Posted: 02/06/2013 2:18 pm
Former NASA researcher;
computational scientist; emeritus professor of mathematics, James
Madison University; author, 'Reason and Wonder'
"The very act of observing alters the thing being observed."
--Werner Heisenberg
Since
Jan. 2'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.
* * * * *
The discussion above hints at another type of dualism, better termed
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.
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