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Time traveling flatlanders

Disclaimer:

This toy story is not an endorsement of buddist, hindi wheels of time (such as Bhavacakra and Kalachakra) or other religious beliefs in circular time. I’m not a religious person and know next to nothing about different religions beliefs of time.

Nor should this toy story be seen as an scientific attempt to describe time and space in our 3D (plus time) world. It should not even be seen as a model, it should more accurately be seen as a hybrid of the films Toy Story and Star Trek (the flatlanders can teleport themself just as in Star Trek 🙂 ). But I do think that the story might help readers that have a hard time understanding time dilation (that occur when something travels close to the speed of light or are close to a black hole) get an intuitive grasp. With that said, let the story begin

Time traveling flatlanders

Underlying the flatland lies a spinning wheel of time. The flatlanders can’t see the time wheel since they can’t look up or down. There is a black hole in the middle of the time wheel where time is only one time frame. Surrounding the black hole is a ring that contain two time frames, next ring contain 4 time frames, next eight and so on (we use base two and let the outer ring contain 32 time frames for simplicity) as shown below:

Flantlanders live at a distance away from the black hole:



 The underlying spinning wheel of time describes how many time frames that occur during a full rotation. The flatlanders living in the fifth ring will experience 32 time frames during one cycle as illustrated below:


Flatlanders found by studies that something strange seems to be happening to the curvature of space and time in some regions. Scientist concluded that there must be a black hole in the center that they couldn’t see (since the wheel of time is hidden beneath the flatland plane).

Two twins discovered a way to teleport a person to which ever position on the 2D plane. One of them teleported himself to the third ring:


 The two twins started to age at different pace as the wheel spun. The outer twin aged 32 time frames during one cycle while the inner twin only aged 4 time frames.:


When the twin teleported himself back to the 32 ring they both noticed the difference in aging. The two twins planed that next time one of them should be teleported into the black hole. But they wished to avoid aging at different pace. Their solution was that the twin who stayed in the 32 ring should stay in the same time frame. This could be achieved by traveling as fast as the spinning wheel:

 

The twins continued to experiment with different configurations of teleporting themself to different rings in the wheel of time. They discovered that a the twin stationed in a inner ring, closer to the black hole, would age faster then the other twin if the outer twin could stay in the same time frame traveling as fast as the time wheel. The outer twin didn’t age at all while the inner twin aged four time frames during one cycle.


 The twins experiment caused much confusion among the flatlanders and some philosophers started speculating in the possibility that time wheels could be nested in time wheels, that in turn are nested in other time wheels all the way up and down.


 Some philosophers even thought that a black hole could contain another universe rotating around a another black hole that in turn could contain another universe that rotate around another black hole and so on. Some of these philosophers got insane.

 


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