Zeno's Quantum Paradox Reversed: Watching A Flying Arrow Increase Its Speed

For over 2,500 years, scientists and philosophers have been grappling with Zeno of Elea's famous paradox. More recently, scientists believed that the counterpart of this paradox, known as the quantum Zeno paradox, is realizable in the microscopic world governed by quantum physics. Now, scientists from the Weizmann Institute of Science have shown that in most cases, the quantum Zeno paradox should not take place. An article describing the calculations that lead to this surprising conclusion appears in today's Nature. The article is also surveyed in the journal's News and Views section.

The Greek philosopher Zeno, who lived in the 5th Century B.C., decades before Socrates, dedicated his life's work to showing the logical paradoxes inherent to the idea of indefinite divisibility in space and time (i.e., that every line is composed of an infinite number of points). One of these paradoxes is known as the arrow paradox: if the motion of a flying arrow is divided ad infinitum, then during each of these infinitesimal moments, the arrow is at rest. The sum of an infinity of zeroes remains zero, and therefore the arrow cannot move. One can imagine how someone giving a flying arrow quick, repeated glimpses, can actually freeze it in place. Zeno inferred from this that movement cannot happen. Indeed, he was a true follower of Parmenides, his teacher and mentor, who advocated that any change in nature is but an illusion.

This philosophical view was rejected by Aristotle, as well as by scientists and philosophers of the 19th century, who resolved Zeno's paradox by showing that non-zero velocity can exist in the limit of infinitesimal divisions of a trajectory. However, the paradox was bolstered in the 1960s by the physicist Leonid A. Khalfin, working in the former USSR, and by physicists E.C.G. Sudarshan and Baidyanath Misra, working in the USA during the 1970s. Using quantum theory, they concluded that if an "observer" makes repeated quick observations of a microscopic object undergoing changes in time, it is highly probable that the object will indeed stop changing. The frequent observations divide the trajectory along which the object evolves into infinitesimal segments in which there is no change. In other words, in the quantum world an observer can freeze the evolution of an object, in accordance with Zeno's paradox.

Skeptics who doubted those calculations must have been genuinely surprised when, in 1990, Colorado University physicist John Wineland proved in an experiment that "freezing glimpses" do work in the real world (or at least in a "simple" world with only two energy levels). Ever since, physicists have been struggling to understand the implications of the experiment. Can the Zeno paradox, for example,"glimpse-freeze" radioactive nuclear decay, thus stopping radiation? The prevailing answer during the past 30 years has been that such a freeze should be possible, provided the successive observations are made frequently enough.

Prof. Gershon Kurizki and Dr. Abraham Kofman of the Weizmann Institute of Science have recently shown that, for better or for worse, such "freezing" does not take place in reality, and decay cannot actually be stopped by "bombarding" the system with glimpses. According to their calculations, the ability to "freeze" changes through quick glimpses depends on the ratio between the memory time of the decay, and the time interval between successive observations. Every process of decay has a memory time. In the case of radioactive decay, for instance, this is the period in which the radiation has not yet escaped from the atom, allowing the system to "remember" its state prior to the decay. The memory time in a radiative decay process of an excited atom (an atom occupying an unstable energy level) is less than one billionth of a billionth of a second. To "freeze" this decay, the observations would have to be at intervals of much less than a billionth of a billionth of a second.

However, a sequence of observations so close in time would cause the appearance of new particles, changing the system completely and destroying it, and thus the question of stopping the decay would become meaningless. On the other hand, if the time interval between observations is longer than the decay's memory time, the rate of decay and radiation is actually increased. Not only does Zeno's paradox not take effect in such a case but there is actually an opposite effect: the "anti-Zeno effect".

Prof. Kurizki: "In other words, if we make the analogy between an object undergoing changes in time, for example a decaying nucleus or an excited atom, and Zeno's moving arrow, the arrow will increase its speed as the rate of the 'glimpses' increases. The surprising conclusion of this research is that the anti-Zeno effect (i.e., the increase of decay through frequent observations) can occur in all processes of decay, while the original Zeno effect, which would slow down and even stop decay, requires conditions that only rarely exist in such processes."

Professor Gershon Kurizki is the holder of the George W. Dunne Chair of Chemical Physics.