For many decades, the often strange and counterintuitive effects of Einstein’s theory of special relativity, including length contraction and time dilation, have been known. However, a new theory is poised to reveal another of its unusual aspects: its long-hidden influence on fluids.
The effect, dubbed “fluid thickening,” is detailed in a new paper by physicist Alessio Zaccone, which outlines a unique microscopic theory involving fluid viscosity and its influence under relativistic conditions. By employing a framework that combines elements from relativistic equations with current theory underlying the displacement of particles, Zaccone’s theory shows how fluid viscosity might behave under conditions nearing the speed of light.
The groundbreaking research may help to bridge the gap between existing concepts involving relativistic hydrodynamics and classical fluid behavior and could even point to the requirement for a new fundamental law of physics.
Relativity and Fluid Dynamics
With the arrival of Einstein’s theory of special relativity in 1905, a range of concepts were introduced that began to unveil the stranger elements of relativistic effects. Among these were length contraction, the phenomenon that causes objects traveling close to the speed of light to appear shorter along their direction of motion.
While such effects have been well established in physics now for decades, relativity theory’s implications for other areas of physics have yet to be fleshed out entirely, including its effects on fluid thickness, otherwise known as viscosity.
That is, until now. Zaccone, a physicist at the University of Milan, Italy, has produced the first work that addresses this with the development of a microscopic model for viscosity that can account for its effects at relativistic speeds.
Relativistic Viscosity, Explained
Employing the relativistic Langevin equation, which deals with the motion of a system experiencing certain varieties of random force, and nonaffine linear response theory, a framework that can be used to derive a microscopic formula for the viscosity of solids and liquids, Zaccone presents a general theory of the viscosity of gases in a new paper published in Physical Review E.
According to Zaccone, the newly proposed theory can explain the behavior of viscosity for gases under everyday conditions, considering factors like mass, temperature, and particle size, an explanation that remains consistent even when gases aren’t moving close to light speed. Further, the theory also reveals the way viscosity changes as fluids approach extreme speeds.
Zaccone’s theory also accounts for fluids at very hot temperatures moving close to the speed of light, with a simple formula that describes how their viscosity increases in proportion to temperature. These previously overlooked effects of relativity, Zaccone says, are consistent with past research involving dense, hot substances like the quark gluon plasma, a highly-energized form of matter believed to have existed shortly after the Big Bang.
Fundamentally, Zaccone’s new framework accounts for the movement of particles with flow, and their deviation resulting from collisions and interactions with other particles, which gives rise to “nonaffine” motions responsible for a significant amount of momentum dissipation.
Proper Momentum
Of particular significance in Zaccone’s theory is the concept of “proper momentum,” which is the momentum relevant to the relative motion of an object as seen by an observer. This is essentially defined by the normal momentum of a particle multiplied by the Lorentz factor (a number always greater than one and becoming extremely large when approaching near-light speeds).
This factor plays a crucial role in the way loss of momentum—as therefore viscosity—is perceived under relativistic conditions in fluids.
When checking his theory alongside classical scenarios, Zaccone was surprised to find that it appears to accurately recover known dependencies of viscosity on temperature, particle mass and size, and Boltzmann’s constant, with relation to classical gases. According to Zaccone, this is consistent with experimental observations, as well as kinetic theory.
Meanwhile, on the end of the spectrum involving high-energy fluids moving at very high speeds (as in the case of quark gluon plasma), Zaccone’s theory predicts a cubic temperature dependence that is a good match for current evidence and offers a unified understanding of fluid behavior from ordinary to extreme conditions.
Significantly, Zaccone says that the new model supports the introduction of “a new fundamental law of physics,” which he says can unite “the most important fundamental constants in nature.”
A Hidden Effect of Einstein’s Relativity Theory?
An additional intriguing observation Zaccone makes involves what appears to be the unveiling of a previously unacknowledged effect of Einstein’s relativity theory.
The effect, which the physicist calls “fluid thickening,” represents a counterpart to previously observed strange effects that include length contraction and time dilation, but with respect to fluids.
According to Zaccone, the unveiling of this effect, which suggests that fluids behave differently at high velocities, could play a crucial role in helping physicists understand relativistic plasmas and their significance in astrophysical contexts and in high-energy physics experiments.
Fundamentally, the discovery offers a significant enhancement to our understanding of special relativity’s reach, while also laying the groundwork for future studies involving high-speed, high energy fluid dynamics.
Zaccone’s paper, “Relativistic theory of the viscosity of fluids across the entire energy spectrum,” appeared in Physical Review E.
Micah Hanks is the Editor-in-Chief and Co-Founder of The Debrief. He can be reached by email at micah@thedebrief.org. Follow his work at micahhanks.com and on X: @MicahHanks.