principle

principle of constancy of the speed of light

The principle of constancy of the speed of light states that light in vacuum travels at a fixed speed independent of the source or observer.
17 related articles · 4 formulas · 1 who worked here

Description

Light is a true sprinter of the Universe, always running at the same speed. No matter whether you are chasing a flashlight beam or rushing towards it, its speed will remain unchanged for you — about 300,000 km/s. This is unlike the everyday world: if you walk on a moving escalator, your speed adds to the speed of the steps. With light, this trick doesn't work! It is this strange property that leads to time dilation and length contraction in relativity.

History

The first indications of the constancy of the speed of light came from Maxwell's equations (1861), from which c = 1/√(μ₀ε₀) was calculated. Attempts to detect the ether wind through the Michelson–Morley experiment (1887) yielded a null result. Hendrik Lorentz and Henri Poincaré developed the preparatory mathematical apparatus, but it was Albert Einstein in 1905 who elevated the constancy of c to a fundamental postulate, discarding the ether and building the theory of relativity.

How it works

The principle underlies all modern high-energy physics and astrophysics. It is necessary for the correct operation of particle accelerators, satellite navigation systems, and understanding the evolution of the Universe. Limits of applicability: special relativity does not account for gravity, so in strong fields (near black holes or at extreme densities) general relativity is required, where the speed of light is locally constant, but its global behavior is more complex.

Fun fact

Imagine a light bulb turning on in the center of a carriage flying at near-light speed. A passenger inside will see the light reach the front and back walls simultaneously. For an observer on the station, the light will first catch up with the back wall, which is moving towards it, and only then the front wall. To both, it will seem that the light traveled at the same speed! It's just that time flows differently in different frames — such wonders.

Concept graph →

Formulas

$$c_s^2 = \frac{dP}{d\varepsilon}$$
Speed of sound squared is the derivative of pressure with respect to energy density.
What is in the formula
c_svariablespeed of sound — speed of sound metre per second
Pvariablepressure — pressure pascal
εvariableenergy density — energy density joule per cubic metre
d/dεoperatorderivative with respect to energy density — derivative
c_s^2=\frac{dp}{d\varepsilon}>\frac{1}{3} · 2606.03707v2
$$c_{\text{coord}} = c \sqrt{-g_{tt}/g_{rr}}$$
Speed of light in curved spacetime coordinates.
What is in the formula
c_coordvariableCoordinate speed of light — speed metre per second
cvariableSpeed of light in vacuum — speed of light metre per second
g_ttvariableTime-time component of metric tensor — metric tensor component
g_rrvariableRadial-radial component of metric tensor — metric tensor component
√operatorSquare root operation — square root operator
c_{{coord}}=c(1-\frac{r_s}{r}) · 2605.09783
$$c_s = \sqrt{\frac{K}{\rho}}$$
Sound speed depends on stiffness and density.
What is in the formula
c_svariableSpeed of sound in the medium — speed of sound metre per second
KvariableBulk modulus (stiffness) of the medium — bulk modulus pascal
ρvariableMass density of the medium — mass density kilogram per cubic metre
√operatorTakes the square root of the argument — square root
c_s(t)=\sqrt{\frac{j_0(t)}{\kappa_0(t)}} · 2607.08353
$$c_s^2 = \left(\frac{\partial P}{\partial \rho}\right)_s$$
Sound speed squared is adiabatic pressure derivative with density.
What is in the formula
c_svariablespeed of sound — sound speed metre per second
Pvariablepressure — pressure pascal
\rhovariablemass density — mass density kilogram per cubic metre
\left(\frac{\partialoperatorpartial derivative with respect to density at constant entropy — partial derivative at constant entropy
c_s^2=(\frac{\partialp}{\partial\varepsilon})_s · 2607.15588v2

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