How Collective Behavior Creates Physical Reality

The electron is as inexhaustible as the atom
— Vladimir Lenin

This note is inspired by the book “A Different Universe: Reinventing Physics from the Bottom Down” by Nobel Laureate in Physics, Robert Laughlin.

I. Introduction

Physics seeks fundamental laws and quantities that govern the world. At first glance, many of these quantities and regularities can be divided into two categories: fundamental (associated with simple, basic objects and interactions) and statistical (collective, emergent, arising from the consideration of a large number of objects).

The difference is easiest to explain with examples. From school physics, we know that the sum of the angles in a triangle is 180 degrees (at least on a plane). We can take a protractor and measure the angles in any triangle — small or large, regular or irregular, isosceles or right-angled — and their sum will always be 180 degrees. Thus, we can call this law fundamental — it is inherent to the simplest object, the triangle itself.

Now, imagine we measure passenger traffic at a subway station in a large city during rush hour. It turns out that the number of people passing through repeats day after day with remarkable accuracy — the flow pattern is stable and predictable. However, if we shift our observations to a bus stop in a quiet residential neighborhood with far fewer people, the picture becomes less defined. Here, random events in individual lives have a more noticeable impact: a power outage in one house causing alarms to fail; a local kindergarten suddenly closing on another day, preventing parents from commuting. As a result, both the total number of passengers and the very timing of the “rush hour” become poorly predictable and can vary from day to day. The clear pattern observed in the subway simply “blurs” here.

It turns out that neither the measured quantity (passenger traffic) nor the patterns associated with it (when rush hour occurs) are fundamental properties of an individual person. Instead, they have a collective, statistical, or emergent nature. Such quantities and laws are perfectly measurable and verifiable for systems consisting of many elements, but gradually lose their precision as the number of these elements decreases.

II. Gas Laws

The era of the Industrial Revolution, with its steam engines — from factories and mines to the first steamships and locomotives — gave a powerful impetus to the study of gases. Physicists empirically derived a series of laws that were later united into the Universal Gas Law. It states that for a gas in a closed container, the ratio of the product of pressure and volume to temperature is always a constant. This constant was named, without much ado, the universal gas constant.

This value remains the same no matter where we measure it: from paddle steamers on the Mississippi to locomotives of the Trans-Siberian Railway, and from the boilers of the Titanic to the laboratories of the Paris Academy of Sciences. The accuracy of these measurements is so high that since 2019, the SI system has considered the constant to be known absolutely exactly and uses it as a standard for defining other units.

It would seem, here is the perfect candidate for a fundamental constant of the universe. But is it?

By the end of the 19th century, it became definitively clear that gas consists of many individual particles — atoms or molecules. It became possible to create an extremely rarefied gas (i.e., containing far fewer molecules than normal) and perform the same experiments that had previously led to the discovery of the Universal Gas Law. As one might guess from our previous example with subway passengers, it turned out that the Universal Gas Law was not so universal after all.

As the number of molecules in a container decreases, the accuracy of determining the universal gas constant drops and drops, to the point where it becomes virtually impossible to define. The very terms “volume occupied by the gas” or “temperature” lose their meaning for a small number of molecules.

It became clear: the phenomenal accuracy of the gas law is not a consequence of the properties of an individual molecule (like the sum of angles in a triangle), but a product of the collective behavior of trillions of particles. By observing a single molecule, it is impossible to predict the existence of the universal gas constant.

III. The Charge of the Electron

Physics did not stop at the discovery of molecules and atoms. It was soon established that the atom itself has an internal structure: a heavy positive nucleus is surrounded by light, negatively charged particles — electrons.

Modern science considers electrons to be truly fundamental particles — the simplest, having no internal structure, and all electrons in the Universe are exact clones of one another. There are not many quantities that characterize an electron, and one of them is its electric charge. If the particle is fundamental, shouldn’t its properties be fundamental as well?

Robert Millikan, the 1923 Nobel Laureate, conducted the following experiment to determine the charge of the electron. Tiny oil droplets were sprayed into ionized air, where they could capture some amount of electric charge. They then entered a chamber with a known electric field. By analyzing the motion of the droplets in this field, it was possible to determine the specific electric charge they had acquired. It turned out that these values were always multiples of the same value — a certain elementary, indivisible charge, which is the charge of the electron.

In subsequent years, other macroscopic experiments confirmed the discovered value of the electron’s charge. Once again, the value was established so reliably that since 2019, the SI system has considered it absolutely exact and uses it as a standard.

All was well until we moved to microscopic measurements of the electron’s charge. In the second half of the 20th century, the predecessors of the Large Hadron Collider made it possible to accelerate elementary particles to tremendous speeds close to the speed of light and then study how they behave at such high energies. Suddenly, the measured charge of the electron began to increase more and more as its energy grew.

The explanation was not long in coming. Quantum field theory posits that a vacuum is not emptiness. Energy fluctuations are possible within it, which can lead to the birth of electron-antielectron (positively charged positron) pairs. These pairs live for an extremely short time, and their existence usually goes unnoticed — we even call these particles virtual. However, near an electron, they have time to orient themselves — the positive charge is attracted to the electron, while the negative one is repelled.

Such pairs are constantly being created and annihilated in great numbers, and together they form a kind of “cloud” or “polarization coat” around the electron, which partially screens its charge. The theory predicts that the “bare” charge of the electron is infinite! When the electron has low speed (energy), we interact with it fully “dressed” in this cloud, while at high energies we can partially “punch through” it and get closer to the “bare” electron, which is why the measured charge becomes energy-dependent.

Thus, all the time we were measuring the electron’s charge, we were dealing not with a bare particle, but with a complex quantum object — an electron dressed in a cloud of virtual particles. The nature of their collective interaction determined the observed charge of the electron, which therefore bears an emergent, not a fundamental, character.

IV. Newton’s Second Law

Let’s go back to the origins. The foundation of all classical physics is Newton’s Second Law: the acceleration of a body is directly proportional to the force acting upon it and inversely proportional to its mass. Combined with our understanding of various forces, this law of motion allows us to describe completely different phenomena, from a cart moving on a road to planetary orbits.

The law was tested experimentally countless times and found to work flawlessly with immense precision. When the molecular nature of gases was established in the 19th century, there was a temptation to apply Newton’s laws to describe the motion of these new objects. It was impossible to conduct an experiment verifying Newton’s law on such a microscopic scale at the time, but the belief in the fundamentality and universality of this law was too great — a Newtonian theory of gases was constructed. Within its framework, atoms and molecules were implied to be like billiard balls — after all, Newton’s law applies only to bodies (even small ones). The theory’s macroscopic predictions matched the experimental gas laws discussed earlier, and thus it was brilliantly confirmed.

A short time later, in the early 20th century, quantum theory overturned our understanding of atoms. It turned out that atoms, like other particles, are waves. For instance, an atom can pass through two slits in a screen simultaneously — something hardly achievable for a billiard ball. In the microcosm, there are no bodies to which force can be applied, nor acceleration in the Newtonian sense. Newton’s Second Law not only doesn’t work there — it does not exist.

This leads to at least three significant implications:

1. Newton’s Law is emergent. Interestingly, a direct derivation of the law from quantum mechanics still does not exist, despite the common assertion that classical physics is merely a special case of quantum physics at the macro-level.
2. The very existence of “bodies” is emergent. Individual atoms are qualitatively different objects than bodies composed of them. A “body” with its definite trajectory, velocity, and acceleration is a property of a collective, not an individual particle.
3. It is remarkable that we were able to perfectly describe the behavior of gases using a theory that is fundamentally incorrect for the task. This proves that Newton’s Second Law is a law of statistics for large ensembles. It doesn’t matter what the elements of the ensemble are — billiard balls or quantum waves. Their collective behavior obeys the same macroscopic rules.

V. Conclusion

Thus, our picture of the world becomes more complex. Many laws and constants that we measure with high precision seem fundamental to us. But if we look deeper — by reducing the number of particles or increasing the energy — this fundamentality crumbles, revealing the emergent, collective nature of reality. Newton’s laws, the gas constant, even the charge of the electron — all these are not the primary “building blocks” of the universe, but complex phenomena born from the collective behavior of trillions of particles. This forces us to reconsider the very task of physics: perhaps we should search not for the simplest elements, but for the principles of their organization, which give rise to the familiar world around us.

We will discuss the philosophical implications Laughlin draws from this conclusion next time. To read about how psychohistory is connected to emergence, click here.