concept

spacetime

Spacetime is the four-dimensional continuum combining space and time, which can be curved by gravity.
28 related articles · 4 formulas · 2 who worked here

Description

Spacetime is like a fabric that unifies space and time into a single whole. Imagine the Universe as a giant trampoline. If you place a heavy ball (a star) on it, it will sag, and everything around will start moving toward that depression. Time also slows down near massive objects—as if clocks run slower when they are near the ball.

History

In 1905, Henri Poincaré and Albert Einstein independently laid the foundations of special relativity, where space and time ceased to be absolute. In 1908, Hermann Minkowski formulated four-dimensional spacetime. In 1915, Einstein completed the general theory of relativity, where the field equations (Einstein equations) linked curvature with energy-momentum. In 1916, Karl Schwarzschild found the first exact solution for a spherical mass, predicting black holes. In 1927, Georges Lemaître applied the equations to cosmology, showing the expansion of the Universe, later confirmed by Edwin Hubble.

How it works

The properties of spacetime are described by the metric tensor g_{\mu u}, which defines distances and causal structure. Mass curves spacetime, and curvature dictates motion, as expressed in Einstein's equations: G_{\mu u} + \Lambda g_{\mu u} = \frac{8\pi G}{c^4} T_{\mu u}. Special relativity is based on the principle of the constancy of the speed of light, which states that the speed of light in vacuum is the same for all inertial observers. Motion along geodesics explains gravity without forces. In cosmology, the Friedmann equations, derived from Einstein's equations, together with Hubble's law describe the expansion of spacetime on large scales.

Fun fact

If you could travel at a speed close to the speed of light, time would flow slower for you, and you could "travel into the future" faster than people on Earth!

Concept graph →

Formulas

$$\vec{v}_{\text{sky}} = \vec{v} - (\vec{v} \cdot \hat{d})\hat{d}$$
Tangential velocity is total velocity minus its radial component.
What is in the formula
\vec{v}_{\text{sky}}variabletangential (sky-projected) velocity — velocity metre per second
\vec{v}variabletotal velocity vector — velocity metre per second
\hat{d}variableunit vector along the line of sight — unit vector
\cdotoperatorscalar product of two vectors — dot product
\vec{v}_{{sky}}=\vec{v}-(\vec{v}*\hat{d})\hat{d} · 2606.05344v1
$$d = v t$$
Distance equals speed multiplied by time.
What is in the formula
dvariableDistance traveled — distance metre
vvariableConstant speed — velocity metre per second
tvariableTime elapsed — time second
d=c*t · 2607.13485
$$f(r) = 1 - \frac{2GM}{c^2 r} + \frac{G k_e Q^2}{c^4 r^2}$$
Describes spacetime around a charged non-rotating mass.
What is in the formula
rvariableRadial coordinate from the center — radial distance metre
f(r)variableMetric function determining spacetime geometry — metric function
GconstantNewtonian constant of gravitation — gravitational constant = 6.67430e-11 cubic metre per kilogram per second squared
cconstantSpeed of light in vacuum — speed of light = 299792458 metre per second
k_econstantElectrostatic force constant in Coulomb's law — coulomb constant = 8.9875517923e9 newton metre squared per coulomb squared
f(r)=1-\frac{2gm}{c^2r}+\frac{gk_eq^2}{c^4r^2} · 2605.10587v1
$$d\tau = \frac{dr}{\sqrt{f(r)}}$$
Increment of proper time for radial motion in curved spacetime.
What is in the formula
τvariableProper time — proper time second
rvariableRadial coordinate — radial coordinate metre
f(r)variableMetric function — metric function
doperatorInfinitesimal change — differential
dτ=\frac{dr^2}{σ^2f(r)} · 2607.14626

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