versions of quantum mechanics, supporting their corresponding solutions to the paradox, shines a new light on quantum weirdness. It is shown, in particular, that the solution obtained in the framework of Orthodox Quantum Mechanics is defective.

Highlights

Introduction and OutlookThe Greek philosopher Zeno of Elea (ca. 490-430 BC) supported Parmenide’s doctrine. This philosophy states that, contrary to the evidence of our senses, the belief in plurality and change is mistaken; in particular motion is nothing but an illusion
Introduction and OutlookThe Greek philosopher Zeno of Elea supported Parmenide’s doctrine
The first as a straightforward application of the postulates of Orthodox Quantum Mechanics; the other is derived from a Spontaneous Projection Approach to quantum mechanics previously formulated

Summary

Introduction and Outlook

The Greek philosopher Zeno of Elea (ca. 490-430 BC) supported Parmenide’s doctrine. This philosophy states that, contrary to the evidence of our senses, the belief in plurality and change is mistaken; in particular motion is nothing but an illusion. Differing from other references to the quantum Zeno effect, the present paper highlights a True Quantum Zeno paradox (TQZ paradox for short): we show that the usual version of Time Dependent Perturbation Theory (TDPT) leads to the conclusion that transitions between stationary states cannot happen.

Formulation of TQZ Paradox

Solving TQZ Paradox

SPA versus OQM

Conclusions