4 questions to Lionel Martellini about his research in finance and... in astrophysics and quantum physics!

A PhD in finance from Berkeley in 2000, a PhD in astrophysics from Nice in 2019... and dozens of articles in international journals. How did you develop these two passions?

Lionel Martellini : Since my earliest childhood, I have always been deeply fascinated by the unreasonable efficacity of mathematical abstractions in accounting for the physical phenomena of the real world. ‘The great book of nature is written in the language of mathematics,’ said Galileo, and one cannot help but marvel at the mystery of the ability of the finite human mind to decipher even a few fragments of this immense book. This constant astonishment is perfectly summarised by Albert Einstein's phrase, ‘what is truly incomprehensible is that the world is comprehensible.’

Despite this keen personal interest in physics, I was so deeply disappointed by the teaching of the subject at high school, which took a highly formatted approach and encouraged neither reflection nor critical thinking, that I ultimately chose to focus instead in college on the use of mathematics and statistics for modelling random phenomena in finance and economics. It was after an academic career that began in the United States (PhD at the University of California, Berkeley, then a position as Assistant Professor of Finance at the University of Southern California in Los Angeles) that I finally joined EDHEC, where I founded the EDHEC-Risk Institute alongside Noël Amenc.

It was only much later, during a sabbatical at Princeton University in 2011-2012, that I took my first formal step towards studying physics. It must be said that Princeton is extraordinarily steeped in the history of theoretical physics, which has been home to giants such as Albert Einstein and Kurt Gödel within its Institute of Advanced Study, but also John Von Neumann and Robert Oppenheimer, and more recently Edward Witten, the only physicist to date to have received the Fields Medal in mathematics. It is really difficult to stay in this environment without being caught up in the strange attraction of theoretical physics! I took two doctoral courses at Princeton, one on general relativity and the other on cosmology, which was then taught by the great physicist Paul Steinhardt, renowned for his work on the cyclic model of the universe.

This experience reaffirmed my interest in these subjects, and I decided, back in France, to pursue doctoral studies with a focus on relativistic astrophysics at the University Côte d'Azur. I was lucky enough to be welcomed there by an astrophysicist, Tania Regimbau, who showed great open-mindedness in inviting a financial economist to join her research work on the stochastic gravitational wave background!

These seemingly opposite domains nevertheless appear to be very close in your mind and in your ‘practices’. Could you tell us more?

Lionel Martellini : 

At first glance, the main point of intersection between finance and physics is that they are two fields that share a common language, that of mathematics. A deeper examination shows that there are certain similarities, but also, of course, fundamental differences, between these disciplines.

To better understand these nuances, it is first useful to remember that physical phenomena seem to be governed by laws, which themselves seem to stem from fundamental principles, such as the principle of least action, the principle of relativity, or the principle of conservation of energy. These somewhat mysterious principles, whose primary existence must first be guessed at, place useful constraints on the admissible laws, thus guiding the physicist in his blind trial and error attempts at understanding the physical worlds.

On the subject of the conservation principle and how it illuminates the physicist's path, it is instructive to consider the parallel drawn by physicist Richard Feynman: ‘Let us imagine that physics, or rather nature, is a vast game of chess with millions of pieces, and that we are trying to discover the rules of the game. The great divinities who play do so very quickly, and we find it difficult to follow and understand. However, we manage to grasp certain rules, and among those we discover there are some that do not require us to observe all the movements. For example, suppose there is only one white pawn on the chessboard; since the pawn moves diagonally and therefore always remains on squares of the same colour, if we look away for a moment while the gods are playing and then look at the game again, we can expect to find a white pawn on the chessboard, its position may have changed but the colour of its square will have remained the same. This is the very essence of a law of conservation. We do not need to get involved in the game to learn at least the basics.’

It is therefore not only the observation of physical phenomena, but also the supposed existence of these principles, that guide the physicist in his approach. Thus, while it is commonly accepted that the ability to offer empirical predictions not yet invalidated by experience is what constitutes the basis for the validity of a physical theory, it is sometimes necessary to think ‘against reality’. The archetypal example of this approach is the extraordinary thought experiment proposed by Galileo to justify the principle of the universality of free fall on purely logical grounds, even though the presence of frictional forces systematically induces in free fall experiments (not carried out in a vacuum) different fall times for objects of different mass, size and composition.

If we now turn to financial theory, it appears that it is also based on a few fundamental principles, in particular the principle of absence of arbitrage (according to which two assets paying the same cash-flows must have the same price), but their validity is based on a form of rationality of economic agents (in this case their desire to exploit price differences between these assets to generate a risk-free profit, which tends to align prices). 

Beyond the frictions (transaction costs, regulatory constraints, etc.), which, like frictional forces in physics (of which they are the natural equivalent), hinder the pure and perfect application of the fundamental principles of finance, certain behavioural biases of investors can compromise the validity of these principles.

So, while we have never seen an apple that we let go not fall to the ground at a speed that is more or less independent of its mass (or the approximation is explained by the presence of friction in the air), we have seen closed-end investment funds trade at prices significantly different from the net value of their underlying assets, with a difference that may be greater than that explained by the impact of frictions, and which is due in particular to the presence of behavioural or informational biases (brand effect, recommendations, lack of knowledge about net asset value, etc.).

In 2016, the detection of gravitational waves rightly caused a stir in the scientific world. Your work and collaborations contributed to this exceptional momentum. What has been the follow-up? What have you been working on since then?

Lionel Martellini : The existence of gravitational waves is indeed an absolutely major discovery that has provided further confirmation of the theory of general relativity, in this case in the so-called strong field domain, with very massive black holes moving at very high speeds. 

This discovery has opened up a new era in astrophysics and cosmology, that of gravitational astronomy, which will make it possible to observe phenomena that are inaccessible by traditional methods based on signals of electromagnetic origin (gamma rays, X-rays, ultraviolet rays, visible light, infrared rays, radio waves, etc.).

The new frontier now consists, thanks to the introduction of increasingly sensitive detectors, some of which will be based in space, of managing to detect gravitational waves of cosmological origin, which are ripples in the geometric structure of space-time produced in the primordial Universe, a few moments after the Big Bang. Unlike gravitational waves of astrophysical origin, the only ones detected to date, which are emitted by violent astrophysical events such as the fusion of black holes or neutron stars, those of cosmological origin come from phenomena that occurred in the very first moments of the Universe through processes predicted by certain cosmological models but whose existence is yet to be confirmed by observations (cosmic inflation, phase transition phenomena, cosmic strings, etc.).

Personally, and even though my own work was on an exploratory subject with no direct link to this major discovery, I experienced it as an immense pleasure and privilege to have the opportunity to join an international collaboration involving more than 2,000 researchers from all over the world, embarking on an absolutely extraordinary intellectual adventure, and this precisely during a period marked by the first detection on 14 September 2015.

My interests have evolved considerably since that first excursion into the world of physics, and my work now focuses on an entirely different field, that of the foundations of quantum physics. While astrophysics and cosmology are concerned with the large-scale objects and structures that make up our universe, quantum physics aims to describe the behaviour of matter at its most fundamental level, that of elementary particles. Precisely 100 years after Werner Heisenberg and Erwin Schrödinger introduced the two competing but equivalent formulations of quantum mechanics, it is fascinating to note that there are still fundamental open questions in the field today.

During another sabbatical, this time at MIT in 2022-2023, I had the opportunity to meet a physicist, Mathieu Beau, now leader of the mathematics and science department at the International School of Boston, with whom we are conducting, in our spare time, an ambitious research programme on the measurement of time in quantum mechanics, which remains one of the fundamental unresolved questions today. While the Born's rule gives the probability distribution of a position measurement at a given instant (with a view of answering the question ‘where is the particle now?’), there is in fact no rule in the standard formalism of quantum mechanics for obtaining the probability distribution of a measurement of the time of passage at a given position (with a view to answering the question ‘when will the particle arrive here?’). What is known as the ‘arrival time problem’ has been widely debated in the scientific literature, where various competing approaches have been proposed, but no consensus has emerged to date. The absence of an accepted formalism for the analysis of arrival time can be considered one of the main blind spots in our quantum description of physical phenomena.

The work we are conducting, which has resulted in several international publications in leading journals, provides a general framework for approaching this question of the arrival time of a quantum system at a given state, without departing from the standard formalism of quantum mechanics but rather by exploiting the full extent of its spectrum! We have thus provided a set of new empirical predictions, some of which are quite surprising, such as the presence of a violation of the universality of free fall in the quantum domain (in the sense that the average fall time of a quantum particle in a gravity field depends on its mass), the existence of a new position/time uncertainty relation (which complements Heisenberg's position/velocity relation) or the presence in certain cases of interference phenomena which may explain that the average time to reach a more distant position can be less than the average time to reach a less distant position!

The next stage now consists in extending these results to discrete systems such as spin systems that form the basis of quantum computing, and also of experimentally validating these predictions, and we are in contact with various teams of experimenters to consider setting up such experiments that could confirm (or invalidate!) the theoretical results we obtained by seeking to exploit the mathematical coherence of the quantum formalism.

Role models are essential in all professions, including research and teaching. If you could look back on your career, what messages would you like to send to current students?

Lionel Martellini : 

Yes, you are right to emphasise the importance of role models in a career. I, for one, have been deeply influenced by the profound freedom of certain physicists such as Albert Einstein or Richard Feynman, who forged their own path in a very bold manner and sometimes without regard for common sense, and their example has served as inspiration throughout my academic and personal experiences.

In the light of a journey that has enabled a young, somewhat dreamy teenager to reconcile a career as an amateur physicist with a professional career in finance, the first message I would like to deliver to our students is to encourage them to hold a form of loyalty to their childhood dreams. This loyalty seems to me to be a very useful guide in the derisory but extraordinary adventure that is human destiny. 

Quantum physics teaches us that at the heart of the universe's creation lies a gigantic wave function, which can be defined as the generative source of infinite possibilities, and human life is a continuous journey of surpassing oneself, of growth, of realisation and expansion of these potentialities.

If within clay lies the statue-to-be, if a blank page a novel in the making, it takes time, but also the vision, talent and hard work of an artist to make real that which existed only in potential. It is therefore a question of each of us building our destiny step by step, assuming full responsibility for being the sole architect of this long and patient process of giving birth to what will ultimately be our life. All this is perfectly captured in a few words by the famous Nietzschean injunction: ‘Become what you are. Do what only you can do.’

And the second message that I would be tempted to deliver, perhaps ultimately the most important, is that of cultivating a taste for gratitude throughout this process as a form of salutary wisdom. Of knowing how to take the time to say thank you, thank you to life, which is offered to us as a gift, thank you to others, those who accompany us, sometimes from our earliest childhood, through our successes and our failures. 

For my part, I was fortunate enough to spend most of a somewhat atypical career at an institution, EDHEC, which is itself quite atypical, standing out from French and international business schools with a unique development model that allows for great intellectual and also entrepreneurial freedom. I have received a lot from our fine school, and for that I feel a deep sense of gratitude. In return, I have tried to give, to give my energy to the service of our ambitious projects within the EDHEC-Risk Institute, to share my enthusiasm in the context of my interactions with the generations of extraordinary students that I have had the immense pleasure of rubbing shoulders with.

So thank you to them, thank you all, all the best in your journey, and enjoy the ride!

………………

Readers interested in further exploring the fascinating world of theoretical physics can find interesting references by following the links below.

The Theoretical Minimum

The Theoretical Minimum by Leonard Susskind, Stanford University is a series of lectures and books on theoretical physics created by Leonard Susskind, a professor at Stanford, in collaboration with Art Friedman. The objective is to teach theoretical physics in a rigorous but accessible way, going beyond simple popularisation and introducing essential mathematical concepts.

• https://theoreticalminimum.com/

The Biggest Ideas in the Universe

The Biggest Ideas in the Universe is a series of videos and books produced by Sean Carroll, theoretical physicist and professor at Johns Hopkins University, aimed at explaining the fundamental concepts of physics with equations, but in a way that is accessible to non-specialists.

• https://www.preposterousuniverse.com/biggestideas/