The more science helps us explain the world, the less we need our imaginations. We strip reality of everything that is uncertain and intangible. Nevertheless, fantasizing is still something worthwhile—so let’s embark on a bold journey to the very edge of modern physics.
The World Has Become Boring to Us.
Just a few centuries ago, local villages and forests were teeming with mystical beings: house spirits and water nymphs, banshees, ghouls, and ghosts, in addition to various minor deities. Far-off lands were thought to be inhabited by bizarre creatures such as monopods and dog-headed men, and sailors returning from distant voyages spoke of encountering mermaids and monstrous krakens—provided they hadn’t fallen off the edge of the earth. The inferno of hell raged beneath our feet, while the heavens above us—divided into sublunar, superlunar, and ethereal realms—were vibrantly inhabited by the spirits of our departed, fairies, angels, archangels, seraphim, celestial thrones, and God knows who or what else. Within us, in the profound depths of our souls, flickered the faint echoes of divine wisdom and subtle whispers from muses and demons.
What a fantastical world it once was!
But now? There’s nothing but atoms in a void. How utterly mundane . . .
Dreamers among Accountants
The longing persists, of course. A handful of determined cryptozoologists still continue to debate the existence of elusive creatures lurking in mountains and lakes, while a small cadre of visionary archeologists still ponder the alleged remnants of ancient, technologically advanced civilizations. But these are just mere shadows of the former glories of human imagination. Successive centuries of hard empiricism have made it so that few today have the courage to publicly deny the prevailing belief that everything is ultimately made up of just a few basic types of subatomic particles, arranged in space that scintillates with activity but is nevertheless basically void. No gods, spirits, souls, creatures, or heavens. It’s as if our current view of the universe were meticulously crafted by an accountant—precise and ordered, devoid of mystical enchantment.
However, within the scientific community, there exists a group of enthusiasts who still continue to stoke the fires of our collective imagination. These are the physicists—particularly those who venture beyond the boundaries of solid observations and revel in the boundless possibilities afforded by mathematics. Particle physicists, with their tales of plectons, sfermions, curvatons, inflatons, pomerons, and meson molecules, are delving into realms that no microscope or telescope has ever glimpsed. Similarly, when astrophysicists tire of studying conventional stars, they turn their attention to hypothetical exotic celestial bodies like preonic, bosonic, and strange stars, or even to the theoretical concept of white holes. A particularly adventurous group of cosmologists has, over recent decades, proposed so many mathematical models for the proliferation of our universe that we’ve moved beyond talking about a multiverse of universes and are instead now considering multiverses of multiverses.
These are, of course, sensible scientific hypotheses—at least to the extent necessary to justify grant applications. They usually draw a tenuous link connecting these imaginative concepts to the reality we know. And so, in fact, these are physical fantasies rather than metaphysical ones. A person longing for the good old times may therefore feel some disappointment: is the best we can do today really just a slightly different kind of particle or a quite strange kind of star? Conversely, truly metaphysical fantasies—talking about the existence of completely different realms of existence, such as a universe of souls, hellish abysses, or a world of gods—struggle to gain a foothold in serious modern discourse.
But is there a middle path? A way to explore reality imaginatively yet concretely, one that does not offend the twenty-first-century rationalist? Indeed, there is. The method involves venturing into the perilous world of metaphysics—albeit beginning within the established boundaries of science (to maintain subtlety) and infusing it all with a touch of philosophical elegance. This way, our inner “accountant” will not panic, but we can also indulge the whims of the free-spirited dreamer that lingers inside us.
Made of Foam
Let’s begin cautiously, stepping just a tiny bit beyond the boundaries of established science. There was a time when the notion that the world has a fractal structure was quite popular. This idea proposed that the universe’s structure at one scale repeats itself at other scales, larger or smaller. This concept originated from the planetary model of the atom, which seemed to suggest that the atom is like a small solar system. And vice versa: electrons are like small planets orbiting around the nucleus. Someone might even ask: Are there maybe aliens living on those electrons?
However, this planetary model was ultimately recognized as an oversimplified interpretation. Modern understanding reveals that atoms don’t actually mirror the solar system, as it had once seemed to early physicists. Despite this, the allure of such comparisons persists. For instance, on the internet one can come across images juxtaposing a vividly colored map of the universe with a similarly colored image of brain tissue, insinuating that the cosmos basically mirrors the brain. In reality, this is merely a strained visual analogy between two appropriately selected representations of objects that are not really similar at all. Nevertheless, the underlying concept, while speculative, isn’t entirely out of the realm of possibility.
Let’s start by exploring how far we could go if we ventured “up” to larger structures or “down” to smaller ones. According to mainstream science, at the largest scale, the universe is homogeneous—it extends perhaps infinitely in all directions, but with consistent properties. So, out of the clusters and superclusters of galaxies, on higher scales a cosmic foam emerges. But this same foam is everywhere—that means there are no larger, supercosmic structures made of differently shaped foam. If we look “downward,” on the other hand, we eventually encounter a realm of sameness and uniformity: elementary particles, like electrons, are thought to lack any detail. They don’t have any gears, threads, or bubbles inside them.
However, if this is what mainstream science concludes, it is not because an absence of structure at these extreme scales has been observed, but rather because these scales remain as-yet unobserved. History offers optimistic hope for those seeking cosmic order. Everywhere we’ve looked so far, we’ve discovered new structures and phenomena. There are theoretical reasons why a homogeneous universe and structureless particles suit physicists’ models, and some even argue that these aspects are derived from the very principles of physics. But fear not: physicists are inventive by nature. Should observations reveal supercosmic structures or sub-electronic details, a fitting and elegant theory will surely emerge to explain them.
Suppose we are intrigued by the “fractal model” of the universe, hypothesizing the existence of miniworlds hidden deep within atoms and vast superworlds of which our cosmos is but a component. How can we sensibly fantasize about this?
We have several rational starting points. First, the universe is never perfectly fractal: at least not like mathematical fractals, which often replicate themselves with exact precision on various scales. We shouldn’t expect to find miniature planets orbiting inside electrons. Second, the universe does evidently favor certain motifs and patterns, recurring across vast scales. Vortices and spirals are a common stylistic element, observable from the microscopic to the galactic scale. The universe also shows a penchant for repeated branching, seen in microscopic rock fractures, lightning patterns, and river networks on continents. However, it seems to shy away from straight lines and smooth surfaces—these forms are rare, and, when they do occur, they usually exhibit various small imperfections.
There are also subtler themes that might easily get overlooked. Consider this one: a large, relatively uniform space, with most of the interesting things occurring on its thin boundary. Planets follow this pattern, as do stars and even magma chambers—it is on their walls that the most interesting minerals are formed, while the inside is a fairly uniform soup of molten rock. In a flatter context, this motif also recurs in oceans, lakes, and puddles, where biodiversity thrives mostly at the edges, not in the expansive middle. There’s even a one-dimensional expression of this cosmic tendency: long periods of time where little happens, punctuated by brief, intense episodes, when everything seems to happen all at once. “War is long periods of boredom punctuated by moments of sheer terror”—this is an adage often attributed to war correspondents from World War I, which reflects the same idea.
For those who delight in populating the unexplored realms of the cosmos with imaginative beings, the key is to remain observant of various leitmotifs of this kind.
Law, Chaos, and Rebels
Here’s another example of something that essentially could be the case but already pushes us well beyond the realms of established science. Physics is underpinned by fundamental laws that are generally accepted to be universally applicable. However, that is really just a first hypothesis. Scientists have come to recognize that, under extreme conditions, these laws could possibly diverge slightly or even get turned upside-down. Go far enough back in time—contemporary cosmology suggests—and the normal forces binding matter today might turn into something completely different. Go back even further, and the very identities of elementary particles might become blurred, and who knows if the laws of spacetime itself might not break down.
While most mainstream physicists steer clear of such speculative territories, there fortunately are some more audacious ones—in addition to throngs of philosophers, of course, unburdened by concerns for protecting their scientific reputation. Let’s try following along with them for a bit, as they present a rather intriguing perspective.
If the laws of physics can change or warp, is it possible for them to completely vanish? Perhaps our universe originated from chaos, where no governing laws applied? This idea, once entertained by the Greeks, differs from the Christian notion of creation out of nothingness; instead, here the cosmos is thought to have emerged out of primordial chaos. The Greeks contemplated a universe orchestrated by a demiurge—a kind of artistic director of the cosmos. Nowadays, in our current understanding, more appreciative of self-organization, we might prefer the notion that the universe itself self-assembled out of chaos. It’s something akin to the kind of spontaneous order that emerges at a bustling fish market just before the holidays—a scene I’ve witnessed firsthand, lending this theory a hint of metaphysical credibility.
This presents an intriguing prospect: what if the laws of nature are not really rigid rules but rather conventions or even habits? This isn’t as far-fetched as it might sound—many seemingly “designed” aspects of nature are actually products of spontaneous emergence. The atoms in a crystal, for instance, all lined up as orderly as soldiers in a parade, are not arranged in this way by some demanding sergeant, but naturally find a way to become aligned in harmony.
If the “laws of physics” are truly the result of spontaneous self-organization, they might not be universally applicable, without exception. Particles that are somehow kept sufficiently well isolated (much like a child raised by wolves) might not adhere to any general laws. There’s also room for defiance: a rebellious electron might veer left in a magnetic field instead of right. Imagine whole colonies of such dissenting particles, establishing communes where conventional laws like energy conservation are disregarded.
Of course, this all sounds like playful speculation, but a more cautious and serious interpretation is possible. Laws of physics that emerged through self-organization might vary across different regions of the cosmos. A good analogy can again be found in crystallization: when a hot soup of atoms solidifies into a crystal, adjacent regions can arrange themselves differently, forming distinct patterns, resulting in a rock composed of various mineral grains of differing shapes and orientations.
If physical laws themselves crystallized out of more primitive chaos, different cosmic regions might have slightly different or even wholly unique sets of laws. Physicists have long entertained a milder version of this hypothesis: every so often they publish an article confirming that the stars and galaxies in distant cosmic regions seem to exhibit familiar behavior, and so the properties of particles there must be quite similar to ours. For now, the universe seems to be homogeneous.
However, differing particle parameters are just the tip of the iceberg. In the boldest version of this theory, all forms of order are the result of spontaneous self-organization. Perhaps the organization of primal energy into convenient packets called particles is just one of these local conventions, whereas far-flung regions of space are still seething with primordial chaos? Maybe our cosmos itself is just a drop of order amidst an ocean of chaos, and a hypothetical traveler venturing beyond our known cosmic horizon would watch in horror as all forms of order and regularity, including mathematics and logic, gradually fade away.
The World on a Pin
My, how far we have wandered . . . The next, third example leads us fully into the territory of metaphysics. But let’s start, again, with a few reasonable questions about the basic notions of physics.
Democritus of Abdera posited that the universe consists solely of atoms and voids. Fast forward twenty-five hundred years, and we’ve progressed slightly from that, now saying that the universe only consists of elementary particles and spacetime, supplemented by an array of types of fields. But what exactly is an elementary particle? What is a field? What is spacetime?
These questions can be answered philosophically, but it’s more interesting to have a look into the physics textbooks, especially at the university level. A deep dive into quantum field theory or relativistic cosmology reveals that concepts like “particle,” “field,” or “space” are defined there in purely mathematical terms, by means of such concepts as “operator,” “solution,” or “symmetry group.” The straightforwardness of this is truly interesting: a particle, for example, is not defined as “a small portion of matter that can be mathematically described by a certain operator.” Rather, it’s simply defined as an “operator” (or a “vector,” depending on the approach). Physics doesn’t have precise definitions for “portion” or “matter,” but it does have them for such terms as “vector” or “complex plane.” Moreover, mathematics—as is its nature—gives physicists the ability to calculate various things, allowing theorists to tell experimentalists that, after conducting experiment “x” on their instruments, the number 1374 will appear. This is a powerful argument in favor of the mathematization of physics.
This notion is both fascinating and philosophically unsettling. If a “particle” is fundamentally a mathematical object, and I, myself, am composed of particles, does that make me a mathematical object, too? The typical, reassuring response goes like this: relax, the world is obviously the world, and we are merely describing (or “representing”) it using mathematical objects. The world isn’t inherently mathematical; it’s simply mathematizable: it lends itself well to being depicted through mathematics. The world is also “pastelizable,” capable of being beautifully rendered in pastels, for instance, and also moderately “limerickable,” or amenable to being expressed through limericks. However, even when one has longer conversations with physicists, particularly those focused on quantum mechanics, quarks, and the cosmos, it’s practically impossible to tease out anything non-mathematical from their description of the world. To them, the suggestion that limericks and pastels are in any way on the same plane as mathematics might provoke anything from irritation to downright indignation. What’s more, physicists’ “particles” and “spacetimes” behave in ways that are virtually inconceivable in the tangible world, yet these behaviors seem to be perfectly comprehensible to mathematicians. It is far from straightforward to identify what this “real world,” which mathematics is thought to merely represent, actually looks like.
Let’s consider what all this implies. No answer is truly reassuring. The “conservative” version—that a particle is still just a particle and mathematics is just a tool to describe it—also opens up a can of worms. What does it really mean that a particle is just a particle? What exactly is this “particle”? Is it a tiny sphere? A cloud? A dot? A wave? And what is it made of? Matter? Energy? And what is this “energy,” anyway? Basic physical concepts are just as elusive and incomprehensible as basic mathematical concepts. When we try to properly imagine the world, it eludes us, and we are left with naïve visual metaphors of what “spacetime” and “particles” are like: endless sheets of graph-paper and tiny fireflies. Yet, if we give any credence to mathematics, the world doesn’t resemble this at all. But then what is its true nature?
If we align ourselves with the “mathematicists,” things seem even bleaker. What would it truly mean to claim that the world is mathematics? Consider this helpful analogy illustrating the magnitude of the metaphysical dilemma we face: the number pi extends infinitely—3.14159265 . . . and so on. Because it’s an infinitely long sequence, and the digits are arranged in every conceivable order, somewhere within it lies a series of digits encoding my birth date. What is more, we can be certain that the entire Bible, if translated into a numerical language (e.g., “a” is 00, “b” is 01, etc.), is even embedded somewhere within the digits of pi. If the world is indeed a mathematical object, it’s like a sequence of digits but without its “real” counterpart.
So, is the entire cosmos, including all its events, embedded in an immutable, eternal matrix of mathematical structures, interwoven by a web of logical relationships? The thought that I am no different from a number sequence is repugnant to me. Intuition tells us the world must be something more than this. Look around—the world is unfolding; things are really happening! Yet, to a mathematical physicist, this poses no issue. If time is merely another numerical parameter in the physical world, then even its passage is just an illusion of our minds. The world isn’t actually unfolding—it’s really a four-dimensional (three spatial and one temporal) construct made up of diverse vectors, operators, groups, and sets, anchored in a universe brimming with all possible such constructs, much like a butterfly pinned in a display. Ultimately, everything that exists is essentially no different from an equilateral triangle (which simply exists, by virtue of the laws of pure form)—albeit with a bit more complexity.
Take Heart!
These forays to the edges of modern physics only partly quench our thirst for profound metaphysical exploration. Yet, before one embarks on a Himalayan expedition, it’s a good idea to do some training in the foothills. Even there we can enjoy a gulp of fresh air and face the risk of a twisted ankle—experiences which we won’t ever have in the concrete world of twenty-first-century scientistic metaphysics. The latter really isn’t metaphysics at all, because, to deserve that title, it would have to transcend physics, even if only slightly.
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