Yakir Aharonov

Yakir Aharonov
Known for	Aharonov–Bohm effect; weak values; two-state vector formalism
Nationality	Israeli
Institutions	Tel Aviv University; Chapman University
Awards	Wolf Prize in Physics (1998)
Fields	Physics; Quantum mechanics; Quantum foundations
Born	28 August 1932; Haifa, Mandatory Palestine
Wikidata	Q721892

Yakir Aharonov (born August 28, 1932) is an Israeli theoretical physicist celebrated for foundational discoveries in quantum mechanics. His most famous result, with David Bohm, was the 1959 prediction of the Aharonov–Bohm effect, a striking demonstration that charged particles can be influenced by electromagnetic potentials even in regions with no force. Aharonov has also introduced novel concepts like weak measurements and weak values, and developed a time-symmetric formulation of quantum theory that has deepened our understanding of quantum paradoxes. Over a long career at universities in Israel and the United States, he has earned many honors (including the 1998 Wolf Prize and the 2009 U.S. National Medal of Science) and influenced generations of physicists working on quantum foundations.

Early Life and Education

Yakir Aharonov was born on August 28, 1932, in Haifa, in what was then British Mandate Palestine. Shortly after finishing high school, he served in the Israeli Army. In 1956 he graduated with a Bachelor of Science degree from the Technion in Haifa. That fall he moved to England to pursue doctoral studies at the University of Bristol under the guidance of David Bohm. In 1960 Aharonov earned his Ph.D., writing a thesis on problems in collective quantum measurements.

After Bristol, Aharonov held a postdoctoral position at Brandeis University (1960–1961) and then joined the physics faculty of Yeshiva University in New York. In 1967 he returned to Israel and became a professor of physics at Tel Aviv University. He later held joint positions at Tel Aviv and the University of South Carolina (1973–2006), and taught at George Mason University (2006–2008). From 2008 onward he has been the James J. Farley Professor of Natural Philosophy at Chapman University in California, while serving as Professor Emeritus at Tel Aviv University. He has also been a Distinguished Professor at the Perimeter Institute for Theoretical Physics (2009–2012). Throughout his career Aharonov has led and participated in research centers devoted to quantum science, and currently is president of Israel’s Institute for Advanced Research (IYAR).

Major Contributions

Aharonov’s work spans many areas of quantum theory, but the theme running through much of it is the exploration of nonlocal and topological effects in quantum mechanics, and the nature of quantum measurement.

Aharonov–Bohm Effect

While still a graduate student, Aharonov and his adviser David Bohm discovered the effect now bearing their names. In their 1959 paper, they showed that an electron moving around (but never touching) a confined magnetic field, such as a long thin solenoid, acquires an extra measurable phase in its wavefunction. This Aharonov–Bohm (AB) effect means that quantum particles are affected by the electromagnetic potential even in regions where the classical electric and magnetic fields are zero. The phase shift accumulated by the electron is proportional to the magnetic flux enclosed by its path. In practice, the AB effect produces a shift in the interference pattern when electrons pass on two sides of a solenoid, even though all field lines are confined inside it.

The AB effect has become a paradigm of quantum nonlocality and topology. It was initially controversial (even Niels Bohr was skeptical of its implications for the classical correspondence principle but experimental verifications followed in the 1960s and beyond (for example, Robert Chambers’ 1960 interference experiment and Akira Tonomura’s definitive electron holography in 1986). Today the AB phase is a standard example of a “geometric” or “Berry” phase in quantum mechanics, and it underpins important phenomena in condensed matter physics (e.g. mesoscopic rings and topological insulators). For the discovery of the AB effect (which profoundly demonstrated the physical significance of potentials), Aharonov shared the 1998 Wolf Prize in Physics with Bohm.

!!! image titled "Illustration of the Aharonov–Bohm effect"

Illustration of the Aharonov–Bohm effect: Electrons (blue paths) pass on either side of a long solenoid (red) containing magnetic flux φ, which is completely confined inside the solenoid (no field leaks outside). Quantum mechanics predicts a relative phase shift between the two paths proportional to φ, producing a displaced interference pattern This shows that the electromagnetic potential (associated with the enclosed flux) affects the electrons even in field-free regions.

Weak Measurements and Weak Values

In the late 1980s, Aharonov and collaborators developed the idea of weak measurements as a novel way to probe quantum systems. A weak measurement gently (i.e. only very lightly) couples an external device to a quantum system and then re-prepares (post-selects) the system in a final state. The result is a weak value, which can lie outside the range of the observable’s normal eigenvalues. For example, Aharonov, Albert, and Vaidman famously showed in a thought experiment that a spin-½ particle could seemingly yield a spin component value of 100 under such conditions These weak values do not represent ordinary measurement outcomes; rather they reflect subtle correlations given both pre- and post-selection. The procedure provides information about a system’s “hidden” properties without fully collapsing its state.

Weak measurements have proved useful in precision metrology (amplifying tiny effects) and in exploring conceptual issues such as the paradoxical separation of a particle and its properties (“Quantum Cheshire Cat”). However, weak values are also controversial: critics argue they are merely conditional averages with no direct physical meaning, and that they can be explained by standard quantum statistics. Supporters (including Aharonov and co-workers) maintain that weak values are valid properties of pre- and post-selected quantum systems Aharonov introduced weak measurements as part of his broader effort to develop a two-state description of quantum systems.

Two-State Vector Formalism and Time Symmetry

Aharonov has long advocated a time-symmetric view of quantum mechanics. In the two-state vector formalism (TSVF), a quantum system between measurements is described by both a forward-evolving state (from the initial preparation) and a backward-evolving state (from the final post-selection). In 1964 he, Peter Bergmann, and Joel Lebowitz formulated a “time symmetry” principle in quantum measurement theory (Aharonov–Bergmann–Lebowitz rule) foreshadowing this approach. The TSVF quantitatively accounts for counter-intuitive quantum correlations by treating past and future measurements on an equal footing. This framework was the backdrop for introducing weak measurements: by post-selecting on a final state, one can ask how earlier weak experiments were influenced by later conditions.

These ideas are part of Aharonov’s broader philosophy that quantum events can, in some sense, be influenced by both initial and final boundary conditions. This has generated much discussion in the foundations community: some researchers embrace it as a powerful interpretative tool, while others criticize it as allowing “retrocausal” effects that seem to let the future modify the past. Regardless, Aharonov’s formalism has inspired many studies and pedagogical insights about quantum paradoxes and nonlocality.

Other Contributions

Beyond these headline topics, Aharonov has contributed to many areas of theory. In 1984 he and Aharon Casher predicted the Aharonov–Casher effect, a dual of the AB effect in which a magnetic dipole acquires a phase by moving around a line of electric charge. He introduced concepts like modular variables (phase-like quantities important for interference) to analyze quantum nonlocality. His early work with Bohm on the Einstein–Podolsky–Rosen (EPR) problem and hidden variables helped stimulate John Bell’s famous investigations. Aharonov co-authored a popular-level book “Quantum Paradoxes: Quantum Theory for the Perplexed” (with Daniel Rohrlich, 2008) that surveys many quantum puzzles from his perspective.

Methodological Approach

Aharonov is known for bold, unconventional theoretical methods. His research often emphasizes gauge and topological aspects of quantum mechanics. By focusing on the quantum phase and potentials, he highlighted how global features (like magnetic flux) have real physical effects. In measurements, he pioneered the idea that one can learn about a system with only partial, gentle disturbance (weak coupling to an apparatus).

Central to his method is the use of pre- and post-selection. Unlike the usual approach of specifying only an initial state, Aharonov regularly considers ensembles of particles that are later chosen to have a given final result. This two-time perspective leads to predictions (via the two-state vector formalism) that are not evident in standard textbook quantum theory. For example, he introduced the use of weak coupling probes that barely affect the system, allowing multiple “weak measurements” in succession. The results of these measurements, conditioned on a particular final outcome, reveal weak values that can be anomalously large or otherwise unusual. This method has provided a new lens on what quantum theory can say about measurements without causing full wavefunction collapse.

Mathematically, Aharonov’s work often leverages interference integrals and gauge-invariant formulations. He treats quantum phase as an observable quantity and applies symmetry arguments (for instance, under time reversal and translation). His approach melds deep conceptual reasoning (thought experiments and paradoxes) with precise formal calculations, exemplifying a style of theory that is both mathematically sound and philosophically probing.

Influence

Yakir Aharonov’s ideas have had a major impact on modern physics. The Aharonov–Bohm effect is now a textbook example in quantum mechanics, with experimental analogs in electron interferometry and mesoscopic rings. It has guided developments in topological quantum field theory, quantum Hall physics, and even proposed designs for topological quantum computing where geometric phases are harnessed. References to the AB effect appear in hundreds of research articles and books on quantum physics and technology.

His concept of weak measurement has opened up avenues in precision measurement techniques (for example, amplifying small beams deflections or phase shifts) and prompted new experiments testing the foundations of quantum mechanics. The TSVF and related ideas have influenced many theoretical works on time symmetry, post-selected ensembles, and the interpretation of quantum paradoxes. Students and collaborators of Aharonov’s—such as Lev Vaidman, David Albert, Avshalom Elitzur, and others—have continued to develop these themes, spreading his methods through quantum foundations and quantum information research. Aharonov has supervised numerous doctoral students and lectured worldwide, helping to mentor the next generation of theorists.

He has often been mentioned as a leading candidate for the Nobel Prize in Physics; a Thomson-Reuters survey even ranked him “most likely to win” in the future (around 2009). While the prize has eluded him so far, he has received many major honors: the 1989 Israel Prize in physics, the 1991 Elliott Cresson Medal, the 1998 Wolf Prize (shared with David Bohm), the 2009 U.S. National Medal of Science, and (in 2024) election as a Foreign Member of the Royal Society (London). He is also a fellow of the American Physical Society and a member of the U.S. National Academy of Sciences and other academies. These accolades reflect the esteem in which the physics community holds his contributions.

Critiques and Debates

Some of Aharonov’s ideas have sparked lively debates. The original AB effect faced early criticism on grounds of classical reasoning; Niels Bohr and others questioned whether the electron shouldn’t exert a back-action on the solenoid to preserve classical intuitions Aharonov and Bohm responded with follow-up papers clarifying that the effect is fully consistent with quantum theory. In the end, precise experiments (such as Tonomura’s) showed that no local force was acting outside the solenoid, vindicating the predicted phase shift.

Weak measurements and weak values have been even more controversial. Critics (e.g. some statistical physicists) have argued that weak values are just complex conditional averages with no new physics. In particular, mathematicians like Jeffrey Tollaksen and Ruth Kastner have written that anomalous weak values are more a curiosity of post-selection. Defenders (including Lev Vaidman and Aharonov himself) counter that weak values are legitimate physical quantities characterizing single quantum systems under the two-state formalism They note that even if weak values require ensemble averaging to measure, their appearance outside the eigenvalue range reveals deep aspects of quantum statistics. The usefulness of weak values for precision experiments has also been argued (providing practical "weak-value amplification" in optics and metrology).

Aharonov’s time-symmetric viewpoint has its skeptics, especially among those favoring the more conventional view that only past conditions affect the future. Some philosophers of physics find the idea of backward-in-time influence troubling or metaphysical. Others maintain that TSVF is simply a reformulation of standard quantum mechanics with the same predictions, so the controversy is more about interpretation. Aharonov’s school acknowledges that multiple quantum formalisms are possible and emphasizes that TSVF provides intuitive insight into certain puzzles (such as the “three-box” paradox or Hardy’s paradox).

None of these debates undermine the mathematical correctness of Aharonov’s formulas; rather, they exemplify how his concepts often push the boundaries of our understanding. In all cases, Aharonov’s work has provoked careful analysis and alternative explanations, which is itself a hallmark of influential theoretical ideas.

Legacy

By now, Yakir Aharonov’s name is firmly attached to several fundamental phenomena in quantum physics. The term “Aharonov–Bohm effect” is one of the first things any quantum physicist learns about the non-classical role of potentials. His work on quantum phases and on measurement theory has been cited thousands of times and woven into the fabric of quantum theory teaching. Even when his specific theoretical frameworks are debated, they consistently inspire new experiments (such as elaborations of weak measurements) and new theoretical tools (post-selective studies, modular variances, etc.).

Aharonov’s career also bridges Israeli and American physics; he helped build the Tel Aviv University physics department and later contributed to research centers like the Perimeter Institute. As professor emeritus in Israel and active researcher in the U.S., he has been a key link between these communities. His presidency of IYAR reflects his ongoing role in fostering scientific research in Israel.

Beyond the technical legacy, Aharonov’s style of thinking–boldly visualizing quantum processes in space and time–continues to influence how physicists approach the foundations of quantum mechanics. In interviews he remains a popular explainer of “quantum weirdness,” and he has lectured extensively to both experts and the public on topics like measurement paradoxes. In short, his legacy is that of a creative phenomenologist: one who asks provocative “what if” questions and then works through the math to see what nature allows.

Selected Works

Y. Aharonov and D. Bohm, Physical Review 115, 485 (1959): “Significance of Electromagnetic Potentials in the Quantum Theory” – original paper predicting the Aharonov–Bohm effect.
Y. Aharonov, P. G. Bergmann, and J. L. Lebowitz, Physical Review 134, B1410 (1964): “Time Symmetry in the Quantum Process of Measurement” – introduction of time-symmetric quantum rule.
Y. Aharonov, A. Casher, Physical Review Letters 53, 319 (1984): “Topological Quantum Effects for Neutral Particles” – theoretical prediction of the Aharonov–Casher effect.
Y. Aharonov, D. Z. Albert, and L. Vaidman, Physical Review Letters 60, 1351 (1988): “How the Result of a Measurement of a Component of the Spin of a Spin-1/2 Particle Can Turn Out to Be 100” – introduction of weak measurement and weak values.
Y. Aharonov and D. Rohrlich (book), Quantum Paradoxes: Quantum Theory for the Perplexed, Wiley (2008) – guided tour of quantum puzzles from Aharonov’s viewpoint.

Timeline

1932 – Born in Haifa, British Mandate of Palestine (now Israel).
1956 – B.Sc., Technion (Haifa).
1960 – Ph.D. (quantum theory) from University of Bristol under David Bohm.
1960–61 – Postdoctoral researcher, Brandeis University (USA).
1961–67 – Faculty at Yeshiva University (USA).
1967–2001 – Professor of Physics, Tel Aviv University (Israel).
1973–2006 – Professor of Physics, University of South Carolina (USA).
1984 – Awarded Israel’s Weizmann Prize in Physics.
1989 – Received the Israel Prize (national award) in exact sciences.
1998 – Awarded the Wolf Prize in Physics (with David Bohm).
2008–present – Professor of Theoretical Physics, Chapman University; continues as Professor Emeritus at Tel Aviv University.
2009 – Awarded U.S. National Medal of Science.
2024 – Elected Foreign Member, Royal Society (UK).

Sources: Reputable biographies, interviews, and reference works on Yakir Aharonov’s life and work