The understanding of science at its most fundamental level has given rise to an unprecedented technological revolution. From the operation of GPS systems and space travel to the invention of transistors and the dawn of the computational era, none of these advances would have been possible without first understanding certain fundamental physical concepts. In the case of GPS, for example, it is essential to account for relativistic physics and, with it, the idea of a finite speed for the propagation of information. In the case of semiconductors, it was quantum mechanics that made it possible to understand behavior that depends on purely quantum phenomena.
When Information Does Not Arrive Instantly
But what does it really mean for an interaction to have a speed? A simple way to think about it is to remember that the image of the Sun we see does not correspond to the exact present, but rather to how it looked approximately eight minutes ago. This happens because sunlight takes that long to travel from the Sun to the Earth. Yet within this everyday fact lies a much deeper idea: it is not only light that takes time to arrive, but also the physical information associated with the influence that one system exerts on another. If the Sun were to suddenly disappear, we would not find out immediately. Both the light and the information about its influence would take some time to reach us.
The maximum speed at which a physical influence is transmitted from one point to another can be called the interaction speed. In Einstein's relativistic physics, this limiting speed in a vacuum is the speed of light, c. Taking this fact into account is not merely a theoretical matter: without considering these delays in the propagation of information, systems like GPS could not function correctly, because accumulated errors in synchronization and position determination would always be present.
The physics that incorporates this finite propagation speed is relativistic physics, and it has been one of the most successful theories in modern science. However, it is not the only way to describe nature. There also exist effective theories that capture certain physical regimes very well, even if they are not the most fundamental description.
The best-known example is Newtonian physics. For centuries it has been the foundation of much of engineering, classical astronomy, and applied science. In that framework, interactions are treated as instantaneous, as if the interaction speed were infinite. Today we know this is not the deepest picture of the universe, but it remains an extraordinarily useful approximation. In most everyday situations, the speed of light is so large compared to typical speeds that treating interactions as instantaneous produces very accurate results.
The Other Possible Extreme: When Spatial Propagation Nearly Halts
A natural question then arises. If a physics like Newton's appears when the interaction speed is taken, in some sense, as infinite, what happens at the opposite extreme? Can there exist a theory in which that speed tends to zero?
The answer is yes. That regime is known as Carrollian physics. Just as Newtonian physics can be seen as a limit in which interactions are instantaneous, Carrollian physics arises in the opposite case: when the spatial propagation of information becomes extremely restricted. In that scenario, different points in space become nearly disconnected from one another. It is no longer a universe where influences arrive immediately, but one where they can barely be transmitted spatially.
At first glance, this may sound like a purely mathematical construction. However, in recent years Carrollian physics has attracted growing interest because it can arise in some very striking physical contexts. For instance, this symmetry emerges in certain limits of general relativity, such as in analyses near the event horizon of a black hole. It can also appear in some condensed matter systems, where the effective propagation speed becomes very small compared to the speed of the particles. It has even been proposed that fluids with this type of symmetry could serve as effective models in discussions about dark energy. Beyond these applications, the underlying question is especially compelling: how does our description of the world change when information can no longer propagate in the usual way?
A Precise Connection Between Two Ways of Describing Quantum Reality
That question is at the heart of the research work of Jose Rojas, Dr. Melvin Arias, and Enrique Casanova. If Newtonian physics and Carrollian physics can be seen as two opposite limits with respect to the interaction speed, then a suggestive idea emerges: is it possible to find a connection between both extremes? In other words, if one has a quantum system described in the usual way, could that same system also be viewed from the opposite perspective, as if both descriptions were two sides of the same coin?
That is one of the central ideas of the first article. In standard quantum mechanics, time is the evolution parameter. In the Carrollian regime, however, the theory can be reorganized so that space takes on that central role.
This leads to a profound question: if one works in one temporal and one spatial dimension, can the same system be viewed from both perspectives and still be, in some sense, the same system? Can there exist a transformation that allows one to move from one description to the other? The article published in Scientific Reports studies precisely this question and derives explicitly the transformation law connecting the standard Schrödinger equation with its Carrollian counterpart. The idea is not simply to compare two different theories, but to show that a precise structural relationship can exist between them.
What Happens When This Idea Is Extended to Many-Particle Systems?
But once that connection is established, another natural question arises. If these Carroll-symmetric systems admit an alternative quantum formulation, how do they behave when one is no longer studying a single particle, but many? In physics, moving from one particle to a many-particle system is not a minor change. It is precisely in that context where collective behaviors, new effective dynamics, and phenomena that cannot be anticipated from the simpler case tend to emerge.
That is the next step addressed in the second article by Jose Rojas and Dr. Melvin Arias, where the discussion is extended to many-particle Carroll–Schrödinger systems. In this way, the initial question is no longer limited to whether a single particle can be described from two complementary perspectives, but also to how that picture reorganizes itself when the system contains many degrees of freedom. In that step, new questions arise about collective dynamics, effective observables, and the way in which such an extreme symmetry modifies the structure of quantum theory.
Taken together, these works examine the same idea from two distinct levels: first in simple systems and then in many-particle systems. The starting point is to ask what happens when the manner in which information propagates in a physical theory changes. From there, a rather unusual connection between different descriptions of quantum dynamics comes to light, allowing for a rethinking of the roles of space and time in certain limiting regimes.
References
-
Rojas, J., Casanova, E., & Arias, M. (2026). Structural dualities between the Schrödinger equation and its ultra-slow-light counterpart in one spatial and one temporal dimension. Scientific Reports. https://doi.org/10.1038/s41598-026-42922-0
-
Rojas, J., & Arias, M. (2026). Dynamics of multiparticle Carroll–Schrödinger quantum systems. Physical Review D. https://doi.org/10.1103/kt92-y6j6