Fear of a Black Universe Read online

  A faithful picture of a quantum field is to imagine the field as the height of a blanket supported by oscillators (springs). At different points on the surface of the blanket the spring will vibrate differently. Now imagine that all these springs are connected to each other. Then the vibrational pattern of the blanket could be quite complicated. There are special vibrations of the springs that can oscillate in sync with each other. Let’s carry the analogy further and imagine that there is a mass on each spring. Straightforward spring mechanics tells us that the rate of vibration of the spring, its frequency, is proportional to the mass. The heavier the spring, the faster the spring bobs back and forth. So, when the field vibrates at the frequency equivalent to the mass of the electron, the electron can be created as a particle from the field’s sympathetic vibration, or resonance. The particle’s creation from its underlying field is analogous to Zen master Suzuki’s water droplet that emerges from the cosmic ocean.2 Likewise, particles are transient entities that could emerge and return back to their mother field. Where do these fields live? The electron field is omnipresent and like the electromagnetic field occupies space-time of the universe. De Broglie’s hypothesis, which we discussed, is realized because the vibrational standing wave pattern of the electron’s field can manifest itself as an electron particle: the particle is nothing but quanta of the electron’s field vibration.

  This leads to a new question about the rest of the matter around us—could it all be emerging from an excited field? We have a hint from de Broglie’s hypothesis that relates the mass of a quantum particle to its wavelength. Amazingly, all matter fields including the electron share exactly the same building blocks in that they are all fermionic fields, named after inventor Enrico Fermi. Fermions, the basic building blocks for all matter, include quarks—the building blocks of protons and neutrons—neutrinos, and other heavier and more exotic particles. They all have the key property that they refuse to occupy the same quantum state. This property is called the exclusion principle and was discovered by Wolfgang Pauli, who also discovered the particle called the neutrino. Fermion states are given by their position and spin. So, if a fermion is at a given position with, say, spin up, then another fermion with spin up can never occupy the same position. But because of the exclusion principle, if we continue to pile up fermions due to their exclusionary behavior, they will form atoms, molecules, and the various macroscopic forms of matter in our world.

  FIGURE 9: The depiction of the quantum field as a collection of oscillators that can resonate to create quanta of particles from the field’s vacuum state.

  Here is a story of blackness in physics. The book Atom and Archetype, which Chris Isham had introduced me to, includes letters exchanged by Pauli and Jung that reveal that the exclusion principle presented itself to Pauli in a series of dreams. Pauli had a reputation for being a harsh critic of other theorists and would swiftly catch mathematical errors and inconsistencies. He is famously known for humiliating those with bad ideas by saying, “Your theory is not even wrong.” In other words, a theory can be incorrect, but at least the process and intellectual sharpness in developing the theory can still be valid. Pauli’s statement implies a denigration of the theorist’s intelligence and process as being laughable. So, it would make some sense that he kept secret his interactions and dream analysis with Carl Jung. It’s especially ironic that the kernel of the exclusion principle came from dreams. Would he have been taken less seriously or shunned by other colleagues if they knew this?

  So, if all matter fields are fermions, what gives them their distinct flavor? In other words, what makes an electron different from a quark or a neutrino, given that they are all fermions? The quick answer is that fermion species can carry different types of charges (electric charge being one familiar example). We should return to a quick discussion of fermion field and see what it says about these differences. Let’s consider the electron field, whose electric charge sources an electric field that fills space. How does the electric charge relate to its parent fermion field? It so happens that the electric charge is beautifully encoded in the fermion field as a special phase of the field’s vibration. The important idea of phase is central to both wave and field properties. Imagine two boats rocking up and down due to the surface-of-ocean waves. If both boats were bobbing at the same frequency and their high and low points matched, they are said to be in phase. On the other hand, two identical waves can be out of phase if their positions do not exactly match up. Here’s an interesting fact: the phase of the electron field controls the value of its electric charge. Now there is no reason for the phase of an electron field at different locations to exactly match, much as rocking boats at different parts of a tumultuous sea would only be in phase by an unlikely coincidence. Nevertheless, experiments have revealed that the value of the electron’s charge is the same regardless of the location, on Earth, the moon, or anywhere. This means that the electron field has the same phase, like a couple of miraculous boats. But what prevents a physics demigod from making the phase of the electron in New York and Trinidad different, so that Trinidadians get more electric charge for their dollar? A special form of the principle of invariance comes to the rescue—this is famously known as local phase invariance.

  Quantum mechanics does allow our demigod to mess with the phases of fields at different locations, and this will problematize the fact that we see the same charges everywhere. But it so happens that there is a magical way to undo the damage the demigod can make to the phases. If we introduce a photon field to interact with the electron field the right way, then every time the demigod changes the phase of the electron, the photon field also makes a compensatory change in its phase so as to erase the change in the would-be difference of the electron’s charge. And this magically happens if the photon field interacts with the electron in a simple way.3 This type of invariance was invented by the genius Hermann Weyl, and he called it phase invariance, or more commonly gauge invariance or its German origin Eichinvarianz. Gauge invariance requires that the electron field interact with light and guarantees the universality of the electron’s charge!

  Now we can understand what makes the fermion matter fields all different from each other—it’s their charges, or phase symmetries, which turn out to be the organizing principle of the standard model of particle interactions. Once I tell you that the electron has a phase invariance, you can immediately write down the full electromagnetic theory, with the unique interaction between the electron and the photon. And it turns out, the same reasoning goes into determining the other two nuclear forces, the weak and strong forces, as they are simply applications of phase symmetries applied to electromagnetism. The phases of the weak and strong interactions have more symmetries and give more involved interactions between the force-carrying particles and the matter fields that carry the weak and strong charges with which the force-carrying particles interact, but all these forces strictly come from Einstein’s principle of invariance, this time applied to the phases of the fermion fields.

  Consider electrons in a star millions of light-years away from Earth. While there are many electron particles, there is only one electron field that they are born from. Those electrons, and the electrons that are in you and me, were created as quantum excitations from the same universal electron field in the early universe. In fact, every other particle, including quarks and neutrinos, in the universe are quanta that emerge from their corresponding field vibrations. It’s in this Suzuki sense that we are tethered to the fundamental fabric of the universe. All the particles that comprise us are quantum vibrations of the same quantum fields that extend across the universe. But does it end here? What is the relationship between space-time and the quantum fields that permeate it? What incited these quantum fields to generate the particles that occupy our universe to turn into stars, planets, and us? And why, since Dirac demonstrated that antimatter must have been created pairwise with all that matter, do we not see very much of it around?

  Underneath the answers to those
questions lies our third principle: emergence.

  5

  EMERGENCE

  A handful of elements from the periodic table come together to create living things like you and me. Yet, the elements themselves are lifeless. How does life emerge from these building blocks? This question is at the heart of emergence. The first two principles we discussed, invariance and superposition, combined to give us the quantum fields we recognize as the building blocks of matter and subatomic forces. Following Paul Dirac’s prediction of the positron, new symmetries in nature were discovered as shorter distance scales, and these new symmetries were experimentally probed with high-energy particle colliders. And these symmetries also functioned to specify the nature of the interactions that fields exhibited with other fields and their associated zoo of particles.

  Throughout the last century, physics has been dominated by the quest to identify the natures of those subatomic forces and a theory of everything that unifies them. The idea has been that one day we would be able to find all the fundamental building blocks of the universe, as well as the rules for their interactions. This approach is referred to as reductionism, and is essentially motivated by trying to figure out how to build the universe from the ground up. Superstring theory is an example of such a unified theory. In string theory, the basic building blocks are one-dimensional strings. However, even if we were able to discover such a unified theory, it isn’t clear that it would be able to explain phenomena such as life or consciousness. To the contrary: there’s a very good chance that the fundamental theory could not arise from a reductionist approach.

  So we are at a crossroads. On one hand, a major program of twentieth-century physics took us down the successful road of reductionism. The symmetries that were discovered informed us about the patterns and relationships between the elementary forms of matter and the precise ways that they interacted with each other. Indeed, the notion that what is fundamental became synonymous with unveiling more symmetries, at least to some leaders in physics, and that perspective played a prominent role in my own career. I was just starting my dissertation work using the exotic symmetries in superstring theory to solve some of the problems in early universe cosmology. We know from astrophysical observations that the universe is expanding. At the earliest stages of the universe’s history, its environment was exceedingly energetic, hot and dense—conditions not at all unlike those at a collision of particles in a collider like the Large Hadron Collider (LHC). So, from the patterns found in collider experiments, we expect that these symmetries generated by superstrings were activated in the very early universe, where superstrings are expected to be the key players. My thesis exported a special symmetry from string theory into cosmology, called target space duality, or T-duality, which treats the physics in a large region of space and a small region of space as being the same. So, as we approach the big bang singularity, where the universe approached microscopic distances, we could avoid the big bang singularity with T-duality. The dream was to use cosmology to test unified theories like string theory, or other approaches to quantum gravity. Superstring cosmology is still an important topic in cosmology, and I still devote some of my research efforts in this direction. So far, the expectation to unveil more symmetries at the shortest distance scales works theoretically.

  On the other hand, there were clear failures of the reductionist regime in particle physics. One of the most famous examples of emergence in quantum physics is superconductivity—really, it’s the poster child of emergence in physics. In 1911, Nobel laureate Heike Kamerlingh Onnes observed that when he lowered the temperature of a metal close to absolute zero, the electric current would flow with zero resistance. There was no reason to expect how and why the billions of electrons, which repel each other as well as experiencing impurities in the metal, should superconduct. After all, lowering the temperature does not seem to prevent the electrons from repelling each other or get rid of the impurities in the metal. Many great physicists, like Einstein, Schrödinger, Heisenberg, Lev Landau, and Feynman, worked on superconductivity. During this time, many thought that completely new physics was needed, perhaps a new law, to account for superconductivity. And it took forty-six years for the trio of John Bardeen, Leon Cooper, and John Robert Schrieffer (developers of the “BCS” theory) to show that good old quantum mechanics and electromagnetism were enough. Superconductivity doesn’t supplant them. It emerges from them.

  The Principle of Emergence: Systems with interacting elementary constituents can exhibit novel properties that are not possessed by the constituents themselves.

  The reason I am promoting the phenomenon of emergence to a principle is based on Einstein’s criteria for a principle, because, to borrow his words, “[A principle is realized by] perceiving in comprehensive complexes of empirical facts certain general features which permit of precise formulation.” What are the complexes of empirical facts in emergence that can transcend its context? There are many examples of disparate and seemingly unrelated physical and biological systems where we see emergence. Emergent behavior also happens in populations of living organisms. Groups of ants can collectively build a bridge of ants so that others can cross a barrier of water. The origin of life itself is argued to be an emergent phenomena. A unicellular bacteria has autonomous properties, such as motility, replication, and metabolism that its individual molecules, like proteins, do not exhibit.

  But what is at the heart of emergence? How does a system “know” to exhibit novel collective behavior? These are hard questions that are currently being researched, and there are some partial answers. A universal aspect of emergence is the relationships between the emergent system and the parts that make it up. Although the emergent property is novel relative to its constituents, there is an interdependence between the emergence and the constituents. For example, the system of atoms that gives rise to an emergent liquid property depends on the collective behavior of the individual atoms. However, in the solid state, the atoms are on average located in a repeating array, forming a large-scale crystal. A simple example of emergence can be seen right in front of your face.

  The renowned theoretical physicist Nigel Goldenfeld, who now directs an institute that focuses on finding links between emergence in physics and biology, has an experiment that we can all do to demonstrate an emergent phenomenon. Here is how it goes. First, push your hand forward in empty space. Second, get a chair and push the chair until it falls on the floor. The fact that the chair moved and fell on the floor is emergence at work.

  This might sound strange, but it’s true. When you moved your hand, it was interacting with the air, which is actually a fluid made up of air molecules. The chair, on the other hand, is a solid. The atoms of the fluid and the solid obey the same laws of atomic interactions, yet, despite the sameness of their atomic interactions, the solid state has new emergent laws of physics. That is, it has new long-range forces, such as a rigid elastic response from your hand pushing against it. The origin of these new forces in the solid state arises from the statistical properties, or collective behavior, of the billions of atoms. If we work at the level of the description of the solid, we can’t deduce what the underlying interactions of the atoms are. At the level of the solid state, all we can deduce is that the continuum description, rigidity, elasticity, and so on emerges from the collective behavior of the atoms.

  The same goes for superconductivity. What I find interesting in that story is how BCS hacked superconductivity, not just because it’s interesting science, but because it gives some guidance for current problems that we are trying to solve. After all, some of the problems that we consider to be impossible to solve have been around for a shorter period than superconductivity.

  I had the good fortune to hear some of the story of superconductivity directly from Leon Cooper, who was my first PhD adviser before I changed fields to quantum cosmology. During my first year of graduate school, I didn’t know who Cooper was, and no one told me that he had won the Nobel Prize. He had the flair of a Shakesp
earean actor, wore fine Italian suits, and sported shades on a well-groomed head of jet black, wavy hair. During our weekly departmentwide talk, where famous researchers would present their results, Cooper would sit at the front of the room and ask what seemed to be naive questions, the type a schoolchild would ask. And this was exactly the quality of mind that, among other things, enabled him to access the ingenuous insight that would crack the nearly fifty-year-old problem of superconductivity.

  Superconductivity was couched in the subfield of the physics of solids, known as solid-state physics.1 One of the leaders of the field, John Bardeen, who previously shared a Nobel Prize for the discovery of the transistor, had been tirelessly working on superconductivity for years with no luck. Bardeen was well aware of the decades of failed attempts to explain superconductivity, and he decided he had to get an outsider’s perspective and tools to bring new life to the problem. So, he sought out a theorist that had a fresh pair of eyes and wasn’t jaded by the biases that may be formed by experts in the field.