Many-minds interpretation

The various interpretations of quantum mechanics typically involve explaining the mathematical formalism of quantum mechanics, or to create a physical picture of the theory. While the mathematical structure has a strong foundation, there is still much debate about the physical and philosophical interpretation of the theory. These interpretations aim to tackle various concepts such as:

1. Evolution of the state of a quantum system (given by the wavefunction), typically through the use of the Schrödinger equation. This concept is almost universally accepted, and is rarely put to debate.
2. The measurement problem, which relates to what is called wavefunction collapse – the collapse of a quantum state into a definite measurement (i.e. a specific eigenstate of the wavefunction). The debate on whether this collapse actually occurs is a central problem in interpreting quantum mechanics.

The standard solution to the measurement problem is the "Orthodox" or "Copenhagen" interpretation, which claims that the wave function collapses as the result of a measurement by an observer or apparatus external to the quantum system. An alternative interpretation, the Many-worlds Interpretation, was first described by Hugh Everett in 1957[3][4] (where it was called the relative state interpretation, the name Many-worlds was coined by Bryce Seligman DeWitt starting in the 1960s and finalized in the 1970s[5]). His formalism of quantum mechanics denied that a measurement requires a wave collapse, instead suggesting that all that is truly necessary of a measurement is that a quantum connection is formed between the particle, the measuring device, and the observer.[4]

In the original relative state formulation, Everett proposed that there is one universal wavefunction that describes the objective reality of the whole universe. He stated that when subsystems interact, the total system becomes a superposition of these subsystems. This includes observers and measurement systems, which become part of one universal state (the wavefunction) that is always described via the Schrödinger Equation (or its relativistic alternative). That is, the states of the subsystems that interacted become "entangled" in such a way that any definition of one must necessarily involve the other. Thus, each subsystem's state can only be described relative to each subsystem with which it interacts (hence the name relative state).

Everett suggested that the universe is actually indeterminate as a whole. For example, consider an observer measuring some particle that starts in an undetermined state, as both spin-up and spin-down, that is – a superposition of both possibilities. When an observer measures that particle's spin, however, it always registers as either up or down. The problem of how to understand this sudden shift from "both up and down" to "either up or down" is called the Measurement problem. According to the many-worlds interpretation, the act of measurement forced a “splitting” of the universe into two states, one spin-up and the other spin-down, and the two branches that extend from those two subsequently independent states. One branch measures up. The other measures down. Looking at the instrument informs the observer which branch she is on, but the system itself is indeterminate at this and, by logical extension, presumably any higher level.

The “worlds” in the many worlds theory is then just the complete measurement history up until and during the measurement in question, where splitting happens. These “worlds” each describe a different state of the universal wave function and cannot communicate. There is no collapse of the wavefunction into one state or another, but rather an observer finds itself in the world leading up to what measurement it has made and is unaware of the other possibilities that are equally real.

The many-minds interpretation of quantum theory is many-worlds with the distinction between worlds constructed at the level of the individual observer. Rather than the worlds that branch, it is the observer's mind that branches.[6]

The purpose of this interpretation is to overcome the fundamentally strange concept of observers being in a superposition with themselves. In their 1988 paper, Albert and Loewer argue that it simply makes no sense for one to think of the mind of an observer to be in an indefinite state. Rather, when someone answers the question about which state of a system they have observed, they must answer with complete certainty. If they are in a superposition of states, then this certainty is not possible and we arrive at a contradiction.[2] To overcome this, they then suggest that it is merely the “bodies” of the minds that are in a superposition, and that the minds must have definite states that are never in superposition.[2]

When an observer measures a quantum system and becomes entangled with it, it now constitutes a larger quantum system. In regards to each possibility within the wave function, a mental state of the brain corresponds. Ultimately, only one mind is experienced, leading the others to branch off and become inaccessible, albeit real.[7] In this way, every sentient being is attributed with an infinity of minds, whose prevalence correspond to the amplitude of the wavefunction. As an observer checks a measurement, the probability of realizing a specific measurement directly correlates to the number of minds they have where they see that measurement. It is in this way that the probabilistic nature of quantum measurements are obtained by the Many-minds Interpretation.

Consider the case where there is no sentient observer, i.e. no mind present to observe the experiment. In this case, the detector will be in an indefinite state. The photon is both passed and absorbed, and will remain in this state. The correlations are withheld in that none of the possible "minds", or wave function states, correspond to non correlated results.[8]

Now expand the situation to have one sentient being observing the device. Now, they too enter the indefinite state. Their eyes, body, and brain are seeing both spins at the same time. The mind however, stochastically chooses one of the directions, and that is what the mind sees. When this observer views the second detector, their body will see both results. Their mind will choose the result that agrees with the first detector, and the observer will see the expected results. However, the observer's mind seeing one result does not directly affect the distant state – there is just no wave function in which the expected correlations do not exist. The true correlation only happens when they actually view the second detector.[8]

When two people look at two different detectors that scan entangled particles, both observers will enter an indefinite state, as with one observer. These results need not agree – the second observer's mind does not have to have results that correlate with the first's. When one observer tells the results to the second observer, their two minds cannot communicate and thus will only interact with the other's body, which is still indefinite. When the second observer responds, his body will respond with whatever result agrees with the first observer's mind. This means that both observer's minds will be in a state of the wavefunction that always get the expected results, but individually their results could be different.[8]

As we have thus seen, any correlations seen in the wavefunction of each observer's minds are only concrete after interaction between the different polarizers. The correlations on the level of individual minds correspond to the appearance of quantum non-locality (or equivalently, violation of Bell's inequality). So the many world is non-local, or it cannot explain EPR-GHZ correlations.