# Physical laws: from pandemics to black holes

- Post by: Maureen Voestermans
- 4 juni 2021
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Three “NWA Kleine Projecten” with the title ‘Physical laws: from pandemics to black holes’ will be funded via the NWA Bouwstenen Route. The idea of these projects is to 1) see if mathematical techniques normally used in quantum mechanics could, surprisingly, also be used to model societal issues such as pandemic outbreaks; 2) explore the building blocks of matter in an original approach that will look at elasticity, one of the most common behaviours in nature – starting from bendable rubber to biological structures to even the crust of neutron stars; 3) explore other surprising aspects of spacetime, namely the existence of event horizons (a point of no return marking the existence of a black hole) and the creation of Hawking radiation around these horizons.

More information about the three subprojects:

**A quantum approach to population dynamics**

“In recent years the field of quantum information has been the focus of great interest both from academia and from industry. The evolving development of the quantum computer has led to claims of ‘quantum supremacy’, but it also underlines the relevance of the question: what kind of problems are quantum computers good at? And, particularly fitting the broad remit of the NWA: is it possible to look outside the domains of computer science or quantum chemistry and physics for interesting problems?

A surprising new direction here could come from population dynamics, which can be highlighted with an example from epidemiological models of the spread of infectious disease. To model the spread of a disease through a population, one could take each individual to be in a specific state and assign rules for their interactions, creating a deterministic, agent-based model.

In the real world, there is always an uncertainty about the status of an outbreak. This uncertainty is active at the level of each individual. One does not know if they are infected until a test has been performed or clear symptoms appear. Is it possible to hardwire this uncertainty into the model? One way to do this is to use a concept familiar from quantum mechanics: the superposition of states. By presenting individuals as being in a superposition, we can also create entanglement between individuals. In this way we can start using the well-developed mathematical tools from quantum mechanics to create what could be called non-deterministic agent-based models, which yield probabilities for individuals to be infected.

The purpose of this research is to explore the application of mathematical tools from many-body quantum systems and quantum field theory to problems in population dynamics. The ultimate goal is to develop a mathematical framework for the understanding of dynamical interacting populations as many-body quantum systems. Examples of tools which can be applied in this context are: the path integral formulation of quantum mechanics, tensor networks techniques to represent large tensors as products of matrices, and renormalization group methods. Within the timeframe of 8 months that fits this funding instrument, an understanding of the SIR (Susceptible, Infectious Recovered) model of epidemiology as a quantum many-body system will be developed. Specifically, the spread of an infectious disease through a population will be modeled using the growth of operator size in a quantum chaotic system. There are already indications that this is possible for simpler models of epidemiology in relation to a well-known model in quantum many-body physics (see “Quantum Epidemiology: Operator Growth, Thermal Effects, and SYK”, Xiao-Liang Qi, Alexandre Streicher, JHEP 08 (2019) 012) in which dualities between gravitational physics and SYK-type models of condensed matter physics are explored).

The proposed research direction would open up new avenues in both the fields of population dynamics and quantum information. It could lay the groundwork for developing a better understanding of the spread of quantuminformation through complex systems, such as the interaction networks within populations.

This project fits perfectly within the goals of NWA route 2 as it aims at establishing a dialogue between physics, mathematics and computer science in an area where aspects of emergence are investigated, as part of the Dutch Institute for Emergent Phenomena, DIEP.

**Hydrodynamics of active odd elastic matter**

“Almost all materials in nature exhibit some form of elasticity in certain regimes. Despite being a centuries old subject, it was recently shown that the traditional methods of elasticity theory need to be revisited in order to be able to describe activity (e.g. self-driven agents such as bacteria) – see Odd Elasticity. The main goal of this proposal is to understand what happens when such materials start flowing. In other words, it aims at developing a hydrodynamic theory of new potential phase of matters – active and odd elastic materials – as well as exploring experimental setups using metamaterials.

In recent years, active matter hydrodynamic equations have played a very important role in understanding pattern formation and flocking in birds, animals, and fishes. The close relationship between the continuum model equations of active matter and those describing liquid crystals has stimulated new directions of research for physicists over the last quarter-century. Recently, such approaches have been extended to include the effect of chirality of the active agents. In real biological systems, there are various examples in which chirality emerges naturally, such as in the swimming strokes of sperm cells. Consequently, successful modeling of chirality in the active matter equations has become a clear milestone to be achieved in the study of active matter, including modifications of active matter hydrodynamics.

A second hot-topic area in the investigation of active matter has been by using equations of motion that break Newton’s third law. The idea of breaking Newton’s third law might sound fanciful, but considering interaction between active agents which carry their own energy source this is a potential reality. As a result, the investigation of non-reciprocity both in the field of active matter and elsewhere is a burgeoning field of ongoing research. In particular, bringing together the two threads introduced here, the combination of chirality and non-reciprocity leads to the presence of novel response functions like odd viscosity and odd elasticity. This NWA project aims at studying the effect on these and other response functions as uncovered in the solutions of the hydrodynamic equations.

To be more specific, the project plans are: (1) to investigate numerically and analytically the hydrodynamic equations of chiral active matter for the flow structures that emerge in these systems; (2) to develop and investigate the hydrodynamic equations of certain classes of non-reciprocal active matter to study flow structures using effective field theory methods; (3) to investigate the emergence and the phenomenology of odd viscosity and odd elasticity in active matter systems using both analytical and numerical methods; (4) to devise potential experimental setups using metamaterials.

Recent study of non-reciprocal active materials and chiral materials have shown how these materials can display a wide range of novel behaviors. This proposal centers on studying the behavior of new classes of active materials and in the development of their comprehensive theoretical understanding.”

**Do neutron stars Hawking radiate?**

“In 1974 and 1975 Stephen Hawking published his ground-breaking papers “Black Hole Explosion?” and “Particle Creation by Black Holes”, proposing that black holes radiate. This was part of the early attempts to describe quantum fields in a curved spacetime, which is very difficult of course because quantum and gravity (still) do not go together very well. In summary, an impressive calculation shows that quantum effects cause a classically stationary back hole to emit thermal radiation, now called Hawking radiation. The black hole even evaporates eventually, leaving a perfect thermal state in the distant future, in which we observers find ourselves. For a clear overview we refer to the books by Wald (1994) and Parker & Toms (2009).

From these (or Hawking’s) expositions one realizes that it is essential that there is an event horizon in Hawking’s calculation and in response to an original question whether neutron stars might also emit “Hawking radiation” the applicant has devoted a short calculation to it and this in turn led to a very interesting discussion. Most importantly, if you want to describe quantum fields for the neutron star + gravity system, you need to extend Hawking’s calculation to a spacetime in which some region is separated – namely the interior of the neutron star – and know something about the quantum effects at the surface, but work without the presence of an event horizon.

More precisely, the sought-for radiation could arise from the more general principle of “particle creation from the curvature of spacetime”. In the early work of Leonard Parker (1968, 1969, 1971) this was explained carefully for expanding universes. The main and crucial assumption in both the black hole and cosmological case is that one can identify asymptotically flat spacetimes, where the ordinary principles of quantum fields make sense. An ingoing vacuum state is then mapped to an outgoing state by Bogoliubov transformations that can in principle be derived from the wave equation in the curved background. The resulting outgoing state is typically not the vacuum state any more; this is the sought-for particle creation, or, in other words, the radiation we are after.

The main challenge in the present project is thus to come up with a (simplified) model for the collapse of matter into a neutron star, where one can identify an asymptotically flat past (well outside the body and at early times) where geodesics begin that end at future null infinity – again assumed to be a flat region of spacetime. After suitable assumptions (spherically symmetric collapse, etc.) on the body, one expects the vacuum state at minus infinity to be transformed to a non-trivial thermal state at future null infinity. The properties of that state are then expected to be related to the physical properties of the (neutron) star.

About the importance of such a project: the outcome could say something about Hawking radiation for more general bodies, and would therefore go much further, especially in astronomy, than the still elusive black holes. In addition, there is a great deal of speculation and discussion in the popular media, but not so extensively in the scientific literature. For example, this article recently appeared in Forbes (with a slightly too bold title).

In addition to a somewhat exaggerated correction of an analogy used by Hawking in his popular science book to explain his 1974 work, it also suggests that Hawking radiation should indeed exist for every body, but of course without details. This project is intended to provide at least some of these details, which would be ground-breaking if the idea works.”

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