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.
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.
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.
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.
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
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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