Editor’s Note: I am most certainly not an expert on quantum mechanics. While I strive to be as accurate and academically rigorous as possible in my blogposts, please take everything below with a grain of salt. I cite some very advanced quantum theory, so it’s certainly possible that I have misrepresented some information. Please notify me of any errors that you find. Also, a lot of this essay will be a formal explication of some concepts that I touched on in my previous blogpost (“Interlude”), so it won’t open with a story.
Everything is changing all the time, even though many of the objects in the world around us appear to be totally still. As the philosopher Heraclitus declared over two millennia ago, “Everything gives way and nothing stays fixed … You could not step twice in the same river.”
The leaves change color. Buildings decay. Your body grows old.
Yet most of us subscribe to the idea that there is a stable identity that underlies all of this metamorphosis. A leaf that is now green isn’t, we think, a separate entity from the version that was originally red. And we most certainly don’t believe that someone changes into a different person as he or she ages. Many of us even support the claim that a ship remains the same object after all of its components have been replaced.
If we didn’t have this preconceived notion that something about an object remains the same in spite of the transformations applied to it, then we would attribute a new identity to every thing at each distinct moment in time. If we were to refer to someone as Jim at time t1, we might call him Albert once a single hair falls off his head at at t2. But obviously we don’t do that. We just call that person Jim. Even if we were to make a distinction between Jim and “Jim-with-a-single-hair-fallen-off” – or, to offer a more dramatic example, “alive Jim” and “dead Jim” – we would tacitly be suggesting that the changes to Jim only qualify his identity but nonetheless do not fundamentally alter it, since we are implying that there is just one person, Jim, behind the different forms and guises that he might take on.
Thus, when we label something, we are labeling the thing that persists through change. You might think that this metaphysical definition of identity runs into problems, especially in instances of very substantial transformations. For instance, once a caterpillar turns into a butterfly, we no longer refer to it as a caterpillar. One might point out, in response, that though the name ascribed to it has changed, there is some part of the organism that has essentially stayed constant. A biologist might say that its genetic constitution hasn’t been altered; some metaphysicians like this one might argue that an immaterial soul is the defining essence of a man or a creature, and that it is unaffected by all the superficial changes that may go on at the level of its appearance. I side with neither the biologist nor the metaphysician on this issue. The reason why the creature stays the same is that its relation to itself hasn’t changed. Relation to itself? Isn’t that a mere tautology, since its relation to itself is the same as, well, just itself? you might be thinking. Not quite.
Shifting this example to the human level is probably more illuminating. As you age from an infant to an old man, your appearance changes so much that it might be impossible for someone else to identify you based on how you looked when you were many decades younger. Yet you experience your entire life as a single unity because your conscious perception of the world is never interrupted. You stand in a certain relation to yourself, which is that you perceive yourself as a whole, individual unit of experience (which is experiencing itself). (Incidentally, Kierkegaard came to a similar conclusion, but I won’t quote him directly because his central idea about the self is very hard to unpack.) The caterpillar-butterfly stands in this same relation to itself.
Of course, things get more complicated when we start talking about inanimate matter. To claim that a spoon maintains a certain relation to itself would suggest that the spoon is conscious. While that’s a very fascinating idea – and one that’s starting to accrue a fair deal of academic legitimacy – it is quite difficult to defend. I will save that topic, also known as panpsychism, for another time. So we must have some alternative explanation for what it is within inanimate objects that remains invariant through change. Here, I turn to quantum physics.
This move on my part might seem perplexing, at first. After all, one of the most striking accomplishments of quantum physics is that it totally demolishes the notion that objects in the universe can fundamentally be steady and unvarying. It would even be difficult to support the seemingly indisputable assertion that subatomic particles, the central focus for much of quantum theory, are “things” as we traditionally conceive of them. As the philosopher Bertrand Russell put it in his Outline of Philosophy, “The main point for the philosopher in the modern theory is the disappearance of matter as a ‘thing.’ It has been replaced by emanations from a locality … All sorts of events happen in the physical world, but tables and chairs, the sun and the moon, and even our daily bread, have become pale abstractions, mere laws exhibited in the successions of events which radiate from certain regions.”
Why such a radical departure from the way we normally think about matter? Very outdated, but conventionally-minded, models of the atom depict an electron orbiting a nucleus in a similar way that the Earth revolves around the sun. Yet this model is incredibly deceptive because we describe the position of an electron within an atom as a “cloud” that specifies the probability of finding it at any given area in space. Yet while the electron is probably contained within the cloud, the laws of quantum mechanics dictate that it is entirely possible for it to be located at any point in space. Because of our inability to sharply define the spatiotemporal properties of an electron, it is scientifically expedient for us to model it as a field rather than a particle – specifically, a quantized excitation of the electron field, which represents the location with the highest probability in the cloud.
Thinking about quantum physics in terms of fields rather than particles immediately clears up a lot of confusion. The Heisenberg uncertainty principle, which states that information a particle’s momentum trades off with our ability to know its position, lends itself to a very accessible interpretation once we start to conceptualize the nature of an electron as a field. For instance, if we know the position of a quantum field excitation, it is like knowing the location where we drop a pebble in a lake. Yet the excitation will move out in all directions, just like the resulting waves from the pebble. Viewing the excitation as a particle or as a wave leads to a head-scratching paradox, since neither one, it seems, could be propagating in every direction at the same time. Quantum mechanics, as it is commonly taught to high school students, would like us to think that the electron has a “wave-particle duality”; it behaves like a particle in certain contexts and as a wave in others, so neither term is sufficient to capture the totality of its behavior. Yet trying to understand the electron as both wave and particle is bewildering for obvious reasons, the foremost of which is that the fundamental identity of the electron would vary by environment and circumstance. The electron qua field is both an internally consistent concept and something that persists through change; it aligns with the metaphysical conception of identity that I laid out earlier. Consider, for instance, the Unruh effect. As described in the physicist Art Hobson’s paper “There are no particles, there are only fields,” an accelerating observer in a vacuum will observe quanta whereas one that is traveling at constant velocity, or at rest, will not. In a particle-centric mindset, a single quantum would have to manifest different properties to separate observers. Yet if we treat the quantum as a field, then the effect will no longer seem like a self-contradictory enigma. There is only one field, but the acceleration of one person transforms the vacuum fluctuations in such a way that the other observer sees only emptiness (0).
Indeed, quantum theory paints a picture of a reality that is much more objective – that is, one that remains constant under changes in perspective – and less observer-dependent when we define particles as fields. The reason for this invariance lies in a fundamental principle known as symmetry, which governs many quantum fields. A thing is symmetrical, as one physicist very broadly defined it, “if there is something we can do to it so that after we have done it, it looks the same as it did before.” There are several different classes of symmetries, including global symmetries that hold at all points in spacetime and local symmetries that hold at only some points. Laws of physics are globally symmetrical, such that that an experiment performed at a different time or location in space (with all the relevant environmental features transposed accordingly) will yield the same results, and it should come as no surprise that each conservation law in physics is associated with a symmetry. Most of the symmetries that occur on the level of particle physics are internal symmetries, which means they don’t involve transformations on spacetime. As a result, they aren’t subject to straightforward interpretation, unlike, for example, the rotational symmetry of a circle. Suffice it to say that the symmetries in quantum field theory are algebraic structures described by something known as group theory.
As an example, particles like quarks and leptons are known to rapidly transform into one another through the exchange of gauge bosons. In fact, the identity of the particle is contingent on the frame of reference in which it is perceived; one observer might see a proton, while another would see a neutron. Were it not for the differences in their electric charge, the proton and the neutron would be virtually indistinguishable, devoid of any metaphysical individuality. The particles themselves are merely signposts that exist for the purpose of expressing a more fundamental symmetry. Indeed, protons and neutrons are nothing more than up and down states of a single entity that displays an internal symmetry known as the isospin, which, critically, is invariant when particles change into new ones. It is important to mention that the isospin is not a spin in physical space but rather one in an abstract space with no associated angular momentum, demonstrating that the symmetry belongs to a deeper layer of reality. The identities of the individual particles are conditional on the peculiarities of subjective experience, but the symmetrical state in which they participate remains constant in spite of the various transformations that may be applied to it, or the different frames of reference from which it might be observed. In that sense, the symmetry is the objective reality, since, by definition, it persists through change.
Furthermore, as the philosopher of science Kerry McKenzie writes, “knowledge of the symmetries associated with a law can also allow us to describe the particles whose behavior is described by that law.” This is a startling observation, because it indicates that the existence of the particle is derived from the symmetry of the particle and not the other way around. We tend to think that the elementary objects of the physical world aggregate like building blocks to form a larger structure, one in which those objects are related to each other through their relative positions and other features, but our most contemporary understanding of particle physics subverts this conventional worldview. Rather, the identity and individuality of the objects in our world are contingent on the underlying structure that relates them to one another, even though it would seem that the converse is true: that a relation between things is conditional on the existence of the things that are being linked together. This seemingly radical view – that structure is the ultimate physical reality – is known in philosophical circles as ontic structural realism (OSR).
OSR in its most extreme form might immediately seem implausible to you because, as many of its critics argue in response, there are “no relations without relata.” There can be no symmetries, it would appear, unless there are some objects to be symmetrically related to each other in the first place. Yet as the philosopher of science Aharon Kantarovich notes, a hypothetical universe that is deprived of all hadrons (recall that these are composite particles that are comprised of quarks) is nonetheless still governed by internal symmetries, since it is the symmetry that determines the kinds of hadrons that can be produced when, say, two photons collide with each other. (1) The symmetry is therefore more fundamental than the particles themselves because it is impossible for the particles to exist without the underlying symmetry, yet possible for the symmetry to exist without the particles.
The essence of an individual particle, then, is totally recast by OSR. As Steven French, one of the core developers of the theory, claims, “the [fundamental] elements themselves, regarded as individuals, have only a heuristic role in allowing for the introduction of the structures which then carry the ontological weight.” In fact, all that an elementary particle is – its essence, as McKenzie points out – is an irreducible representation, or “irrep,” of the symmetry associated with the family/species to which that particle belongs. In 1939, the Nobel Prize-winning mathematician Eugene Wigner found that the irreps of a fundamental symmetry in particle physics, the Poincaré invariance, should have either some determinate mass ∈ R > 0 and spin ∈ Z/2 or some determinate mass = 0 and helicity ∈ Z (where R and Z represent the real numbers and the integers, respectively). Since all the particles in the Standard Model (2) have exactly these properties, Wigner’s analysis enabled physicists to predict the existence of most of the elementary particles by identifying them with irreps of symmetry groups, long before they were confirmed through experiment. As a pair of theoretical physicists wrote, “Ever since the fundamental paper of Wigner on the irreducible representations of the Poincare group, it has been a (perhaps implicit) definition in physics that an elementary particle ‘is’ an irreducible representation of the group, G, of symmetries of nature.”
Fig. 1. Measurable quantities of particles in quantum theory are derived from the symmetry groups of nature. From the blog Soul Physics, run by philosopher of physics Bryan Roberts.
Yet symmetry can often be broken in the universe, often through a spontaneous process. One of the most classic examples of spontaneous symmetry breaking is the Higgs mechanism, which is associated with the famed and highly-reported Higgs boson and field (for more details on the precise difference between the Higgs field, boson, and mechanism, see footnote 3). The primary significance of the Higgs boson/field lies in its manifestation of a particular kind of symmetry breaking (4). In fact, the discovery of the Higgs boson/field was primarily motivated by a mathematical inconsistency that relates to a symmetry between two of the four fundamental forces in nature: the electromagnetic force and the weak force. At particularly high temperatures, these two forces are unified into a single one, the electroweak interaction. Yet quantum field theory could not explain how the quantum of the electromagnetic field, the photon, and that of the weak field, the W and Z bosons, could both be contained within a symmetrical state. Since it turns out that the photon is massless and the two bosons are massive, Higgs’ quest to sort out this mathematical incongruity also ended up answering questions about the origins of mass. The Higgs field, it was suggested, is responsible for spontaneously breaking the symmetry associated with the electroweak force, and this process consequently produces the photon and the W and Z bosons.
While protons would carry mass in a world without the Higgs mechanism, electrons would be totally massless, thereby precluding all interaction between atoms and chemistry itself. In that sense, symmetry breaking is crucial to our very existence; as Marie Curie stated in the late 1800s, the process is responsible for nothing less than the creation of phenomena (5). Indeed, a totally symmetric universe must look the same no matter where an observer is located or oriented in space, which is only possible, as quantum field theory predicted, if there isn’t any mass whatsoever. Additionally, as the physicist Dave Goldberg explains, symmetry mandates that all matter in the universe is accompanied by antimatter, and indeed, particles always emerge out of the quantum vacuum in quark-antiquark pairs. Yet these pairs never exist for more than a very fleeting period of time because they necessarily annihilate each other. Therefore, at some point immediately after the Big Bang, there must have been a slight imbalance in the quantity of matter and antimatter; otherwise, there wouldn’t be anything at all! The reasons for this disparity, on a purely physical or cosmological level, are totally unknown.
But perhaps our metaphysics can shed some more insight. If we lend any credence at all to OSR, then symmetry is probably one of the best candidates for the underlying structure that unifies reality. Symmetry is definitionally a feature of a system that remains invariant under transformation. Therefore, objects preserve their identities through time because they stand in relation to a certain kind of symmetry. A particle-field doesn’t have to be treated any differently when it is rotated 30 degrees, but only because the laws of physics are globally symmetrical. Only by virtue of internal symmetry is there some sense in which a particle remains the same even when the most dramatic transformations occur to it, including those that would appear to change its fundamental identity (e.g. from proton to neutron and vice versa). When the symmetry is broken, the particle exists as something apart from the broader structure that would otherwise constrain its identity. No longer a mere representation of a symmetry, it assumes the status of an individual and therefore bears some relation to itself. Yet symmetry breaking doesn’t eliminate symmetry altogether; rather, it brings an existing symmetry to a “lower level,” or in more technical terms, it splinters the initial symmetry group to one of its subgroups. Therefore, a particle-field is an asymmetrical relation to itself that nonetheless depends on its relation to the relevant symmetry group for its persistence through change. The appearance of the particle at one moment is no more than a temporary mask that conceals the deeper symmetry in which it participates.
And what are you but the person behind the many disguises that you relate yourself to?
(0) Though I agree with Hobson that, at the quantum level, there are only fields and no particles, I will continue to refer to particles throughout this essay.
(1) Note that, in Kantarovich’s proposed thought experiment, the universe isn’t totally “particle-less” since he allows for the existence of leptons. But this distinction doesn’t really matter.
(2) The Standard Model is physicists’ best model for classifying the elementary particles of the universe and describing three of the four fundamental forces (strong, weak, and electromagnetic).
(3) Peter Higgs and several other physicists proposed in the early 1960s that space is permeated with the quantum Higgs field, which creates the resistance that particles encounter whenever they try to move. Highly complex interactions between this field and the bosons, described by the Higgs mechanism, gave mass to the latter. However, it is impossible to directly observe the Higgs field, since it is invisible and hypothesized to be totally massless. The only way to empirically validate the existence of the field is to collide subatomic particles at remarkably high velocities, which will cause a Higgs boson to flick out of the field in the same way that part of a wall will get chipped off whenever someone throws a rock at it. Since all quantum fields are associated with a certain particle (known simply as the quantum), evidence of the Higgs boson essentially serves as confirmation of the Higgs field. When the Large Hadron Collider at CERN finally detected the Higgs boson in the summer of 2012, physicists finally had, as cosmologist Michael Turner put it, an explanation for how mass came about in the physical universe.
(4) The masses of nuclei – or, more accurately, the quarks that constitute hadrons like protons or neutrons – are indeed attributable to their interactions with the Higgs field. But the three quarks in a hadron constitute only 0.2% of its mass, so it turns out that the Higgs field actually plays a relatively insignificant role in accounting for mass in space.
(5) What are the physical ramifications of this/what does this mean on a more scientific level? I spent at least five hours trying to search for an answer to this question on Google, but I came away empty-handed. Email me if you have any insights.