Fear of a Black Universe Read online

  —RICHARD FEYNMAN

  It was sophomore year and the moment we physics majors had been waiting for. The last year and a half had been a tedious grind of problem sets that involved boring blocks sliding down inclined planes and systems of masses hanging on pulleys. But that day we sat attentively. It was our first quantum mechanics class, and we were waiting for Professor Lyle Roelofs, a tall man with a thick mustache in a plaid shirt, to deliver his first lecture. He began by saying, with a straight expression on his face, “I can assure you that after learning quantum mechanics, there will be no need to drop acid.” I thought he was joking. Twenty-eight years later, however, I can report that he was right. Just when you think you understand it, when you stop to think of what quantum mechanics is saying about reality, there is really no need to drop acid—your mind has already experienced alternate reality.

  Quantum physics underlies our electronic technology, and although we think about it as the physics of the very small, it is likely to apply to galaxies, too, as it probably describes the behavior of whatever particles make up dark matter. And, as we’ll see, quantum mechanics is probably central to the existence of the universe, too. In fact, one of the reasons I became a physicist was Stephen Hawking and James Hartle’s proposal of the wave function of the universe, which posits that the entire universe is a quantum mechanical system.

  Perhaps it comes as no surprise that, just as no one ever described the general theory of relativity as being like an acid trip, quantum mechanics wouldn’t offer up an obvious central principle like the principle of invariance. That doesn’t mean we can’t try to find one. If I had to choose one (which I guess I do!), it would be the principle of superposition of states.

  Of all the strange things about quantum mechanics, I believe superposition is the main point of departure of the microscopic quantum world from the ordinary world of large things (like dogs and airplanes) of classical physics that we experience. Once we have this principle, it invokes strange features such as nonlocality, the uncertainty principle, and complementarity, which, if you’re familiar with quantum mechanics, are all pretty strange, and if you’re not, you’re about to! These will form the basis of much of the cutting-edge mysteries we are currently wrestling with and exploring in these pages.

  To appreciate the bizarre world that the principle of superposition of states describes, we should first understand the concepts of superposition and state independently. In classical mechanical systems, the physics of the macroworld you inhabit, every object has two attributes that describe what physicists call its physical state. One is its position, which is where the object is. The other is the object’s momentum, which is defined by its mass and its velocity. This means that momentum is a vector, and includes both the speed of the object and the direction it is traveling in, as well as the object’s mass. We can think about the physical state as a point in a two-dimensional space, where the y-axis denotes the momentum and the x-axis denotes the position. This space is called phase space. Phase spaces are key tools in analyzing all dynamical classical systems, whether a baseball or a spaceship—or even classical particles.1 Each occupies a unique point in phase space. So if we have something simple, such as a ball in motion, we are able to predict with certainty what its state in the phase space will be in the future, once we apply to it the dynamical laws in classical physics. This is called determinism. A classical object can only be at a unique position and velocity at a given moment of time. I hope so far this makes good common sense.

  FIGURE 5: A phase-space diagram showing a particle’s momentum and position.

  You might think that, if states make good common sense, then it must be superposition that doesn’t. But it can make common sense, too. In fact it is a common and useful property of waves. If we drop a stone on a calm pond, a periodic wave will propagate radially outward from where the stone hit the water. If we drop other stones nearby, other periodic waves will also propagate radially outward from those points as well, and sooner or later those waves will encounter each other and combine. This will result in a more complicated pattern of waves, where they can either add up or subtract from one another. The ability of waves to combine to make more interesting waves is at the heart of superposition: in fact, the word superposition literally means the process by which simple periodic waves of differing frequencies are added up to make a complicated-looking wave. An intricate-looking water wave is made up of billions of water molecules that collectively superpose to take the shape it has. This isn’t just something that happens in bodies of water; it’s why there can be dead spots if stereo speakers aren’t set up correctly, and it is also how electronic music synthesizers work. Conversely, a complicated-looking wave can be decomposed—mathematically, anyway, if not in a pond—into a large collection of periodic simpler waves.

  FIGURE 6: To the left, solid and dashed periodic waves can superpose (be added) to form a more complex wave to the right. Conversely, the right-hand wave can be decomposed into the two periodic waves on the left.

  The ability of waves of water atoms to superpose made it all the more confusing for physicists when they first encountered the bizarre behavior of electrons in their experiments. In a nutshell, individual electrons were thought to be particles, but they exhibited wavelike behavior instead. Quantum mechanics was invented, in part, to deal with those experiments.

  Here is the punch line: A single electron can exist as a superposition of many states at the same time. In other words, a single electron can be in many places, or have many momenta, at once. More generally, behavior of electrons or any quantum entity can be stated as follows:

  The Quantum Superposition Principle: A quantum system is expressed by adding many distinct states at the same time.

  A common example of quantum superposition concerns the position of an electron moving in space. The superposition principle says that the state of an electron’s unique position in space is equivalent to the same electron having a wide array of velocities at the same time. The converse is also true. If the electron has a state describing it to have a given velocity, it can equally be expressed as a superposition of one electron having a very large range of positions.

  You can see why Professor Roelofs thought this was crazier than tripping on acid: all your physical intuition about the classical world should go out the window. How can one electron be in several places at once? How can one particle be moving at many different velocities at the same time?

  One of the most mysterious experimental displays of the quantum strangeness of superposition is the double slit experiment. Richard Feynman calls the double slit experiment “impossible, absolutely impossible to explain in any classical way, and has in it the heart of quantum mechanics.” Here is how it goes: One electron at a time is shot toward a screen, which lights up where the electron lands. Between the electron gun and the screen is a barrier with two small holes that allow the electrons to pass through. At first, we see nothing out of the ordinary, just electrons landing and lighting up the screen like fireflies. After a large number of individual electrons arrive on the screen, however, they distribute themselves in a bizarre way. Since the electrons are particles, we expect them to pile up in two bundles directly behind the holes. However, the electrons land on the screen to create what’s called a wave interference pattern, with areas with lots of light spots and areas with few. How did the individual electron particles know to avoid the location of the previous electrons to collectively exhibit a wave pattern later? What exactly is the electron doing when it arrives at the double slit? Is it behaving like water waves that go through both holes and interfere after they pass through?

  We could partially explain the interference pattern if we assume that the electrons behave like a wave as it approaches the two nearby holes. The electron wave would split up and pass through both holes and recombine forming an interference pattern. Experimenters tried to find out if that’s what was going on by putting detectors at one opening to see where the electron went through.
What they saw instead was that the interference pattern on the screen completely disappeared. So, when we are not looking at the electrons during their flight, they behave like waves, and when we try to pin their positions down, they lose their wavelike properties and collapse into one location out of the many possible places they could have been. It’s as if the electrons knew when they were being watched to change their wavelike properties. Ever since this bizarre situation presented itself, many physicists have attempted to reconcile it with either modifying quantum mechanics or giving it a new interpretation. There is still no general agreement!

  Although experiments like the double slit experiment were and still are quite shocking, it turns out that most of our modern technology stems from the quantum mechanical understanding and ability to control the electron. My favorite is the solid state laser. Another is the nuclear magnetic resonance technology, which drives the MRI machine used to do brain scans in hospitals. Electrons carry a negative electric charge and have another property that physicists call half-integer spin. Spin is called that because, mathematically, it’s something like the spinning of a top. Tops spin clockwise and counterclockwise; electrons have elementary spins we call up and down, and they behave like tiny magnetic north and south poles. Spins can be flipped by the application of a precise magnetic field, and this is at the heart of an MRI.2

  The double slit experiment also inspired those in other disciplines, including both neuroscience and mysticism, with the behavior of the observed electron indicating that perhaps there is some undiscovered link between quantum mechanics and consciousness. These speculations continue to stir mystery, controversy, and confusion, even among Nobel Prize–winning physicists, and there may even be some truth to these intuitions. I will present my own suppositions later, but for now, it is important to see that this weird behavior stems from two ideas: that the electron’s location in space is a superposition of position states, and when we make an observation we can only see the electron realize itself at one position.

  This property is seen in a wide array of quantum mechanics and is currently being exploited to make quantum computers a reality. This conundrum is at the root of an issue in quantum mechanics called the measurement problem, a subject we must confront. The bizarre quantum superposition could also be a useful attribute for a superhero. Like many youngsters, I was hooked on Marvel comic books and imagined creating my own superhero. It turned out that it didn’t matter that much that Stan Lee and I went to the same high school. Also, my drawing skills weren’t that great, so I didn’t end up pursuing that path. I am now amazed to see how quantum physics has entered in Marvel movies, such as Ant-Man and The Avengers.3 If I were to create a new character, I can think of a few properties of the quantum world that would fit the bill of major new attributes for a superhero. If my hero was fighting many villains at once, then he or she would have a major advantage over a nonquantum hero. A quantum superhero with the ability to be superposed in many positions at the same time could fight many villains at once. Of course, this raises some deep questions. If an electron causes trouble for us once we interact with it going through a slit, what’s going to happen when the quantum hero interacts with classical villains? We will return to this issue when we discuss the measurement problem inherent in quantum mechanics.

  But first it’s useful to explore more quantum weirdness.

  In 1923 a French prince named Louis de Broglie claimed that all matter possesses wavelike properties. First, by paradoxical fiat, de Broglie related the momentum of an electron to its wavelength, and further that all matter—anything with mass and momentum—also has a wavelength associated with it. This hypothesis was used to correctly explain one of the great mysteries of early twentieth-century physics, which is why negatively charged electrons don’t go crashing into the positively charged nucleus of atoms. If we identify the wave as the electron’s orbit around the nucleus, then the longest wavelength predicted by its mass would correspond to the closest orbit that it could make around the nucleus. The electron would not be allowed to go to lower orbits and fall into the nucleus because no lower wavelength orbitals would exist for the wave. This picture was also consistent with Niels Bohr’s model of the atom, and why he had hypothesized that electrons existed in orbits that could only have discrete, integer values. This model correctly predicted and explained the absorption and emission spectrum of gasses that classical physics could not explain. Despite having a host of models, such as the Bohr atom and de Broglie’s orbits, to account for the wavelike behavior of electrons, physicists still lacked a precise equation to describe what was going on. At least they did until Erwin Schrödinger returned from a short ski trip in the Swiss Alps with a most beautiful and elegant dynamical wave equation describing the wavelike superposition of quantum matter.

  Schrödinger is one of my heroes in physics, and he inspired many young physicists of my generation as well. He wasn’t the stereotypical “geeky” physicist that is often portrayed in movies and in TV shows like The Big Bang Theory. He had a host of other interests such as poetry, color theory, and Eastern mysticism, and I am convinced that his polymath tendencies influenced his creativity. While no one knows exactly how he came up with it, Schrödinger discovered a differential equation—which we call the Schrödinger equation—for all quantum systems. It is an intriguing fact that all our theories are described by differential equations; for some reason, after all the elegant formulations of a physical theory, when the rubber hits the road, physicists end up solving differential equations. The solution of the Schrödinger differential equation is a mathematical function that contains all information, including superposition of states, about quantum systems: the wave function ψ.4

  The Schrödinger equation is so aesthetically beautiful, I can’t help but write it down.

  This singular equation determines the behavior of the wave function, denoted by the variable, spoken as psi (and sounds like sigh). It describes how the wave function of a quantum system interacts, and changes in time. This equation predicts all quantum phenomena, including the periodic table, physics of a neutron star, and even the semiconductor device in your smartphone. The equation simply says that the temporal change, or evolution, of a quantum wave function (right side) depends on the energy, which encodes interactions acting on it (left side). Once we know the evolution of the wave function, we get new insights into and predictions for the quantum system at hand. Some of these properties led to the invention of gadgets like transistors, the heart of all computer-driven technology. The superposition principle emerges naturally from it. This is because the Schrödinger equation is what is known as linear. This means that if one finds two independent solutions of the wave function, then the sum of those solutions would also be a solution. Periodic waves obey this mathematical property of linearity. Thus, the wave function describes waves that can be decomposed into an infinite set of simple harmonic waves of differing frequencies.

  So what is the electron doing, according to the Schrödinger equation? Schrödinger interpreted the electron as a highly peaked material wave, like a pulse: the wave is the electron. But with this interpretation a natural paradox presents itself: If a highly peaked wave function is to describe a single electron, what does it mean when the electron wave function hits a barrier and splits in two? One common feature of a moving wave is that if it starts off highly peaked, at some later time it will spread. But what becomes of the particle when the wave loses its shape and splits into many pieces? Are we to think that the electron will split up into many electrons? Precision experiments from particle accelerators reveal that the electron is an elementary particle and is not a composite of any smaller unit of matter. So if the wave splits, the electron certainly does not split in two. It could be that the electron does lose its identity when it encounters an environment that enables it to shape-shift. We will return to this issue. For now, let’s accept the electron as an indivisible and independent unit.

  Schrödinger’s interpretation that the w
ave function represents a material wave whose shape describes the position of a particle was problematic, and it forced physicists at the time to seek an interpretation of the wave function to also make sense out of a quantum particle being in many states at once, as is suggested by the double slit experiment. Max Born, another leading quantum physicist, provided an ingenious interpretation of the Schrödinger equation that dealt with the problem of a splitting wave: he argued that the wave function is not a material wave but a wave of possibilities, so that where the wave has the largest amplitude the particle is more likely to be there, and correspondingly less likely to be where the wave’s amplitude is lower. Applying the Born interpretation to the double slit experiment, the wave pattern we see is the result of a probability wave that goes through both slits. When we look to see which hole the electron is at, the probability superposition collapses into one position outcome and the interference pattern disappears. This still doesn’t solve every problem with the double slit experiment. You should scratch your head and wonder how the act of observation collapses this probability distribution in the wave function to the observed value. Also, what does it mean for a probability wave to go through the slit?

  The competing interpretations of the wave function forced the architects of quantum mechanics to take philosophical stances about how to interpret quantum mechanics generally. Albert Einstein, one of the founders of the theory, took a realist stance. Realism demands that there is an objective physical world that is independent of our existence. This seems reasonable since the universe had existed billions of years before stars, planets, and humans came on the scene. Saying that a probability wave goes through a hole avoids saying exactly what the electron is actually doing in that region of space. In accounting for the double slit experiment, a realist posits that the quantum theory should explain what the electron does when it encounters the two open slits and the resulting interference pattern, with or without the presence of a measuring interaction.