Volume 19: Pages 75-82, 2006

Physical Laws Must Be Invariant over Quantum Systems

Paul Merriam

133 B Cayuga Street, Santa Cruz, California 95062 U.S.A.

Decoherence may not solve all of the measurement problems of quantum mechanics. It is proposed that a solution to these problems may be to allow superpositions to describe physically real systems in the following sense. Each quantum system “carries”around a local space‐time in whose terms other quantum systems may take on nonlocal states. Each quantum system forms a physically valid coordinate frame. The laws of physics should be formulated to be invariant under the group of allowed transformations among such frames. A transformation of relatively superposed spatial coordinates that allows an electron system to preserve the de Broglie relation in describing a double‐slit laboratory system — in analogy to a Minkowskian transformation — is proposed. In general, “quantum relativity” says h = 1 is invariant under transformations among quantum reference frames. Some conjectures on how this affects gravity and gauge invariance are made.

Keywords: quantum mechanics, entangled, superpositions, measurement problem, decoherence, relational, special relativity, de Broglie relation, Schrödinger's equation, quantum relativity, invariance, transformations, quantum Einstein equation, 5‐manifold

Received: February 7, 2005; Published online: December 15, 2008