Schrödinger’s Capital: Two Rules to Ring Them All

NOTE 25: The strange parallels between Schrodinger’s equation and microeconomic theory

In his book, From Eternity to Here, Sean Carroll discusses the peculiar nature of the universe as seen from the perspective of the Copenhagen school. This peculiar nature can be described by four characteristics of matter at the quantum scale:

1. Matter behaves both like a discrete particle and like a less discrete wave.

2. Matter suddenly changes from wave-like behavior to particle-like behavior whenever we attempt to observe it. i.e., whenever we interact with it.

3. The instantaneous transition from wave-like behavior to particle-like behavior is such that it is, a. irreducibly random: Which is to say, we can only approximate its final result in advance; and, b. irreversible: which is to say, we cannot know the previous state of the particle, our interaction with a particle irretrievably destroys the information regarding its previous state.

4. There is an irreducible level of uncertainty when we try to measure a process.

In classical physics the development of a process can be accounted for by a single set of rules based on Newtonian physical laws; but in the natural world described by quantum mechanics the development of a process appears to be governed by two completely different sets of rules, which Carroll explains this way:

“1. When we’re not looking at it, a wave function evolves smoothly and predictably. The role that Newton’s laws play in classical mechanics is
replaced by the Schrödinger equation in quantum mechanics, which operates in a precisely analogous way. Given the state of the system at any one time, we can use the Schrödinger equation to evolve it reliably into the future and into the past. The evolution conserves information and is completely reversible.

2. When we observe it, a wave function collapses. The collapse is not smooth, or perfectly predictable, and information is not conserved. The amplitude (squared) associated with any particular outcome tells us the probability that the wave function will collapse to a state that is concentrated entirely on that outcome. Two different wave functions can very easily collapse to exactly the same state after an observation is  made; therefore, wave function collapse is not reversible.”

The Copenhagen interpretation of quantum physics proposed that one set of rules applied to a process until we actually observe it, at which point the process is instantly determined by another set of rules. The transition between the two ‘states’ is not smooth and involves a significant loss of critical information so that the state of the process prior to the collapse cannot be known. Moreover, according to Carroll, two completely different processes (wave functions) can collapse to the same state once observed.

Which ‘state’ the process will collapse into is entirely random, such that we can only assign probabilities to the outcome. However, once the process fall into this state, all subsequent observations will produce the same results, until affected by other forces.

One economy, two sets of rules

Oddly enough, in neoclassical theory, as in quantum mechanics, there are two completely distinct and separate sets of rules that operate side by side: microeconomic theory and macroeconomic theory. In much the same way the quantum mechanics assumes the existence of two sets of rules governing the natural world, economic theory assumes that two different sets of rules govern the behavior of the economy.

However, there is still another even more interesting characteristic shared between quantum mechanics and microeconomics: in both Schrödinger’s equation and microeconomic theory, the system unfolds in a steady and predictable fashion. Bizarrely, Schrödinger’s equation does not actually predict a collapse of the wave-form. Similarly, microeconomic theory does not predict capitalist crises of overproduction.

According to Wikipedia,

“A physical process of measurement can be described in two distinct ways. In the first way it can be described as occurring in an isolated system, described by a single quantum state that remains coherent and obeys the Schrödinger equation throughout the process. There is no reduction of the wave function in this description. It does not exhibit a definite result, because the Schrödinger equation describes only the unbroken and reversible evolution of probabilities.”

Similarly, any one familiar with microeconomic theory will know that it too does not predict any breakdown or periodic interruption of economic activity owing to overproduction of capital. Thus, when the Great Depression hit, Keynes had to advance an entirely different theory that accepted the idea an economy could fall into a permanent state of stagnation — macroeconomic theory was born.

Was the emergence of the Copenhagen interpretation and microeconomic theory a coincidence

The question raised by the appearance of the Copenhagen interpretation in physics and the division of bourgeois political economy into macro and micro rules is whether it is just a coincidence the two emerged side by side in their respective fields? Historical evidence suggests it was not.

According to E. Roy Weintraub, in his book, How Economics Became a Mathematical Science, in response to the labor theory of value in the late 19th century there was a struggle over the way to do economics, whose resolution, says Weintraub, was shaped by similar conflicts going on in the fields of mathematics and physics:

“Economists believe that the last third of the nineteenth century played a pivotal role in the evolution of their modern discipline. ‘The Marginalist Revolution,’ with its introduction of homo oeconomicus making consumption decisions at the margin, reshaped economics into a modern science. The controversies over the scientific status of economics were quite alive at the end of the nineteenth century as the German Historical School, American Institutionalists, the Austrian School, and other contested the nature and limits of economic science. The best way to do economics was in fact an open question in 1900. … this contest shadowed similar contests in mathematics and physics, and its resolution was to be shaped by the resolution that eventually stabilized those other fields of inquiry.”

This is suggestive of more than coincidence between the rise of the Copenhagen school and the emergence of the macro/micro split in neoclassical economic theory. Ultimately, “the introduction of homo oeconomicus making consumption decisions at the margin”, required the creation of two sets of rules in economics to explain the behavior of the economy: There is microeconomic theory to describe the behavior of economic agents at the level of the firm and macroeconomic theory to describe the behavior of the economy as a whole.

Ignoring the implication of two sets of rules

In physics, the similar introduction of two sets of rule to describe the macro and micro behavior of matter led in practice to a rather jarring situation. According to Carroll, most physicists who accept the Copenhagen interpretation carry on their research by mostly ignoring the implications of the standard interpretation:

“Most physicists, even those who use quantum mechanics every day in their research, get along perfectly well speaking the language of the Copenhagen interpretation, and choosing not to worry about the puzzles it presents. Others, especially those who think carefully about the foundations of quantum mechanics, are convinced that we need to do  better. Unfortunately there is no strong consensus at present about what that better understanding might be.

In a similar fashion, economists today accept the split between micro and macro economics as if this split has no obvious implications for the field itself. As if, in other words, micro and macro economic theory does not point to the fundamentally incomplete character of economic theory. The economy appears governed by one set of economic rules at one point, but then by a completely different set of rules at another point.

Einstein waged a lifelong struggle against the Copenhagen interpretation based not on the assertion it was wrong in its predictions, but that the theory itself was incomplete, since it could not explain its result.

Fortunately, unlike physicists, who have not yet been able to identify a law that unites both the macroscopic and microscopic behavior of matter, we know what is missing in the split in economic theory between macro and micro economic theory. In its desire to overthrow the classical assumption that labor is the sole source of value (and thus profit), neoclassical theory concerns itself solely with “consumption decisions at the margin”, never realizing that consumption is itself essential to production.