Curved Space-time
We now move to Einstein’s formulation of the theory in terms of curved (non-Euclidean) spacetime.
- Example: imagine you were on a merry-go-round which was rotating at a fast speed. If you were asked to find the shortest distance between points A and B in the diagram, you would pick the “curved” line rather than the dashed line. Why?
- Your meter sticks would shrink less at a smaller radius, therefore you would need fewer of them on the “curved” path!
- Similarly, you would find “curved paths” to be the shortest routes between A & C and B & C. Therefore the sum of your angles in the triangle ABC would be < 180°! You would measure your space to be curved!
- Applying the equivalence principle once again, we are led to the conclusion that what we call a gravitational field can be viewed as just the “physical manifestation” of curved space-time!