The Universe has an unsurpassable speed limit, applicable to all matter and information. This constraint does not arise from a particular force but directly from the structure of spacetime, as described by the fundamental laws of physics.
In 1873, James Clerk Maxwell (1831-1879) published his final treatise, begun in 1861, "A Treatise on Electricity and Magnetism". This treatise synthesizes and develops his entire theory of electromagnetism, predicting the existence of waves propagating through a vacuum.
The speed of these electromagnetic waves is given by the relation: \( v = \frac{1}{\sqrt{\varepsilon_0 \, \mu_0}} \) where \(\varepsilon_0\) represents the permittivity of free space and \(\mu_0\) the permeability of free space. This equation shows that the speed \(v\) is an intrinsic property of the vacuum, not a speed of matter transport. It gives exactly the value of the speed of light in a vacuum, \(c\) = 299,792,458 m·s-1. The letter \(c\) to represent the speed of light was popularized by Albert Einstein (1879-1955) in his 1905 work on special relativity.
At the time of Maxwell, the exact values of \(\varepsilon_0\) and \(\mu_0\) were not defined with current precision, and the calculated speed was therefore only approximate. Maxwell himself compared this speed to the known measurements of the speed of light at the time. In 1862, Léon Foucault (1819-1868) succeeded in measuring the speed of light with great precision. Using an ingenious device combining mirrors and a toothed wheel, he obtained a value of about 298,000 km/s. Maxwell, noting this agreement, suggested that light is an electromagnetic wave.
N.B.:
The permittivity of free space (\(\varepsilon_0\)) is a physical constant that characterizes the ability of a vacuum to "host" an electric field. It is expressed in farads per meter (F·m-1) and appears in Coulomb's law and Maxwell's equations.
The permeability of free space (\(\mu_0\)) characterizes the response of a vacuum to a magnetic field. It is expressed in henries per meter (H·m-1) and appears in Ampère's law and Maxwell's equations.
In 1905, Albert Einstein (1879-1955) postulated that this speed is the same for all inertial observers, thus founding special relativity.
In this theory, the total energy of a particle of mass \(m\) moving at speed \(v\) is written as: \( E = \gamma m c^2 \) with: \(c\) the speed of light and \(\gamma\) the Lorentz factor \( \gamma = \frac{1}{\sqrt{1 - \frac{v^2}{c^2}}} \).
Thus, as \(v\) approaches \(c\), the factor \(\gamma\) increases sharply and diverges to infinity (\(\gamma \to +\infty\)):
For a 1 g object moving at a speed such that \(\gamma \approx 70710\), the total energy: \(E = \gamma \, m_0 c^2\) would be: \(\approx 6.35 \times 10^{19}\ \text{J}\). In other words, a small 1 g object would require all the energy consumed by the entire planet for about a month.
This enormous energy shows that even for a very small object with rest mass, reaching a speed extremely close to \(c\) requires an energy that is practically impossible to provide. The speed \(c\) thus appears not only as a speed limit but as an insurmountable energy barrier for any object with rest mass.
Photons have no rest mass (\(m_0 = 0\)), their energy is entirely associated with their momentum (\(E = pc\)). In the context of relativity, this relationship implies that their speed is necessarily \(c\). They can neither slow down nor exceed this speed, as any variation would violate the relativistic equation linking energy, mass, and momentum.
| Physical Context | Equation | Meaning | Reference |
|---|---|---|---|
| Electromagnetism | \( v = 1 / \sqrt{\varepsilon_0 \mu_0} \) | Propagation speed of electromagnetic waves | James Clerk Maxwell |
| Special Relativity | \( \gamma = 1 / \sqrt{1 - v^2/c^2} \) | Time dilation and energy increase | Albert Einstein |
| Mass-Energy | \( E = m c^2 \) | Mass-energy equivalence | Albert Einstein |
| Relativity and Photons | \( E^2 = (m_0 c^2)^2 + (pc)^2 \) | For \(m_0 = 0\), \(E = pc\); photon speed = \(c\) | Albert Einstein |
Sources: NIST - Fundamental Physical Constants, Royal Society Publishing.
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