David Pines and Robert Laughlin introduced a very important concept of physics namely ‘Quantum Protectorate’ through an article with the title ‘The Theory of Everything’ published in 2000. Followed by this another great theoretical physicist endorsed that same idea. Through their writing they wanted to highlight the importance of many body systems which are relevant for matter in condensed form. Nowadays in many body systems because of the complicated interactions among the constituent elements lead to exotic emergent properties of matter. The question remains even by substantially understanding the constituent elements and its basic organizing principles are we able to explain the relevant emerging exotic properties of the matter! Or we need to invoke some other degrees of freedom. In the following text we will try to highlight some of the important aspects of the concept of ‘Quantum Protectorate’.

What is reductionism?

How do we try to understand a very complex thing in our life! Best strategy is to divide this complex matter into many small parts, and then try to understand the small parts individually. That is to say that breaking down complex things into simpler parts. Most active and rational modern scientists would at least accept this idea. Some philosophers may pose different opinions, though. In terms of science and philosophy, this is called reductionism. The properties of many complex phenomena can be reasonably explained in terms of the dynamics of several other less fundamental elements. How do our body and mind work? This is a very fundamental question in our life. Do we really understand these completely! Today the majority of scientists and philosophers are inclined to accept the idea that all the living and non-living matters of which we have substantial knowledge are based on certain fundamental principles. It is assumed that these principles are enforceable in normal state conditions. In extreme conditions the effectiveness of these basic principles remains in question, though.

Let us begin with a very simple example. Isaac Newton's laws of gravitation can explain a mango falling from a tree to the ground, a stone thrown into the sky will fall to the ground, just as the Earth revolves in a particular orbit around the Sun, other planets do the same rotating around the Sun or some satellites rotating around our blue Earth. The same principle is sufficient to explain why objects revolve in a certain orbit around the Earth. If one can understand the properties of an atom substantially, a chemical reaction can be understood. The same organizing principle can be used to explain the color of a flame. To simply put, most of the events in this Universe can be explained by knowing some basic principles. This is the main idea of reductionism. So far, this idea has been accepted by most scientists and philosophers. In the current and previous century many outstanding minds from around the world have placed a significant effort to formulate a beautiful mathematical equation called the ‘Theory of Everything’, which would explain all natural phenomena in the Universe. This would have been a real success and paradigm shift formulation. Naturally many outstanding and famous minds were and are involved in this effort. Imagine a situation – a single mathematical equation, this explains all the fundamental properties of Nature. Sad part of the story is that this has not been realized so far. Over the years various complex phenomena of Mother Nature by varying different external parameter ranges have been discovered by the scientists in the laboratory. How far human beings have understood these emergent wonders! To what extent the idea of reductionism is applicable to understand this emergent Universe. This is an important question which deserves critical thinking and comprehensive discussions. Superconductivity is such an emergent many body effect. Magnetism is a many body effect too. Now the question is can we reasonably apply the idea of reductionism to explain these phenomena or do we need to invoke some other conceptual building blocks! This is what we are going to discuss in the following.

What is superconductivity?

Superconductivity is a fascinating property of matter. This is a new state of matter mostly occurring at low temperatures, a state with zero resistivity and a state with the repulsion of applied external magnetic fields. Our daily life observation tells that current is sent through a wire (normal conductor), i.e., streams of electrons are passing through a conductor, these electrons cannot move from one end of the wire to the other without experiencing any resistance. These electrons are scattered for various reasons. They generate heat known as the Joule heating effect. Because of that Joule heating effect, a significant amount of energy is wasted. But in superconducting material in the superconducting state current can go through a superconducting material without experiencing any resistance. If there is no resistance, then there is also no question of wasting energy by means of Joule heating. The second important property of a superconductor is when an external magnetic field is applied in the superconducting state; the magnetic field is repelled from the superconducting material. Now the relevant question is that can one apply the idea of reductionism in superconductor. Before we discuss this point, let us try to understand what the ‘Theory of Everything’ is in condensed matter system!

What is the ‘Theory of Everything’ in condensed matter systems?

In condensed matter physics the theory of everything means the Schrödinger equation. Austrian-Irish physicist Erwin Schrödinger constructed this equation in 1925 and published this in 1926. Almost at the same time (1925) German physicist Werner Heisenberg gave another new equation, a new law of motion. These new equations help to explain the mysteries of the atomic world. But the problem was solving Heisenberg's equation, which is not very easy. The branches of mathematics used to formulate that equation were completely unknown to physicists at that time. So, applying Heisenberg's equation was not an easy task. On the other hand, physicists of that time were already familiar with the mathematical basis of the equation given by physicist Erwin Schrödinger. In fact, these two equations created by Heisenberg and Schrödinger carry the same basic message. Only the language of expression is different. For example, if the same truth is told in Hindi and German language, they sound different to both, but those who know both languages can understand the truth. The application and corresponding success of quantum mechanics for unraveling the atomic mystery is unquestionable. It was started by Heisenberg and Schrödinger. Both of them won the Nobel Prize for their invention. Heisenberg won the Nobel Prize in 1932 and Schrödinger in 1933, respectively.

Schrödinger equation

In condensed matter physics Schrödinger's equation can be called the ‘Theory of Everything’. Though one can call this as the ‘Theory of Everything’, nevertheless many limitations are there. The equation can be solved when it deals with a small system that is a small number of atoms or molecules. In fact, the beauty of this equation is that the relevant solutions meet the experimental results with high precision. But what would be the case when the system is large having many atoms or molecules. Can we find a solution by making calculations reasonably! The answer is it is difficult. For example, if the system contains more than 10 molecules, then this is already going to be a close to impossible task not only for intelligent human beings but also even for a supercomputer. As the number of molecules increases, this makes the task even harder. We know that a small amount of material contains approximately 10^23 of atoms or molecules. This is a huge number. Where the exact solution of the Schrödinger equation becomes almost impossible if there are more than 10 molecules, how can a material containing 10^23 molecules be solved? Just as a computer of that size does not exist at present; it is also a big question whether it will ever be possible to make it in the near future. However, the amount of material that we deal with, usually, is not less than that. In a large-scale system, where a large number of molecules are present, some calculations must nevertheless be possible. These calculations help us to demonstrate and/or to predict the shape of a molecule, the length scale and energy values of chemical bonds, and the elastic properties of matter. Why some materials are transparent, why some materials reflect light, why some materials absorb light – all these can be calculated at the elementary level. If we have a small amount of basic experimental results, then it can also be calculated, the rate or speed of simple chemical reactions, the change of state of the substance, magnetism, and sometimes even the temperature of the transition of superconductivity can be estimated. But if one thinks that one can predict the emergent properties of matter based on fundamental principles just by performing mathematical calculation, without relevant experimental inputs, this is simply disillusion. It is almost impossible to predict the emergent Universe out of only numerical calculations without the availability of relevant experimental data. There are several examples one can easily highlight. The phase diagram of liquid Helium3 isotopes, the entire phenomenology of high-temperature superconductivity has not yet been explained by these mathematical equations. What's more, the functionality of proteins, the functionality of the human brain cannot be explained by Schrödinger-equation. The point is that there are certain limits of the validity of the idea of reductionism.

We ask ourselves how useful the concept of reductionism is in explaining the emergent states of solid state matter. Contextually, the article by American Nobel laureate physicist Philip Anderson was published in Science magazine in 1972 with the title “More is Different ''. This is breakthrough texts not only in the study of solid state matter, but also in the philosophy of science as a whole and in understanding the fundamental principles of Nature. This is, perhaps, what he also wanted to advocate. A real system consists of many molecules. Even a small portion of matter contains approximately 10^23 numbers of molecules. The exact numbers naturally depend on the molecular weights and/or the constituent elements of the compound. Let us begin with a single isolated molecule. This single isolated molecule reflects intrinsic properties of this molecule. Now if we add many molecules there, and then these molecules are combined. The question is whether the properties of the isolated molecule and a system with a large number of molecules show the same properties. Often the case their properties are not same as varying external parameters. To simply put, the properties of a single molecule may not be necessarily the same as of the whole system. More constituent elements you put in the system; the system is prone to provide different properties than the single or isolated system.

What is ‘Quantum Protectorate’!

Superconductivity is an emerging property of matter. A laboratory test result. In many materials these exotic properties have been observed. One can have a bulk amount of superconducting materials and the bulk system shows the superconducting properties. That is a state with zero resistance and complete/partial magnetic flux repulsion. In fact, the effect is substantial enough so that one can visualize this effect by the so-called magnetic levitation experiment, where superconducting material in the superconducting state in the presence of a moderate magnetic field is lifted in the air. Superconductivity is a many body effects. While superconductivity has opened up outstanding fundamental research directions, superconductivity has the potential extraordinary future applications. Some of them are already in place. Now the straightforward question is can one understand superconducting properties of matter by solving Schrödinger's equation. The answer is certainly not. The truth is that some emerging properties of matter, such as superconductivity, magnetism, quantum hall effect, and superfluidity depend on higher order organizing principles. This is where the word ‘Quantum Protectorate’ plays a significant role. Two physicists namely David Pines and Robert Laughlin coined the term ‘Quantum Protectorate’ in 2000. Literally protectorate means a state which is protected by another state. Like children are protected by their parents. In quantum matter the emergent properties of matter, which originated because of the relevant mutual interactions among the constituent particles, are governed and protected by the laws of quantum mechanics. This essentially gives rise to the stable state of a matter. This doesn’t depend on the individual properties of an atom or molecule. This doesn’t depend on the small impurity effect or defect, doesn’t depend on the tiny fluctuations of the temperature and/or other relevant external parameters. This is a highly organized principle of a matter in the emergent Universe.

Higher Organizing Principles

Superconductivity works because higher organized principles are active there. In a superconducting state two electrons are coupled and they form a Cooper pair. As a result of the law of quantum mechanics two electrons are strongly entangled. These numerous pairs of these electrons work coherently to make this superconducting state. Now the question is that if one breaks the Cooper pair, and two electrons act separately, can one get superconductivity out of this break out scenario? The straightforward answer is simply no. To get superconductivity, a relevant system needs a collective effort. For a superconducting system which contains, say, 1023 atoms, if one atom is being isolated from the system, this atom will not show superconductivity individually, but the system as whole, though. In the same line of discussion, in case of a ferromagnetic material, if one isolates a single spin out of the whole system, can this spin individually exhibit ferromagnetic properties! It requires a collective effort among all the spins to get to the ferromagnetic state. To simplify this let us consider a Fair in a town, where there is a huge crowd of people. We get an average sound of human noise, but we hear nothing distinctly. A strange sound is heard. Each person talks to each other in their own place, in different tones, on different topics. That is there is a mixture of different frequencies. In fact, the outcome is that even if we don’t understand each other a general sound will appear to us, but there is no collective effort as such. Thus, this is not a higher organized principle. Let us give another example. Let's assume that we went to enjoy a symphony orchestra musical event. The musical event plays several musical instruments to create a beautiful melodic ambience. This is a collective effort. Are we really interested in what individual instruments play! Do we really pay significant attention to what sounds an individual instrument reflects! No actually as a listener, as an outsider we don’t pay much attention to the individual details. But the overall or collective outcome is important for our ears and minds. It can be considered as the simplified but real-life analogy (metaphor) of a higher organized principle. Superconductivity, magnetism, superfluidity represent such higher organized principle.

The main point is the following: modern science has to be viewed in different perspectives. Whatever science we talk about fundamental, deep or profound, in all places we cannot restrict ourselves to only molecules or atoms. We have to go beyond that. We have already discussed many properties of matter (Nature) that can be understood by some basic principles or some simple set of equations. We must admit and acknowledge these. As far as science is concerned, we have achieved tremendous success. At the same time, we must also admit the real World is much more complex and much more dynamic. The underlying mechanisms for all the emerging phenomena are equally complex. Superconductivity, magnetism are such complex problems. Similarly human emotions, human feelings, human brain activity, chaos, weather etc. fall into these complex categories. To understand the underlying mechanism of these phenomena requires highly organized principles. We need to have a new vision, much sharper and clear new ideas.

Rajib Sarkar

Scientist

Technical University of Dresden, Germany

References:

1. The Theory of Everything, R. B. Laughlin and David Pines

PNAS 97, 28-31 (2000) https://doi.org/10.1073/pnas.97.1.28

2. Sources of Quantum Protection in High-Tc Superconductivity, Philip W. Anderson, Science 288, 480 (2000)

3. Magnetism: A Very Short Introduction, Stephen J. Blundell (Oxford)

4. Superconductivity: A Very Short Introduction, Stephen J. Blundell (Oxford)