Yakir Aharonov

A time-symmetric formulation of quantum mechanics

Quantum mechanics allows one to independently select both the initial and final states of a single system. Such pre- and postselection reveals novel effects that challenge our ideas about what time is and how it flows.

Revisiting Hardy's Paradox: Counterfactual Statements, Real Measurements, Entanglement and Weak Values

Hardys paradox is revisited. Usually the paradox is dismissed on grounds of counterfactuality, i.e., because the paradoxical effects appear only when one considers results of experiments which do not actually take place. We suggest a new set of measurements in connection with Hardys scheme, and show that when they are actually performed, they yield strange and surprising outcomes. More generally, we claim that counterfactual paradoxes point to a deeper structure inherent to quantum mechanics.

Measurement of the Schrödinger Wave of a Single Particle

We show that it is possible to measure the Schrodinger wave of a single quantum system. This provides a strong argument for associating physical reality with the quantum state of a single system, and challenges the usual assumption that the quantum state has physical meaning only for an ensemble of identical systems.

THE UNITARITY PUZZLE AND PLANCK MASS STABLE PARTICLES

Abstract We suggest that the ultimate remnant of an evaporating black hole is an infinitely degenerate particle at the Planck mass. Arguments are presented for the stability of these objects and their cosmological and theoretical implications are briefly discussed.

Measurement of time of arrival in quantum mechanics

It is argued that the time of arrival cannot be precisely defined and measured in quantum mechanics. By constructing explicit toy models of a measurement, we show that for a free particle it cannot be measured more accurately then

Quantum Cheshire Cats

\ensuremath{\Delta}{t}_{A}\ensuremath{\sim}{1/E}_{k},

Quantum interference experiments, modular variables and weak measurements

where

The mean king's problem: Prime degrees of freedom

{E}_{k}

Modular variables in quantum theory

is the initial kinetic energy of the particle. With a better accuracy, particles reflect off the measuring device, and the resulting probability distribution becomes distorted. It is shown that a time-of-arrival operator cannot exist, and that approximate time-of-arrival operators do not correspond to the measurements considered here.

Some mathematical properties of superoscillations

In this paper we present a quantum Cheshire Cat. In a pre- and post-selected experiment we find the Cat in one place, and its grin in another. The Cat is a photon, while the grin is its circular polarization.