Characterized by some counter arguments to such views

 

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)

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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

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