November 16, 2018

THE CAT THAT ATE THE COGITO:

The Defeat of Reason: a review of What Is Real?: The Unfinished Quest for the Meaning of Quantum Physics by Adam Becker (TIM MAUDLIN, Boston Review)

Becker does not discuss the earliest signs that something was amiss in the theory of light and matter, but the fundamentals are well known. The first hints of particle-like behavior in electromagnetic waves were dropped by Max Planck in his treatment of blackbody radiation, the light given off as a body heats up. In 1905 Albert Einstein took a decisive step with his analysis of the photoelectric effect, the current that flows in certain metals exposed to light. Einstein postulated that the light wave delivers its energy to the metal in small packets or quanta. The energy per packet varies with the color (frequency) of the light, and the number of packets with the brightness (amplitude). Below a critical frequency, no current flows, no matter how bright the light. Above that frequency, some flows no matter how dim.

Light is not just absorbed by matter; it is also emitted. The emission from atoms occurs at only certain precise frequencies. These constitute atomic spectra, which permit us to determine how much of each element there is in a distant star.

In 1913 Niels Bohr devised the Bohr atom. Electrons orbit the nucleus just like planets orbiting the sun. Only certain orbits--which Bohr gave rules for--are available to the electron, and when an electron jumps from a higher orbit to a lower one, it emits light of a frequency determined by the energies of the orbits. The challenge was figuring out how these quantum jumps happen. Over the next decade, Bohr failed to find any precise electron motions. The spectra and intensities of emitted light never came out right. This is the period of the "old" quantum theory.

Becker's main historical narrative begins dramatically at the October 1927 Fifth Solvay International Conference in Brussels. In 1925 Werner Heisenberg had invented matrix mechanics. Heisenberg's mathematical formalism got the predictions that Bohr had been seeking. But the central mathematical objects used in his theory were matrices, rectangular arrays of numbers. The predictions came out with wonderful accuracy, but that still left the old puzzle in place: how does the electron get from one orbit to another? You can stare at a matrix from morning to night, but you will not get a clue.

Bohr took an unexpected approach to this question: instead of asking if the theory was too young to be fully understood, he declared that the theory was complete; you cannot visualize what the electron is doing because the microworld of the electron is not, in principle, visualizable (anschaulich). It is unvisualizable (unanschaulich). In other words, the fault lay not in the theory, it lay in us. Bohr took to calling any visualizable object classical. Quantum theory had passed beyond the bounds of classical physics: there is no further classical story to tell. This became a central tenet of the Copenhagen interpretation of quantum theory.

Imagine Bohr's motivation to adopt this extreme conclusion. For over a decade, he had been seeking exact, visualizable electron trajectories and failed. He concluded that his failure was rooted in the impossibility of the task.

But in 1926 Erwin Schrödinger produced a mathematically different theory, wave mechanics. Schrödinger's mathematics was essentially just the classical mathematics of waves. The atomic system was not designated by a matrix, it was described by a wavefunction. And waves may not be particles, but they are certainly visualizable objects from everyday life.

What is Real? and The Ashtray are spellbinding intellectual adventures into the limits, fragility, and infirmity of human reason.

Schrödinger's theory proved easier to use than Heisenberg's, in part because it is more intuitive. Furthermore, first Schrödinger and then Paul Dirac proved that the two theories are equivalent. In physics any two theories that make precisely the same observable predictions are observably equivalent. And one of the predominant philosophical views of the age--logical positivism--held that any two observably equivalent theories are really one and the same theory. That is, although the two theories may seem to be giving completely different accounts of the world, they are not. The total content of an empirical theory consists in the predictions it makes about the observable. No more and no less.

Logical positivism is a very attractive view for people who do not want to worry about what they cannot observe. It is ultimately a theory about meaning, about the content of a theory. According to the positivists, a theory says no more than its observable consequences.

Logical positivism has been killed many times over by philosophers. But no matter how many stakes are driven through its heart, it arises unbidden in the minds of scientists. For if the content of a theory goes beyond what you can observe, then you can never, in principle, be sure that any theory is right. And that means there can be interminable arguments about which theory is right that cannot be settled by observation.

So the situation in 1926 was rather confused. Matrix mechanics and wave mechanics were, in some sense, thought to be the same theory, differently expressed. But if you use the mathematics to derive a certain matrix yet have no notion of how the physical situation associated with the matrix would appear, how do you get a prediction about what you will observe? And wave mechanics is not much better off. Waves are certainly visualizable, but the world we live in, the world of laboratory experiments, does not present itself as made of waves. It presents itself, if anything, as made of particles. How do we get from waves to recognizable everyday stuff?

This, in a nutshell, is the central conundrum of quantum mechanics: how does the mathematical formalism used to represent a quantum system make contact with the world as given in experience? This is commonly called the measurement problem, although the name is misleading. It might better be called the where-in-the-theory-is-the-world-we-live-in problem.

For Bohr and Heisenberg, the measurement problem is how the unvisualizable can influence the observable (and hence visualizable). For Schrödinger it is how waves can constitute solid objects such as cats. In wave mechanics, the little planetary electron of the old quantum theory gets smeared out into a cloud surrounding the nucleus. If quantum mechanics provides a complete description of the electron--as Bohr insisted--this diffuseness is not merely a reflection of our ignorance about where the electron is, it is a characteristic of the electron itself. As Schrödinger memorably wrote to Albert Einstein, "There is a difference between a shaky or out-of-focus photograph and a snapshot of clouds and fog banks." This unexpected (but perfectly visualizable) mistiness of the electron was fine by Schrödinger: after all, we have no direct experience of electrons to contradict it. But the dynamics of the theory could not confine the smeariness to microscopic scale. In certain experimental situations, the haziness of the electron would get amplified up to everyday scales. The electron that is nowhere-in-particular gives birth to a cat that is no-state-of-health-in-particular. Schrödinger found this result manifestly absurd: something must have gone wrong somewhere in the physics.

For his part, Bohr insisted--as he had to--that the description of an experimental procedure and its outcome be classical, which is to say visualizable. Otherwise, you could not tell what experiment was done and how it came out. But at some point, if we are probing the microscopic realm, we must reach the unvisualizable. And the interaction between the two must itself be unvisualizable, since one part is. So all one can ask for is a mathematical rule: if an interaction occurs, what are the probabilities of the various possible classical outcomes? There is no more to be sought from quantum theory than these numbers. And matrix mechanics typically does not provide a precise prediction but a set of probabilities for different outcomes. The deterministic world of classical physics has been lost.

Which is all well and good, so long as you know what counts as the point of interaction between a quantum system and a classical one. But this Bohr could never nail down. We are left with the question: under what conditions does such an interaction (a measurement of the quantum state) occur? Do we need a human observer? Some conscious detection device, even if not human? Will a mouse do? Some detection device, even if not conscious? The Copenhagen interpretation never answered.

For Schrödinger, we get a different problem. We can visualize the microworld: it is a wave. But at some point, waves must manage to appear as particles, things located at definite positions in space. And just as the Copenhagenists advert to measurement here, so too does Schrödinger. The sudden change from an electron wavefunction being spread all over space to being located at a point is called "the collapse of the wavefunction." So for wave mechanics, the measurement problem becomes: When and how does the wavefunction collapse? And the tentative answer is, upon measurement.

We are all Designist now; the Anglosphere was fortunate to never stray from that truth.
Posted by at November 16, 2018 10:22 AM

  

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