Randomness and Irreversiblity in Quantum Mechanics: A Worked Example for a Statistical Theory

The randomness of some irreversible quantum phenomena is a central question because irreversible phenomena break quantum coherence and thus yield an irreversible loss of information. The case of quantum jumps observed in the fluorescence of a single two-level atom illuminated by a quasi-resonant laser beam is a worked example where statistical interpretations of quantum mechanics still meet some difficulties because the basic equations are fully deterministic and unitary. In such a problem with two different time scales, the atom makes coherent optical Rabi oscillations between the two states, interrupted by random emissions (quasi-instantaneous) of photons where coherence is lost. To describe this system, we already proposed a novel approach, which is completed here. It amounts to putting a probability on the density matrix of the atom and deducing a general “kinetic Kolmogorov-like” equation for the evolution of the probability. In the simple case considered here, the probability only depends on a single variable θ describing the state of the atom, and p(θ,t) yields the statistical properties of the atom under the joint effects of coherent pumping and random emission of photons. We emphasize that p(θ,t) allows the description of all possible histories of the atom, as in Everett’s many-worlds interpretation of quantum mechanics. This yields solvable equations in the two-level atom case.

E. Schrödinger’s 1931 paper “On the Reversal of the Laws of Nature” [“Über die Umkehrung der Naturgesetze”, Sitzungsberichte der preussischen Akademie der Wissenschaften, physikalisch-mathematische Klasse, 8 N9 144–153]

We present an English translation of Erwin Schrödinger’s paper on “On the Reversal of the Laws of Nature‘’. In this paper, Schrödinger analyses the idea of time reversal of a diffusion process. Schrödinger’s paper acted as a prominent source of inspiration for the works of Bernstein on reciprocal processes and of Kolmogorov on time reversal properties of Markov processes and detailed balance. The ideas outlined by Schrödinger also inspired the development of probabilistic interpretations of quantum mechanics by Fényes, Nelson and others as well as the notion of “Euclidean Quantum Mechanics” as probabilistic analogue of quantization. In the second part of the paper, Schrödinger discusses the relation between time reversal and statistical laws of physics. We emphasize in our commentary the relevance of Schrödinger’s intuitions for contemporary developments in statistical nano-physics.

Light Cones as Quantum Phenomena

Quantum erasure experiments push the boundary between the quantum and classical worlds by letting delayed events influence the state of previously recorded and potentially widely distributed classical information. The only significant restriction to such unsettling violations of forward-only causality is that the distribution of forward-dependent information cannot cross out of the light cone boundaries of the event in the past, a feature that ensures no violations of causality — no rewriting of anyone else's recorded histories — can occur. The erasure interpretation of this conundrum requires rewriting of information recorded and distributed in the past, which would itself be a violation of causality. The quantum predestination interpretation removes the causal rewriting issue. However, quantum predestination requires detailed coordination of inputs from outside of the forward-dependent event's light cone, thus massively violating the same limit that prevents causality violations in such events. Yet another approach is to invoke the Schrödinger's cat variant of quantum erasure in which arbitrarily complex classical events within the light cone become quantum dependent upon the future event. As with all Schrödinger's cat interpretations of quantum mechanics, this variant of quantum erasure violates causality by discarding local classical histories such as the information-rich state of the cat's body. The most straightforward interpretation of erasure experiments is to follow the lead of the equations themselves, which transform on paper as if their components are independent of ordinary space and time limits, up to the limits imposed on them by the speed of light. Interpreting the light cone of each quantum system as an atemporal, aspatial unit in which classical time and space have no meaning results in a multi-scale, matter-dependent definition of spacetime in which every light cone is a singular quantum entity. In such a universe, both time and space are defined not as pre-existing, mass-independent continuums but as the consensus of vast numbers of constantly interacting and mutually limiting quantum-entity light cones.

On the meaning of EPR’s Reality Criterion

This essay has two main claims about EPR’s Reality Criterion. First, we claim that the application of the Reality Criterion makes an essential difference between the EPR argument and Einstein’s later arguments against quantum mechanics. We show that while the EPR argument, making use of the Reality Criterion, does derive that certain interpretations of quantum mechanics are incomplete, Einstein’s later arguments, making no use of the Reality Criterion, do not prove incompleteness, but rather point to the inadequacy of the Copenhagen interpretation. We take this fact as an indication that the Reality Criterion is a crucial, indispensable component of the incompleteness argument(s). The second claim is more substantive. We argue that the Reality Criterion is a special case of the Common Cause Principle. Finally, we relate this proposal to Tim Maudlin’s recent assertion that the Reality Criterion is an analytic truth.

The Virtues of Separability and Locality

This chapter presents the argument for wave function realism that it is the only realist interpretation of quantum theories that can maintain a fundamentally separable and local metaphysics. It is commonly seen as a consequence of entanglement and Bell’s Theorem that quantum mechanics entails quantum nonseparability and nonlocality. Yet although all rival realist ontological interpretations of quantum mechanics involve either a nonseparable or a nonlocal fundamental metaphysics, the metaphysics of wave function realism is fundamentally both separable and local, although the view also makes room for nonfundamental nonseparability and nonlocality. The chapter considers several arguments that could explain why one should prefer interpretations of quantum theories that are separable and local, and concludes with a defense of intuitions in quantum interpretation.