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Playing in Space-Time: Information Theory and Intervals in Space-time

225 views · Published 25 November 2016 · 21:02 · Indexed 18 October 2026

Channel: Doug Sweetser · 2016 · Science & Technology

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Information theory takes a problem and tries to make it more abstract. It asks how much information is needed to solve this problem? While science loves reductionism, Nature practices information transformation: what goes in is equal to what goes out.

For calculating invervals in curved space-time, the standard approach needs four for the event, ten for the metric tensor, and 20 for how the metric tensor changes in space-time to calculate the one interval, a reduction of 34 to 1.

To calculate an interval using space-time numbers, a variation on quaternions, a quaternion operation always yeilds another quaternion. This means you cannot get an interval out, but must get an interval and three other terms. To do the calculation, the difference of a quaternion is squared. Thus one starts with four pieces of information and after transforming by squaring, ends with four pieces of information.

An honest observer of events has the data. Can they tell if they are an inertial or non-inertial observer? I argue that they cannot. If another honest observer sees the same set of events, they can compare the squares of their observed differences and determine if they are moving at a constant speed relativite to each other. They can also determine if they are in the same space-times-time equivalence class which is my new proposal for gravity.

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