Emergence vs. Reductionism

Fundamental laws governing ordinary matter appear well-established. Equations and laws determine or describe the behaviour of individual particles, like the Schrödinger Equation, exploring the deepest structures of matter. However, the fundamental laws cannot predict why materials conduct electricity without resistance, magnets form, copper oxides superconduct at unexpectedly high temperatures.

This tension between macroscopic and microscopic laws sparks important questions. Is all macroscopic behaviour reducible to its fundamentals, or do new laws emerge?

This question is central to modern physics as it leads the way for future research, especially in terms of how to approach a Theory of Everything or many-particle systems like superconductors. Even if microscopic equations are known, they often become computationally intractable for many-particle systems.

Reductionists

Scientists who believe everything is reducible to fundamental laws are called reductionists. Reductionists argue that by exploring the realms of particle and quantum physics, we could learn about the laws that rule nature. „They aim at explaining the properties of a system in terms of its constituents and their properties“ (1). It appears logical to explain nature in terms of hierarchies (particle physics -> atoms -> molecules -> cells -> universe)

Key arguments for reductionists are the mathematical elegance and the unity of physics. This includes the Principle of Parsimony, meaning that the best explanation is often the simplest one. Reductionism has also achieved remarkable success, like in thermodynamics reduced to statistical mechanics, chemistry reduced to quantum mechanics, or optics reduced to electromagnetism. The hope is to eventually find a Theory of Everything that combines all fundamental laws that lead to the macroscopic world. A central field of research is combining the four fundamental forces (electromagnetism, strong and weak nuclear forces, and gravity). Theories like string theory or quantum gravity try to unify quantum mechanics with general relativity.

Emergentists

Emergentists believe that the fundamental laws become irrelevant for many-particle systems and the macroscopic world follows different rules than the microscopic one. New laws often arise at larger scales that cannot be directly predicted from the microscopic structure. Emergentists argue that although fundamental laws underlie everything, new laws arise at higher levels, which are not directly derivable from microscopic structures.

One can differ between strong and weak emergence. Strong emergence refers to phenomenons that are unpredictable form their underlaying components (like consciousness), suggesting independent laws of nature. Weak emergence involves unexpected properties of a system that are reducible to their components, but surprising.

Emergence covers a broad range of complex systems for physical to biological to philosophical and social ones. Language demonstrates this principle, although just an illustrative analogy, as Oriol Artime and Manilo De Domenico show in a paper (4). For example, the letters C-A-T individually have no meaning, but their arrangement creates a higher-level meaning, therefore considered an emergent phenomenon.

Nobel Laureates on Emergence

Noble Laureate Philip Warren Anderson famously states „more is different“, which is the centre of emergence. He further explains „the ability to reduce everything to simple fundamental laws does not imply the possibility to start form those laws and reconstruct the universe. (…) At each level of complexity entirely new properties appear, and the understanding of the new behaviours requires research which I think is as fundamental in its nature as any other“ (2). Anderson considers symmetry breaking as central to the hierarchical structure of science. Symmetry means the fundamental laws of a system are independent of change. For example, a system in symmetry does not prefer any state, but breaking it means a state is preferred, like in a crystal lattice.

Nobel Laureate Robert Laughlin addresses the search for a Theory of Everything from reductionists. He proposes the Schrödinger equation as a prototype of the Theory of Everything. However, this Theory of Everything is of no use to the macroscopic world. „We know that this equation is correct because it has been solved accurately for small numbers of particles and found to agree in minute detail with experiment. However, it cannot be solved accurately when the number of particles exceeds about 10. (…) We have succeeded in reducing all of ordinary physical behavior to a simple, correct Theory of Everything only to discover that it has revealed exactly nothing about many things of great importance.“ (3)

Examples for Emergence

Nobel Laureate Anthony Legget points out the example of Ohms Law in his article „On the nature of research in condensed state physics“ (6). „As far as I know, no-one has ever come even remotely within reach of deriving Ohm‘s law from microscopic principles without a whole host of auxiliary assumptions“, says Legget. He suggests that once a macroscopic theory proves right, microscopic theories are oftentimes derived from necessary approximations that lead to the desired result.

Examples for strong emergence are consciousness or life. Although neuroscience explores neural connections and can assign certain properties to parts of the brain, consciousness remains a mystery. It seems irreducible to brain components or neural activity. Life, as well, seems to be independent of individual DNA molecules, proteins and other molecules, but rather an emergent phenomenon.

Additionally, many consider the effective mass of an electron as an emergent phenomenon. While the rest mass is constant, the mass depends on the electron’s environment. For instance, the effective mass in a semiconductor differs form its rest mass. The same applies to the lifetime of neutrons which depends on its state and environment, an example of how effective properties are context dependent.

Other perspective

Reductionists argue that the progress of science will prove emergentists wrong. In the 19th and 20th century, for example, emergentists used chemistry and biology as their main argument. Complex biological structures could not arise from the fundamental laws of physics. However, the success of quantum chemistry explaining the periodic table and properties of DNA reduced to its molecules and atoms undermined strong emergentists claims that chemistry and biology could not be grounded in physics.

Additionally, critics argue that emergentists don’t provide an exact theory either. Arguing that macroscopic properties just emerge form complex structures might not be an appropriate explanation.

There is a scientific debate about whether nature is fully reducible to its fundamentals. A powerful and important example is superconductivity.

Superconductivity

Superconductors, first discovered by Dutch physicist Kamerlingh Onnes in 1911, conduct electricity with zero electrical resistance. Normally, electrons repel each other due to Coloumb interaction, but superconductors below the critical temperature form bound pairs (Cooper pairs) that allow electricity to flow without resistance. Normal electron flow experiences resistance because individual electrons scatter off imperfections, impurities, and lattice vibrations.

Below a critical temperature, electrical resistance of a superconductor abruptly drops to zero, indicating a a sudden phase change. Electrons stop behaving like individuals but rather form Cooper pairs and condense into a macroscopically coherent quantum state, called a charged superfluid. The critical temperature is usually very low as the energy at high temperatures breaks Cooper bounds.

Superconductivity is considered an emergent phenomenon because it emerges only from the collective interaction of many electrons forming Cooper pairs. It is a state of many Cooper pairs sharing one macroscopic wave-function. This means a quantum property becomes macroscopic and opens new doors for physicists.

Nobel Laureate Robert Laughlin argues that superconductors are „quantum protectorate“, meaning that their properties (like zero resistance) are stable because they are governed by higher organising principles. According to him, the underlying Theory of Everything becomes irrelevant.

BCS theory

Many reductionists explain superconductivity with the Bardeen-Cooper-Schrieffer (BCS) theory for which the scientists won the Nobel Prize in Physics in 1972. Although I will only give a brief overview of the theory, it had remarkable impact.

BCS theory provides a microscopic explanation for Cooper pairs, named after Leon N. Cooper, based on electron-phonon interactions. The key idea is that electrons distort nearby positive ions when flowing through the lattice, which creates slightly positive regions. Those regions attract other electrons, „resulting in an effective attractive interaction between the two electrons. This interaction is mediated by lattice vibrations known as phonons“(5).  According to the BCS theory, electron-phonon interactions are the key to Cooper pairs, responsible for electrical flow without energy loss.

However, the discovery of high-temperature superconductors in the late 1980s revealed limitations of the BCS theory. Conventional electron-phonon interactions seem to not fully explain them, as „superconductors with high superconducting transition temperatures have unusual properties that cannot be explained by conventional Fermi liquid theory or the Bardeen-Cooper-Schrieffer (BCS) theory“, says Director of the National Lab for Superconductivity at the Institute of Physics. (7)

Percolation in cuprate materials and current research

High temperature superconductors are called cuprates. It remains a mystery why they become superconductors at much higher temperatures than conventional metals. Additionally, in some cuprate materials signs of superconductivity appear even above the critical temperature. As the material cools, nanoscale inhomogeneities cause prior superconducting patches. The parts connect like a network, referred to as percolation. Only when the patches form a continuous path, global superconductivity emerges.

A lot of research is going on for high temperature superconductors as its applications have enormous potential. For example, ARPES might deliver promising results: „Over the past three decades, angle-resolved photoemission spectroscopy (ARPES) has played a key role in unveiling the electronic structure and gap structure of high- temperature superconductors. (…) ARPES can directly measure the electron self- energy, which is intimately related to electron scattering and electron pairing.“ (7)

Those recent developments increased the quest for superconductivity at room temperature. „In 2015, we serendipitously found an ‘Earth temperature’ superconductivity of 203 K in H3S at a pressure of 150 GPa. Later, superconductivity at 250-260 K in LaH10 was found, and, recently, super conductivity at 287 K was announced in a material that is likely to be H3S modified by carbon. ‘Hot’ superconductivity at 200 °C has been predicted for a ternary hydride. This dramatic progress has resulted from the symbiosis of theory, computation and experiment.“(7)

Additionally, recent experiments show that stacking two layers of graphene at a precise angle causes superconductivity from a strongly correlated state. This ‚magic-angle twisted bilayer graphene‘ is a prime example of emergence by design where rearranging the layers creates new laws.