British philosophers Simon Saunders and David Wallace claimed that fellow British philosopher Michael Lockwood is wrong to say that there's no answer to who we will become upon branching[2a]. Instead, they suggest that we'll become one particular mind after we branch in agreement with American philosophers David Albert and Barry Loewer.
An observer should expect to experience either one outcome or another after a quantum interaction, and this creates an element of subjective uncertainty.
Wallace described how "when I say 'who will I become'" before initiating a quantum experiment with two possible results, "that statement should actually be ascribed to two versions of me"[2b]. We do not notice the fact that we have numerous minds because, from a subjective point of view, they will be indistinguishable, all seeing the same things and thinking the same thoughts at the same time.
1.1 Weight ↑
Wallace showed that Lockwood's many minds approach is false because his interpretation of 'weight' does not make sense. There's no observable difference between worlds with a low or high weight and so pain will not be more intense in a world with higher weight.
Wallace showed that Lockwood's many minds approach to quantum mechanics violates the functional definition of probability because it implies that it's logical to try to maximise the weight of the world we're in. This is impossible because branching occurs all the time and we have no way to keep track of this weight.
Wallace described how it would lead to:
"[a person being] faced with the impossible task of calculating how much branching will occur across the entire lifetime of the Universe (contingent on [their] choice of action) in order to weigh up the value, now, to [them] of carrying out a certain act".
If we don't care about our own weight, then we shouldn't care about the weights of our future-selves. Wallace argued that weights can only apply to events and not to people or worlds.
In 2005, Wallace suggested that we can replace Lockwood's notion of a 'weighted branching universe' with that of an 'emergent branching universe'. Emergent branching universes can be thought of as approximate descriptions that emerge "from some underlying physical reality" where "there is no 'finest-grained' structure of branches but only a vaguely-defined cut-off point below which 'branching' talk ceases to be useful".
An observer should be rationally compelled to act as if they are in a weighted branching universe, except for the fact that the concept of weight is meaningless when applied to people.
1.2 The preferred basis problem ↑
Wallace also showed that we don't need Lockwood's many minds approach in order to account for the preferred basis problem. Wallace suggested that it doesn't matter that the basis of decoherence is approximate if you accept a functional definition of the mind.
Wallace claimed that all macroscopic objects should be understood "in terms of certain structures and patterns which emerge from quantum theory"[6a].
Wallace argued that we already use the concept of patterns to provide functional definitions and gave the example of our definition of a tiger. We can define the word 'tiger' from many perspectives, and choose the one that is easier or most useful for us.
We could, for example, try to learn about the behaviour of tigers by studying them at an atomic level, but this would be overly complicated. We could study them at a cellular level, but again this would provide us with too much irrelevant information. We learn most about the behaviour of tigers by studying them in terms of single, individual tigers, patterns that arise from a background of energy and matter.
Wallace claimed that we define a tiger as "any pattern which behaves as a tiger"[6b].
In the case of Schrödinger's cat, the superpositional state of the inside of the box can be described as containing patterns of both a dead and alive cat as well as "all possible macroscopic objects made out of the cat's subatomic constituents"[6c].
Cats are described as patterns and so cannot be in superpositions themselves, cats can only be duplicated. This level of description is not usually needed however, because decoherence will quickly remove all observable effects of the superposition.
Wallace agreed with American philosopher Daniel Dennett, who claimed that a pattern is real if it's useful for us to refer to it when explaining theories. Usefulness is defined in terms of explanatory power and predictive reliability. Patterns are subjective, just as worlds are, and so it's possible that different types of minds perceive patterns, and hence define macroscopic objects, in different ways.