209 Visualization of Spacetime
A picture of curved spacetime that is used to show how mass warps the fabric of space and time so that nearby matter follows that curve.
Note: Also called a rubber-sheet model of gravity. Also called a spacetime embedding diagram.
Earth sits in a deep dip of the spacetime grid, and the Moon follows a closed path around that curve.
The Sun warps spacetime across the solar system, while Earth and the Moon sit in smaller dips inside that larger curve.
209.1 From the Gravity Probe B Guide
In Einstein’s general theory of relativity, spacetime is a four-dimensional structure whose shape is curved and twisted by the presence and motion of matter and energy. Mass warps the fabric of spacetime in a manner similar to a bowling ball warping a spandex sheet. A smaller mass near a larger mass is not pulled by a distant force; it follows the structure of curved spacetime near the larger mass. Planets orbiting the Sun follow the curvature of spacetime produced by the Sun.
209.2 References
- Range, S. K. Educator’s Guide to Gravity Probe B: Investigating Einstein’s Spacetime with Gyroscopes. Stanford University / NASA, 2004 (HQ PDF, 2008). Page 10. Public domain. PDF
- Annihilation
- Constancy of the Speed of Light
- Contracted Length
- Coordinate Transformations
- Derivation of Elastic Potential Energy Formula
- Derivation of Gravitational Potential Energy Formula
- Derivation of Kinetic Energy Formula
- Derivation of Newtonian Kinetic Energy Formula
- Derivation of Potential Energy Formula
- Derivation of Relativistic Kinetic Energy Formula
- Electromagnetic Field Transformations
- Energy-Momentum Relation
- Events
- Field Tensor
- Four-Current
- Four-Momentum
- Four-Potential
- Frame
- Inertial Frame
- Inertial Reference Frames
- Kinetic Energy
- Length Contraction
- Light Cone
- Lorentz Factor
- Lorentz Transformations
- Magnetism as a Relativistic Effect
- Mass-Energy Equivalence
- Massless Particles
- Minkowski Metric
- Minkowski Space
- Moving Clocks
- Non-Inertial Frames
- Nuclear Energy
- Particle Creation
- Photon Energy
- Potential Energy
- Principle of Relativity
- Proper Length
- Proper Time
- Rapidity
- Reference Frames
- Relativistic Electrodynamics
- Relativistic Momentum
- Relativistic Momentum and Energy
- Relativity Principle
- Rest Energy
- Simultaneity
- Spacetime
- Spacetime Interval
- Time Dilation
- Total Energy
- Twin Paradox
- Velocity Addition
- Visualization of Spacetime
- Worldlines