Tuesday, January 6, 2009

Smooth Quantum Mechanics: 2. Registry and Time Evolution

In the Smooth Quantum Mechanics, the evolution is deterministic, but the initial data is not determined. The registry is a collection of partial initial data, which is in general incomplete. This leads in particular to a version of the Many Worlds Interpretation: the Many Registries Interpretation.

Registry and Time Evolution

In the Smooth Quantum Mechanics, the evolution is, for the complete system, deterministic and unitary. The randomness appears because of the incomplete knowledge of the initial conditions. Not only that we don’t know these initial conditions, but they are even not defined, until we perform the measurement. This is because of Bell’s theorem. We can choose what observable to measure, and each observable limits the possible outcomes in a different way. We can have two observables so that it is clear that their outcomes are relatively incompatible. When we choose one of them, we chose what already happened. We determine the past in the active sense of the word “to determine”.

Each observation we make increases the constrains of the solution of the evolution equation. The set of (delayed) initial conditions known at a time is named “the registry”. This registry increases as new measurements are related causally to the registry. For the observer, the time evolution correlates with the registry expansion. Some measurements are independent, and others are correlated, since they measure entangled particles or degrees of freedom. The registry is a network of such events, and the way it expands is correlated with the time arrow. The physical laws being time symmetric at a fundamental level, the relations between the measurements are probably correlated with the thermodynamic time arrow. Therefore, the registry can be viewed in a timeless way, providing a block world (or block universe, or BU) view. On the other hand, it can be viewed as being correlated with the time’s arrow, providing an evolving world view.

Many Registries Interpretation of Quantum Mechanics

The way the registry expands by adding new observations is not determined by the present state of the registry (except when the registry is complete, providing a full description of initial data). This means that we can expand the registry in many ways. These multiple possibilities remind us the Many Worlds Interpretation of Quantum Mechanics, in which the world splits with each new measurement, according to each outcome. There is a difference, in that the split in the MWI is due to the indeterministic character of the wavefunction collapse (although the “total” wavefunction evolves deterministically). In the Many Registries Interpretation, each world is deterministic, but the observer has not identified/chosen yet her world, so she perceived the evolution as indeterministic. By adding new observations to the registry, she can increase the information about the world. Thus, she selects the world, and she even seems to have a small possibility of choosing the world, by choosing the observable.
By adhering to Smooth Quantum Mechanics, we can keep the idea of MWI, in the form of Many Registries Interpretation. The idea of “registry” reconciles the indeterminism perceived by the observer, with the fundamental determinism of the unitary evolution.
Even if we don’t know if we will ever be able to provide experimental support for one or another version of the MWI, I think that the MWI has at least a great pedagogical value. Also, it allows a better reconciliation of the block world with the apparent openness of the future.

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