“The very act of observing alters the thing being observed.”–Werner Heisenberg

Since Jan. 8th’s post, we’ve been discussing assumptions that science initially embraced either explicitly or tacitly, later to abandon them as invalid or unnecessary. In the last post we rang the death knell for *determinism*. Today let’s ring it for *dualism*.

The flavor of dualism most germane to science is *Cartesian dualism*, in reference to the 17th-century French philosopher and mathematician René Descartes, who partitioned the cosmos into two domains: the *res extensa* (matter) and the *res cogitans* (mind). Foundational for classical physics, the *Cartesian partition* presupposed the independence of subject (the observer) and object (the thing observed). Implicit in the *subject-object dichotomy* was the presumption of an independent reality “out there” that remains undisturbed during scientific observation.

Science proceeded objectively along until 1900, when German physicist Max Planck stumbled onto the subatomic *quantum*, the daintiest morsel of the material world. Matter and energy, it turns out, are *quantized* into discrete parcels that defy further subdivision. A little thought experiment helps expose the crack that the quantum opened in the bedrock of physics.

Imagine being ticketed for speeding, say for driving at 65 miles per hour on a road posted at 55. You didn’t spot the patrol car until well past it. The trooper’s radar gun got you from behind. In traffic court you attempt a quantum-mechanical defense: “Your Honor, I was traveling at the posted speed limit. When the officer fired his radar gun, the colliding radio-frequency *photons* transferred their combined momentum to my car, bumping up its speed to 65 mph. Had the officer not fired the radar gun, I would not have been speeding.”

Of course, you must now pay the speeding fine *and* a fine for contempt of court, because your argument is patently absurd. However, it contains a germ of truth. Momentum was exchanged between the photons and your car. Moreover, the momentum lost by the reflected photons shifted their *frequency* — similar to the familiar auditory *Doppler shift* — allowing the patrolman to infer your speed. But the effect on your vehicle was immeasurably small, because a car’s momentum so vastly exceeds the combined momentum of a few photons.

But suppose we wish to similarly detect the position and velocity of a moving *electron* rather than an automobile. An electron is too small to observe directly, so we infer its presence by beaming energy at it and observing the pattern of reflected energy. The essential difference from the previous case is that electrons are exceedingly small, and each therefore carries only a tiny amount of momentum. When a light photon, for example, collides with an electron, the impact occurs among virtual equals.

In the quantum world we have some choice in the color (frequency) of the photon projectiles. We can use “blue” photons, by which we mean highly energetic ones, or wimpy “red” ones. Suppose we first try wimpy ones, like the radio-frequency photons of a radar gun. An advantage of low-frequency photons is that they carry little momentum and, upon collision, scarcely disturb the electron’s velocity, which can be inferred accurately. But what can be said of the electron’s position? Very little. The *wavelength* of the photon provides the natural “tick marks” of our distance-measuring “yardstick.” For low-frequency, long-wavelength photons, the tick marks are exceedingly sparse. Therefore, we obtain only a crude measurement of position.

Then let’s try highly-energetic “blue” photons. In this case we determine the electron’s position accurately, but its trajectory is so utterly altered that its velocity cannot be inferred.

There must be a way out of this corner. Let’s try subdividing high-frequency photons into smaller parcels that won’t disturb the electron so violently. That is, let’s use one half, or one fourth, or one millionth of a photon. However, the central tenet of quantum mechanics precludes this scheme: Quanta are not subdivisible. Try as we might, the electron’s position and velocity cannot simultaneously be determined precisely. This is the essence of *Heisenberg’s uncertainty principle*.

*duality*, for it refers to differing aspects of a

*single*entity. We have caricatured the photon as if it were a particle, like a small billiard ball. But we have also spoken of its frequency and wavelength, attributes of a

*wave*. Quantum mechanics reveals that all material objects — not just photons and electrons — manifest in two fundamentally different ways: as waves or as particles. Waves are distributed in space; particles are localized. Two waves may occupy the same place at the same time through

*superposition*. Two particles cannot. The forms are mutually exclusive. Which facet one observes depends upon the design of the experiment. Some experiments reveal an electron’s wave nature, for example, and others its particle nature. No experiment reveals both aspects concurrently.

The oracle of quantum mechanics, Niels Bohr, spoke of *complementarity* rather than duality. Matter has two faces. Both faces reveal something about the object. By analogy, I, despite being a unitary human being, am both a party animal and a contemplative person. If you want to truly know me, observe me both at a party, interacting with others, and while meditating alone on my yoga mat.

Decades of attempts to resolve wave-particle duality failed. Every material object possesses an inherent wavelike nature expressed mathematically by its *wavefunction*. What does a quantum object’s wavefunction reveal? The startling consensus of physicists is that the wavefunction encodes the *probability* of the object being detected at a given location when observed. Apparently, until observed, quantum objects manifest only a *tendency to exist*.

Again, an analogy helps (thanks to Charles Peskin of Courant Institute). Imagine skiing down a steep slope. A tree grows in the middle of the run near the bottom, presenting a hazard. The tree lies immediately ahead if you maintain your current course. Several possible scenarios exist, each associated with a *probability*. There exists a nonzero probability of striking the tree and perishing or sustaining injury. You could veer to the right of the tree, an option with a probability of slightly less than 50 percent. With equal probability you could veer left. The possibilities can be more finely graded, as in the very small probability of missing the tree by one mile to the right or the relatively high probability of missing it by six inches to the left. At the instant of your awareness of impending danger, all possibilities exist as *potentia*, each characterized by a probability. Time is of the essence. You decide to adjust course to the left. At the moment of conscious intent — that is, decision — all potentia but one dissolve, and there remains a single reality: You miss the tree to the left. In quantum mechanics, this is known as *collapse of the wavefunction*.

In his delightful book *Uncertainty*, David Lindley summarizes: “Measurements are not passive accountings of an objective world, but interactions in which the thing measured and the way it is measured contribute inseparably to the outcome.”

Heisenberg’s uncertainty principle removes the partition separating mind from matter, rendering a fatal blow to Cartesian dualism. But complementarity remains. Possibly foreshadowing a paradigm shift for physics, Nobel laureate Wolfgang Pauli envisioned: “It would be most satisfactory of all if psyche and matter could be seen as complementary aspects of the same reality.”

*This blog post was adapted from Chapter 11 of my recent book* Reason and Wonder and also appeared at HuffingtonPost.com.

### Dave Pruett

Dave Pruett, a former NASA researcher, is an award-winning computational scientist and emeritus professor of mathematics at James Madison University (JMU) in Harrisonburg, VA. His alter ego, however, now out of the closet, is a writer. His first book, Reason and Wonder (Praeger, 2012), a "love letter to the cosmos," grew out of an acclaimed honors course at JMU that opens up "a vast world of mystery and discovery," to quote one enthralled student. For more information, visit reasonandwonder.org

Since you are into math, I wonder if you can tell me if there is a factor for malevolence, akin to the ones for addition, subtraction, multiplication and division. A malevolent factor would differ from the mutual functions in that it would be a third force out to destroy the partners in a normal mathematical equation.

Also, aren’t equations dualistic? If so, have you destroyed it? If it’s just a model, can it be destroyed?