The Many Minds Approach
The many minds approach looks at the consequences of the Everett approach to quantum mechanics from the perspective of the mind. The motivation for doing this is that the multiverse as a whole does not change; it is our perspective of it that changes. This happens after decoherence has taken place, when we become aware of the result of a quantum interaction. Others prefer the term many worlds because the superpositional multiverse contains an infinite amount of universes regardless of our perspective.
The Everett approach challenges classical notions of identity. Everett first considered this in an early draft of his 1957 proposal. He stated that "as an analogy one can imagine an intelligent amoeba with a good memory. As time progresses the amoeba is constantly splitting, each time the resulting amoebas having the same memories as the parent. Our amoeba hence does not have a life line, but a life tree. The question of identity or non identity of two amoebas at a later time must be rephrased. At any time we can consider two of them, and they will have common memories up to a point (common parent) after which they will diverge according to their separate lives after this point. It becomes simply a matter of terminology as to whether they should be thought of as the same amoeba or not, or whether the phrase 'the amoeba' should be reserved for the whole ensemble...We can get a closer analogy if we were to take one of these intelligent amoebas, erase his past memories, and render him unconscious while he underwent fission, placing the two resulting amoebas in separate tanks, and repeating this process for all succeeding generations, so that none of the amoebas would be aware of their splitting. After awhile we would have a large number of individuals, sharing some memories with one another, differing in others, each of which is completely unaware of his 'other selves' and under the impression that he is a unique individual. It would be difficult indeed to convince such an amoeba of the true situation short of confronting him with his 'other selves'". Everett claimed that the same was true for his approach to quantum mechanics; "any single individual is at all times unaware of his 'other selves' with which he has no interaction from the time of splitting".
An analogous situation arises in television shows, like Star Trek, when a transporter goes wrong and two copies of an individual are made. It is often argued that they both have an equal right to existence, and all of their former privileges and belongings, yet they may go on to lead very different lives, and become very different people. There appears to be three options for what could happen to us when this sort of branching takes place; either we become one of the potential observers, all of the potential observers, or none of them.
The term 'many minds' was coined by American philosophers David Albert and Barry Loewer in 1988. Albert and Loewer relied on a dualistic theory of the mind and first suggested that we must have one mind before, and after, branching. The problem with this is that the other observers will be 'mindless hulks', people who act in every other way like a person but are not 'ensouled', and there would be no way to know the difference between the two. In response to this problem, Albert and Loewer suggested that every brain must be associated with an infinity of minds, so that they can be distributed after a split in accordance with the Born rule. Albert and Loewer suggested that Deutsch's probability justification can be transposed to the many minds approach, with the uncertainly relating to which world any one particular mind will end up in.
In Mind, Brain & the Quantum: The Compound "I", first published in 1989, British philosopher Michael Lockwood suggested that the many minds approach does not have to rely on a dualistic theory of the mind. Lockwood claimed that the many minds approach is the first scientific theory that implies subjective experiences are necessary, and that the "irreducibly perspectival character to what is revealed in consciousness" arises "quite naturally, and independently" within it. This is because the many minds approach leads directly to a view "of the world as, in some sense, a sum of perspectives…the inevitable selectivity involved in a point of view is automatically accommodated, via the idea that consciousness is tied to one amongst a potential infinity of what, in the context of quantum mechanics, are known as representations".
Lockwood referred to the superpositional brain as the 'Mind' and to our subjective consciousness as 'maximal experiences'. He described the sum of maximal experiences that correspond to one Mind as a 'biography'. Branching occurs relative to a biography when there is a branching of maximal experiences, this happens when we become aware of the macroscopic effects of a quantum interaction.
Lockwood argued that it is already accepted that we can have mutually incompatible experiences which are wholly our own, they simply occur at different times.
Lockwood showed that biographies can be represented by a cylinder; with time as the vertical dimension and biographies as the horizontal dimension. The distribution of maximal experiences at any particular time are seen by looking at a cross-sectional area of the cylinder, this will be made up of a number of different colours, each representing different experiences. Before the measurement, the surface could be green, for example, but after the 'split', it will divide into yellow and blue regions.
Image credit: Mind, Brain & the Quantum: The Compound "I" by Michael Lockwood, 1989.
One advantage of Lockwood's many minds approach is that it can give a definite solution to the preferred basis problem, whereas decoherence is only approximate. Lockwood's theory resolves the preferred basis problem by stating that the conscious mind is only capable of comprehending definite states. He argued that the reason why consciousness selects this particular basis is no more of a mystery than why we are unaware of other parts of our mind. This basis is subjective, however, and so it is still relevant to ask why our minds behave this way. Lockwood considered whether creatures could have evolved to observe macroscopic objects in superpositional states, but it is debatable as to whether this is physically possible since it is difficult to understand how they could interact.
In contrast to Albert and Loewer, who claimed that you will only become one of the observers present after a quantum interaction, Lockwood appears to suggest that you become them all. In fact, Lockwood argued that it does not make sense to ask who you will become. In 1986, British philosopher Derek Parfit considered a number of thought experiments involving the mind being duplicated, or modified, until it is no longer logical to ask when 'you' cease to exist. Parfit concluded that it is meaningless to ask, before branching, which of a multiple set of people you will become. This is an empty question because there is no determinate answer even if we know everything there is to know. In a way, you will be none of them, and, in a way, you will be them all. Parfit suggested we replace the notion of identity with that of personal survival, here we care about what happens to our future-selves but recognise that they are not us.
It seems that there is no room for subjective probability if we accept this view, yet this is not the case. Lockwood argued that the world can be considered to branch after an observer interferes with a quantum system, but before they become aware of the results, in this time it is meaningful to ask which measurement they will observe. Israeli physicist Lev Vaidman offered an analogy; if a person is given a sleeping pill before they interact with a quantum system and are then placed in one of two rooms, corresponding to the outcome, it is meaningful to ask the person on awaking what the probability of them being in either room is.
Lockwood's many minds approach suggests that there is an importance attached to the measure, or weight of a world. Lockwood claims that saying that a world has twice the weight as another "is parallel to saying, for example, that this pain lasted twice as long as the last one" or that "this pain is, superpositionally speaking, twice as extensive as that". Lockwood went on to argue that it is "rational for an instantaneous mind to care equally about all of its successors" and that "this is analogous to preferring the longer to the shorter of two alternative pleasures, when they are of equal intensity".
Lockwood appears to advocate a utilitarian approach to morality. Utilitarianism is a theory of morality first proposed by British philosopher Jeremy Bentham in 1789. The principle of utility states that an action is permissible if, and only if, it increases the total sum of utility, where utility is defined as the pleasure that comes from happiness. In order to quantify happiness Bentham considered intensity, duration, certainty or uncertainty, propinquity (closeness) or remoteness, fecundity (the ability to produce more happiness in the future), purity (the amount of pain associated with an event), and extent (the amount of people it effects). Lockwood suggested that we should add the potential weight of a world to the list with the following example; "Imagine that I am wired up to a pleasure machine, capable of administering some pleasurable sensation, of a fixed intensity, for different durations, and that these different durations are associated, respectively, with distinct outcomes of a quantum measurement." In order to calculate how much pleasure "the machine will confer on the successors of this instantaneous mind" we must calculate "the total area of that region within my experiential manifold, in which the sensation in question occurs".
Vaidman argued that someone should not agree to play games, such as quantum Russian roulette, because the version of them that survives will be in a world with a low weight. Quantum Russian roulette is similar to Russian roulette, except that the gun is triggered by a quantum event. This means that the players will branch every time they pull the trigger, so that they both live and die.
The concept of quantum suicide extends the idea of quantum Russian roulette in order to differentiate between the collapse and Bohm approaches, and different versions of the Everett approach. The idea behind quantum suicide is that, if you are somehow all of the observers after branching, then you would never observe a world where you instantaneously die and so, from your perspective, every time you pull the trigger you must live. This idea was first proposed by Austrian mathematician Hans Moravec in 1987 and French philosopher Bruno Marchal in 1988. Swedish-American cosmologist Max Tegmark extended the idea in 1998. Moravec considered a situation where scientists are unable to turn on a particle accelerator, because every time they try something stops them. He suggested that this is the only thing that we could possibly observe if the effect of the particle accelerator was to instantly destroy the Earth.