Negative Kinetic Energy between past and Future State Vectors

An analysis of errors in measurement yields new insight into classically forbidden quantum processes. In addition to " physical " values, a realistic measurement can yield " unphysical " values; we show that in sequences of measurements , the " unphysical " values can form a consistent pattern. An experiment to isolate a particle in a classically forbidden region obtains a negative value for its kinetic energy. It is the weak value of kinetic energy between past and future state vectors. 1. Introduction. When the word " quantum " first entered the language of physics, it meant a restriction on possible values of energy; and it is still axiomatic that the only observable values of a physical quantity are the eigenvalues of a corresponding quantized operator. When we obtain values that are not eigenvalues, we interpret them as errors. Still, measurements are uncertain in practice, and can even yield classically forbidden, " unphysical " values. We have uncovered remarkable regularities in the way that " unphysical " values can appear in sequences of measurements, suggesting that these values may not be unphysical at all. In quantum theory, it seems, not only are physical quantities not restricted: they can take