Can a material have a positive index of refraction less than unity? Why or why not?

The speed of light in a vacuum is a fundamental constant of nature, denoted by the symbol c. Its value is approximately 299,792,458 meters per second. This speed is the cosmic speed limit; according to current scientific understanding, nothing can travel faster than light in a vacuum.

When light passes through a medium, such as water or glass, it slows down. This slowing is quantified by the index of refraction (n), which compares the speed of light in a vacuum to its speed in the material. We write this as: \(n = \frac{c}{v}\), where v is the speed of light in the material. For all known materials, n is always greater than or equal to one, indicating that light always slows down in a material compared to its velocity in a vacuum.

An index of refraction less than unity implies an impossible scenario where light travels faster in a medium than it does in a vacuum. This concept conflicts with our empirical observations and the theoretical foundations rooted in physics, leading to the conclusion that such materials with n<1 do not exist.

The principle of causality, also known as cause and effect, is a foundational concept in physics and the philosophy of science. It states that every effect has a specific cause, and this cause precedes its effect in time. This principle underpins the chronological ordering of events in our universe.

In the context of light and information transmission, causality implies that no information or material object can travel faster than the speed of light, as doing so would mean the effect (the arrival of information) could precede its cause, resulting in paradoxes and contradictions with observed reality. Therefore, the principle of causality is a core reason why the idea of a material with an index of refraction less than unity (implying faster-than-light speeds in the medium) cannot be reconciled with established physical laws.

Einstein's theory of relativity is divided into two parts: special relativity and general relativity. Special relativity deals with physical phenomena in the absence of gravity and introduces the concept that the laws of physics are the same for all observers in uniform motion relative to each other. It asserts that the speed of light in a vacuum is constant and independent of the motion of the light source.

General relativity extends this to include gravity, describing how it affects time and space. Both theories uphold the constancy of the speed of light as a cornerstone. According to relativity, increasing an object's speed requires exponentially more energy as it approaches the speed of light, and surpassing this limit would require infinite energy, which is impossible. This limitation reinforces the physical improbability of a material having an index of refraction less than one, as it contradicts the relativistic framework that governs the behavior of light and matter at high speeds.