Exactly, final speed must be equal, not average speed.valenumr said:
docnet said:
The phrase "the longer path is quicker" often refers to scenarios in physics where a particle or wave takes a longer route that results in a shorter travel time due to varying speeds in different mediums or paths. This concept is particularly relevant in optics and wave mechanics, where light can take different paths to reach the same destination, and the path that appears longer can sometimes be faster due to the properties of the medium.
A classic example is light traveling through different media, such as air and water. When light passes from air into water, it slows down. If there are two paths—one through air and a shorter one through water—the longer path through air may allow the light to arrive at the destination faster than the shorter path through water, illustrating that the longer path can indeed be quicker.
Fermat's principle of least time states that light will travel between two points along the path that takes the least time, not necessarily the shortest distance. This principle underpins the idea that the longer path may be quicker if it allows the light to travel through a medium where it moves faster, demonstrating that time, rather than distance, is the critical factor in these scenarios.
Yes, this concept is not limited to optics. It also applies in fields like quantum mechanics, where particles can take multiple paths simultaneously, and the path that contributes most to the probability amplitude may be longer but quicker. Additionally, it can be seen in classical mechanics, such as in the analysis of trajectories and motion where forces and resistances affect the speed of travel along different routes.
Yes, the principle of the longer path being quicker has practical applications in various fields, including telecommunications and fiber optics, where the design of pathways for signals can optimize speed and efficiency. It is also relevant in engineering and architecture, where the layout of structures and materials can influence the speed of heat transfer or fluid flow, leading to more efficient designs.