Mass, geometry and gravity
Einstein's general relativity (1915) replaced Newton's force of gravity with the geometry of curved spacetime. In John Wheeler's summary, "spacetime tells matter how to move; matter tells spacetime how to curve." Objects in free fall follow the straightest possible paths — geodesics — through a spacetime that mass and energy bend. This picture predicts light bending, gravitational time dilation, the precession of Mercury's orbit and gravitational waves, all since confirmed.
The rubber-sheet analogy and its limits
The familiar picture of a bowling ball denting a rubber sheet is a 2-dimensional analogy, and this simulator is that analogy made interactive. It is genuinely useful, but imperfect: it shows curvature of space only, while much of everyday gravity actually comes from the curvature of time; and it quietly uses ordinary downward gravity to roll objects into the well. Treat it as intuition-building, not the literal four-dimensional geometry, which is described by Einstein's field equations.
How to use the simulator
Add masses and move them around. The deformation of the grid stands in for spacetime curvature, and the paths of passing test particles bend toward the masses — the visual counterpart of an orbit or a gravitational slingshot.
Note: this is a pedagogical analogy, not a solution of the Einstein field equations. It illustrates the idea that mass curves spacetime and that curvature guides motion, but it does not reproduce quantitative general-relativistic predictions.
Frequently asked questions
What is spacetime curvature?
In general relativity, mass and energy bend the four-dimensional geometry of spacetime, and this curvature is what we experience as gravity. Objects in free fall follow the straightest available paths, called geodesics, through the curved spacetime.
Is the rubber-sheet analogy accurate?
It is a helpful but imperfect analogy. It depicts only the curvature of space, whereas most everyday gravity comes from the curvature of time, and it relies on ordinary gravity to pull objects into the well. It builds intuition but is not the real four-dimensional geometry.
What is general relativity?
General relativity is Einstein's 1915 theory of gravity, in which mass and energy curve spacetime and that curvature governs how matter and light move. It predicts light bending, gravitational time dilation and gravitational waves, all experimentally confirmed.
Does light bend due to gravity?
Yes. Because light follows geodesics through curved spacetime, its path bends near massive objects. This gravitational lensing was first confirmed during the 1919 solar eclipse and is now routinely observed by astronomers.
References
- A. Einstein (1916), "Die Grundlage der allgemeinen Relativitätstheorie" ("The Foundation of the General Theory of Relativity"), Annalen der Physik 354(7):769–822.
- J. B. Hartle, Gravity: An Introduction to Einstein's General Relativity (Pearson).
- C. W. Misner, K. S. Thorne & J. A. Wheeler, Gravitation (W. H. Freeman / Princeton University Press).