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.
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 is happening in nature. His research programme for fixing up the theory has a number of non-standard elements.
First, Lazarovici is aware that quantum electrodynamics suffers from the quantum measurement problem, and thinks that we ought to adopt a solution proposed by David Bohm, positing the existence of point particles that are distinct from the quantum wave function. Second, he wants to build quantum electrodynamics from a version of classical electrodynamics without fields, where particles interact directly with one another (such as Wheeler and Feynman’s). Third, he adopts Dirac’s controversial idea that space is filled with a vast ‘sea’ of negative energy electrons. This Dirac sea was central to early research in quantum electrodynamics but has fallen out of favour in most contemporary presentations of the theory.
These ideas fit together well, and Lazarovici hopes that they will allow us to avoid certain unpleasant infinities that arise in quantum electrodynamics. I’m curious to see where this approach leads. In favour of research that deviates from the mainstream, Feynman said (at the end of his Nobel lecture) that progress in physics might well be made by someone who teaches himself ‘quantum electrodynamics from a peculiar and unusual point of view; one that he may have to invent for himself’.
In my contribution to the debate, I advocated a different point of view on quantum electrodynamics. Following Faraday, I argued that we should get rid of particles and just have fields. However, I don’t think the electromagnetic field alone is enough. We need another field as well: the Dirac field. It is this field that represents the electron (and also the antiparticle of the electron, the positron).
In classical electrodynamics, this approach replaces the point electron particle with a spread-out lump of energy and charge in the Dirac field. Because the charge is spread out, the electromagnetic field that is produced by this charge will not get infinitely strong at any point in space. That makes the self-interaction problem less severe. But it is not solved. If the electron’s charge is spread out, why don’t the various parts of the electron repel one another so that the electron rapidly explodes? That’s something I’m still working to understand.
We saw this problem before, for the idea that the electron is a little ball. However, the style of this new proposal is quite different. The goal here is not to invent a model of the electron but, instead, to find one in the existing equations of quantum electrodynamics.
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.