Why is the Speed of Light a Constant?

The speed of light is one of the fundamental physical constants, believed to be applicable over the entire universe and to remain fixed over time. Its value in vacuum is 299,792,458 meters per second.

What makes this constant a constant? Why do so many quantities depend on this? And why do many equations in physics include this constant?

Early approach

A journey of its evolution through last few centuries leads us to answer these questions. Until the beginning of 17^th century there was no generalized concept of light having any speed. Light was thought to appear instantaneously then. It was in 1676, when the speed of light was first measured. Remarkably it was serendipitous. Two researchers—Giovanni Domenico Cassini and Ole Roemer—were trying to study certain discrepancies in the eclipses of one of the moons of Jupiter. Roemer guessed that the discrepancies occurred because light has some finite speed and it takes certain time to reach Earth. Following some rough calculations, Roemer concluded that the light has a finite speed of about 225,000 kilometers per second.

Considering significant inaccuracy in data available at that point of time, this estimate doesn't sound bad at all.

To explain the origin and significance of the speed of light, two remarkable theories appeared in course of time--Maxwell's theory of electromagnetism in mid 19th century and Einstein's special theory of relativity in 1905. At the time of Maxwell, electricity and magnetism had been studied extensively. He was working on the idea that electricity could be generated by changing magnetic field. Maxwell found the solution of his famous equations to be wave like and hence concluded that electric and magnetic fields, when change in time, interact to produce a travelling electromagnetic wave. He proceeded to calculate the speed of these waves and obtained the value to be 310,740 kilometers per second. He realized that this was indeed the speed of light. This strongly suggested that the light is an electromagnetic wave and was confirmed by later experiments.

However, Maxwell suggested that there must be an ambient medium--ether--through which the light propagates.

Myth about ether

Two decades later, two scientists Michelson and Morley attempted to detect the ether by observing the relative change in light as Earth changed its direction of travel with respect to the Sun during the the course of a year. Surprisingly, they failed to detect any change. This triggered further debates and ideas behind the existence of ether.

Einstein--with his Special Theory of Relativity--argued that the whole idea of ether being the medium for the light to travel was unnecessary as he showed that the speed of light through vacuum is the universal limit (c) and nothing can move faster than the speed of light. However, he didn't prove the constancy of speed of light. Indeed, It was one of the underlying assumptions of his special theory of relativity (other one being the principle of invariance--an idea, first expressed by Galileo, showing uniformity of all physical laws in an inertial system). Combining these two assumptions, Einstein showed that the speed of light is independent of the speed of observer as well as the speed of the source of light and that everything else in the universe. So, no matter how fast anything moves, it will always measure the speed of light to be equal to 300,000 kilometers per second.

Quantum Field Theory

Neither of the theories--Maxwell's Electromagnetic Theory of Light and Einstein's Special Theory of Relativity--explain what determines the speed of light? Maxwell calculated the speed of light using the parameters μ₀ and ε₀. Now the question arises is that what do these quantities mean in vacuum since electricity and magnetism arise due to some elementary particle such as electrons, and no matter is supposed to be present in vacuum. We need Quantum Field Theoretical concept in order to complete Maxwell's theory.

Quantum Field Theory says that no vacuum is ever empty. Vacuum is the lowest energy state of the quantum system. Though the uncertainty principle, i.e. fluctuations and inconsistencies associated with physical measurements, doesn't affect our life at microscopic level; but these fluctuations produce energy (or matter) in form of elementary particles in quantum vacuum. These excitations are short lived, but they appear as pairs of particles and antiparticles with equal and opposite charge, such as electron and positron. An electric or magnetic field when applied to the vacuum, will distort these pairs to produce electromagnetic response. This helps us to measure the electromagnetic properties of quantum vacuum, and thereby to calculate the value of c.

In 2010, a group of physicists at Max Planck Institute for the Science of Light performed an experiment, where they created virtual pairs in quantum vacuum and calculated the constants μ₀ and ε₀ which was within a factor of 10 to the correct value used by Maxwell. In 2013, scientists at University of Paris-Sud calculated the value of c from the electromagnetic properties of quantum vacuum and claimed it to be correct. This connection between the quantum fluctuations and classical electromagnetism is indeed fascinating.

Constancy of the constants

The speed of light is considered one of the several universal constants along with quantities like Gravitational constant G and Plank's constant h. Numerical values of these constants are known to great precision. But are these quantities really constant and fundamental throughout the universe? Well, modern science assumes that the laws of physics are same everywhere in space-time. However this is just an assumption after all asking to be tested. Plenty of attempts have been made in this regard. Paul Dirac, in 1937, raised doubts over the value of gravitational constant G, but probably there are no conclusive evidences to validate his suggestion that G decreases with time (or space). The same is for the case of c.

Another doubt arises whether the constants such as G or c or h are fundamental. Well, fundamental constants are the ones which are pure number and do not depend on any dimension. So, the likes of fine structure constant α, which is the ratio of speed of the electron in Hydrogen atom to c, with value 1/137 and the ratio of proton mass to electron mass with value 1836.2 are fundamental.

No matter whether G, c or h are fundamental constant or not, these are still constants. These quantities have fixed magnitude. So do the fundamental constants. But why this c has the value of 300, 000 km/s, or for the matter why is α equal to 1/137? What if α was something else? What if c was something else? Why could these quantities not take any other value?

As it turns out, we do not have the answer for these questions. To play with, you can change the speed of light by making it pass through some medium and show that it takes longer time than it should, but the fact is that its speed remains to be 300,000 km/s as it strikes and keeps bouncing back inside the atoms in that particular medium.

Philosophical point of view

Why do these fundamental constants possess a certain value? Well, may be these values are set for our universe by nature and the magnitude of these constants have to do something with our existence. We see these values how we see. We don't see any other value to these constants because it probably would describe some other universe. This is a puzzle we can't solve because we are part of it and so is our existence.