The Speed of Light: A Universal Constant

Light, an Invariant Phenomenon

Light travels in a vacuum at a constant speed of \(\approx 299,792,458\) m/s, denoted \(c\). This speed does not vary with the speed of the emitting source or that of the observer. This property, experimentally confirmed in 1887 by the work of Albert Abraham Michelson (1852-1931) and Edward Morley (1838-1923), is one of the two fundamental postulates of Albert Einstein's (1879-1955) special relativity (1905).

Why is this constancy so strange?

In classical Newtonian systems, velocities add up. If a train is moving at 100 km/h and a passenger throws a ball at 50 km/h, an observer on the ground will measure 150 km/h. But light does not obey this rule: no matter the speed of the train or the object thrown, the emitted light will always be measured at \(c\) by all observers, regardless of their relative speed.

A direct consequence of Maxwell's equations: Universal Constants

Maxwell's equations predict that electromagnetic waves propagate in a vacuum at a speed given by: \(\displaystyle c = \frac{1}{\sqrt{\varepsilon_0 \mu_0}}\) where \(\varepsilon_0\) is the permittivity of the vacuum and \(\mu_0\) is its magnetic permeability. These constants are universal, which imposes \(c\) to be as well. This property deeply shook classical mechanics and led to the abandonment of the ether concept.

A speed limit for the transmission of information

The speed of light also represents a causal limit: no information can propagate faster. This constraint structures all the causality of our universe. If we could exceed \(c\), temporal paradoxes would appear, threatening the coherence of physics.

Example 1: The GPS system and clock synchronization

GPS satellites must account for the time it takes for the light signal (radio waves) to travel the Earth-satellite distance (about 20,000 km). Since this transmission is limited by the speed of light \(c\), an error of one microsecond would result in a positioning inaccuracy of more than 300 meters. Without respecting this speed limit, GPS coordinates would be inconsistent and unsynchronized. Additionally, the GPS system also corrects relativistic effects due to the speed of the satellites and the gravitational potential difference with the Earth's surface.

Example 2: Quantum entanglement and the no-communication theorem

Even in the phenomenon of quantum entanglement, where two correlated particles seem to react instantaneously to each other regardless of the distance, no information can be transmitted faster than the speed of light. This constraint is guaranteed by the no-communication theorem, which prevents any exploitable transfer of information between two entangled events. Thus, relativity remains coherent: non-local quantum effects do not violate the causality imposed by the limit \(c\).

A relativistic universe

By accepting that \(c\) is the same for everyone, it becomes necessary to redefine time and space. Time dilates and lengths contract according to relative speed, according to the formulas: \(\displaystyle t' = \frac{t}{\sqrt{1 - v^2/c^2}}, \quad L' = L \sqrt{1 - v^2/c^2}\)
These effects, although weak at low speed, become predominant at speeds close to \(c\).

The speed of light: foundation of spacetime

The constancy of \(c\) allows defining fundamental units (the meter is defined from \(c\)), synchronizing atomic clocks in GPS, and measuring cosmic distances. It is therefore much more than just a speed: it is a structural property of spacetime.

Sources: Michelson & Morley (1887), Wikipedia – Special Relativity, NIST – Definition of the meter.