Which interpretations of quantum mechanics require a fundamental "arrow of time"?

Question

As I understand the various interpretations of quantum mechanics, it seems like certain interpretations require the "arrow of time" to taken as fundamental, while others do not. By the arrow of time, I mean any qualitative asymmetry between the future and the past, beyond the asymmetry of time required by CPT symmetry. By fundamental, I mean included in/as a postulate, and not derivable from other postulates or the boundary conditions of the universe. For example, the 2^nd Law of Thermodynamics introduces an arrow of time (in terms of entropy), but it is not fundamental because it can be derived from statistical mechanics and the boundary conditions of the universe.

As I understand it, the Copenhagen interpretation involves a fundamental arrow of time, since wave function collapse only occurs in one direction in time. Whereas, in the Everett interpretation, the fact that decoherence only occurs in one direction in time is not fundamental because it is explained by our position in time relative to the Big Bang. But I am not sure I correctly understand what is fundamental in each interperetation.

So, my question is: Do any interpretations of quantum mechanics (say, of the four listed by the Internet Encyclopedia of Philosophy - Copenhagen, Many-Worlds, Hidden Variable Theories, and Spontaneous Collapse Theories) include a fundamental arrow of time as defined above? If so, which interpretation(s), and which specific postulate introduces an arrow of time?

Answer 1

The spontaneous collapse theory is an alternative to quantum theory with different equations of motion:

https://arxiv.org/abs/2310.14969

This theory has an arrow of time built into its postulates because collapse would discard information contained in the phases of the states eliminated by the collapse.

The Copenhagen interpretation doesn't clearly explain what's happening in reality and so doesn't clearly explain anything including implications for time symmetry. The same is true for almost all variants of hidden variables, except for pilot wave theory, which has time symmetric equations of motion. The second law is explained along similar lines to how they would be explained in classical physics:

https://arxiv.org/abs/1906.10761

The MWI also has time symmetric equations of motion. The analysis of irreversibility isn't much different from time symmetric classical physics although probability is explained differently since it is based on symmetry properties of quantum states not on ensembles:

https://arxiv.org/abs/2104.11223

https://arxiv.org/abs/1806.03532

Answer 2

Mechanics is reversible - whether quantum or classical. The irreversibility (arrow of time) appears either in statistical physics/thermodynamics or in cosmology. For technical discussion see Where does the irreversiblity came from if all the fundamental interaction are reversible?. Indeed, the problem of irreversibility emerged before (or about the same time) as quantum mechnaics, and had been viewed as one of the few remaining major goals of physics... before quantum mechanics and relativity crushed the party.

In this sense, QM brings nothing new - its laws are reversible (if we mean by QM the specific discipline, as meant in physics - not just "everything quantum", which would then include quantum statistical physics.)

Measurement is needed insofar as quantum phenomena are accessible to our observation only via non-quantum results, which are observed via the quantum objects entering in contact with macroscopic objects, that is objects subject to the laws of thermodynamics/statistical physics.

Statistical physics vs. thermodynamics
Thermodynamics is a phenomenological theory - it simply postulates the arrow of time, and introduces entropy as a mathematical quantity describing the direction of time - in other words, it simply describes what we observe.

Statistical physics shows that macroscopic systems evolve in a certain direction (with overwhelming probability), but it comes at the expense of making other assumptions - like ergodicity (equivalence of statistical and time averaging.)

But the bottom line: the laws of quantum mechanics are reversible.

Answer 3

As a law of thumb, one can say that in all deterministic interpretations the laws are reversible. This includes MWI (Everett's) and de Brogle-Bohm interpretations.

Your assumption regarding Everett's interpretation seems wrong. In fact, it does not have a fundamental arrow of time because, in this interpretation entropy does not grow at all. As such, there was never any Big Bang. All entropy grows, explosions and bangs are merely illusions that we see in our branch of the universal wave function. There are branches where apparent Big Bang happened differently, at different time (compared to present) or started and then reversed. At the same time, the universal wave function eternally remains in the lowest-entropy state.