The question of whether it is rigorous to invoke mathematical notions such as infinity in discussions about the impossibility of faster-than-light travel is an interesting one. While infinity itself may not have a direct physical counterpart, it is often used in mathematics as a useful concept to explore certain theoretical limits and possibilities.
In the context of faster-than-light travel, the concept of infinity is often invoked to discuss the consequences of special relativity, a well-established physical theory. According to special relativity, the speed of light in a vacuum is the maximum speed at which information or matter can travel. This principle is supported by a wealth of experimental evidence.
Mathematical tools, including the concept of infinity, can be used to derive various consequences and limitations arising from the constancy of the speed of light. For example, when an object with mass approaches the speed of light, its relativistic mass increases without bound, implying that an infinite amount of energy would be required to accelerate it to the speed of light. This is a consequence derived from mathematical equations based on the principles of special relativity.
While infinity itself may not be physically realizable, mathematical reasoning using infinity can still be meaningful within the framework of physics. It helps us understand the behavior and limitations imposed by physical theories. These mathematical tools, including infinity, have been extensively tested and have made accurate predictions about a wide range of physical phenomena.
It is worth noting that our understanding of the physical world is based on a combination of empirical observations, experimental data, and mathematical models. Mathematics provides a powerful language for describing and understanding the natural world, and its use, including concepts like infinity, has been a successful approach in explaining and predicting physical phenomena.
In summary, while infinity may not have a direct physical counterpart, its use in mathematical reasoning can be rigorous and useful for understanding the limitations imposed by physical theories, such as the impossibility of faster-than-light travel as predicted by special relativity.