What’s Everything Made of?
is an assistant professor of
philosophy at the California Institute of Technology. He is interested in the
foundations of quantum mechanics, classical field theory, and quantum field
theory.
Edited by Nigel Warburton
[[An excellent review article
describing how little is settled concerning the composition of matter.]]
Long before philosophy and physics
split into separate career paths, the natural philosophers of Ancient Greece
speculated about the basic components from which all else is made. Plato
entertained a theory on which everything on Earth is made from four fundamental
particles. There are stable cube-shaped particles of earth, pointy and painful
tetrahedron-shaped particles of fire, somewhat less pointy octahedron-shaped
particles of air, and reasonably round icosahedron-shaped particles of water.
Like the particles of contemporary physics, Plato thought it was possible for
these particles to be created and destroyed. For example, an eight-sided air
particle could be created by combining two four-sided fire particles (as one
might imagine occurring when a campfire dies out).
Our understanding of nature has come
a long way since Plato. We have learned that much of our world is made of the
various atoms compiled in the periodic table of elements. We have also learned
that atoms themselves are built from more fundamental pieces.
Today, philosophers who are
interested in figuring out what everything is made of look to contemporary
physics for answers. But, finding answers in physics is not simply a matter of
reading textbooks. Physicists deftly shift between different pictures of
reality as it suits the task at hand. The textbooks are written to teach you
how to use the mathematical tools of physics most effectively, not to tell you
what things the equations are describing. It takes hard work to distil a story
about what’s really happening in nature from the mathematics. This kind of
research is considered ‘philosophy of physics’ when done by philosophers and
‘foundations of physics’ when done by physicists.
Physicists have developed an
improvement on the periodic table called ‘the standard model’. The standard
model is missing something very important (gravity) and it might turn out that
the pieces it describes are made of yet more fundamental things (such as
vibrating strings). That being said, the standard model is not going anywhere.
Like Isaac Newton’s theory of gravity or James Clerk Maxwell’s theory of
electrodynamics, we expect that the standard model will remain an important
part of physics no matter what happens next.
Unfortunately, it’s not immediately
clear what replaces the atoms of the periodic table in the standard model. Are
the fundamental building blocks of reality quantum particles, quantum fields,
or some combination of the two? Before tackling this difficult question, let us
consider the debate between particles and fields in the context of a classical
(non-quantum) theory: Maxwell’s theory of electrodynamics.
Bottom of Form
Albert Einstein was led to his 1905
special theory of relativity by engaging in foundational research on
electrodynamics. After developing special relativity, Einstein entered into
a debate with
Walther Ritz about the right way to formulate and understand classical
electrodynamics. According to this theory, two electrons placed near one
another will fly apart in opposite directions. They both have negative charge,
and they will thus repel one another.
Ritz thought of this as an
interaction directly between the two electrons – each one pushing the other,
even though they are not touching. This interaction acts across the gap in
space separating the two electrons. It also acts across a gap in time. Being
precise, each electron responds to the other’s past behaviour (not its current
state).
Einstein, who was averse to such
action-at-a-distance, understood this interaction differently. For him, there
are more players on the scene than just the particles. There are also fields.
Each electron produces an electromagnetic field that extends throughout space.
The electrons move away from one another not because they are directly
interacting with each other across a gap, but because each one is feeling a
force from the other’s field.
Do electrons feel forces from their
own electromagnetic fields? Either answer leads to trouble. First, suppose the
answer is yes. The electromagnetic field of an electron gets stronger as you
get closer to the electron. If you think of the electron as a little ball, each
piece of that ball would feel an enormous outward force from the very strong
electromagnetic field at its location. It should explode. Henri Poincaré
conjectured that there might be some other forces resisting this self-repulsion
and holding the electron together – now called ‘Poincaré stresses’. If you
think of the electron as point-size, the problem is worse. The field and the
force would be infinite at the electron’s location.
If the electron does not interact
with itself, how can we explain the energy loss?
So, let us instead suppose that the
electron does not feel the field it produces. The problem here is that there is
evidence that the electron is aware of its field. Charged particles such as
electrons produce electromagnetic waves when they are accelerated. That takes
energy. Indeed, we can observe electrons lose energy as they produce these
waves. If electrons interact with their own fields, we can correctly calculate
the rate at which they lose energy by examining the way these waves interact
with the electron as they pass through it. But, if electrons don’t interact
with their own fields, then it’s not clear why they would lose any energy at
all.
In Ritz’s all-particles no-fields
proposal, the electron will not interact with its own field because there is no
such field for it to interact with. Each electron feels forces only from other
particles. But, if the electron does not interact with itself, how can we
explain the energy loss? Whether you believe, like Einstein, that there are
both particles and fields, or you believe, like Ritz, that there are only
particles, you face a problem of self-interaction.
Ritz and Einstein staked out two
sides of a three-sided debate. There is a third option: perhaps there are no
particles, just fields. In 1844, Michael Faraday explored this option in an
unpublished manuscript and
a short published ‘speculation’. One could imagine describing the physics of
hard, solid bodies of various shapes and sizes colliding and bouncing off one
another. However, when two charged particles (such as electrons) interact by
electric attraction or repulsion, they do not actually touch one another. Each
just reacts to the other’s electromagnetic field. The sizes and shapes of the
particles are thus irrelevant to the interaction, except in so much as they
change the fields surrounding the particles. So, Faraday asked: ‘What real
reason, then, is there for supposing that there is any such nucleus in a
particle of matter?’ That is, why should we think that there is a hard core at
the centre of a particle’s electromagnetic field? In modern terms, Faraday has been
interpreted as proposing that we eliminate the particles and keep only the
electromagnetic fields.
On 8 August, at the 2019
International Congress on Logic, Methodology and Philosophy of Science and
Technology in Prague, I joined four other philosophers of physics for a debate
– tersely titled ‘Particles, Fields, or Both?’ Mathias Frisch of the Leibniz
University Hannover opened our session with a presentation of the debate
between Einstein and Ritz (see his Aeon essay, ‘Why Things Happen’). Then, the remaining three
speakers defended opposing views – updated versions of the positions held by
Einstein, Ritz, and Faraday.
Our second speaker, Mario Hubert of
Caltech, sought to rescue Einstein’s picture of point-size particles and fields
from the problem of self-interaction. He discussed the current status of
multiple ideas about how this might be done. One such idea came from Paul
Dirac, a mathematical wizard who made tremendous contributions to early quantum
physics. Dirac’s name appears in the part of the standard model that describes
electrons.
In a 1938 paper, Dirac
took a step back from quantum physics to study the problem of self-interaction
in classical electrodynamics. He proposed a modification to the laws of
electrodynamics, changing the way that fields exert forces on particles. For a
point-size particle, his new equation eliminates any interaction of the
particle with its own electromagnetic field, and includes a new term to mimic
the kind of self-interaction that we actually observe – the kind that causes a
particle to lose energy when it makes waves. However, the equation that Dirac
proposed has some strange features. One oddity is ‘pre-acceleration’: a
particle that you’re going to hit with a force might start moving before you
hit it.
In the 1930s and ’40s, a different
strategy was pursued by four notable physicists: Max Born (known for ‘the Born
rule’ that tells you how to calculate probabilities in quantum physics),
Leopold Infeld (who coauthored a popular book on modern physics with
Einstein: The Evolution of Physics), Fritz Bopp (who was part of the
German nuclear research programme during the Second World War and, after the
war, cosigned a manifesto opposing
nuclear weapons and advocating nuclear energy in West Germany), and Boris
Podolsky (a coauthor of the paper that spurred Erwin Schrödinger to coin the term
‘entanglement’ and introduce his enigmatic cat). These physicists proposed ways
of changing the laws that specify how particles produce electromagnetic fields
so that the fields produced by point particles never become infinitely strong.
When you change these laws, you
change a lot. As Hubert explained in his presentation, we don’t fully
understand the consequences of these changes. In particular, it is not yet
clear whether the Born-Infeld and Bopp-Podolsky proposals will be able to solve
the self-interaction problem and make accurate predictions about the motions of
particles.
You might feel that all of this talk
of classical physics has gotten us very far off topic. Aren’t we supposed to be
trying to understand what the standard model of quantum physics tells us about
what everything is made of?
As in a time-travel movie, the
future can influence the past
The part of the standard model that
describes electrons and the electromagnetic field is called ‘quantum
electrodynamics’, as it is the quantum version of classical electrodynamics.
The foundations of the two subjects are closely linked. Here’s how Richard
Feynman motivates a discussion of the modifications to classical
electrodynamics made by Dirac, Born, Infeld, Bopp, and Podolsky in a chapter of
his legendary lectures at Caltech:
There are difficulties associated
with the ideas of Maxwell’s theory which are not solved by and not
directly associated with quantum mechanics. You may say, ‘Perhaps there’s no
use worrying about these difficulties. Since the quantum mechanics is going to
change the laws of electrodynamics, we should wait to see what difficulties
there are after the modification.’ However, when electromagnetism is joined to
quantum mechanics, the difficulties remain. So it will not be a waste of our
time now to look at what these difficulties are.
Indeed, Feynman thought these issues
were of central importance. In the lecture that he gave upon receiving the Nobel Prize in
1965 for his work on quantum electrodynamics, he chose to spend much of his
time discussing classical electrodynamics. In collaboration with his graduate
advisor, John Wheeler (advisor to a number of other important figures,
including Hugh Everett III, the inventor of the Many-Worlds interpretation of quantum mechanics, and Kip Thorne, a
corecipient of the 2017 Nobel
Prize for gravitational-wave detection), Feynman had proposed a
radical reimagining of classical electrodynamics.
Wheeler and Feynman – like Ritz – do
away with the electromagnetic field and keep only the particles. As I mentioned
earlier, Ritz’s field-free theory has particles interact across gaps in space
and time so that each particle responds to the past states of the others. In
the Wheeler-Feynman theory, particles respond to both the past and the
future behaviour of one another. As in a time-travel movie, the future can
influence the past. That’s a wild idea, but it seems to work. In appropriate
circumstances, this revision yields accurate predictions about the motions of
particles without any true self-interaction.
In a talk titled ‘Why Field Theories
are not Theories of Fields’, the third speaker in our debate, Dustin Lazarovici
of the University of Lausanne, took the side of Ritz, Wheeler, and Feynman. In
the action-at-a-distance theories put forward by these physicists, you can’t
tell what a particle will do at a particular moment just by looking at what the
other particles are doing at that moment. You also need to look at what they
were doing in the past (and perhaps what they will do in the future).
Lazarovici argued that the electromagnetic field is merely a useful
mathematical bookkeeping device that encodes this information about the past
and future, not
a real thing out there in the world.
Lazarovici then moved from classical
to quantum electrodynamics. Like many other philosophers of physics, he
believes that standard formulations of quantum electrodynamics are
unsatisfactory – in part because they don’t give a clear picture of what
I was driven to this all-fields
picture not by studying the self-interaction problem, but by two other
considerations. First, I have found this picture helpful in understanding a
property of the electron called ‘spin’. The standard lore in quantum physics is
that the electron behaves in many ways like a spinning body but is not really
spinning. It has spin but does not spin.
If you think of electrons as a
field, then you can think of photons the same way
If the electron is point-size, of
course it does not make sense to think of it as actually spinning. If the
electron is instead thought of as a very small ball, there are concerns that it
would have to rotate faster than the speed of light to account for the features
that led us to use the word ‘spin’. This worry about faster-than-light rotation
made the physicists who discovered spin
in the 1920s uncomfortable about publishing their results.
If the electron is a sufficiently
widely spread-out lump of energy and charge in the Dirac field, there is no
need for faster-than-light motion. We can study the way that the energy and
charge move to see if they flow in a circular way about some central axis – to
see if the electron spins. It does.
The second consideration that led me
to an all-fields picture was the realisation that we don’t have a way of
treating the photon as a particle in quantum electrodynamics. Dirac invented an
equation that describes the quantum behaviour of a single electron. But we
have no similar
equation for the photon.
If you think of electrons as
particles, you’ll have to think of photons differently – either eliminating
them (Lazarovici’s story) or treating them as a field (Hubert’s story). On the
other hand, if you think of electrons as a field, then you can think of photons
the same way. I see this consistency as a virtue of the all-fields picture.
As things stand, the three-sided
debate between Einstein, Ritz and Faraday remains unresolved. We’ve certainly
made progress, but we don’t have a definitive answer. It is not yet clear what
classical and quantum electrodynamics are telling us about reality. Is
everything made of particles, fields or both?
This question is not front and
centre in contemporary physics research. Theoretical physicists generally think
that we have a good-enough understanding of quantum electrodynamics to be
getting on with, and now we need to work on developing new theories and finding
ways to test them through experiments and observations.
That might be the path forward.
However, sometimes progress in physics requires first backing
up to reexamine, reinterpret and revise the theories that we already have. To
do this kind of research, we need scholars who blend the roles of physicist and
philosopher, as was done thousands of years ago in Ancient Greece.
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