Abstract
Conservation principles are essential to describe and quantify dynamical processes in all areas of physics. Classically, a conservation law holds because the description of reality can be considered independent of an observation (measurement). In quantum mechanics, however, invasive observations change quantities drastically, irrespective of any classical conservation law. One may hope to overcome this nonconservation by performing a weak, almost noninvasive measurement. Interestingly, we find that the nonconservation is manifest even in weakly measured correlations if some of the other observables do not commute with the conserved quantity. Our observations show that conservation laws in quantum mechanics should be considered in their specific measurement context. We provide experimentally feasible examples to observe the apparent nonconservation of energy and angular momentum.
Highlights
Conserved quantities play an important role in both classical and quantum mechanics
We have shown that conservation laws in quantum mechanics need to be considered with care since their experimental verification might depend on the measurement context even in the limit of weak measurements
The conservation is violated if extracting objective reality from the weak measurements
Summary
Conserved quantities play an important role in both classical and quantum mechanics. According to the classical Noether theorem, the invariance of the dynamics of a system under specific transformations [1] implies the conservation of certain quantities: Translation symmetry in time and space results in energy and momentum conservation, respectively, and rotational symmetry in angular momentum conservation and gauge invariance in a conserved charge. Unlike the standard projection, which is highly invasive, the extraction of objective values from weak measurements requires a special protocol involving the subtraction of a large detection noise. Such objectivity is debatable [24,25]. Weak quantum measurements are the closest counterparts of classical measurements [26], so they are prime candidates to define objective reality and, conservation principles are expected to hold in systems with an appropriate invariance. We show that for quantum measurements in the weak limit superconservation holds, but quantities such as energy, momentum, and angular momentum apparently violate conservation even if an appropriate symmetry results in classical conservation law. Considering an imperfect conservation or measurement of the quantity, we develop a Leggett-Garg-type test of objective realism
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