Characterized to be

spread out in the 3N-dimensional space we know as configuration space, with

both phase and amplitude at each point in this space, the wavefunction is the

most integral part of describing our world with quantum mechanics. So, what is

it to be a realist about this most paramount feature of the quantum mechanical

description? To advocate wavefunction realism one believes that the fundamental

ontology of the world we inhabit is realised by the wavefunction being a field

in a highly dimensional spacetime. An overview of the leading realist

interpretations of quantum mechanics will be given in the coming writings that

will be followed by some counter arguments to such views from Allori, Maudlin

and their collaborators. From both the for and against arguments to

wavefunction realism I will be arguing that we cannot be complete realists

about the wavefunction but rather an adapted realist view, that of

functionalism, gives the most logical ontological description of our world.

Bohmian mechanics,

theorized by David Bohm in 1952, rejects the position that the wavefunction

completely describes the universe. For there are two things which govern the

universe, the wavefunction and what is known as the ‘world particle’. The wavefunction

itself exists in configuration space and evolves deterministically governed by

the schr?dinger equation

and the particle exists in a 3D space. The particle is also deterministically

governed by a particle equation, describing its position in space evolving over

time as a function of the wavefunction state. Due to what we know as ‘hidden

variables’ the particles always have definite position. Hidden variables, is a

name given to parameters of the particles that are not themselves described by

the wavefunction, as they give position to the particle when the wavefunction

describing it is not in an eigenstate. It is essential for this theory that the

wavefunction is considered a field to act upon the particle. And hence why it

is realist. As was said by John Bell “No one can understand

this theory until he is willing to think of ? the wavefunction as a real

objective field … Even though it propagates not in 3- space but in 3N-space.”(1987,

p. 128)

Hugh Everett did not agree with the interpretation of

Bohm, he had a fundamental issue with Bohmian interpretation in that he

believed the quantum ontology was not that which required anything more than

the wavefunction. In his own words “Our

main criticism of this view is on the grounds of simplicity – if one desires to

hold the view that ? is a real field then the associated particle is

superfluous since, as we have endeavoured to illustrate, the pure wave theory

is itself satisfactory.” (Everett, Theory of the Universal Wavefunction,

section VI). Thus Everett developed another interpretation, sometimes known as

the many worlds interpretation. Built on the notion that the schr?dinger equation is the only law required for the

guiding quantum systems. In this interpretation, no collapse of the

wavefunction occurs. Representation of the universal wavefunction is that of a

superposition of different states known as ‘branches’ occurring upon

observation. Each branch is a real, possible and concurrent outcome from the

measurement. Hence why it is known as many worlds interpretation.

The final realist

interpretation I will describe as it will be refer to later on in the text, as

will the others, is that of Ghirardi-Rimini-Weber (GRW hereafter). In this

interpretation, once again the world consists of a singular universal

wavefunction. The dynamics of this however is not governed simply by the schr?dinger equation. The second law governing dynamics

along with the schr?dinger

is one which accurately defines the odds of the wavefunction undergoing a

collapse. Hence this interpretation is not deterministic nor always local. Here

collapses are the result of completely random chance and hence occurs absent of

measurement. Even due to this, the interpretation is just as precise as the

previously stated interpretations.

For all the above

interpretations that posit an ontology for the world in which we live, the

manifest image we experience and observe, the wavefunction must be considered a

field and configuration space more than just abstract non-physical space. The

work of Allori, Maudlin and their colleagues posits an opposing view. They dispute

the notion that the primitive ontology, that is, the foundations upon which all

other aspects of the theory must be constructed, includes the wavefunction in configuration

space. From this stand point the wavefunction is attributed with a

non-primitive nomological character. It is argued that the wavefunction not

inhabiting our 3D space manifest image is cause for the wavefunction to not be

the most fundamental part of quantum mechanics. Allori and Maudlin’s argument

is based around the school of thought “that in order to account

for the appearance of a three-dimensional world, the fundamental physical

ontology must be three-dimensional.”(The Status of our Ordinary Three Dimensions

in a Quantum Universe, Alyssa Ney) From this way of thinking Allori puts

forward simply that the wavefunction is a product of necessity, simply an abstraction

that must be called upon to describe the behaviours of quantum mechanical

systems.

The reasoning stated in

the previous paragraph is very sound of mind and easily comprehensible, it is

postulation based upon everyday observation of the manifest image – our 3D

everyday experience of the world around us. Quantum mechanics as we know it

however does not adhere to everyday experience of the manifest image in the

phenomena it exhibits. The reasoning for the primitive ontology being devoid of

the wavefunction, I would say, may come across as following a thought pattern

reminiscent of Occam’s razor. There is a seemingly great amount of simplicity in

the argument. Therefore, I refer to the work of Tim Maudlin in greater detail

to explain his reasoning. Maudlin believes it is imperative, that for any theory

to hold realist status it must have what are known as local beables within its

ontology. A term coined by John Bell a local beable is an object within our 3D

space possessing definite positions. Described by Maudlin “local beables do not

merely exist: they exist somewhere” (2007, p. 3157). Put simply, local beables

inhabit physical 3D space and so must be part of the primitive ontology. The wavefunction

itself exists in configuration space and hence cannot have location in 3D

space. This is true for all of the interpretations of quantum mechanics stated

at the beginning of this paper. The argument made by maudlin then stands that

because of this the wavefunction simply cannot be part of the primitive

ontology of quantum mechanics, nor have a physical space of which to inhabit. If

this reading of quantum theory is correct then the primitive ontology of such

exists in 3D space and not in configuration space. Hence from this it is argued

that we cannot be realist about quantum mechanics by being realists about the

wavefunction, we must be realists about the primitive ontology of quantum

mechanics being ultimately about the manifest image inhabiting local beables. In

the next section of this paper I will now briefly state considerations of John

Bell on Bohmian mechanics.

If we think of the above

musings in such a way as John Bell did in the quote mentioned in the second

paragraph of this paper it is reasoned that Bohmian mechanics cannot be thought

of in such a way if one wishes to understand and realise Bohm’s interpretation

with completeness. For instance, in Bohmian mechanics the wavefunction is

thought to possess a causal capacity in that it governs the state of the world

particle. If the wavefunction was that described by Allori then it could not

have such a capacity as laws give a description of the causal capacity of

entities, not themselves possess it. The wavefunction is governed itself by the

schr?dinger equation, the schr?dinger equation is what would appear to be the law and

not the wavefunction. Hence, prima facie, the wavefunction seems to be of

primitive ontological status. It follows from these considerations to look at works

which hold this central idea of the wavefunction having such an ontological

status but in a differing school of thought.

We are now to think

functionally about the objects which we observe within our manifest image. The

works of David Albert, Barry Loewer and David Wallace require this of us. Such works

take the wavefunction realist interpretations of GRW and Everett to be true. Due

to this let us consider that the configuration space of quantum mechanics is

the fundamental space of the universe. From this we consider also a real

wavefunction that’s evolution with time is such that it may enact our 3D

manifest image of the world, for an object in this enacted manifest image to be

so, there needn’t actually be the said object but rather something able to play

the functional role of the object. Hence, we can think of the 3D space we

inhabit as non-fundamental. Such a view point allows us to negate the views of

Allori and Maudlin. Another extremely interesting prospect arises from such a

description of space. If the manifest image is enacted functionally, then there

is no requirement for our manifest image to be more than a simulation. This allows

us to counter argue the position of Maudlin that any realist interpretation of

quantum mechanics must contain local beables within its ontology. If 3D space

is little more than a simulation then it follows that so is a local beable and

therefore is nothing but a functional projection of the wavefunction onto our

manifest image.

It is my belief now that

one’s favoured interpretation of quantum mechanics and therefore one’s view of

wavefunction realism is to be decided upon subjective appeal. The interpretations

mentioned at the beginning of this paper have been expanded upon throughout and

have been argued for and against by views with stark contrast. Questions of

dismissing the wavefunction as an entity residing in a fundamental

3N-dimensional configuration space and questions of accepting the former but

disregarding our manifest image to be anything more than an enacted simulation

being played out upon the stage of configuration space by the behaviour of a real

wavefunction over time have been raised. From considering the works of the

philosophers and physicists I argue that the works of Albert and Loewer is the

best description for the ontology of quantum mechanics. It serves to me

tremendous logical significance that wavefunction be fundamental. We know from

comparison between theory and experiment that quantum mechanics is a theory

that is extremely succesful