Many-minds interpretation

The many-minds interpretation of quantum mechanics extends the many-worlds interpretation by proposing that the distinction between worlds should be made at the level of the mind of an individual observer. The concept was first introduced in 1970 by H. Dieter Zeh as a variant of the Hugh Everett interpretation in connection with quantum decoherence, and later (in 1981) explicitly called a Many-(or multi-)consciousness Interpretation. The name many-minds interpretation was first used by David Albert and B. Loewer in their 1988 work Interpreting the Many Worlds Interpretation.

The central problems
One of the central problems in interpretation of quantum theory is the duality of time evolution of physical systems:
 * 1) Unitary evolution by the Schrödinger equation,
 * 2) Nondeterministic, nonunitary change during measurement of physical observables, at which time the system "selects" a single value in the range of possible values for  the observable. This process is known as wavefunction collapse. Moreover, the process of observation occurs outside the system, which presents a problem on its own if one considers the universe itself to be a quantum system. This is known as the measurement problem.

In the introduction to his paper, The Problem Of Conscious Observation In Quantum Mechanical Description (June, 2000) H. D. Zeh offered an empirical basis for connecting the processes involved in (2) with conscious observation:


 * "John von Neumann seems to have first clearly pointed out the conceptual difficulties that arise when one attempts to formulate the physical process underlying subjective observation within quantum theory. He emphasized the latter’s incompatibility with a psycho-physical parallelism, the traditional way of reducing the act of observation to a physical process. Based on the assumption of a physical reality in space and time, one either assumes a coupling (causal relationship — one-way or bidirectional) of matter and mind, or disregards the whole problem by retreating to pure behaviorism. However, even this may remain problematic when one attempts to describe classical behavior in quantum mechanical terms. Neither position can be upheld without fundamental modifications in a consistent quantum mechanical description of the physical world."

The Many-worlds Interpretation
Hugh Everett described a way out of this problem by suggesting that the universe is in fact indeterminate as a whole. That is, if you were to measure the spin of a particle and find it to be "up", in fact there are two "yous" after the measurement, one who measured the spin up, the other spin down. This relative state formulation, where all states (sets of measures) can only be measured relative to other such states, avoids a number of problems in quantum theory, including the original duality - no collapse takes place, the indeterminacy simply grows (or moves) to a larger system. Effectively by looking at the system in question, you take on its indeterminacy.

Everett claims that the universe has a quantum state, which he called the universal wavefunction, that always evolves according to the Schrödinger equation or some relativistic equivalent; now the measurement problem suggests the universal wavefunction will be in a superposition corresponding to many different definite macroscopic realms (`macrorealms'); that one can recover the subjective appearance of a definite macrorealm by postulating that all the various definite macrorealms are actual---`we just happen to be in one rather than the others' in the sense that "we" are in all of them, but each are mutally inobservable.

Continuous infinity of minds
The idea of many minds was suggested early on by Zeh in 1995. He argues that in a decohering no-collapse universe one can avoid the necessity of macrorealms by introducing a new psycho-physical parallelism, in which individual minds supervene on each non-interfering component in the physical state. Zeh indeed suggests that, given decoherence, this is the most natural interpretation of quantum mechanics.

The main difference between `many minds' and `many worlds' interpretations then lies in the definition of the preferred quantity. The `many minds' interpretations suggests that to solve the measurement problem, there is no need to secure a definite macrorealm: the only thing that's required is appearance of such. A bit more precisely: the idea is that the preferred quantity is whatever physical quantity, defined on brains (or brains and parts of their environments), has definite-valued states (eigenstates) that underpin such appearances, i.e. underpin the states of belief in, or sensory experience of, the familiar macroscopic realm.

In its original version (related to decoherence), there is no process of selection. The process of quantum decoherence explains in terms of the Schrödinger equation how certain components of the universal wave function become irreversibly dynamically independent of one another (separate worlds - even though there is but one quantum world that does NOT split). These components may (each) contain definite quantum states of observers, while the total quantum state may not. These observer states may then be assumed to correspond to definite states of awareness (minds), just as in a classical description of observation. States of different observers are consistently entangled with one another, thus warranting objective results of measurements.

However Albert and Loewer suggest that the mental does not supervene on the physical, because individual minds have trans-temporal identity of their own. The mind selects one of these identities to be its non-random reality, while the universe itself is unaffected. The process for selection of a single state remains unexplained. This is particularly problematic because it is not clear how different observers would thus end up agreeing on measurements, which happens all the time here in the real world. There is assumed to be a sort of feedback between the mental process that leads to selection and the universal wavefunction, thereby effecting other mental states as a matter of course. In order to make the system work, the "mind" must be separate from the body, an old duality of philosophy to replace the new one of quantum mechanics.

In general this interpretation has received little attention, largely for this last reason.

Objections
Objections that apply to the many-worlds interpretation also apply to the many-mind interpretations. On the surface both of these theories expressly violate Occam's Razor; proponents counter that in fact these solutions minimize entities by simplifying the rules that would be required to describe the universe.

Another serious objection is that workers in no collapse interpretations have produced no more than elementary models based on the definite existence of specific measuring devices. They have assumed, for example, that the Hilbert space of the universe splits naturally into a tensor product structure compatible with the measurement under consideration. They have also assumed, even when describing the behavior of macroscopic objects, that it is appropriate to employ models in which only a few dimensions of Hilbert space are used to describe all the relevant behavior.

In his ‘What is it like to be Schrödinger's cat?’ (2000), Peter J. Lewis argues that the many minds interpretation of quantum mechanics has absurd implications for agents facing life-or-death decisions.

In general, the many minds theory holds that a conscious being who observes the outcome of a random zero-sum experiment will evolve into two successors in different observer states, each of whom observes one of the possible outcomes. Moreover, the theory advises you to favor choices in such situations in proportion to the probability that they will bring good or bad results to your various successors. But in a life-or-death case like getting into the box with Schrödinger’s cat, you will only have one successor, since one of the outcomes will ensure your death. So it seems that the many minds interpretation advises you to get in the box with the cat, since it is certain that your only successor will emerge unharmed. Compare: Quantum suicide and Quantum immortality