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Entropy and the arrow of time

Greek philosophers some millennia ago and since then many philosophers over the centuries round the world had been raising the deep-rooted perennial questions: what is life, where was its beginning and where is its end, what makes life continue and many more intractable questions like these. These are perennial questions of profound significance, which had so far been answered in many divergent ways – in pure incomprehensible philosophical terms, in supernatural religious terms and so forth.

However, scientifically inclined people, who used to be branded centuries ago as natural philosophers, would pose the same questions in somewhat different terms: how did life begin, when is the beginning of life, how did it evolve, what is the nature of time and what is the flow of time etc? Again, these questions are not easy to answer, but at least scientists have structured and sequenced the questions so that answers become easier.

Natural philosophy evolved from pure philosophical inquiry and inquisitiveness. Scientific disciplines were considered effectively the extension of wider philosophical queries. That is why even today the highest academic degrees, both scientific and non-scientific, are titled as Doctor of Philosophy (PhD). Physical sciences are the ones which describe physical processes of natural sciences in numerical and quantitative terms.  

Heat, temperature, enthalpy, entropy, energy etc are quantities within the subject matter of thermodynamics and statistical mechanics. These subject matters along with Newtonian physics, electricity and magnetism, optics etc were bundled together as the ‘classical physics’. This naming of ‘classical physics’ does not mean that these subjects have become ‘classical’ – sort of outdated and outmoded – and there is nothing more to learn from these subjects; far from it. It only means that these traditional subjects have been set aside in order to concentrate on newer disciplines (roughly from the beginning of 20th century) like the general theory of relativity, quantum mechanics, particle physics, cosmology etc. which are called the ‘modern physics.’

This traditional segregation of branches of physics into classical physics and modern physics is purely arbitrary. There is no boundary line, no demarcation either in terms of time or disciplines between classical and modern physics. Entropy, the parameter which was invented in the 19th century as a thermodynamic quantity, has profound implications in the concept of space-time continuum and the big-bang theory of modern physics!

Entropy measuring disorder and the arrow of time.

First of all, we need to understand what heat is before we can go to understanding entropy. In olden days – 17th century or earlier – people used to visualise heat as some sort of fluid called ‘caloric’. In fact, this caloric is composed of two parts – hot and cold parts. A body is hot because it has more hot fluid and less cold fluid. On the other hand, a body is cold because it has more cold fluid than hot fluid. When hot and cold bodies come in contact with each other, hot fluid moves from the hot to the cold body and thereby rendering the cold body somewhat hotter! Nonetheless, those scientists did manage to identify a very important parameter called ‘temperature’ that measures the body’s ‘hotness’ or ‘coldness’.  

In reality, heat is the thermal energy which arises due to vibration, oscillation or physical motion of atoms and molecules that make up the body. When a body at a higher temperature comes in contact with another body at lower temperature, the excess vibrational energies of the atoms and molecules are transferred to the body at lower energy. It is the temperature that dictates the direction of flow of heat.

Let us now consider what entropy is. Entropy is a thermodynamic quantity that is the ratio of amount of heat energy that flows from one body (hot) to another body (cold) at a certain (absolute) temperature. As the probability of energy flowing from higher energy to the lower energy is much higher than the other way around, it has always been found heat flows from a hotter body to a colder body and entropy is assigned to be positive in that situation. Should heat flow from a colder body to a hotter body – its probability being very low indeed -, entropy could theoretically be negative. But in nature heat never flows from colder to hotter body and entropy is never negative. The very nature of heat (arising from motions of atoms and molecules) being transferred from hot to cold bodies, entropy is a measure of disorder in the composite system. As disorder increases, so does entropy.

It may be pointed out that when heat is shared between the bodies, it does not matter the relative sizes of these bodies. For example, A hot tea spoon dipped in a bucket of water would have some amount of heat transferred from the spoon to the water, although the total energy of the bucket of water may be much higher than that of the spoon. As stated above, it is the temperature which dictates the flow of heat and thereby the increase in entropy.

This increase in entropy or the degree of disorder is intricately linked to the flow of time or in physics terminology, the arrow of time. As neither time nor entropy does flow in reverse, they are always moving in the forward direction. From our previous example, the heat from the spoon is transferred to the bucket of water as time passes and that is the arrow of time. A situation can hardly be visualised (although theoretically possible with infinitesimally low probability) when heat flows in reverse, that is, the dipped spoon would recover heat from the bucket and become hot again!

From the time of big-bang, the entropy had been going up i.e. the degree of disorder had been spreading. That is quite natural as heat flows from one hotter part of the universe to another colder part of the universe and that means entropy is always increasing.

With the advancement of biological sciences, it had been speculated that a time will come when human beings will live for a very long time and may even become immortal. Living longer with better medical care is already happening. People on the average now live almost double the age of what they used to live about a couple of centuries ago. But being immortal means humans will not age in time and that implies that the past, present and future will all merge into one – no change in age, no change in body functions or flow of nutrients from one part of the body to another! It is a continuation of the same thing over and over again. In other words, human beings will live in suspended animation – neither alive nor dead – as energy flow will stagnate to zero entropy and there is no arrow of time. If that is what is meant by immortality, then probably that can be achieved. But, in reality, human beings, or for that matter, any form of life can never be immortal in true sense of the term. A body can live for a long period of time and gradually decay, but can never last forever.

– Dr A Rahman is an author and a columnist