Dr. Meinard Kuhlmann

Physicists speak of the world as being made of
particles and force fields, but it is not at all clear
what particles and force fields actually are in the
quantum realm. The world may instead consist
of bundles of properties, such as color and shape.

Physicists routinely describe the universe as being made of tiny subatomic particles that push and pull on one another by means of
force fields. They call their subject “particle physics” and their instruments “particle accelerators.”

They hew to a Lego-like model of the
world. But this view sweeps a little-known
fact under the rug: the particle interpretation
of quantum physics, as well as the field interpretation,
stretches our conventional notions
of “particle” and “field” to such an extent that
ever more people think the world might be
made of something else entirely.

The problem is not that physicists lack a valid theory of the
subatomic realm. They do have one: it is called quantum field theory.
Theorists developed it between the late 1920s and early 1950s
by merging the earlier theory of quantum mechanics with Einstein’s
special theory of relativity. Quantum field theory provides
the conceptual underpinnings of the Standard Model of particle
physics, which describes the fundamental building blocks of matter
and their interactions in one common framework. In terms of
empirical precision, it is the most successful theory in the history
of science. Physicists use it every day to calculate the aftermath of
particle collisions, the synthesis of matter in the big bang, the extreme conditions inside atomic nuclei, and much besides.

So it may come as a surprise that physicists are not even sure
what the theory says—what its “ontology,” or basic physical picture,
is. This confusion is separate from the much discussed mysteries
of quantum mechanics, such as whether a cat in a sealed
box can be both alive and dead at the same time. The unsettled
interpretation of quantum field theory is hobbling progress toward
probing whatever physics lies beyond the Standard Model,
such as string theory. It is perilous to formulate a new theory
when we do not understand the theory we already have.
At first glance, the content of the Standard Model appears
obvious. It consists, first, of groups of elementary particles,
such as quarks and electrons, and, second, of four types of force
fields, which mediate the interactions among those particles.

This picture appears on classroom walls and in Scientific American
articles.  However compelling it might appear, it is not at
all satisfactory.

For starters, the two categories blur together. Quantum field
theory assigns a field to each type of elementary particle, so
there is an electron field as surely as there is an electron. At the
same time, the force fields are quantized rather than continuous,
which gives rise to particles such as the photon. So the distinction
between particles and fields appears to be artificial, and
physicists often speak as if one or the other is more fundamental.
Debate has swirled over this point—over whether quantum
field theory is ultimately about particles or about fields. It started
as a battle of titans, with eminent physicists and philosophers
on both sides. Even today both concepts are still in use for
illustrative purposes, although most physicists would admit
that the classical conceptions do not match what the theory
says. If the mental images conjured up by the words “particle”
and “field” do not match what the theory says, physicists and
philosophers must figure out what to put in their place.

With the two standard, classical options gridlocked, some philosophers of physics have been formulating more radical alternatives.

They suggest that the most basic constituents of the material
world are intangible entities such as relations or properties.
One particularly radical idea is that everything can be reduced to
intangibles alone, without any reference to individual things. It is
a counterintuitive and revolutionary idea, but some argue that
physics is forcing it on us.

THE TROUBLE WITH PARTICLES

When most people, including experts, think of subatomic reality,
they imagine particles that behave like little billiard balls rebounding
off one another. But this notion of particles is a holdover
of a worldview that dates to the ancient Greek atomists and
reached its pinnacle in the theories of Isaac Newton. Several overlapping lines of thought make it clear that the core units of quantum field theory do not behave like billiard balls at all.

First, the classical concept of a particle implies something
that exists in a certain location. But the “particles” of quantum
field theory do not have well-defined locations: a particle inside
your body is not strictly inside your body. An observer attempting
to measure its position has a small but nonzero probability of
detecting it in the most remote places of the universe. This contradiction was evident in the earliest formulations of quantum
mechanics but became worse when theorists merged quantum
mechanics with relativity theory. Relativistic quantum particles
are extremely slippery; they do not reside in any specific region
of the universe at all.

Second, let us suppose you had a particle localized in your
kitchen. Your friend, looking at your house from a passing car,
might see the particle spread out over the entire universe. What
is localized for you is delocalized for your friend. Not only does
the location of the particle depend on your point of view, so does
the fact that the particle has a location.  In this case, it does not
make sense to assume localized particles as the basic entities.
Third, even if you give up trying to pinpoint particles and simply
count them, you are in trouble. Suppose you want to know
the number of particles in your house. You go around the house
and find three particles in the dining room, five under the bed,
eight in a kitchen cabinet, and so on. Now add them up. To your
dismay, the sum will not be the total number of particles.  That
number in quantum field theory is a property of the house as a
whole; to determine it, you would have to do the impossible and
measure the whole house in one go, rather than room by room.

An extreme case of particles’ being unpinpointable is the vacuum,
which has paradoxical properties in quantum field theory.
You can have an overall vacuum—by definition, a zero-particle
state—while at the same time you observe something very different
from a vacuum in any finite region. In other words, your
house can be totally empty even though you find particles all over
the place. If the fire department asks you whether anyone is still
inside a burning house and you say no, the firefighters will question
your sanity when they discover people huddled in every room.
Another striking feature of the vacuum in quantum field theory
is known as the Unruh effect. An astronaut at rest may think he
or she is in a vacuum, whereas an astronaut in an accelerating
spaceship will feel immersed in a thermal bath of innumerable
particles. This discrepancy between viewpoints also occurs at the
perimeter of black holes and leads to paradoxical conclusions
about the fate of infalling matter [see “Black Holes and the Information Paradox,” by Leonard Susskind; Scientific American,
April 1997]. If a vacuum filled with particles sounds absurd, that
is because the classic notion of a particle is misleading us; what
the theory is describing must be something else. If the number of
particles is observer-dependent, then it seems incoherent to assume
that particles are basic. We can accept many features to be
observer-dependent but not the very fact of how many basic
building blocks there are.

Finally, the theory dictates that particles can lose their individuality.
In the puzzling phenomenon of quantum entanglement,
particles can become assimilated into a larger system and
give up the properties that distinguish them from one another.
The presumptive particles share not only innate features such as
mass and charge but also spatial and temporal properties such as
the range of positions over which they might be found. When particles are entangled, an observer has no way of telling one from
the other. At that point, do you really have two objects anymore?
A theorist might simply decree that our would-be two particles
are two distinct individuals. Philosophers call this diktat
“primitive thisness.” By definition, this thisness is unobservable.
Most physicists and philosophers are very skeptical of such ad
hoc moves. Rather, it seems, you no longer have two particles
anymore. The entangled system behaves as an indivisible whole,
and the notion of a part, let alone a particle, loses its meaning.
These theoretical problems with particles fly in the face of experience.

What do “particle detectors” detect if not particles?

The answer is that particles are always an inference. All a detector
registers is a large number of separate excitations of the sensor
material. We run into trouble when we connect the dots and
infer the existence of particles having trajectories that can be
traced in time. (Caveat: Some minority interpretations of quantum
physics do think in terms of well-defined trajectories. But
they suffer from their own difficulties, and I stick to the standard
view [see “Bohm’s Alternative to Quantum Mechanics,” by David
Z. Albert; Scientific American, May 1994].)

So let us take stock. We think of particles as tiny billiard balls,
but the things that modern physicists call “particles” are nothing
like that. According to quantum field theory, objects cannot be
localized in any finite region of space, no matter how large or
fuzzy it is. Moreover, the number of the putative particles depends
on the state of motion of the observer. All these results
taken together sound the death knell for the idea that nature is
composed of anything akin to ball-like particles.

On the basis of these and other insights, one must conclude that
“particle physics” is a misnomer: despite the fact that physicists
keep talking about particles, there are no such things. One may
adopt the phrase “quantum particle,” but what justifies the use of
the word “particle” if almost nothing of the classical notion of particles has survived? It is better to bite the bullet and abandon the
concept altogether. Some take these difficulties as indirect evidence
for a pure field interpretation of quantum field theory. By
this reasoning, particles are ripples in a field that fills space like an
invisible fluid. Yet as we will see now, quantum field theory cannot
be readily interpreted in terms of fields, either.

THE TROUBLE WITH FIELDS

The name “quantum field theory” naturally connotes a theory
that deals with quantum versions of classical fields, such as the
electric and magnetic fields. But whatis a “quantum version”?
The term “field” conjures up magnetic fields that cause iron filings
to align themselves around a bar magnet and electric fields
that cause hair to stand up on end, but a quantum field is so different
from a classical one that even theoretical physicists admit
they can barely visualize it.

Classically, a field assigns a physical quantity, such as temperature
or electric field strength, to each point in spacetime. A quantum
field instead assigns abstract mathematical entities, which
represent the type of measurements you could conduct, rather
than the result you would obtain. Some mathematical constructions
in the theory do represent physical values, but these cannot
be assigned to points in spacetime, only to smeared-out regions.
Historically, physicists developed quantum field theory by
“quantizing” classical field theory. In this procedure, theorists
go through an equation and replace physical values with “operators,”
which are mathematical operations such as differentiation
or taking the square root, and some operators can correspond
to specific physical processes such as the emission and
absorption of light. Operators place a layer of abstraction be-
tween the theory and reality. A classical
field is like a weather map that shows the
temperature in various cities. The quantum
version is like a weather map that
does not show you “40 degrees,” but “√—.”
To obtain an actual temperature value,
you would need to go through an extra
step of applying the operator to another
mathematical entity, known as a state
vector, which represents the configuration
of the system in question.

On some level, this peculiarity of
quantum fields does not seem surprising.
Quantum mechanics—the theory on
which quantum field theory is based—
does not traffic in determinate values either
but only in probabilities. Ontologically,
though, the situation seems weirder
in quantum field theory because the supposedly
fundamental entities, the quantum
fields, do not even specify any probabilities;
for that, they must be combined
with the state vector.

The need to apply the quantum field to
the state vector makes the theory very difficult
to interpret, to translate into something
physical you can imagine and manipulate
in your mind. The state vector is holistic;
it describes the system as a whole
and does not refer to any particular location.
Its role undermines the defining feature
of fields, which is that they are spread
out over spacetime. A classical field lets you
envision phenomena such as light as propagation
of waves across space. The quantum
field takes away this picture and leaves
us at a loss to say how the world works.
Clearly, then, the standard picture of
elementary particles and mediating
force fields is not a satisfactory ontology
of the physical world. It is not at all clear
what a particle or field even is. A common
response is that particles and fields
should be seen as complementary aspects
of reality. But that characterization does not help, because
neither of these conceptions works even in those cases
where we are supposed to see one or the other aspect in purity.
Fortunately, the particle and field views do not exhaust the possible
ontologies for quantum field theory.

STRUCTURES TO THE RESCUE?

A growing number of people think that what really matters are
not things but the relations in which those things stand. Such a
view breaks with traditional atomistic or pointillist conceptions
of the material world in a more radical way than even the severest
modifications of particle and field ontologies could do.
Initially this position, known as structural realism, came in a
fairly moderate version known as epistemic structural realism. It
runs as follows: We may never know the real natures of things
but only how they are related to one another. Take the example
of mass. Do you ever see mass itself? No. You see only what it
means for other entities or, concretely, how one massive body is
related to another massive body through the local gravitational
field. The structure of the world, reflecting how things are interrelated, is the most enduring part of physics theories. New theories may overturn our conception of the basic building blocks of
the world, but they tend to preserve the structures. That is how
scientists can make progress.

Now the following question arises: What is the reason that
we can know only the relations among things and not the things
themselves? The straightforward answer is that relations are all
there is. This leap makes structural realism a more radical proposition, called ontic structural realism.

The myriad symmetries of modern physics lend support to
ontic structural realism. In quantum mechanics as well as in
Einstein’s theory of gravitation, certain changes in the configuration
of the world—known as symmetry transformations—have
no empirical consequences. These transformations exchange the
individual things that make up the world but leave their relations
the same. By analogy, consider a mirror-symmetric face. A
mirror swaps the left eye for the right eye, the left nostril for the
right, and so on. Yet all the relative positions of facial features remain.

Those relations are what truly define a face, whereas labels
such as “left” and “right” depend on your vantage point. The
things we have been calling “particles” and “fields” possess more
abstract symmetries, but the idea is the same.
By the principle of Occam’s razor, physicists and philosophers
prefer ideas that can explain the same phenomena with the fewest
assumptions. In this case, you can construct a perfectly valid
theory by positing the existence of specific relations without additionally assuming individual things. So proponents of ontic
structural realism say we might as well dispense with things and
assume that the world is made of structures, or nets of relations.
In everyday life we encounter many situations where only
relations count and where it would be distracting to describe
the things that are related. In a subway
network, for example, it is crucial to know
how the different stations are connected.
In London, St. Paul’s is directly connected
to Holborn, whereas from Blackfriars you
need to change lines at least once, even
though Blackfriars is closer to Holborn
than St. Paul’s. It is the structure of the
connections that matters primarily. The
fact that Blackfriars Tube station has recently
been renovated into a nice new station
does not matter to someone trying to
navigate the system.

Other examples of structures that take
priority over their material realization are
the World Wide Web, the brain’s neural
network and the genome. All of them still
function even when individual computers,
cells, atoms and people die. These examples
are loose analogies, although they are
close in spirit to the technical arguments
that apply to quantum field theory.
A closely related line of reasoning exploits
quantum entanglement to make the
case that structures are the basis of reality.
The entanglement of two quantum particles
is a holistic effect. All the intrinsic
properties of the two particles, such as electrical
charge, together with all their extrinsic
properties, such as position, still do not
determine the state of the two-particle system.
The whole is more than the sum of its
parts. The atomistic picture of the world, in
which everything is determined by the
properties of the most elementary building
blocks and how they are related in spacetime,
breaks down. Instead of considering
particles primary and entanglement secondary,
perhaps we should think about it the other way round.
You may find it is strange that there could be relations without
relata—without any objects that stand in that relation. It sounds
like having a marriage without spouses. You are not alone.

Many physicists and philosophers find it bizarre, too, thinking it
impossible to get solid objects merely on the basis of relations.
Some proponents of ontic structural realism try to compromise.
They do not deny objects exist; they merely claim that relations,
or structures, are ontologically primary. In other words, objects
do not have intrinsic properties, only properties that come from
their relations with other objects. But this position seems wishywashy.

Anyone would agree that objects have relations. The only
interesting and new position would be that everything emerges
purely on the basis of relations. All in all, structural realism is a
provocative idea but needs to be developed further before we will
know whether it can rescue us from our interpretive trouble.

BUNDLES OF PROPERTIES

A second alternative for the meaning of quantum field theory
starts from a simple insight. Although the particle and field interpretations are traditionally considered to be radically differ-
ent from each other, they have something crucial in common.
Both assume that the fundamental items of the material world
are persistent individual entities to which properties can be ascribed.

These entities are either particles or, in the case of field
theory, spacetime points. Many philosophers, including me,
think this division into objects and properties may be the deep
reason why the particle and field approaches both run into difficulties.

We think it would be better to view properties as the one
and only fundamental category.

Traditionally, people assume that properties are “universals”—
in other words, they belong to an abstract, general category.
They are always possessed by particular things; they cannot
exist independently. (To be sure, Plato did think of them as existing
independently but only in some higher realm, not the
world that exists in space and time.) For instance, when you
think of red, you usually think of particular red things and not
of some freely floating item called “redness.” But you could invert
this way of thinking. You can regard properties as having
an existence, independently of objects that possess them. Properties
may be what philosophers call “particulars”—concrete, individual
entities. What we commonly call a thing may be just a
bundle of properties: color, shape, consistency, and so on.
Because this conception of properties as particulars rather
than universals differs from the traditional view, philosophers
have introduced a new term to describe them: “tropes.” It
sounds a bit funny, and unfortunately the term brings inappropriate
connotations with it, but it is established by now.

Construing things as bundles of properties is not how we
usually conceptualize the world, but it becomes less mysterious
if we try to unlearn how we usually think about the world and
set ourselves back to the very first years of life. As infants, when
we see and experience a ball for the first time, we do not actually
perceive a ball, strictly speaking. What we perceive is a round
shape, some shade of red, with a certain elastic touch. Only later
we do associate this bundle of perceptions with a coherent object
of a certain kind—namely, a ball. Next time we see a ball, we
essentially say, “Look, a ball,” and forget how much conceptual
apparatus is involved in this seemingly immediate perception.
In trope ontology, we return to the direct perceptions of infancy.

Out there in the world, things are nothing but bundles of
properties. It is not that we first have a ball and then attach
properties to it. Rather we have properties and call it a ball.
There is nothing to a ball but its properties.
Applying this idea to quantum field theory, what we call an
electron is in fact a bundle of various properties or tropes:
three fixed, essential properties (mass, charge and spin), as well
as numerous changing, nonessential properties (position and
velocity). This trope conception helps to make sense of the theory.
For instance, the theory predicts that elementary particles
can pop in and out of existence quickly. The behavior of the
vacuum in quantum field theory is particularly mind-boggling:
the average value of the number of particles is zero, yet the vacuum
seethes with activity. Countless processes take place all
the time, involving the creation and subsequent destruction of
all kinds of particles.

In a particle ontology, this activity is paradoxical. If particles
are fundamental, then how can they materialize? What do
they materialize out of ? In the trope ontology, the situation is
natural. The vacuum, though empty of particles, contains properties.
A particle is what you get when those properties bundle
themselves together in a certain way.

PHYSICS AND METAPHYSICS

How can there be so much fundamental controversy about a
theory that is as empirically successful as quantum field theory?
The answer is straightforward. Although the theory tells us
what we can measure, it speaks in riddles when it comes to the
nature of whatever entities give rise to our observations. The
theory accounts for our observations in terms of quarks, muons,
photons and sundry quantum fields, but it does not tell us what
a photon or a quantum field really is. And it does not need to,
because theories of physics can be empirically valid largely
without settling such metaphysical questions.

For many physicists, that is enough. They adopt a so-called instrumentalist attitude: they deny that scientific theories are meant to represent the world in the first place. For them, theories are only instruments for making experimental predictions. Still, most
scientists have the strong intuition that their theories do depict
at least some aspects of nature as it is before we make a measurement.

After all, why else do science, if not to understand the world?
Acquiring a comprehensive picture of the physical world requires
the combination of physics with philosophy. The two disciplines
are complementary. Metaphysics supplies various competing
frameworks for the ontology of the material world, although
beyond questions of internal consistency, it cannot
decide among them. Physics, for its part, lacks a coherent account
of fundamental issues, such as the definition of objects,
the role of individuality, the status of properties, the relation of
things and properties, and the significance of space and time.

The union of the two disciplines is especially important at
times when physicists find themselves revisiting the very foundations of their subject. Metaphysical thinking guided Isaac
Newton and Albert Einstein, and it is influencing many of those
who are trying to unify quantum field theory with Einstein’s
theory of gravitation. Philosophers have written libraries full of
books and papers about quantum mechanics and gravity theory,
whereas we are only beginning to explore the reality embodied
in quantum field theory. The alternatives to the standard particle
and field views that we are developing may inspire physicists
in their struggle to achieve the grand unification.

MORE TO EXPLORE
An Interpretive Introduction to Quantum Field Theory.
Paul Teller. Princeton University Press, 1995.
No Place for Particles in Relativistic Quantum Theories?
Hans Halvorson and Rob Clifton in
Philosophy of Science, Vol. 69, No. 1, pages 1–28; March 2002.
Available online at
http://arxiv.org/abs/quantph/0103041
Ontological Aspects of Quantum Field Theory.
Edited by Meinard Kuhlmann,
Holger Lyre and Andrew Wayne. World Scientific, 2002.
Against Field Interpretations of Quantum Field Theory.
David John Baker in British
Journal for the Philosophy of Science,
Vol. 60, No. 3, pages 585–609; September 2009.
http://philsci-archive.pitt.edu/4132/1/AgainstFields.pdf
The Ultimate Constituents of the Material World: In Search of an Ontology for Fundamental Physics.
Meinard Kuhlmann. Ontos Verlag, 2010.
Quantum Field Theory.
Meinard Kuhlmann in Stanford Encyclopedia of Philosophy,
Winter 2012.
http://plato.stanford.edu/archives/win2012/entries/quantum-field-theory
SCIENTIFIC AMERICAN ONLINE
What is a field? For a pithy video explanation, see
http://www.scientificamerican.com/video.cfm?id=what-is-a-field2013-06-19