Prof. Thanu Padmanabhan, one of the stalwarts of theoretical physics, and a shining star of the Indian scientific community, left his mortal abode on the 17th of September this year. With a stellar career spanning over four decades, he has been immortalized through his contributions to advancement of theoretical physics and cosmology. In this article, Dr. Karthik Rajeev brings out the essence of some of Prof. Padmanabhan’s seminal works - ranging from the formation of cosmological large scale structure to the interface of quantum mechanics and gravity.

Thanu Padmanabhan
(10 March 1957- 17 September 2021)

Thanu Padmanabhan, fondly known as Paddy, was an internationally acclaimed Indian theoretical physicist, whose research works are spread across a variety of topics in gravitation, quantum theory and the study of our universe. Progress in theoretical physics happens in two different, but equally important, ways. The first corresponds to significant advances achieved using existing theoretical frameworks, while the second corresponds to, what may be called `paradigm shifts’. Padmanabhan’s immense contributions to physics have been on both of these fronts. About 300 papers in refereed international journals, about 10 books and numerous other articles that he has authored, spread over about four decades of his monumental career, is a testimonial to the impact he made in the field.

In 1977, a 20-year-old Padmanabhan started his research journey by investigating the interaction between gravitational waves and electromagnetic waves. The results of his mathematical study were published in the reputed journal Pramana, while he was still an undergraduate student at University College, Trivandrum. Little did his friends and colleagues know that this was only the start of a stellar career of one of the brightest and fastest thinkers of our time. We shall now briefly glance through some of his contributions in the decades that followed.

It should be mentioned that the following `summary’ does not faithfully cover all of Padmanabhan’s contributions. This article is only an attempt to explain, in simpler terms, a few of his works that have influenced the author the most.

When the Quantum meets Gravity

Quantum mechanics and the general theory of relativity are two of the foundational pillars on which theoretical physics, as we understand it today, is built. While quantum mechanics offers an efficient approach to understand physics at the smallest scales, general relativity furnishes the most satisfactory theory of gravitational interaction at our disposal today. Recall that according to our current understanding, there are four fundamental interactions in nature: the strong nuclear, the weak nuclear, the electromagnetic and the gravitational interactions (see: Fundamental interaction). A thorough understanding of the first three forces is essential to describe physics at the subatomic to the molecular level. On the other hand, while studying physics at these scales, theoretical physicists often ignore even the existence of gravity and get away with it quite safely! However, the effects of quantum mechanics are quite significant at these smallest scales. Hence, any sensible theory that attempts to describe phenomena at these levels must respect the principles of quantum mechanics. Fortunately, we have a remarkable model to describe the strong nuclear, weak nuclear and electromagnetic forces that incorporate quantum theory, namely, the Standard Model of particle physics (for a recent visual description of the Standard Model, see this link).

Then the question arises: What about gravity?. It turns out that quantum mechanics does not play any significant role in the gravitational interactions that, say, govern the dynamics of our Solar system. This is true even for gravitational interactions at much larger scales, say galaxies, galaxy clusters and so on. Does that mean that we should not bother incorporating quantum theory into our models of gravity? The answer is NO! The reason is that there are scenarios in nature where both the effects of quantum mechanics as well as gravitational interactions are believed to be equally significant. One such scenario occurs, for instance, when we consider physics at the very early stages of our Universe. There is a simple trick that physicists use to decide whether a physical scenario demands a quantum theory of gravity. The idea is to check whether the typical length, time and energy scales of a given physical situation is comparable to a set of constants called the Planck length, Planck time and Plack energy, respectively. The reason this works is because the aforementioned Planck quantities are defined solely in terms of the fundamental constants c (the speed of light), h (the Planck’s constant) and G (gravitational constant) (see this link for further information). Recall that Planck’s constant (h) corresponds to quantum mechanics, the speed of light ( c ) to relativity and the gravitational constant (G), of course, to gravity. Therefore, it is reasonable to expect that the Planck quantities (constructed with h,c and G) correspond to quantum theories with general relativistic gravity! Now, imagine the very early stages of the universe, say, just after or during the Big-Bang, when our universe was extremely `tiny’. During that era, the typical length, time and energy scales are believed to become comparable to the corresponding Planck quantities, hence signaling the need for a quantum theory of gravity to explain the physics at that time. A similar argument can also be made for the extremely dense interior of a black-hole, indicating that quantum gravity effects might be relevant there as well!

Therefore, a quantum theory of gravity (translates to “a consistent model of gravitational interaction that incorporates principles of quantum mechanics”) is crucial to understand nature deeply. Unfortunately, however, one of the major challenges in theoretical physics today is to combine the principles of quantum mechanics and general relativity, into a coherent quantum theory for gravity. The reason gravity has not been tamed this way is primarily because it is not simply a `force’ in the conventional sense. To better understand what makes gravity different, let us briefly review how gravity is described in Einstein’s general theory of relativity (GTR).

Einstein taught us that spacetime– the union of space (the ‘where’) and time (the ‘when’)– is the most natural construct to base our understanding of gravity. When there is no matter, spacetime is quite uninteresting and ‘flat’, say, like a flat rubber sheet. The presence of matter introduces non-trivial geometric features on the spacetime, somewhat analogous to how placing a heavy ball on the rubber sheet stretches it. Gravity, it turns out, is just a manifestation of such geometric features of spacetime. The geometry, in turn, can be mathematically described by a quantity called metric tensor. Imagine the metric tensor as an object that tells us two basic pieces of information about the spacetime: ‘distances’ between two nearby points and ‘angles’ between intersecting lines in the spacetime. Einstein’s famous field equations determine the precise manner in which metric tensor behaves in the presence of matter. On the other hand, in the absence of gravity, physicists usually consider the other interactions to play out in a flat background spacetime, much like how dancers (forces and particles) perform in an inert stage (spacetime). However, the presence of gravity has the consequence that the spacetime itself is dynamic! (Imagine the stage itself performing with the dancers!) To combine quantum mechanics with a realistic theory in which the spacetime itself is dynamic is a major challenge that theoretical physicists are facing even now.

In the 1980’s Padmanabhan, along with his supervisor Prof. Jayant V Narlikar, made significant progress in tackling this challenge. An ingenious idea that was the key to some of their works was to consider a simpler scenario in which the dynamic content of gravity is captured by only a ‘piece’ of the metric-tensor, called the conformal factor. Roughly speaking, what this simple scenario meant was that they considered only the distance-providing piece of the metric tensor to be dynamic while restricting the angles to be ‘fixed’ (Recall that metric-tensor gives us ‘distances’ and ‘angles’ in spacetime.). It turns out that this piece of gravity can be combined with quantum theory in a relatively straightforward way. Therefore, they could perform several calculations that would have been difficult or even impossible in attempts towards a ‘full’ quantum theory of gravity. Although their model might sound simple, it leads to important insights about the structure of the universe and spacetime in general, of which here we shall briefly look at only two.

Before going into the insights that emerged from Padmanabhan’s and his collaborators’ studies, we have to understand certain basics of our universe’s past. There is irrefutable evidence now that our universe is expanding at an accelerated pace. What this implies is that if we imagine the evolution of our universe as a movie and play it in reverse, we would expect that the universe is contracting. Now, using the principles of general relativity and the assumption that our universe is made of reasonably realistic matter content , this thought experiment leads to the fact that the universe must have emerged from a single point in the past! Such a point is technically called a singularity and, in physics, the presence of such singularities signifies potential deficiencies of a theoretical framework. It is generally believed that a quantum theory of gravity would cure this problem. One of the important insights that emerged out of the works of Padmanabhan and Narlikar was that this belief is in fact well-founded. For instance, one of the outcomes of their simple model was that the singularity at the beginning of our universe may be absent when quantum theory is considered! This might be viewed as a strong indication that a more complete quantum theory of gravity may also have the cure for singularity.

Another result that came out of their studies was that the distance between two points in spacetime cannot be made arbitrarily small, instead, there could be a lower limit called ‘zero-point length’. This is quite counter-intuitive because our intuition is that as we bring two points closer and closer, the distance between them eventually becomes zero! The reason for the breaking of our intuition is that quantum effects potentially modify the structure of spacetime at the smallest length scales. In fact, it is found that the presence of `zero-point length’, or something resembling that concept, is a universal feature in several approaches to a quantum theory of gravity. This later motivated Padmanabhan and his collaborators to also investigate the implications of the ‘zero-point length’ in several other important contexts in theoretical physics, which eventually led to many useful physical insights.

The grand design of the cosmos

The formation of large scale structures in the universe is probably the problem requiring a solution in cosmology.
— Thanu Padmanabhan

At sufficiently large scales, our universe is quite homogeneous and isotropic. It is important to understand what one means by sufficiently large scale. To understand this better, let us consider a very large white sheet of paper. When looked at with naked eyes, the paper looks the same no matter at what point on the paper we are looking and which direction we are looking. But, if we zoom in using a powerful microscope, we will see that the paper is made of a network of microscopic plant fibres, which are arranged to form a uniform flat sheet at scales visible to our naked eyes. Of course, if we zoom in further, we will also find that the fibres themselves are made of cells, which in turn is made of molecules and so on. Similarly, in our universe, the stars are organized into galaxies, which in turn form galaxy groups that form galaxy clusters. These clusters are then arranged into filament-like structures, sheet-like structures and so on. Such large structures are separated by immense voids, hence creating a somewhat foamy texture to our universe, at a very large scale. Just as a paper looks homogeneous to us at scales greater than, say, a few millimetres (although it consists of intricate microscopic plant fibres), our universe is homogeneous at scales much greater than a few hundred million light-years (although, at smaller scales, it consists of several structures like galaxies, galaxy clusters, filaments etc., at various levels).

The fact that the universe is quite homogeneous at sufficiently large scales and at the same time has elaborate structures at smaller scales provides us an important clue about the state of our universe when it was much younger. Scientists believe that in the very early stages of our universe, the density of matter must have been remarkably uniform (hence, the large-scale smoothness we observe today!). However, there must also have been very small variations in this density, as we move from one place to another in the universe. The large scale structures in our universe, that we described earlier, are believed to have formed due to the gravitational field of such density fluctuations. However, the precise manner in which these `primordial’ density fluctuations led to the formation of large scale structures is still not completely understood analytically. Efficient computer simulations have been developed by several scientists and collaborations to make progress in understanding this problem. Although such simulations are helpful in making concrete predictions, they often do not provide us with clear physical insight. To gain more insight one needs a greater analytical handle. According to Padmanabhan: “This is important since some people in this field use computers the way a drunkard uses a lamppost - for support, not illumination.”

Padmanabhan contributed significantly to this direction by employing a wide range of tools in theoretical physics, which include, in particular, statistical mechanics. For instance, although the problem of cluster formation itself, in its entirety, is difficult to study analytically, Padmanabhan proposed a simple model in which one can divide the process of formation of structure into three convenient regimes. Each of these regimes was defined such that they could be independently dealt with reasonable analytical ease. He then proceeded to show how the results, in the three independent regimes, can be carefully combined to make predictions that are in good agreement with those from computer simulations. Such an approach shed more light on the underlying physics that drives the structure formation.

Cosmological constant and the microstructure of spacetime

Observations show that our universe is expanding at an accelerated rate. The current accelerated expansion, in turn, seems to indicate that our universe is uniformly filled with a rather strange kind of energy called ‘Dark Energy’. Unlike other kinds of matter and energy, dark energy seems to create a sort of repulsive force at large scales, which tends to accelerate the expansion of our universe. It turns out that the effect of a uniform distribution of dark energy is mathematically equivalent to introducing a certain fundamental constant to Einstein’s field equations of general theory relativity. In this picture, dark energy is viewed as the manifestation of a new fundamental constant for our universe, called the cosmological constant. Moreover, to best explain the current observations, the cosmological constant must be a very small positive value, in a suitable unit.

On the other hand, according to the principles of quantum field theory (QFT), which is another pillar of theoretical physics, the ‘vacuum’ has a certain energy content and this energy has the same effect as that of a cosmological constant. I should caution that the term ‘vacuum’ technically means the lowest energy state of a system. Moreover, due to quantum effects, the ‘vacuum’ in QFT, unlike the vacuum in the English dictionary(vacuum = a space entirely devoid of matter), has a richer structure. Consequently, the vacuum, according to QFT, must have a certain energy which is referred to as the ‘vacuum energy’. Since this vacuum energy also has an effect similar to the introduction of a cosmological constant, a certain fraction of the observed value of the cosmological constant must be the contribution from the vacuum energy. The problem, however, is that theoretically, this contribution seems to be gigantically larger than the observed value of the cosmological constant! This embarrassing disagreement between the observed value of the cosmological constant and the theoretical value of vacuum energy is referred to as the cosmological constant problem.

According to Padmanabhan, to resolve the cosmological constant problem, one must start by admitting that at the deeper level, spacetime is not the fundamental object describing gravity. Spacetime and gravity, according to Padmanabhan, must emerge from more fundamental microscopic structures. This is similar to how a large number of microscopic H₂O molecules interact to form the emergent fluid that we call water. He also claimed, with compelling reasons, that a deeper theory of gravity should be sensitive to only the fluctuations of the vacuum energy, instead of the vacuum energy itself. In this framework, one should identify the cosmological constant with the fluctuations of the vacuum energy, instead of the total vacuum energy itself, which we already saw was gigantically large. This furnishes a compelling approach for resolving the cosmological constant problem, which is still being seriously explored by many researchers across the world.

Note that fluids, which is an example of emergent phenomena, are described to some extent by a set of equations called the Navier-Stokes equations. Moreover, the presence of microscopic structure also implies that one can ascribe thermodynamic properties to these fluids. These thermodynamic quantities, in turn, must also satisfy certain thermodynamic identities. On the other hand, we have already seen that the dynamics of spacetime is described by Einstein’s field equations. To summarize, while emergent objects are characterized by certain kinds of features and related equations, gravity (or equivalently spacetime) is described by, what seems like, a totally different kind of equations. How does one reconcile this with the fact that spacetime (gravity) is emergent?

Padmanabhan and his collaborators showed that Einstein’s general relativity itself already contains strong evidence for the claim that spacetime is emergent. For example, they showed that when Einstein’s equations are suitably reformulated, it takes the form of the Navier-Stokes equation! In addition, in a different setting, Einstein’s equations also acquire the form of thermodynamic identities! They also demonstrated that this is a feature of a larger class of theories of gravity that are extensions of Einstein’s general relativity. This, clearly, can be considered as a strong hint of the emergent nature of spacetime and hence, gravity. This raises the deeper question: If spacetime is emergent, like say water, what is its microscopic structure, analogous to how water consists of microscopic H₂0 molecules? In his last decade, Padmanabhan had constantly considered this question, the answer to which would revolutionize physics forever. He also believed that the difficulties with combining quantum theory with gravity primarily arise because one usually assumes spacetime as the fundamental variable to describe gravity, while it is actually only an emergent variable. The answer to the above question could also lead to the simultaneous resolution of two of the most fundamental challenges in theoretical physics: (1) formulating a quantum theory of gravity and (2) the cosmological constant problem. If experimental and theoretical confirmation of Padmanabhan’s revolutionary perspective on gravity emerges in the future, it would mark the third significant paradigm shift in our understanding of gravity, following Newton’s law of gravitation and Einstein’s general theory of relativity!