There are generally two paradigms to understand the environment around us namely reductionism and emergence. The word “environment” means everything around us whether it is living or non-living objects. It includes things that fall under either natural sciences or social sciences. Reductionism is the idea that we can understand bigger objects by understanding the smaller constitutes that make the bigger things. On the other hand, when smaller constituents come together the whole thing might develop novel properties that do not exist at the level of the small constituents. Therefore complete knowledge of the constituents might not be enough to understand the whole thing. The question of which one – emergence or reduction – is more fundamental attracts not only physicists but also philosophers, biologists, among others. In physics, the two ideas at first seem to be mutually exclusive. However, both paradigms have proven to be of high importance to our understanding of nature. Even though there is a big debate about which one is superior, this essay is about the possible mutual benefits between reduction and emergence. I will consider the example given by Piers Coleman [1] about the tie between emergence and reduction that led to our current understanding of conventional superconductivity.

Our everyday electronic devices function because of some electric current that moves inside "wires" buried inside our devices. The electric current is the movement of electric charge inside the material. Since these wires are typically made of a very large number of core nuclei and electrons, the moving electric charge inside the wires will collide with other electrons and nuclei. These collisions are the reasons why our electronic devices get hot! These collisions are what make our electricity bills more expensive than they could be. The solution to the problem of unwanted collisions of electrons inside wires is to make materials that have moving charges that do not collide with anything else! Some of these materials are called superconductors. There are different types of superconductors. We call superconductors that scientists understand conventional superconductors, while the ones that scientists do not understand are called unconventional. In this essay, we are concerned with conventional superconductors because physicists are still trying to understand unconventional ones. 

Ultimately the understanding of superconductivity boils down to understanding the behavior of electrons inside materials and the typical approach to do this is to use quantum mechanics. Conventional superconductivity was explained by John Bardeen, Leon Cooper, and Robert Schrieffer in their Bardeen-Cooper-Schrieffer theory (BCS). This theory is a microscopic theory because it managed to explain the accumulated macroscopic phenomenology in terms of the microscopic constituents of matter namely electrons and phonons. In other words, we say it connected the microscopic details to the macroscopic observations.

During the beginning of the time when physicists started to study superconductivity, the standard tools to understand the behavior of electrons inside materials were the free electron model of Drude (and its variants) and the quantum mechanical band theory. These methods are all considered methods of reductionism.  The Nearly Free Electron theory was very successful to explain the properties of metals. However, it could not give any hints on what makes normal electrons in metals turn into superconducting electrons! Using these reduction methods, the brilliant theorists of their time including Einstein, Bohr, Heisenberg, Bloch, Landau, and many others could not solve the mystery of superconductivity for more than forty years!

Useful hints to solve the mystery came from two avenues. Firstly from more experimental information and heuristic arguments to understand them. Secondly by proposing a first-of-its-kind model for emerging quasiparticles. The first major step in the pursuit of understanding superconductivity was doing more experiments on superconducting materials. This led to discovering the behavior of the superconductivity materials once subjected to an external magnetic field. It was found that a strong enough magnetic field can destroy superconductivity. Additionally, superconductors are diamagnets because they do not allow the magnetic field to penetrate the sample. The magnetic field can only penetrate to a very short distance called penetration depth. This useful observation was used by the two brothers Heinz and Fritz London to argue that this diamagnetic behavior is due to the rigidity of the superconducting wavefunction in the presence of a magnetic field. This advancement gave theoretical hints on the nature of the wavefunction and the type of phase transitions between superconductivity and normal states. It showed that superconductivity is an interesting emergent phenomenon where the transition between normal and superconductivity states leads to a drastic change in the properties of the electrons.

The second hint that helped physicists solve the mystery of superconductivity came in 1950 when experimentalists observed the isotope effect. This means that different isotopes of the same element need different temperatures to reach the superconductivity states coming down from the normal state at high temperatures. Heavier isotopes need lower temperatures to become superconducting. This observation revealed that the motion of atoms inside the materials plays a role in superconductivity. In the beginning, theorists thought that atomic motion would affect the energy of moving electrons inside superconducting materials. However, quickly after that Frohlich proposed in 1952 that the movement of atoms – technically called phonons- is in fact affecting the interaction between electrons. To the surprise of everyone, this phonon-induced interaction between electrons turned out to be attractive. Electrons inside superconductors effectively attract each other! This attractive interaction between electrons of opposite momentum and spin – called Cooper pairs- near the Fermi surface leads to an energy gap that differentiates between the normal and superconducting states. Pairs of electrons below the gap are superconductors and once they get enough energy to jump this emerging energy barrier, the pairs break up and superconductivity degrades.

The third major step in the story of BCS was the realization that these pairs of electrons – Cooper pairs- follow the bosonic statistics. Therefore the pairs can condensate into a superfluid state that allows electrons to move around without collisions with anything else – thus they superconduct. The emergence of bosonic quasiparticles from fermionic matter was then realized which seems to me to be the heart of BCS theory. Based on the idea that phonon-induced attractive interaction couples certain types of electrons –  with opposite momentum and spins- Robert Schrieffer in 1957 wrote his many-body wave function which proved to describe the superconducting state.

Using the previously mentioned  three clues - magnetic effect, isotope effect and Cooper pairs - the trio Bardeen, Cooper, and Schrieffer published their BSC theory in 1957. The Experimental discovery of the magnetic effect and the work by the London brothers fall under the emergence paradigm. Using the isotope effect to infer that electrons might attract each other also falsl unders emergence. However, using the last piece - Cooper pairs-  to come up with the  BCS wavefunction falls under reduction. This shows -as Piers Colemen puts it - how reduction and emergence came together as a perfect storm of discovery.

It did not take the community a long time to realize that BCS theory is the correct theory to describe conventional superconductivity. Moreover, the success of the BCS is not just limited to demystifying the mystery of superconductivity, it also led to brilliant ideas for other problems in physics. It led to the general idea of superfluidity culminating in the discovery of superfluidity in Helium, the idea of nuclear superfluid, and also to the emergence of the quark-gluon condensate proposed by Anderson and Higgs.

From this historical lesson where reduction and emergence married to give birth to BCS, an appropriate strategy to use when confronting mystical unsolved problems in physics is to exploit both reduction and emergence to the maximum extent. One should start by focusing on building a guiding big picture from all phenomenological details congregated from different experimental results. With as many as possible phenomenological observations, one should start by using general macroscopic understanding rather than microscopic.   Focusing on microscopic, detailed arguments might be misleading because it will probably cost a lot of time and effort without great benefit. Instead, thermodynamics and macroscopic arguments should be taken seriously and even be given precedence over following the guidance of microscopic theories. During the journey to gain macroscopic understanding, one should prioritize physical understanding not mathematically complete solutions. The first one might lead to short cuts to practical solutions while the latter can lead to unnecessary mathematical difficulties that delay the progress greatly if not force us to completely abandon the problem. Hints from experiments should be adopted even on a heuristic level instead of insisting on a reductionist approach that starts from the very bottom. Once these heuristic steps proved to be useful one can then go back and try to build models that explain heuristic steps according to the practice of reductionism. With this recipe, one can take advantage of both emergence and reduction to solve scientific problems facing humanity. 


[1] Emergence and Reductionism: an awkward Baconian alliance: arXiv:1702.06884