Daniel M. Greenberger

The role of equivalence in Quantum Mechanics

Abstract On applying Quantum Mechanics to the problem of a particle bound in an external gravitational potential, we find the following results, which violate ones classical conception of the principle of weak equivalence: radii, frequencies, etc., depend on the mass of the bound particle; the binding energy has the wrong mass dependence; inertial forces do not look like gravitational forces; and there are mass-dependent interference effects. These inconsistencies disappear in the classical limit, which must be approached in a particular manner. The conclusion is reached that the classical statements one can make using weak equivalence have no direct quantum analog and thus the principle is somewhat irrelevant in discussing low-lying quantum states.

A representation-free description of the Kasevich–Chu interferometer: a resolution of the redshift controversy

Motivated by a recent claim by Muller et al (2010 Nature 463 926–9) that an atom interferometer can serve as an atom clock to measure the gravitational redshift with an unprecedented accuracy, we provide a representation-free description of the Kasevich–Chu interferometer based on operator algebra. We use this framework to show that the operator product determining the number of atoms at the exit ports of the interferometer is a c-number phase factor whose phase is the sum of only two phases: one is due to the acceleration of the phases of the laser pulses and the other one is due to the acceleration of the atom. This formulation brings out most clearly that this interferometer is an accelerometer or a gravimeter. Moreover, we point out that in different representations of quantum mechanics such as the position or the momentum representation the phase shift appears as though it originates from different physical phenomena. Due to this representation dependence conclusions concerning an enhanced accuracy derived in a specific representation are unfounded.

The scale transformation in physics

Abstract Some criteria are established to test whether invariance under a continuous transformation will lead to a conservation law. The scale transformation is examined as a special case, and shown not only to lead to no general conservation law, but also in fact to be of a trivial nature. This is due to the rather artificial way in which scale invariance is usually introduced. A theory is then constructed by introducing an internal coordinate of dimension (length) in order to allow only the dimensionless ratio of lengths to enter, and by exploiting the gaugelike structure of the scale transformation. In this theory the scale transformation does lead to a new conserved current (as well as to an “almost conserved” one), and the internal coordinate is shown to play the same role for the scale transformation as the internal coordinate spin plays for the case of rotations, and allows the theory to treat massive particles.

An uncertain principal

overenthusiastic optimism that the human intellect was the Earth’s only important resource. Neither attitude advances a serious discourse of complex scientific matters whose understanding helps to shape our fate. For many years, when reading Ehrlich, I wished that his incisive conclusions and passionate advocacies based on his wide-ranging understanding were not couched in such catastrophic tones. That is why I welcome this book: it will not be a revelation to anyone reasonably well versed in modern evolutionary anthropology — but it is a spirited, valuable and enjoyable contribution to an interdisciplinary understanding of our complex natures. ■ Vaclav Smil is at the University of Manitoba, Winnipeg R3T 2N2, Canada.

The Stefan–Boltzmann law: two classical laws give a quantum one

Due to the universality of blackbody radiation the constant in the Stefan-Boltzmann law connecting the energy density and temperature of blackbody radiation is either a universal constant, or built ...

Chapter 8 Planck, photon statistics, and Bose–Einstein condensation

Publisher Summary The chapter emphasizes some of the historical details that surround Plancks work. The chapter draws heavily on Plancks original papers and his book on heat radiation and reproduces comments by Ter Haar. It describes in some detail exactly what Planck did and did not do and the importance of fluctuations in his work. How fluctuations enter into the theory of the laser, and how this theory has been used to treat fluctuations in Bose–Einstein condensation (BEC) are explained. Historically, Einstein was the first to demonstrate the existence of the “Bose” condensate. After Bose had created his “photon as a particle” path to the Planck distribution, Einstein went on to show that there was a critical temperature below which a macroscopic number of atoms would occupy the lowest energy state of the potential holding the atoms. A new approach was found to the N body boson problem that treated the fluctuations very accurately by extending the laser-phase transition analogy to include BEC.

The Impossibility of Keyless Communication in Quantum Cryptography

We define a keyless communication as a message sent from one party (Alice) to another (Bob), such that the message is totally secure. This means that if a third party (Eve) is trying to eavesdrop, she will receive only random bits. She cannot understand the content of the message, even if she is able to intercept it in such away that Alice and Bob do not know it has been intercepted. For such a totally secure message, Alice and Bob do not need to set up any key beforehand, as it can add no further security. Starting with a system that we felt sure met such criteria, we were shocked to find out that it could be broken in at least two ways, by a semi-classical method and by a quantum method, such that Eve could read a message and Alice and Bob would not know it. Alice and Bob can counter such eavesdropping, but only by sending out test messages. This will enable them to ascertain that Eve is on the line, but then she can still occasionally pick up snippets of their conversation. In that case, in order to be totally secure, it is better to establish an unbreakable key beforehand. We postulate and give plausibility arguments that in general it is impossible to establish keyless communication between two parties.