What Is the Measure of Nothingness? Infinity, Virtuality, Justice

Nothingness. The void. An absence of matter. The blank page. Utter silence. No thing, no thought, no awareness. Complete ontological insensibility. Shall we utter some words about nothingness? What is there to say? How to begin? How can anything be said about nothing without violating its very nature, perhaps even its conditions of possibility? Isn't any utterance about nothingness always already a performative breach of that which one means to address? Have we not already said too much simply in pronouncing its name? Perhaps we should let the emptiness speak for itself.

At the very least, listening to nothing would seem to require exquisite attention to every subtle detail. Suppose we had a finely tuned, ultrasensitive instrument that we could use to zoom in on and tune in to the nuances and subtleties of nothingness. [1] But what would it mean to zoom in on nothingness, to look and listen with ever-increasing sensitivity and acuity, to move to finer and finer scales of detail of...? Alas, it is difficult to conceive how one would orient oneself regarding such a task. What defines scale in the void? What is the metric of emptiness? What is the measure of nothingness? How can we approach it? [2]

On the face of it, these questions seem vacuous, but there may be more here than meets the eye. Consider, first, setting up the condition for the experiment: we begin with a vacuum. Now, if a vacuum is the absence of everything, of all matter, how can we be sure that we have nothing at hand? We'll need to do a measurement to confirm this. We could shine a flashlight on the vacuum, or use some other probe, but that would introduce at least one photon (quantum of light) onto the scene, thereby destroying the very conditions we seek. Like turning up the light to see the darkness, this situation is reminiscent of the mutually exclusive conditions of im/possibility that are at issue in Niels Bohr's interpretation of quantum physics.

Measurements, including practices such as zooming in or examining something with a probe, don't just happen (in the abstract)- they require specific measurement apparatuses. Measurements are agential practices, which are not simply revelatory but performative: they help constitute and are a constitutive part of what is being measured. [3] In other words, measurements are intra-actions (not interactions): the agencies of observation are inseparable from that which is observed. Measurements are world-making: matter and meaning do not preexist, but rather are co-constituted via measurement intra-actions.

If the measurement intra-action plays a constitutive role in what is. measured, then it matters how something is explored. In fact, this is born out empirically in experiments with matter (and energy): when electrons (or light) are measured using one kind of apparatus, they are waves; if they are measured in a complementary way, they are particles. Notice that what we're talking about here is not simply some object reacting differently to different probings but being differently. What is at issue is the very nature of nature. A quantum ontology deconstructs the classical one: there are no pre-existing individual objects with determinate boundaries and properties that precede some interaction, nor are there any concepts with determinate meanings that could be used to describe their behavior; rather, determinate boundaries and properties of objects-within phenomena, and determinate contingent meanings, are enacted through specific intra-actions, where phenomena are the ontological inseparability of intra-acting agencies. Measurements are material-discursive practices of mattering. And phenomena are contingent configurations of mattering. At the heart of quantum physics is an inherent ontological indeterminacy. This indeterminacy is only ever partially resolved in the materialization of specific phenomena: determinacy, as materially enacted in the very constitution of a phenomenon, always entails constitutive exclusions (that which must remain indeterminate). Now, it's one thing for matter to materialize differently according to different measurement practices, but is there some way in which the specificity of measurement practices matters if we're measuring the void, when the void is presumably nothing?

Complementarity. [4] Contingency. Indeterminacy. Inseparability. Any attempt to say something, anything, even about nothing, and we find ourselves always already immersed in the play of quantum in/determinacy.

Questions of the nature of measurement-or, more broadly, intra-actions-are at the core of quantum physics. Intra-actions are practices of making a difference, of cutting together-apart, entangling-differentiating (one move) in the making of phenomena. Phenomena –entanglements of matter/ing across spacetimes-are not in the world, but of the world. Importantly, intra-actions are not limited to human-based measurement practices. Indeed, the issues at stake in exploring the vacuum are not merely questions of human exploratory practices in the quest for knowledge, but are thought to be ontologically poignant matters that go to the very nature of matter itself.

When it comes to the quantum vacuum, as with all quantum phenomena, ontological indeterminacy (not epistemological uncertainty) is at the heart of (the) matter... and no matter. Indeed, is it not rather the very nature of existence that is at issue, or rather nonexistence, or rather the conditions of im/possibilities for non/ existence?... Or maybe that's the very question the vacuum keeps asking itself. Maybe the ongoing questioning of itself is what generates, or rather is, the structure of nothingness. The vacuum is no doubt doing its own experiments with non/being.[5]

In/determinacy is not the state of a thing, but an unending dynamism. The play of in/determinacy accounts for the un/doings of no/thingness. From the point of view of classical physics, the vacuum has no matter and no energy. But the quantum principle of ontological indeterminacy calls the existence of such a zero-energy, zero-matter state into question, or rather, makes it into a question with no decidable answer. Not a settled matter, or rather, no matter. And if the energy of the vacuum is not determinately zero, it isn't determinately empty. In fact, this indeterminacy is responsible not only for the void not being nothing (while not being something), but it may in fact be the source of all that is, a womb that births existence. Birth and death are not the sole prerogative of the animate world. "Inanimate" beings also have finite lives. "Particles can be born and particles can die," explains one physicist. In fact, "it is a matter of birth, life, and death that requires the development of a new subject in physics, that of quantum field theory...Quantum field theory is a response to the ephemeral nature of life." [6]

Quantum field theory (QFT) was invented in the 1920s, and its development continues to this day. [7] It is a theory that combines insights from the classical field theory of electromagnetism (mid-nineteenth century), special relativity (1905), and quantum mechanics (1920s). QFT takes us to a deeper level of understanding of the quantum vacuum and its implications. According to QFT, the vacuum can't be determinately nothing because the indeterminacy principle allows for fluctuations of the quantum vacuum. [8] How can we understand "vacuum fluctuations"? First, it is necessary to know a few things about what physicists mean by the notion of a field.

A field is something that has a physical quantity associated with every point in spacetime. [9] Let's consider a very simple example of a field: an infinite drumhead that can be assigned a time-varying displacement value at each point in space. If the drumhead is not vibrating, then it is completely flat and has the same value everywhere–let's call this the zero value, corresponding to no displacement. If a drummer now taps the drumhead, it vibrates, and waves of energy flow outward from where it is tapped. In this case, the field values vary in space and time as the displacement wave moves across the surface. Thus far we have a classical field theory, with a perfectly still drumhead representing the classical vacuum (or zero-energy state), and a vibrating drumhead representing a nonzero-energy state. Now we add quantum physics. Quantizing the field means that only certain discrete vibrational states exist. (If you're not used to thinking about different vibrational modes of a drum, it may be easier to visualize a stringed instrument with only a discrete set of standing waves, or harmonics, possible.) Now we add special relativity, in particular, the insight that matter and energy are equivalent (E = mc2 ). Since vibrations of the field carry energy, and only a discrete set of energy states can exist, and a mass value can be assigned to each energy state, then we can see that a field vibrating at a particular frequency or energy is equivalent to the existence of particles of matter with a particular mass. This correspondence between quantum particles and quantized fields is the cornerstone of QFT.

Now let's return to our question: what is a vacuum fluctuation? Using the drum example, the quantum vacuum would correspond to a state where the average value of the displacements is zero everywhere, that is, there's no drummer tapping the drum. And yet the stillness of the drumhead is not assured, or rather, there is no determinate fact of the matter as to whether or not the drumhead is perfectly still, even in the absence of all external disturbances, including drumming. In other words, vacuum fluctuations are the indeterminate vibrations of the vacuum or zero-energy state.

Putting this point in the complementary language of particles rather than fields, we can understand vacuum fluctuations in terms of the existence of virtual particles: virtual particles are quanta of the vacuum fluctuations. That is, virtual particles are quantized indeterminacies-in-action. Admittedly, this is difficult to imagine, even more so than the account that is usually given. According to the usual lore, virtual particles are very short-lived entities that come into and out of existence so quickly that they can't be detected, and hence are not real, not in the same sense as actual particles. But this way of putting it entails the wrong temporality and ontology. Virtuality is not a speedy return, a popping into and out of existence with great rapidity, but rather the indeterminacy of being/nonbeing, a ghostly non/existence. In other words, the common portrayal of quantum vacuum fluctuations as an arena of covert virtual activity-particle-antiparticle pairs rapidly coming into and out of existence, getting away with something for nothing if only it happens fast enough that we can't know about it, that is, that we can't actually count any divergences from pure nothingness, like a banker playing fast and loose with accounts, taking money out and paying it back before anyone notices anything missing from the ledger-is of questionable validity. The void is not a financial wheeler-dealer, an ethically questionable, shadowy character. [10] Rather, the void is a spectral realm with a ghostly existence. Not even nothing can be free of ghosts. [11] Virtual particles do not traffic in a metaphysics of presence. They do not exist in space and time. They are ghostly non/existences that teeter on the edge of the infinitely thin blade between being and nonbeing. They speak of indeterminacy. Or rather, no determinate words are spoken by the vacuum, only a speaking silence that is neither silence nor speech, but the conditions of im/possibility for non/existence. There are an infinite number of im/possibilities, but not everything is possible. The vacuum isn't empty, but neither is there any/thing in it. Hence, we can see that indeterminacy is key not only to the existence of matter but also to its nonexistence, or rather, it is the key to the play of non/existence.

Virtual particles are not in the void but of the void. They are on the razor edge of non/ being. The void is a lively tension, a desiring orientation toward being/becoming. The vacuum is flush with yearning, bursting with innumerable imaginings of what could be. The quiet cacophony of different frequencies, pitches, tempos, melodies, noises, pentatonic scales, cries, blasts, sirens, sighs, syncopations, quarter tones, allegros, ragas, bebops, hiphops, whimpers, whines, screams, are threaded through the silence, ready to erupt, but simultaneously crosscut by a disruption, dissipating, dispersing the would-be sound into non/being, an indeterminate symphony of voices. The blank page teeming with the desires of wouldbe traces of every symbol, equation, word, book, library, punctuation mark, vowel, diagram, scribble, inscription, graphic, letter, inkblot, as they yearn toward expression. A jubilation of emptiness.

Don't for a minute think that there are no material effects of yearning and imagining. Virtual particles are experimenting with the im/possibilities of non/being, but that doesn't mean they aren't real, on the contrary. Consider this recent headline: "It's Confirmed: Matter Is Merely Vacuum Fluctuations." [12] The article explains that most of the mass of protons and neutrons (which constitute the nucleus and therefore the bulk of an atom) is due not to its constituent particles (the quarks), which only account for 1 percent of its mass, but rather to contributions from virtual particles. Let's try to understand this better. Consider an individual particle. According to classical physics, a particle can stand on its own. We simply place a particle in the void-a Democritean delight. But according to QFT, a physical particle, even a (presumedly) structureless point particle like an electron, does not simply reside in the vacuum as an independent entity, but rather is inseparable from the vacuum. The electron is a structureless point particle "dressed" with its intra-actions with virtual particles: it intra-acts with itself (and with other particles) through the mediated exchange of virtual particles. (For example, an electron may intra-act with itself through the exchange of a virtual photon, or some other virtual particle, and that virtual particle may further engage in other virtual intra-actions, and so on.) Not every intra-action is possible, but the number of possibilities is infinite. In fact, the energy-mass of this infinite number of virtual intra-actions makes an infinite contribution to the mass of the electron. But how can this be when the mass of a physical electron is clearly finite (indeed, it's pretty darn small from our perspective)? The explanation physicists give is that the lone ("bare") point particle's contribution is infinite as well (infinitely negative due to the negative charge of the electron), and when the two infinities (that of the bare electron and that of the vacuum self-energy) are properly added together, the sum is a finite number, and not just any finite number but the one that matches the empirical value of the mass of the electron! [13] In other words, an electron is not just "itself" but includes a "cloud" of an indeterminate number of virtual particles. All this may seem like a farfetched story, but it turns out that vacuum fluctuations have direct measurable consequences (e.g., Lamb shift, Casimir effect, the anomalous magnetic moment of the electron). [14]

So even the smallest bits of matter are an enormous multitude. Each "individual" is made up of all possible histories of virtual intra-actions with all Others. Indeterminacy is an un/doing of identity that unsettles the very foundations of non/being. Together with Derrida we might then say: "identity... can only affirm itself as identity to itself by opening itself to the hospitality of a difference from itself or of a difference with itself. Condition of the self, such a difference from and with itself would then be its very thing... the stranger at home." [15] Individuals are infinitely indebted to all Others, where indebtedness is not about a debt that follows or results from a trans/action, but rather, a debt that is the condition of possibility of giving/receiving. Ontological indeterminacy, a radical openness, an infinity of possibilities, is at the core of mattering. How strange that indeterminacy, in its infinite openness, is the condition for the possibility of all structures in their dynamically reconfiguring in/stabilities. Matter in its iterative materialization is a dynamic play of in/determinacy. Matter is never a settled matter. It is always already radically open. Closure can't be secured when the conditions of im/ possibilities and lived indeterminacies are integral, not supplementary, to what matter is. Nothingness is not absence, but the infinite plentitude of openness. Infinities are not mere mathematical idealizations, but incarnate marks of in/determinacy. Infinities are a constitutive part of all material "finities," or perhaps more aptly, "af/finities" (affinities, from the Latin, "related to or bordering on; connection, relationship"). Representation has confessed its shortcomings throughout history: unable to convey even the palest shadow of the Infinite, it has resigned itself to incompetence in dealing with the transcendent, cursing our finitude. But if we listen carefully, we can hear the whispered murmurings of infinity immanent in even the smallest details. Infinity is the ongoing material reconfiguring of nothingness; and finity is not its flattened and foreshortened projection on a cave wall, but an infinite richness. The idea of finitude as lack is lacking. The presumed lack of ability of the finite to hold the infinite in its finite manifestation seems empirically unfounded, and cuts short the infinite agential resources of undecidability/ indeterminacy that are always already at play. Infinity and nothingness are not the termination points defining a line. Infinity and nothingness are infinitely threaded through one another so that every infinitesimal bit of one always already contains the other. The possibilities jor justice-to-come reside in every morsel of finitude.

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"What Is the Measure of Nothingness? Infinity, Virtuality, Justice" was firstly commissioned as part of "100 Notes - 100 Thoughts" on the occasion of dOCUMENTA 13, 2012 and published in English and German by Hatje Cantz Verlag.