A 125-year-old physics challenge may sharpen climate models, offering breakthroughs in forecasting, disaster prediction, and pure science.
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At the dawn of the 20th century, David Hilbert propounded his famous 23 problems on fundamental mathematics, one of which, in particular, would have profound consequences for theoretical physics if it were ever to be solved. A solution proposed recently has claimed to do just that. If it turns out to be true, it would not only be a major step forward in physics but could also have a sizeable impact on a wide variety of other fields, including the possibility of significantly more accurate climate models. Furthermore, in an era dominated by technological breakthroughs in Artificial Intelligence (AI) and the geopolitical elements surrounding it, the importance of fundamental scientific research often gets overshadowed. A theoretical breakthrough of this magnitude could aid significantly in addressing this issue.
At the second International Congress of Mathematicians held at Sorbonne University, Paris, in 1900, David Hilbert, one of the greatest mathematicians in history, unveiled 23 unsolved problems in mathematics which would define the future of the subject. These included fundamental mathematical problems such as the famous Riemann hypothesis and the Diophantine Equation. While some of these have been solved over the preceding century, several continue to remain elusive.
Though Hilbert’s problems are technically mathematical, a few of them do have implications for other fields. A case in point is his sixth problem, “The Axiomatization of Physics,” in which he pondered whether it was possible to determine the basic mathematical principles from which all physical theories stem. While this is a particularly ambitious problem, which may never truly be solved, a subset of this problem has gained particular traction in the physics community over the years: the prospect of unifying three seemingly disparate theories explaining the motion of fluids at different scales.
The current understanding of fluid motion exists on three scales: microscopic, mesoscopic, and macroscopic. At the microscopic level, we utilise Newton’s laws of motion to determine the behaviour of individual point particles. At the mesoscopic or intermediate scale, the equations of statistical mechanics take over, with the Boltzmann equation serving as its foundation. Statistical mechanics essentially uses the principles of probability and statistics to smooth over the dynamics of individual particles in favour of their collective behaviour and properties. Finally, at the macroscopic level, we no longer track the behaviour of particles, focusing instead on the properties of the fluid as a whole. This is determined by the Euler and Navier-Stokes equations.
Figure 1: Fluid Motion Across Different Scales
Source: Hilbert’s Sixth Problem: Derivation of Fluid Equations Via Boltzmann’s Kinetic Theory, Deng et al
While all three theories work remarkably well in their own respective domains, it is not quite evident what exactly serves as the unifying element, connecting vastly different equations and theories across all three divergent scales. However, in March 2025, researchers at the University of Michigan published a paper claiming to have finally united the three different theories under a unified scheme. While it has not been peer-reviewed yet, the analysis appears promising and may finally resolve a longstanding fundamental issue in theoretical physics.
While uniting three different theories across multiple scales is in itself a remarkable achievement, the paper also has implications for a much more fundamental issue in physics, the arrow of time or why time passes in only one direction. At the microscopic level, the laws of physics are reversible in time, meaning that at the level of atoms, forward in time works essentially the same way as backwards in time as far as the theory is concerned. Yet this is not the case at the macroscopic scale, or what we observe on a daily basis. Instead, time only seems to flow in one direction: forward.
While uniting three different theories across multiple scales is in itself a remarkable achievement, the paper also has implications for a much more fundamental issue in physics, the arrow of time or why time passes in only one direction.
Presently, the laws of thermodynamics justify the arrow of time using the principle of increase of entropy, which roughly states that natural phenomena proceed in the direction which increases the overall disorder within the system, thereby giving rise to what we perceive as the forward flow of time. However, there is no actual proof for why this perceived unidirectional flow of time takes place. Hilbert’s sixth problem highlights the importance of understanding how the macroscopic equations of fluid mechanics emerge from the microscopic behaviour of atoms. Therefore, its potential solution will significantly aid in further understanding why the arrow of time exists and how irreversible behaviour emerges from reversible physical laws.
One of the main challenges impeding accurate climate models is the vast number of parameters involved in their computation. This makes it particularly difficult to run simulations even for the most advanced supercomputers. Models must account for a gamut of macroscopic and microscopic parameters, including wind and water circulation, air molecules, and substrates, while incorporating equations from kinetic theory, statistical physics, and fluid mechanics. A connection between macroscopic and microscopic equations will allow these models to bridge the gap while eliminating redundant parameters, thereby significantly increasing accuracy and efficiency.
A connection between macroscopic and microscopic equations will allow these models to bridge the gap while eliminating redundant parameters, thereby significantly increasing accuracy and efficiency.
The same applies to other fields that use these equations, including chemistry, biology, aerodynamics, condensed matter physics, and materials science.. More accurate models mean more efficient simulations, which, in turn, implies faster technological progress and innovation. Combining these with increasingly efficient AI algorithms, such as Google’s AlphaGeometry, has the potential to accelerate the development of these models.
Virtually all technological breakthroughs that have emerged in the 20th century, including semiconductors, lasers, and more recently, AI chips, are unanimously founded on fundamental research in mathematics and physics. For instance, quantum theory, which is currently celebrating 100 years of continued success, played a major role in paving the way for almost all current technologies. While there are significant efforts to scale up research and training in technologies such as AI, quantum computing, and semiconductors, the same does not seem to be true for fundamental scientific research, as highlighted by the recent federal research funding cuts in the United States. This is further exemplified by the fact that, despite significant achievements in multiple areas of physics in the recent past, according to several prominent physicists, there has been virtually no fundamental advancement in the subject for over 40 years.
That solving a 125-year-old physics problem may contribute to these improvements underscores the vital role of advancing research in the pure sciences.
In this context, the solution to a foundational problem in physics has the potential to reinvigorate interest in advancing fundamental sciences, especially given its applications in other applied sciences. Climate science serves as one such crucial area. Despite their critical importance, climate models have long struggled with inaccuracies, largely due to their inherent complexity and the vast number of variables and parameters involved. Advances in modelling could significantly improve our ability to track climate change, forecast weather, and predict natural disasters such as hurricanes and floods. That solving a 125-year-old physics problem may contribute to these improvements underscores the vital role of advancing research in the pure sciences.
Prateek Tripathi is a Junior Fellow with the Centre for Security, Strategy and Technology at the Observer Research Foundation.
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Prateek Tripathi is an Associate Fellow at the Centre for Security, Strategy and Technology. His work focuses on an emerging technologies and deep tech including quantum ...
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