XIX. Note on the Law of Conservation of Energy

Kaoru Inoue, Masayuki Yamazaki

Chiara Marletto, Vlatko Vedral

We point out that symmetries mandating the conservation of additive quantities, e.g., those induced by the energy and momentum conservation laws, hold in quantum physics not just “on average,” as is sometimes claimed, but exactly in each branch of a quantum state, expressed in the basis where the conserved observable is sharp. We note that for conservation laws to hold exactly for quantum systems in this sense (not just on average), it is necessary to assume the so-called totalitarian property of quantum theory, namely, that any system capable of coupling to a quantum system must itself be quantized, including the measuring apparatus. Hence, if conservation laws are to hold exactly in quantum theory, the idea of a “classical measuring apparatus” (i.e., not subject to the branching structure) is untenable. We also point out that any other principle having a well-defined formulation within classical physics, such as the Equivalence Principle, is also to be extended to the quantum domain in exactly the same way, i.e., branch by branch.

Constantinos Ragazas

In our derivation of Planck's Law (showing that this Formula is an exact mathematical identity that describes the interaction of measurement) the 'accumulation of energy' locally at time t was a key variable. By starting with this as the primary variable and defining energy, momentum and force in terms of it we are able to mathematically derive such basic laws of Physics as Conservation of Energy and Momentum, and Newton's Second Law of Motion. Following the same approach we demonstrate in this short note how Schrodinger's Equation relates to this formulation. This leads to a physical meaning of the wave-function ψ and a plausible explanation of the double-slit experiment.

A. Lees