Question

Why is the speed of light what it is ? Why is it not billions of miles per second? What does the front of the beam look like? What if the speed was infinite?

Answer 1

The speed of light in a vacuum, approximately $299,792,458$ meters per second, is a fundamental constant in our universe. It is not arbitrary but has deep connections to the fundamental structure of spacetime and the properties of electromagnetic radiation. The speed of light being finite, and specifically having the value that it does, has profound consequences for the behavior of the universe as we know it.

1. Why is the speed of light what it is and not faster (e.g., billions of miles per second)?

The speed of light being what it is can be understood through the fundamental laws of electromagnetism and the geometry of spacetime. It is related to the electric permittivity and magnetic permeability of free space (denoted by ${\epsilon }_0$ and ${\mu }_0$, respectively) and is given by:

$c=\frac{1}{\sqrt{{\epsilon }_0{\mu }_0}}$

These constants, ${\epsilon }_0$ and ${\mu }_0$, are fundamental properties of space, and they appear in Maxwell's equations, which describe the behavior of electric and magnetic fields and the propagation of electromagnetic waves (including light). The value of $c$ emerges as a consequence of the underlying laws of electromagnetism and the geometric nature of spacetime.

If the speed of light were significantly different, it would have dramatic effects on the behavior of the universe. For example, if light were much faster, it would drastically alter the way electromagnetic interactions occur, leading to different atomic and molecular structures, changes in the behavior of particles, and likely different physical laws governing our universe.

2. What does the front of the beam look like?

The "front" of a light beam refers to the leading edge of the electromagnetic wavefront as it propagates through space. In the case of a beam of light, the wavefront is a plane wave, which means that the wavefronts are flat and perpendicular to the direction of propagation. In the absence of any obstructions or interactions, the front of a light beam appears as a continuous, coherent plane of oscillating electric and magnetic fields.

3. What if the speed of light were infinite?

If the speed of light were infinite, it would have several far-reaching consequences:

• Causality: The concept of causality, which forms the foundation of cause and effect relationships, would be severely impacted. Information and causal influence could travel instantaneously across any distance, leading to logical inconsistencies and paradoxes.

• Simultaneity: The idea of simultaneous events would become relative and observer-dependent. There would be no absolute notion of "now" for all observers.

• Relativity: The theory of special relativity,