If the speed of light were infinite in classical mechanics, it would have several significant implications and changes to the fundamental principles and equations of physics. Here are a few key differences:
Relativity: The theory of special relativity, which is based on the constancy of the speed of light in a vacuum, would not exist or would be significantly altered. The concepts of time dilation, length contraction, and the equivalence of mass and energy (E=mc^2) would no longer be applicable.
Newtonian Mechanics: Newton's laws of motion, formulated in classical mechanics, would remain valid in most scenarios. However, there would be no upper limit on the velocity of objects. According to Newton's laws, an object could continuously accelerate without bound as long as a force is applied.
Causality: The concept of causality, where cause and effect occur in a definite temporal order, would be simpler. Information and interactions could propagate instantaneously across any distance. This would have implications for our understanding of cause and effect relationships and the predictability of physical systems.
Electromagnetism: The behavior of electric and magnetic fields would be significantly altered. The equations of Maxwell's electrodynamics would be different, as they are derived based on the constancy of the speed of light. This could lead to changes in how electromagnetic waves propagate and interact with matter.
Optics: The study of light and optics would also undergo substantial changes. Phenomena such as refraction, reflection, diffraction, and interference would be different in the absence of a finite speed of light. The propagation of light through different mediums would not be subject to the usual laws of Snell's law and the refractive index.
It's important to note that these points are hypothetical and assume a fundamental change in a fundamental constant of nature. The concept of an infinite speed of light is not consistent with our current understanding of the universe and the theory of relativity. The finite speed of light plays a crucial role in shaping our understanding of the physical laws and behaviors observed in the universe.