Universal Measurements

Are quantum measurements meta-measurements?


What does it mean to perform a measurement?

Usually, a measurement is a process of an interrogative kind, through which to a given question we assign a specific result.

How tall is Goofy? To answer, we must measure the height of Goofy, for example with a meter, and the numerical value obtained corresponds to the result of the measurement.

Before the advent of quantum mechanics, it was believed that measurements always have predetermined outcomes, in the sense that measurement processes can only reveal properties that are already present in the system, i.e., which are already possessed by the entity in question. In short:

The height of Goofy exists, regardless of the fact that we measure it or not.

This state of affairs changed radically with the advent of quantum mechanics. In fact, when performing measurements on microscopic systems, it was found that the outcomes were not always predictable in advance. In other words, it was discovered that:

The interrogative process corresponding to a measurement can only be associated, in general, with a spectrum of possibilities, corresponding to the different outcomes that are in principle actualizable.

Before a measurement is concretely performed, none of these possibilities can be considered as being actual, as it is precisely the measurement process (i.e., the observation) which is capable of actualizing one of these potential outcomes.

Therefore, if measurements were initially considered as a simple processes of discovery, after the advent of quantum mechanics they were understood also, and especially, as a processes of creation.

The very act of measuring, that is, of observing, can bring each time into existence (into actuality) the very property that is observed, which before the measurement did not yet exist, in the ordinary sense of the term.

This process of actualization of potential properties, typical of quantum measurements, has received much attention from physicists, since the early days of quantum mechanics, who have tried to penetrate its mystery. Some went as far as to bring into play the consciousness; others have invented an uncountable number of “parallel” universes!

From my perspective, the Belgian physicist Diederik Aerts proposed, nearly thirty years ago, the most convincing solution, in his hidden-measurement interpretation of quantum probability. His idea is as simple as it is effective:

During a measurement, a different interaction between the measured system and the measuring apparatus is each time selected (i.e., actualized), due to the presence of fluctuations, so that the final outcome cannot be predicted in advance.

In other words, if it is true that a quantum measurement is an indeterministic process, which cannot be predicted in advance, not even in principle, this is because the experimental context, with its intrinsic fluctuations, does not allow the experimenter to control, in no way, which of these different interactions will be ultimately selected.

It is interesting to note that this same process also happens in our mind, when we make a decision.

For example, if someone asks us to mention a fruit that we like, many possibilities will show themselves to us: our mind will immerse in the context generated by the question, bringing it into contact with the different elements of our memory, and at one point a certain interaction will be selected, in a way that we cannot consciously control, thus bringing to the “light of our consciousness” a specific name (or image) of a fruit, among the many that we love, which is the answer to the question that was addressed (i.e., the outcome of the cognitive measurement).

Not surprisingly, many advances have been made in recent times in the understanding of human decision and thought processes, using precisely models of quantum kind. This not in the sense of a modeling of the human brain as a quantum computer, but in the sense that mental processes can be effectively described as processes whose structure is very similar to that described by quantum mathematics.

Without going into details, let me just point out that several typical quantum phenomena, such as interference, entanglement, superposition, emergence and contextuality, have found a striking correspondences in many psychological experiments, for example with respect to the way we humans evaluate different combinations of concepts.

In short, it was found that concepts interacting with a human mind behave in a very similar way to microscopic entities, and are governed by laws which appear to be structurally similar.

And, similarly, as recently pointed out by Aerts in his conceptual interpretation of quantum mechanics, we can also say that the microscopic entities, in turn, have a remarkable conceptual nature, although we must certainly take care not to confuse them with human concepts.

One of the interesting things (for a physicist) of this emerging field of so-called quantum cognition, is that so much so the study of the quantum formalism has proven useful in the understanding of the functioning of the human mind, in the same way the study of our thought processes may prove useful in the understanding of physical systems at a fundamental level.

For instance, we know that in cognitive experiments measurements are carried out not by a single subject, but by an entire collection of different subjects, whose results are in the end averaged out. In other words:

A cognitive measurement is usually a meta-measurement, that is, an average over several measurements.

Moreover, a careful analysis of the process through which we make choices suggests that we do not directly choose an outcome (for example, a particular specimen of a fruit we like), but, at a much more fundamental level, we choose a way of choosing an outcome! This means that:

A measurement, at its most fundamental level, would be an act through which a specific way of measuring would be selected in the first place, from which a final outcome would be in the end created.

This suggests that a measurement process, in general, can be understood as an act expressing a sort of double level of potentiality, i.e., a meta-potentiality, which is much deeper than initially hypothesized.

Years ago, to this fascinating hypothesis Aerts gave the suggestive name of universal measurement, advancing that quantum measurements could very well be an example of measurements of a universal kind.

The validity of his hypothesis has now been placed on a more solid basis, in a recent work that I had the pleasure doing in collaboration with him, in which we have shown, among other things, that:

If the structure of the set of states of an arbitrary entity is Hilbertian, then the universal measurements performed on that entity are quantum measurements, in the sense that the universal measurements will produce the same values for the outcome’s probabilities as those predicted by quantum mechanics.

This result certainly helps us to better understand why the quantum mathematics (and more specifically its probabilistic calculus) has shown such an “unreasonable effectiveness” also in fields of study that have little or nothing to do with physics, such as that of human cognition. This is so because, in particular:

The uniform fluctuations characterizing quantum probabilities can be understood as a first order approximation of a more general non-uniform theory.

Technical Article (Part One)
Technical Article (Part Two)

See also:

Universal Measurements — How to free three birds with one move

May 2017, 148 pages, by Diederik Aerts and Massimiliano Sassoli de Bianchi. Readership: university students and science enthusiasts interested in quantum mechanics or quantum cognition.

This is a book presenting to a wide audience of readers, ranging from fans of science to professional researchers, some of the authors’ recent discoveries in three distinct, but intimately related domains: probability theory (Bertrand’s paradox), observation in physics (the measurement problem) and the modeling of experiments in psychology (quantum cognition). In all three of these domains of investigation, and the associated problems, the authors explain how to advantageously use the key notion of universal measurement, which constitutes the fil rouge of the whole text.