The light we see every day doesn’t always work as we think. It can slow down, bend, speed up and even change the direction of time. These amazing phenomena were studied by a group of Finnish physicists and published their results in the journal Optica.

Accelerating waves are waves whose velocity depends on time. Such waves occur when light interacts with matter. For example, when light hits the surface of glass or water, it experiences acceleration as it passes from one medium to another. This causes light to be reflected and refracted at different angles. This effect is called Snell’s law and is well known in school physics lessons. However, the conventional wave equation that describes the propagation of light does not take acceleration into account. It assumes that the speed of light is constant and equal to the speed of light in vacuum. To explain acceleration, Finnish physicists proposed a new equation called the acceleration wave equation. It can describe the behavior of light in a medium with changing speed.

By solving this equation, physicists discovered some interesting properties of acceleration waves. It turns out that such waves obey Einstein’s law of relativity. That is, they experience relativistic effects such as time dilation and length contraction. Time dilation means that time passes more slowly for accelerating waves than it does for observers in the laboratory. The reduction in length means that the wavelength of the acceleration wave becomes shorter than that of a laboratory observer. These effects explain some of the paradoxes that arise when considering light in the environment. For example, why aren’t light pulses conserved when passing through materials? Momentum is the product of an object’s mass and speed. Light has no mass but has momentum depending on its frequency and wavelength. When light travels slowly through a medium, its frequency does not change but its wavelength decreases. Therefore its momentum will decrease. However, the law of conservation of momentum states that the momentum of a closed system cannot change without the action of an external force. So how can we explain this fact?

The answer lies in the relative impact of length contraction. When light slows down in a medium, it speeds up. As a result, its wavelength is shortened not only for the laboratory observer but also for the light itself. In other words, light is perceived as if it were in a vacuum. Its frequency and wavelength do not change, meaning its momentum does not change. Therefore, the momentum of light is conserved from the light’s point of view, not from the observer’s point of view. This is called the covariance principle: the laws of physics must be the same for all frames of reference.

Another surprising property of acceleration waves is the presence of an arrow of time. The arrow of time is the direction in which time passes. In everyday life, we see time passing from the past to the future. For example, an egg can break but cannot be reattached. Indeed, entropy, a measure of the disorder of a system, always increases over time. This is called the thermodynamic arrow of time. However, in the microscopic world of particles, entropy plays no role. The laws of physics do not depend on the direction of time. For example, an electron can move forward and backward over time. This is called the microscopic arrow of time. There is no exact direction.

Finnish physicists have shown that for accelerating waves, time has only one direction: from the past to the future. This means that the acceleration wave cannot go back in time. They cannot return to their previous state. This property is called cause and effect: the cause must precede the effect. Why does this happen? Because the accelerating wave obeys the accelerating wave equation, this equation has only one solution for each initial condition. That is, if we know the acceleration wave at one time, we can predict what it will look like at any other time. But we cannot do the opposite: we cannot distinguish between the previous wave of acceleration and which is today. This means that the equation of the acceleration wave is not invariant under changing the sign of time. This distinguishes it from the ordinary wave equation, which has two solutions for each initial condition: one for the forward progression of time and one for the reverse progression.

So, Finnish physicists discovered a new way to study light and its properties. They show that acceleration waves can be used to examine relativistic effects and the arrow of time at the microscopic level. This could open up new perspectives in understanding the nature of light and time, as well as the development of new technologies based on wave acceleration. For example, accelerated waves can be used to create ultra-high resolution microscopes capable of seeing objects smaller than the wavelength of light. Additionally, acceleration waves can be used to transmit information faster and more securely because they are harder to intercept and tamper with.

source: https://opg.optica.org/optica/fulltext.cfm?uri=optica-10-10-1398&id=540974