November 7, 2024 by Alessio Zaccone
Collected at: https://phys.org/news/2024-11-fluids-thicken-theory-einstein-real.html
The theory of special relativity is rife with counterintuitive and surprising effects, the most famous of which are length contraction and time dilation. If an object travels at a relative speed, which is a non-negligible fraction of the speed of light, with respect to an observer, the length of the object in the travel direction will appear shorter to the observer than it actually is in the object’s rest frame.
In particular, it will appear shorter by a factor equal to one divided by the Lorentz factor. The latter depends only on the relative speed between the object and the observer and on the speed of light, and can only be larger or equal to one, hence the “length contraction” effect.
While length contraction and time dilation are well established relativistic effects, which have been known since even before Einstein’s 1905 paper on special relativity, one may wonder if other relativistic effects concerning other fundamental physical properties can be predicted by special relativity.
For example, in spite of intense research in the field of relativistic hydrodynamics, a relativistic theory of the viscosity of fluids that is also able to recover the limit of classical gases has been missing so far. This is the revealing symptom that the available relativistic theories of viscosity are, possibly, incomplete.
In a new article published in Physical Review E, I derived a general microscopic theory of the viscosity of fluids, based on the recently proposed relativistic Langevin equation (derived from a relativistic microscopic particle-bath Lagrangian), combined with a microscopic nonaffine theory of particle-level displacements under flow. This framework describes the microscopic motion of particles (atoms or ions) as a result of their interactions and collisions with other particles, under an imposed flow field.
While the particles have a tendency to follow the flow field, they also deviate from it due to the interactions with other particles. These “deviations” are called “nonaffine” motions and greatly contribute to the dissipation of momentum in the fluid in motion.
In special relativity, the “momentum” that is relevant for relative motion of the object with respect to an observer is the “proper momentum”, which is the ordinary momentum of the particle multiplied by the Lorentz factor (again, the latter is a number always larger than 1 and a very large number for objects traveling at or near the speed of light).
The new theory that I derived shows that the viscosity of the fluid, which is proportional to the loss of proper momentum for a fluid moving near the speed of light, is thus proportional to the ordinary viscosity of the same fluid moving at ordinary speeds multiplied by the Lorentz factor.
I was quite surprised when I checked whether my microscopic relativistic theory is able to recover, in the non-relativistic limit of low speeds, the viscosity of classical gases as is known from kinetic theory and many aerodynamic experiments. Indeed, I found that the new formula could recover the correct dependencies of viscosity on temperature, particle mass and size, and Boltzmann’s constant which are known for classical gases (e.g., for air flowing near the wings of an airplane).
In the opposite limit of high-energy fluids moving at extremely high speeds (e.g., quark gluon plasma or classical relativistic plasmas), the theory predicts the cubic dependence on temperature in agreement with evidence and yields a new fundamental law of physics which brings together the most important fundamental constants in nature.
Interestingly, I realized that the new theory might unveil a hitherto neglected effect of Einstein’s relativity theory. For example, in analogy with length contraction and time dilation, we can speak of “fluid thickening” as a new relativistic effect that has been overlooked so far and may have important consequences for our understanding of relativistic plasmas in astrophysics and in high-energy physics, including the quark-gluon plasma obtained from high energy nuclear collision reactions.
This story is part of Science X Dialog, where researchers can report findings from their published research articles. Visit this page for information about Science X Dialog and how to participate.
More information: Alessio Zaccone, Relativistic theory of the viscosity of fluids across the entire energy spectrum, Physical Review E (2024). DOI: 10.1103/PhysRevE.110.L052101. On arXiv: DOI: 10.48550/arxiv.2406.18434
Bio: Alessio Zaccone received his Ph.D. from the Department of Chemistry of ETH Zurich in 2010. From 2010 till 2014 he was an Oppenheimer Research Fellow at the Cavendish Laboratory, University of Cambridge. After being on the faculty of Technical University Munich (2014–2015) and of University of Cambridge (2015–2018), he has been a full professor and chair of theoretical physics in the Department of Physics at the University of Milano since 2022. Awards include the ETH Silver Medal, the 2020 Gauss Professorship of the Göttingen Academy of Sciences, the Fellowship of Queens’ College Cambridge, and an ERC Consolidator grant (“Multimech”).
Research contributions include the analytical solution to the jamming transition problem (Zaccone & Scossa-Romano PRB 2011), the analytical solution to the random close packing problem in 2d and 3d (Zaccone PRL 2022), the theory of thermally-activated reaction rate processes in shear flows (Zaccone et al. PRE 2009), the theory of crystal nucleation under shear flow (Mura & Zaccone PRE 2016), the theoretical prediction of boson-like peaks in the vibrational spectra of crystals (Milkus & Zaccone PRB 2016; Baggioli & Zaccone PRL 2019), the theory of the glass transition in polymers (Zaccone & Terentjev PRL 2013), the theoretical and computational discovery of topological defects in glasses (Baggioli, Kriuchevskyi, Sirk, Zaccone PRL 2021), and the theoretical prediction of superconductivity enhancement effects due to phonon damping (Setty, Baggioli, Zaccone PRB 2020). Research interests range from the statistical physics of disordered systems (random packings, jamming, glasses and the glass transition, colloids, nonequilibrium thermodynamics) to solid-state physics and superconductivity.
Journal information: Physical Review E , arXiv
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