Any material theory of the mind will have to explain why people have subjective experiences. This might be a problem that we'll never be able to solve. However, there might already be a theory that explains the subjective nature of consciousness. This is known as the Everett, or many worlds, approach to quantum mechanics[1a].
1. Problems with quantum mechanics ↑
Quantum mechanics challenges classical notions of space, time, matter, and probability. Proponents of the collapse approach to quantum mechanics state that when we measure a property of a quantum system, the different possibilities given in Austrian physicist Erwin Schrödinger's wave equation collapse into a single result. The probability of any given result can be determined using the Born rule. Yet we have never found these collapse dynamics, and there's nothing like them within quantum theory itself.
We could put this problem aside and hope that these dynamics will be discovered in time, but then we still have to solve the problem of how quantum states can interact with ordinary matter at all. This is known as the measurement problem.
The measurement problem is similar to the problem faced by mind-body dualists like French natural philosopher Rene Descartes, who argued that there are two fundamentally different substances in the universe, which interact, despite exhibiting different properties and obeying different laws.
The Bohm approach to quantum mechanics solves all of these problems by dropping the idea of a collapse, but it must then add dynamics to explain why all but one of the possibilities given in the Schrödinger equation are suppressed.
These problems could all be solved with instrumentalism, the view that we should not take physical theories literally when they invoke objects that we cannot see. Instrumentalists argue that all previous scientific theories have been proven false and so we should not take the invisible entities postulated by our current theories literally either.
This argument is countered by the fact that instruments have been built that rely on these invisible entities to work. In fact, the immense technological progress that we have made may be 'miraculous' if they did not exist.
Instrumentalism and the Bohm approach are both still popular, but their main rival claims to solve the problems of quantum mechanics without relying on any extra dynamics or hidden variables. In 1957, American physicist Hugh Everett III suggested that we should simply take Schrödinger's wave equation literally, applying the theory to everything, including the universe itself[1b].
2. The Everett approach ↑
Everett showed that if there are no collapse dynamics, and no hidden variables that suppress the effects of a superposition, then everything will evolve in accordance with the unitary evolution of Schrödinger's wave function.
This means that an observer is not separated from the quantum system they are measuring. When they measure a property of a quantum system, it will not collapse into a single determinate state. Instead, every possibility given by the Schrödinger equation is actualised and, because they too are in a superpositional state, they will observe them all.
When someone measures the spin of an electron in the vertical plane, for example, it will have a 50% chance of appearing 'up' and a 50% change of appearing 'down'. Both the Bohm and collapse approaches predict that an observer will record only one result in accordance with its probability. The Everett approach predicts that they will record both.
Everett described how:
"there is only one physical system representing the observer, yet there is no single unique state of the observer...Thus with each succeeding observation (or interaction), the observer state 'branches' into a number of different states...each branch represents a different outcome of the measurement"[1c].
Everett referred to his approach as the "relative state formulation" because it shows that everything we experience exists in relative terms. In the example above, the experience of measuring the electron to be 'up' is only real relative to the experience of measuring it to be 'down'. Neither branch is more real than the other, and Everett made it clear that he was not suggesting an instrumental interpretation.
Everett stated that:
"it is completely unnecessary to suppose that after an observation somehow one element of the final superposition is selected to be awarded with a mysterious quality called 'reality' and the others condemned to oblivion".
Everett argued that we do not appear to experience every possible result because we too behave like a quantum object, and:
"all the separate elements of a superposition individually obey the wave equation with complete indifference to the presence or absence ('actuality' or not) of any other elements"[1d].
Everett stated that:
"this total lack of effect of one branch on another also implies that no observer will ever be aware of any 'splitting' process"[1e].
"constantly splitting into a stupendous number of branches, all resulting from the measurement like interactions between its myriads of components. Moreover, every quantum transition taking place on every star, in every galaxy, in every remote corner of the universe is splitting our local world on earth into myriads of copies of itself".
The Everett approach does not contradict the laws of energy convention, however, because the universe does not literally split every time a quantum event takes place. This is because the theory applies to the universe as a whole.
Collapse approaches to quantum mechanics cannot apply their theory to the universe as a whole because an external observer would be required in order to collapse its superpositional state. The Everett approach does not face this problem, and so it can describe the entire universe using Schrödinger's wave equation. This superpositional universe is known as the multiverse.
There are no collapse dynamics within the Everett approach, and so there's no distinct time when a measurement is said to have been made. When we become aware of the result of a quantum experiment, the world does not literally split, we simply realise which world we are already in.
The Everett approach does not face the problem of explaining the appearance of instantaneous action at distance, which is apparent in the collapse approach to quantum mechanics. This is because there's no need to send information between one entangled quantum system and another.
Two entangled particles may be separated and then observed by two scientists. When the first measures a property of their quantum particle, QA, they realise which world they are in and know that the second observer's results will be correlated with theirs. But QA does not need to send a signal to QB in order to 'tell' it the results. This is because all results are actualised and so QB only needs to 'know' that it is in a world which is correlated with QA, and this information was exchanged when the two quantum states became entangled in the first place.
Although Everett only mentioned the word 'branches' in 1957, the realism associated with them soon led to the term 'parallel worlds' being used instead. DeWitt was the first to do so when he popularised Everett's approach in 1970 and by 1977, Everett was defending his theory in these terms.
3. Problems with the Everett approach ↑
Despite solving a number of problems, the Everett approach created new problems of its own. These include:
The preferred basis problem, which asks why the universe is split into the 'separate worlds' we experience.
The problem of probability, which asks why it makes sense for one event to be more probable than another if we really experience all possibilities.
The problem of Ockham's razor, which asks how this theory can be true, since it relies on the existence of an infinite amount of other, unobservable, worlds to account for our experiences in this one.