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Curved Spacetime and General Relativity Explained
Newton described gravity as a force between masses, F = Gm₁m₂/r². Einstein's general relativity (1915) describes it as geometry: mass and energy curve spacetime, and freely falling objects follow the straightest possible paths, called geodesics, through that curved spacetime.
The rubber-sheet picture, and its limits
A heavy ball on a stretched sheet makes a dip, and marbles roll around it. This picture helps, but it is only an analogy: it uses "downwards" gravity to explain gravity, and it leaves out the curvature of time, which is actually what makes slow objects fall.
Newton vs Einstein
In weak gravity and at low speeds, the two theories agree almost perfectly, which is why spacecraft can be navigated with Newton's laws plus small corrections. They differ near very dense objects and for light: Mercury's orbit slowly rotates by an extra 43 arcseconds per century, and light passing the Sun bends twice as much as a naive Newtonian estimate.
Light bending and lensing
Light grazing the Sun bends by 1.75 arcseconds (α = 4GM/c²b), first measured in the 1919 eclipse. Distant galaxies behind massive clusters appear as arcs, multiple images or complete Einstein rings: this is gravitational lensing.
Gravitational time dilation
Clocks run slower deeper in a gravitational field: the rate is √(1 − 2GM/rc²). GPS satellite clocks gain about 45 microseconds a day from weaker gravity (and lose about 7 from their speed). Without correcting for this, GPS positions would drift by kilometres each day.
Frequently asked questions
What does it mean that spacetime is curved?
Mass and energy change the geometry of space and time, so the straightest possible paths (geodesics) bend. Objects in free fall, and light, follow these paths.
Is the rubber-sheet model of gravity correct?
It is a helpful analogy, not a literal picture. Real spacetime curvature includes time, and objects don't sink into anything.
Why do GPS satellites need relativity?
Their clocks run about 38 microseconds a day fast overall (45 gained from weaker gravity, 7 lost from orbital speed). Without corrections, positions would drift by kilometres daily.
Does light bend due to gravity?
Yes. Light passing a mass bends by α = 4GM/(c²b). For the Sun it is 1.75 arcseconds, confirmed in 1919.