Invariance Principles

W. M. Stuckey, Timothy J. McDevitt, Michael Silberstein

Quantum information theorists have created axiomatic reconstructions of quantum mechanics (QM) that are very successful at identifying precisely what distinguishes quantum probability theory from classical and more general probability theories in terms of information-theoretic principles. Herein, we show how one such principle, Information Invariance and Continuity, at the foundation of those axiomatic reconstructions, maps to “no preferred reference frame” (NPRF, aka “the relativity principle”) as it pertains to the invariant measurement of Planck’s constant h for Stern-Gerlach (SG) spin measurements. This is in exact analogy to the relativity principle as it pertains to the invariant measurement of the speed of light c at the foundation of special relativity (SR). Essentially, quantum information theorists have extended Einstein’s use of NPRF from the boost invariance of measurements of c to include the SO(3) invariance of measurements of h between different reference frames of mutually complementary spin measurements via the principle of Information Invariance and Continuity. Consequently, the “mystery” of the Bell states is understood to result from conservation per Information Invariance and Continuity between different reference frames of mutually complementary qubit measurements, and this maps to conservation per NPRF in spacetime. If one falsely conflates the relativity principle with the classical theory of SR, then it may seem impossible that the relativity principle resides at the foundation of non-relativisitic QM. In fact, there is nothing inherently classical or quantum about NPRF. Thus, the axiomatic reconstructions of QM have succeeded in producing a principle account of QM that reveals as much about Nature as the postulates of SR.

Gerald Feinberg

V. J. Stenger

The laws of physics were not handed down from above. Neither are they rules somehow built into the structure of the universe. They are ingredients of the models that physicists invent to describe observations. Rather than being restrictions on the behavior of matter, the laws of physics are restrictions on the behavior of physicists. If the models of physics are to describe observations based on an objective reality, then those models cannot depend on the point of view of the observer. This suggests a principle of point-of-view invariance that is equivalent to the principle of covariance when applied to space-time. As Noether showed, space-time symmetries lead to the principles of energy, linear momentum, and angular momentum conservation--essentially all of classical mechanics. It also leads to Lorentz invariance and special relativity. When generalized to the abstract space of functions such as the quantum state vector, point-of-view invariance is identified with gauge invariance. Quantum mechanics is then just the mathematics of gauge transformations with no additional assumptions needed to obtain its rules, including the superposition and uncertainty principles. The conservation and quantization of electric charge follow from global gauge invariance. The electromagnetic force is introduced to preserve local gauge invariance. Although not discussed here, the other forces in the standard model of elementary particles are also fields introduced to preserve local gauge invariance. Gravity can also be viewed as such a field. Thus practically all of fundamental physics as we know it follows directly from the single principle of point-of-view invariance.

Klaus Mainzer

J. M. Jauch

If a distinction is made between kinematical and dynamical symmetries of a quantum mechanical localizable system it is possible to extend the principle of Galilei-invariance to elementary particles, subject to arbitrary external forces. This principle implies a severe restriction on the possible types of external forces which can act on a particle. In fact we show in this paper that for a scalar particle the only forces which are compatible with this principle are those which derive from a scalar and vectorpotential. The Hamiltonian takes on the usual gauge-invariant form of a charged particle in interaction with arbitrary electromagnetic forces.

Annick Lesne, Michel Laguës