Time Travel in Flatland?

Time Travel in Flatland?

an animated tutorial in physics, light cones and causality

Flatland; a romance of many dimensions is a short novel by Edwin Abbott published in London in 1884. Abbott described his interactions with beings who live in a flat plane of two spatial dimensions, and showed how we might perceive the existence of higher dimensions.

Flatlanders denounce Abbott for dimensional bias.

Abbott wrote Flatland before the unified picture of space and time emerged in early 20th century mathematics and physics. Nowadays we would say that the Flatlanders live in 2+1 dimensional spacetime — two space dimensions and one time.
Einstein’s General Theory of Relativity is much simpler in Flatland (plus time), so that is where we’ll start exploring what it means to travel in time.

Spacetime 101

Here’s some basic background covering how mathematical models of space and time have evolved since ancient times, from the Pythagorean Rule to Newtonian mechanics, Special Relativity and General Relativity.

Time Travel 102

Flatland with gravity – how does that work? In one time and two space dimensions, the Einstein equation is almost too simple, but the results are not! See how spacetime curvature warps light cones, creates ambiguities in causal boundaries, and even allows at least a mathematical possibility for time travel.

Time Travel 103

What about the world of one time and three space dimensions that we (appear to) live in? Can causality go awry in our Universe? Look at spinning black holes and a quantum-field powered wormhole for examples where propagation backwards in time can happen, at least in theory.



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