Fear of a Black Universe

by Stephon Alexander

  There is a realist interpretation that does this, the de Broglie–Bohm pilot wave. In the de Broglie–Bohm theory there is no superposition in the wave function, but a particle and an invisible wave that propagates through the double slit. This electron surfs the contours of the wave and ends up tracing out the interference pattern of the wave. This de Broglie–Bohm interpretation still uses the Schrödinger equation but trades off the probability weirdness for another kind of weirdness, which allows for nonlocal interactions between physical objects. In the de Broglie–Bohm theory, the wave can cause faster-than-light correlations between different electrons. If the wave changes in one region, an electron motion will be instantaneously affected at a distant region.

  FIGURE 7: The double slit experiment as represented by the de Broglie–Bohm pilot wave theory. The lines that emanate from the two slits are the trajectories of the electrons along the contour of the nonlocal quantum potential surface.

  Niels Bohr and his followers rejected realism and actually formulated quantum mechanics, the form that is taught in most textbooks, to avoid asking questions about the electron’s reality when it’s not being observed. Some such as Werner Heisenberg and Born even questioned the existence of particles until an interaction takes place. Influenced by Eastern philosophy such as Buddhism and Taoism, Bohr believed that our classical experience and perceptions were incompatible with the intrinsic duality that quantum entities possessed. According to Bohr, quantum entities possess pairs of contradictory qualities, such as wave and particle, energy and time, electric and magnetic, spin up and spin down. In Taoism the yin and yang represent contradictory or opposing qualities that coexist to describe the whole. Likewise, the whole electron possesses both the contradictory wave and particle properties at the same time. It is through our macroscopic measuring devices that we see either the particle or the wave properties revealed, and not both. Bohr elevated this duality to a principle he called complementarity.

  FIGURE 8: A visual representation of complementarity. There appears to be two independent images. Upon closer inspection, the boundaries of both images define each other.

  Some of Bohr’s brilliant young followers incorporated his complementarity principle into the actual mathematical formalism of quantum theory. The Nobel Prize was awarded to a young Werner Heisenberg, who formulated the uncertainty principle, which is rooted in complementarity. To see this a bit more clearly let’s combine Bohr’s wave-particle complementarity with the superposition principle to see how uncertainty follows naturally. According to the superposition principle, simple periodic waves of different frequencies can be added up (superposed) to give a more complicated wave. I can add up many periodic waves of differing frequencies to give a pulse, which approximates a particle like the electron. A quantum state described by a wave with definite frequency is actually the same as a particle with a definite velocity. This happens because the speed of a periodic wave is proportional to how rapidly it oscillates—its frequency. And according to the superposition principle it takes a very large superposition of many different velocity states to approximate a state of definite position of a particle.

  This feature of duality and uncertainty marks a profound difference between the classical and quantum worlds. In classical systems, the dynamics are given in pairs of physical quantities, for example, as we discussed position and momentum. These dual pairs come together to form phase space, and in principle we can know everything about the position and momentum at the same time with complete accuracy. On the other hand, in quantum mechanics we can only know one of the quantities with precision, at the expense of randomizing the other. The key idea is that dual qualities like position and momentum simply and inevitably disrupt each other’s certainty.

  Heisenberg came up with a thought experiment, the Heisenberg microscope, to highlight this compromise. He imagined that if we observe an electron, light has to bounce off it, exchanging a definite amount of momentum, which will change the electron’s trajectory, hence randomizing its subsequent position. Consider a state with a unique definite frequency. I ask you, where is the wave? If I pick a point on the wave, it looks exactly the same as any other point if I shift along by one complete cycle, so any point on the wave is not a unique position. Therefore, the specific location of the wave is indeterminate. A perfectly periodic wave is everywhere! Now imagine a pulse, similar to what we see on the devices that measure your heartbeat. The position of the pulse is located where the pulse is highest in height. A pulse is a wave that is very localized in space. However, the frequency of a pulse is indeterminate because a frequency is defined to be a quantity that depicts how often a wave repeats itself in a given amount of time. The singular pulse only repeats itself once. So, a periodic wave has a definite frequency but an indefinite position. And a pulse (now think of it as a particle) has a well-defined position but an indefinite frequency. There is a tradeoff. Quantum states that are localized in space are indefinite in their momentum, and those with precise momentum have delocalized in space.

  Einstein was vehemently against the idea that quantum mechanics, and so nature, was fundamentally operating on chance. He famously said, “God does not play dice,” reflecting his realist stance on physics. Bohr responded, “Don’t tell God what to do.” Despite the witticisms and counterarguments, Einstein persisted in disagreeing with Bohr and his followers and set out to find the death blow to the anti-realism of quantum mechanics. Einstein teamed up with his own duo of young researchers, Boris Podolsky and Nathan Rosen. Together, they wrote a paper containing what is known as the EPR paradox. EPR showed that special states exist in quantum mechanics such that two particles can have opposing features; these are called entangled states. A version of this thought experiment involved a pair of photons that is created by the decay of a particle at rest. If the photons start out in a spin-zero state and fly off in opposite directions at astronomical distance, the measurement of the spin of one photon will predict with 100 percent probability that the other spin has to be opposite, because the photons are in a spin-zero entangled state. The other spin will be communicated instantaneously. EPR coined this as “spooky action at a distance,” and it was seen to be in opposition to the fact—a critical feature of Einstein’s special theory of relativity—that no signal can travel faster than the speed of light.

  Ironically for Einstein, what was intended to be a potential death blow to the quantum turned out to be a brilliant prediction when it was experimentally observed. These experiments revealed that quantum particles exhibit nonlocal effects. For example, measuring the polarization of a photon instantaneously determines the spin of its entangled pair. Simply put, nature is nonlocal. The other question was whether the spin was real before it was measured—that is, whether it was determined by what is called a hidden variable of the system, rather than being a random result of the process of measurement, as Bohr and his followers believed. According to the groundbreaking proof of Irish physicist John Bell, this nonlocality in quantum mechanics has to be the result of the action of a hidden variable. Interestingly, Bell used the de Broglie–Bohm interpretation, based on the yet-to-be-observed pilot waves, as an example of a nonlocal hidden variable theory.

  All of this points to a fundamental tension in quantum mechanics. At one level quantum mechanics is completely deterministic. According to the Schrödinger equation, if one knows the initial state of the wave function at some initial time, then one knows exactly what the state will be at a later time. However, because the wave function represents a superposition of possible outcomes—it’s a probability distribution—then if a measurement is made, we will see only one of such outcomes. In other words, an observation collapses the function in an indeterministic way. This tension was rigorously investigated by John von Neumann, one of the great mathematicians of the century. Von Neumann, along with Eugene Wigner and Wolfgang Pauli, argued that the measurement problem required a resolution that would go beyond the current formulation of the theory. They even went so far as to arg
ue that consciousness itself played a role in collapsing the wave function. To the contrary, Bohr and his followers asserted that there was no problem based on complementarity, and they embraced the inherent contradiction in quantum mechanics. According to Bohr, there is a sharp divide between the quantum world and classical measuring device, and the instantaneous collapse of the wave function is a feature of this divide. Decades of Nobel Prize–winning physicists have landed on opposing sides of the measurement problem.

  Despite these ongoing and unresolved issues in quantum mechanics, its formulation as a probabilistic theory where superpositions can collapse upon measurement has passed a century of precision experiments and applications. However, as we shall see, these issues will come back to haunt us when we connect quantum mechanics to gravity and the early universe.

  We’ll get back to that. After all, we’ve still got one more physical principle to go. But before we do, let’s explore what happens when we attempt to merge the invariance with the quantum principle.

  4

  THE ZEN OF QUANTUM FIELDS

  Most mornings as a kid I would hear about my mother’s experiences as a night-shift nurse at Montefiore Hospital in the Bronx. While she was getting me and my brothers ready for school, she would tell us about some of her patients and their various medical predicaments. These stories ignited big questions about my own mortality, about the fact that my time on this planet was finite and even uncertain. In hindsight, this was a driving force behind my decision to study physics, as the field provided a rational approach to understanding the physical world and our place in it, and would help make sense of reality and the big questions I had about existence.

  As the years went by, my questions about what physics should say about our place in the universe got overshadowed by the rat race of publishing articles and landing a permanent faculty position. I didn’t forget about them, however. In recent years, I have come to the conclusion that, at least metaphorically, modern physics is starting to make contact in a non-woo-woo way to some tenets of Eastern philosophy. Now I can see why Schrödinger and Bohr read that stuff. Some of these connections have been made in other works, such as The Tao of Physics. My goal here is to add what I consider to be a sound new metaphor to this mix of connections, based on the fusion of invariance and superposition, that is relevant to the question: Why is there something rather than nothing?

  My first introduction to Eastern philosophy was a book entitled Zen Mind, Beginner’s Mind by Zen master Shunryu Suzuki. Suzuki had a most interesting metaphor for existence. Imagine a stream flowing toward a waterfall. When the water leaves the cliff a droplet of water leaves the stream and at some point, rejoins the stream. Life is like that droplet of water and the stream is like the universe. During the time between when we are “born” and when we “pass away,” we are like that water droplet, feeling like we are separate from the universe as a whole. But before we are born and after we die, we are a part of the stream, the universe. I remember wanting there to be some truth to Suzuki’s metaphor. So, in what way could we be connected with the universe in the poetic manner described by Suzuki? According to Zen philosophy this merging can be only experienced. But I have never experienced Suzuki’s claim, since I experience having a separate and localized body that’s made up of matter as I occupy and move through empty space.1 So in place of experience theoretical physics will have to suffice.

  There was a Zen monastery twenty minutes from Brown University, where I was a graduate student: the Providence Zen Center. My friend and physics classmate Claire was a regular Zen practitioner and brought me and a few friends along to engage in a morning of formal practice. The morning included, among other forms of meditation, my favorite, breakfast meditation—when eating, just eat. There were others: after fifteen minutes of chanting words that I didn’t understand, we sat in silence for three sets of half-hour sitting meditations followed by walking meditation. This cycle of sitting and walking meditation would continue for a few hours. Then the Zen master came out and gave a little talk. She said, “You, me, this table, this universe are all made from the same fundamental substance… form is emptiness and emptiness is form.” I later learned that many Zen practitioners seek to attain a mental state called satori, where they can experience being one with this fundamental substance.

  How amazing that at the same time I was learning the mother language of physics called quantum field theory, and the modern view of physics confirms experimentally what these masters have experienced subjectively about who we are—necessarily connected to the universe. But if this insight is true, it must be linked to the matter that we are made of, atoms and their associated force carriers. And we will now see that our popular and pedagogical view of matter has been flawed. To make this clear, let us first look at one of the fundamental building blocks of matter, the electron.

  One of the biggest misconceptions that is nevertheless routinely taught is that things are made of elementary particles that form the building blocks of atoms and molecules. It is the case that from a historical point of view, atoms and a zoo of elementary particles were discovered first, but when physicists were trying to reconcile the quantum mechanical nature of these particles with special relativity, the particle picture was overthrown by a deeper reality of the quantum field. This field picture of all matter came as a necessity of trying to reconcile the physics of an electron moving close to the speed of light in an atom. To properly understand the electron’s behavior in this relativistic context, we must find a way to merge special relativity with the electron’s controller, quantum mechanics. When you do attempt to merge the quantum with relativity, you immediately see, according to the invariance principle, that the basic equation of quantum mechanics is not invariant under the space-time symmetries of special relativity. The main reason is that ordinary quantum mechanics gives time a preferred status over space, and in relativity, they are on the same footing. In 1929 English physicist Paul Dirac ingeniously found a way to unite special relativity with quantum mechanics.

  In hindsight, the hint of this unification comes from electromagnetism, a classical field theory that Einstein showed is already invariant under special relativity. The idea of the field was first introduced by English scientist Michael Faraday to explain his ingenious experiments involving moving magnets, which he found would create electric currents in nearby circuits. To explain the action at a distance between the magnet and the current-carrying wire, Faraday stated, “I believe that magnetism is actually propagating itself through this invisible field of influence.” Faraday also said, “I believe that Electricity has this invisible field of influence and so does gravity.” His peers rejected the claim about fields as idiotic. This “invisible field” was considered heretical because the paradigm of the time was that of a mechanical universe. Similar types of heresy today would be considered “woo-woo” by critics on YouTube channels. Biographers say that Faraday died of heartbreak because his field idea was not accepted during his lifetime. Ironically, long after Faraday’s rejection from the scientific community, schoolchildren still play with magnetic filings that trace out magnetic field lines emanating between the north and south poles of a magnet.

  If you really stop to think of invisible agents acting to impart forces on objects through empty space, the field concept is actually eerie, the stuff of witchcraft. It was not until later in the century that the field idea became accepted. And as we will now see, the field concept will become a central paradigm underlying modern physics.

  James Clerk Maxwell unified a disparate set of electric and magnetic properties into a coherent framework grounded in the reality of an electromagnetic field. We can think of the electromagnetic field as a continuous substance that is distributed throughout space-time. Electric and magnetic charges will bend the field in definite ways. Conversely, a warped field can exert forces on a charged particle. Disturbances of the electromagnetic field can create waves that move at the speed of light, commonly known as electromagnetic waves. Wh
en these waves vibrate at a frequency on the order of a trillion cycles per second, we perceive it as visible light. Einstein earned the Nobel Prize showing that waves of light can also behave like a quantum particle, the photon, and the wave-particle duality had to be reckoned with. It took Dirac, German physicist Pascual Jordan, and Born to realize that the fundamental substance of the photon is the electromagnetic field that is emitted when the electron makes quantum jumps from an excited state. In this case, harmonic vibrations, or quanta, of the electromagnetic fields gave rise to the photon. If the photon is a particle excitation of the electromagnetic field, what about the other particles of nature—are they related to a field?

  What Paul Dirac discovered was that to unite special relativity with quantum mechanics, the invariance principle with the quantum principle, something radical about the nature of the electron had to be compromised. He finally figured out, in the spirit of Einstein, how to make the Schrödinger equation invariant under the symmetries of special relativity. After succeeding, he found a new symmetry relating the electron with a mirror electron with negative energy. In physics when we encounter situations with negative energy, we run for cover. Negative energy is like falling down a hill with nothing to stop the fall. But it gets worse than that because all of that energy will cascade through quantum interactions to the electromagnetic field, creating an unfathomable explosion that would destroy an entire galactic system. In Dirac’s case, he used symmetry to ingeniously reinterpret and repackage this negative energy electron as a new particle with positive charge and positive energy and called it a positron, the antiparticle of the electron—a new particle was born! Two years later the Nobel Prize–winning discovery of the positron was made by Carl Anderson, confirming quantum field theory. With the reality of the positron this meant that when an electron and a positron interact, they annihilate each other and their masses convert to energy to produce a photon, according to Einstein’s famous equation that states that matter is equal to energy. Or an electron and positron can spontaneously be created from a photon with an energy twice as much as the rest mass of the electron and positron. This led Dirac and others to no longer think of the electron particle as a fundamental entity, but a part of one underlying electron-positron field.