New Wave Equation Connects Wave Mechanics, General Theory of Relativity, and Time
Researchers from Tampere University and the University of Eastern Finland have made a groundbreaking discovery in the field of wave mechanics. They have derived a new wave equation that links wave mechanics with the general theory of relativity and the arrow of time. This achievement not only resolves long-standing debates in physics but also opens up possibilities for the development of novel materials.
The researchers focused on accelerating waves and found that their new wave equation provides a unique perspective on wave mechanics. Previously, wave mechanics only accounted for waves with constant speed. By allowing for variations in the speed of waves over time, the researchers were able to formulate an accelerating wave equation.
“While writing down the equation was simple, solving it was another matter,” explained Assistant Professor Matias Koivurova from the University of Eastern Finland. Initially, the solution seemed nonsensical, but upon closer examination, the researchers realized that it exhibited behaviors reminiscent of relativistic effects.
Working together with the Theoretical Optics and Photonics group led by Associate Professor Marco Ornigotti from Tampere University, the researchers made progress in understanding the implications of the new wave equation. They discovered that the accelerating wave equation only allows solutions where time flows forward, establishing a well-defined direction of time, or an ‘arrow of time.’
The direction of time is typically determined by increasing entropy, which reflects the flow of time in thermodynamics. However, in the case of accelerating waves, the direction of time is fixed regardless of entropy. This indicates a fundamental property of nature that determines the direction of time for single particles.
The researchers also found that their wave equation could model continuous waves across interfaces, contributing to the resolution of a long-standing controversy known as the Abraham–Minkowski controversy. This debate revolves around the change in momentum when light enters a medium. The researchers demonstrated that, according to their wave equation, the momentum of the wave is conserved, thus reconciling the opposing perspectives.
The new wave equation also has implications for time-varying materials. It allows for the analytic modeling of situations that were previously only accessible through numerical methods. One such application is the study of disordered photonic time crystals, an exotic hypothetical material. The researchers found that their wave equation explained the observed changes in energy and demonstrated local violations of energy conservation in such materials.
This research has far-reaching implications, from everyday optical effects to laboratory tests of the general theory of relativity. It sheds light on the preferred direction of time and provides a framework for understanding wave mechanics in a broader context.
The study, titled “Time-varying media, relativity, and the arrow of time,” was published in the journal OPTICAL. The researchers involved were Matias Koivurova, Charles W. Robson, and Marco Ornigotti.
This exciting breakthrough paves the way for further advancements in physics and material science, promising a deeper understanding of the universe and the principles that govern it.