I cannot claim to actually understand quantum theory. I’m a writer, trained in the English language, literature, and humanist principles, not a degreed scientist nor any kind of a mathematician. In fact, I have an ingrained distrust of mathematics. I sense that, like the grammar of a language, mathematics is a human-devised system. Mathematics reflects, first, our groping toward a current understanding of the nature of reality, which is constantly subject to revision; and second, the inherent workings and prejudices of the human mind, which has grown out of complexity and cannot always justify itself.^{1}

But I thought I understood—at least in part, without all the equations to solve—the purpose of quantum mechanics in dealing with systems that cannot be directly observed. Observation is a basic tool of science. You might almost say that without observation and analysis, science does not exist. Without observation and reality testing, science becomes conjecture, metaphysics, and mysticism.

The effects of the act of observing upon the outcome of an experiment or observed situation were never much of a problem for scientists during most of its flowering during the Renaissance and the Enlightenment. Astronomy, the study of the cosmos beyond Earth’s atmosphere, is all about observation without experimentation that might affect the outcome. You look directly at the light from stars and galaxies, you study that light as it reflects off planets and moons. Nothing you can do to that light—refract it, break it, analyze it—can have any effect on the stars and galaxies themselves. Most of the objects under observation are also light-minutes, if not light-years, distant from the observer. A great many of them have already changed position, changed their nature, or even burned out and ceased to exist.

Since then, we have discovered that many objects and events out there in the cosmos either do not shine and so cannot be directly observed—think of brown dwarf stars and dark matter—or they are so far away that they can only be observed indirectly—think of exo-planets whose very presence must be inferred from their orbital and luminary effects on their anchoring suns. Still, all we can do is study, observe, and infer. Until we launch spacecraft and expeditions, we cannot change the objects of study.^{2}

Down here on Earth, under the atmosphere, we have always run the risk of an observation effect. You can study the physics of motion, action, and reaction with billiard balls. But you must always allow that a human hand wields the cue stick, or that humans designed and built the spring-loaded machine that gives the ball its first impetus, or that humans at least milled the slate bed of the billiard table and applied the felt that covers it. Human eyes watching the balls do not affect their paths, but human hands and inputs are present at every phase of the experiment.^{3} And even the human eyes that see the results and human brains that interpret them are subject to variabilities of perception.

But still, scientists did not have to contend directly with the observation effect until they entered the realm of the very small, the quantum realm of atoms and flying particles. These individual objects are not only too small to see by reflected light in a microscope, but the medium of observation—flying photons in a light-based microscope, flying electrons in an electron microscope—will interfere with the location and direction of motion attributable to an observed proton or neutron. You can know where a flying proton was coming from by capturing it in a sensor. You can know where it once was by hitting it with a smaller particle and studying the latter’s deflection. But you can’t know where a flying particle is and where it’s going at the same time. To observe it is to send it somewhere else.

This is not a problem that can be overcome by using better instruments, manufactured to closer tolerances, more finely tuned, using a more fine-grained medium of observation. Working with atoms and particles and their associated energies, you can only know after the fact: after you have disturbed their original motion and inadvertently changed it. Or you can know something by observing great masses of such particles operating together, cancelling out individual variations, moving in a bunch as, perhaps, thousands or millions of atoms adhering together to become a dust particle that’s big enough to bounce a photon off without sending it somewhere else.

Quantum mechanics governs the study of individual objects at this sub-microscopic level. As I understand quantum mechanics—and remember, I’m an English major standing outside looking in—it accepts this after-the-fact uncertainty and has principles for dealing with it. Quantum mechanics accepts that an electron buzzing around an atomic nucleus has no observable location or path.^{4} If you want to talk about the electron, you write an equation about the probability of where it might be and where it’s headed. But trying to nail the electron by actually observing it is futile. First, because you can only obtain old, that’s-where-it-was-then data. Second, because you’ve interfered with the electron in the wild and changed it by your very act of observation and experiment.

The story of Schrödinger’s cat is intended to represent this acceptance of uncertainty. Put a live cat in a box with a vial of poison and a mechanism to break the vial only if a random event—the decay of a radioactive atom—occurs. Close the box and wait. As you wait, the cat may still be alive or may already be dead. You can’t know until you open the box. Quantum mechanics says the cat’s fate is suspended in a wave function, which is an equation that describes the probability of the atom decaying and the chances of the cat being alive and of the cat being dead.

Something I learned recently—and I’ll get to where in a minute—is that we can think of probability and statistics in two different ways, as frequentists or as Bayesians. The frequentist calculates a likelihood by studying the frequency of an occurrence among a large number of random events, such as the frequency of heads coming up in a long run of coin tosses. With a lot of data taken under identical circumstances, you can calculate the probability of the toss almost exactly: 50% of the time heads comes up, and 50% tails. For the frequentist, the proposition that a coin toss will have these results establishes a kind of predictable reality. By contrast, the Bayesian—so named after the work of 18th-century mathematician and theologian Thomas Bayes—measures the plausibility of an event when you have incomplete knowledge. The Bayesian knows you can never do enough coin tosses to fix that 50-50 as an exact number. And even if you tried, other factors might affect the tosses, such as air currents in the room, tiny imperfections in the coin’s balance, and microgravities due to plate tectonics. So Bayesians are careful about making assumptions, know their calculations may include subjective elements, and are quick to change or abandon their predictions as new data come to light.

A frequentist looking at Schrödinger’s box can take what he knows about previous decay events in the triggering atom and write a simple equation showing the likelihood of the cat being either alive or dead. For standard quantum mechanics, that equation *becomes* the observer’s reality. Until the box is opened, the observer must believe that the cat exists in two states, both alive and dead, an unresolved wave function—which only resolves itself, or “collapses,” when the observer opens the box. In the same way, a physicist can only know about the position and direction of an electron as a probability function. The electron isn’t anywhere in particular nor is it going anywhere else in particular until it’s knocked off its course by observation.

I had always thought of the wave function as a physicist’s cautionary tale: “You can’t know until you look, and looking changes the results. So when studying individual events at the sub-microscopic scale, you just have to deal with probabilities rather than certainties. The only certainties are in mass effects, taking the average of movements among a large number of randomly moving particles.” After all, that works for billiard balls. Even though the atoms composing the ball’s ivory or resin may individually be oscillating or moving in different directions as the polymer chains writhe and adjust to impact, the ball itself is going in a predictable direction, has a specific location at any one point in time, and is not deflected by the act of our looking at it.

That it, the probabilities described by the wave function are a statement about the limits of human knowledge.

It turns out this quantum caution works on a macro scale, too. We can’t know what every consumer in the nation thinks about a new laundry detergent or how every voter will cast his or her ballot. And the simple act of meeting them all individually and asking can have the effect of changing the data. “Hmm, why did the pollster ask me *that?* That’s an aspect of the product [or candidate] I’ve never considered before.” Or “the man asking me these questions looks sneaky and untrustworthy. He must be trying to dupe me or make me change my mind in some way. I’d better not tell him what I *really* think.”

But we believe we can sample enough data to come up with a reliable probability. When you study the average thoughts or opinions of a large enough number of randomly thinking individuals—not the whole population, certainly, but a “statistically meaningful” percentage—we all accept that you can come up with a pretty close approximation of an election’s outcome or a product’s success in the marketplace.^{5}

As I said, it’s always been obvious to me that Schrödinger’s cat and the wave function represent a cautionary tale. It never occurred to me that physicists might think the cat actually was *both* alive and dead until the box was opened, or that the electron might not have *any* location or direction until observed. That is, I never suspected anyone believed that their wave functions, their probability calculations, were real things, representing any kind of ultimate reality. Thinking that can lead to the absurdities—like the cat’s being both alive and dead at the same time—which have plagued quantum mechanics from the beginning. When you think you can write an equation that includes conjectures about probability and yet still represents reality, you are halfway to metaphysics and mysticism.

Call me a natural-born Bayesian.

I’ve just finished reading an article in the June 2013 *Scientific American,* “Quantum Weirdness? It’s All in Your Mind” by Hans Christian von Baeyer. The upshot is that a new model developed by three physicists dealing in quantum information theory^{6} is currently resolving the absurdities found in most interpretations of quantum mechanics. They call their work “Quantum Bayesianism,” or QBism for short.^{7}

Quantum Bayesianism applies the Bayesian view of statistics and probability—fluid in its hypotheses, subjective in its approach, driven by direct observation of the data, and mindful of the nature of conjecture—to the observational restrictions of quantum mechanics. According to QBism, the boxed cat may be alive or dead. The conundrum has nothing to do with the cat, which already knows its own fate. The wave function is a construct in the observer’s mind to balance the two probabilities—live cat, dead cat—until the box is opened to confirm one or the other. According to QBism, the wave form of an electron or any other flying particle is a construct in the observer’s mind to capture all of the particle’s possible locations and directions—anywhere inside the nave of our hypothetical cathedral (see Note 4 below), maybe heading toward the altar or heading toward the door, but certainly not out on the Pont Neuf or somewhere in Rheims heading for Belgium. But this equation has no more to do with the electron’s actual situation than our refracting a spectrum from the light of Arcturus affects the star in any way.

This is a quantum mechanics I can believe in and follow, even if I can’t write the wave function equations myself. This is a realization of my supposition about the physicist’s cautionary tale. And that only leaves one question.

This new Bayesian interpretation suggests that earlier physicists working in quantum mechanics have all along been thinking that their equations, rather than a statement about the limits of knowledge, are actually statements about the nature of reality: the electron indeed has no location or direction except in a probability equation; the cat really is both alive and dead. This seems to have been the contention of the orthodox, or Copenhagen Interpretation, of quantum physics for the past eighty or so years. If so, then my question is: what other craziness will they believe and/or have they promulgated? It’s one thing to be pure in adhering to your cautionary tales, to state with conviction and absolute belief that you cannot know a thing but only theorize about it. It’s quite another to believe that your theories thereby replace reality.

To me, QBism represents an awakening from a long, dark period of conjecture. We may be back at a ground state of unknowing. But I find that more comforting than for human science to continue climbing the ladder of mathematics and internal logic, past the point at which the rungs actually coexist with observable reality, and then onward, upward, higher, onto rungs that are purely theoretical. At a certain point, you have to open your eyes, look down … and fall.

1. See my earlier postings Fun With Numbers (I) and (II) from September 19 and 26, 2010.

2. However, this premise is changing, now that we can land humans on the Moon and human-made machines on Mars, and litter the space in between with satellites and their detritus. Mission planners make every attempt to sterilize their landers, so that the possibility of carrying an Earth microbe to Mars is greatly reduced. But we can no longer say that the transmission of Earth-borne microbes to Mars and their later, mistaken “discovery” there is an impossibility. We are no longer simply observing Mars with distant telescopes; we are doing hands-on science with all its perils.

3. Similarly, any physics experiment not involving sight and light, such as work with sound waves or seismic waves, depends on the design and manufacturing quality of the detecting device—the microphone or motion detector.

4. And the possible number of locations and paths are huge. I’ve heard an atom described in terms that, if the nucleus of a hydrogen atom were the size of a pea, and you placed it at the center of Notre Dame in Paris, the electron might be anywhere inside the cathedral and headed almost instantaneously anywhere else inside the cathedral.

5. But there still is a residual observation effect. Human minds are far more complex than flying electrons. They are also clever, subtle, self-conscious, and suspicious. The kinds of questions asked in a poll or product survey, the framing of each question, and the hidden bias that might or might not be revealed to an alert or cautious respondent—all work to skew the data. Compared to opinion polling, the vagaries of quantum physics are crystal clear.

6. Carlton M. Caves of the University of New Mexico, Christopher A. Fuchs who is now at the Perimeter Institute in Ontario, and Ruediger Schack of the University of London in a 2002 paper titled “Quantum Probabilities as Bayesian Probabilities.”

7. And if you mentally read that contraction as “cubism,” you’re not alone.