One of the plot points of the movie Interstellar centers around the idea that travelling through a wormhole to get someplace distant and then returning would result in the same time dilation as if the astronauts travelled at near light speed in normal space to and from the same object. That is, if you travelled through a worm hole and came back, what you returned to would be much older than what you left.
It would be fun to take a cellular automata model of physical space which was correct for relativity, and fold it over and pinch it to connect two distant points in the cellular space, and then see if the predicted time dilation effect was reproduced in the model.
I Googled “cellular automata relativity” and it seemed the only two papers written on this topic are by two Canadian electrical engineers, Tom Ostoma and Mike Trushyck, in 1999. They never published again. I read through these papers and they talk about cell propagation and the number of rules per cell, with the cells being of volume related to Planck constant and the universal clock time for the whole automata, operating outside of time within the automata, such that the speed of light, viewed as velocity of propagation of information between cells, was reproduced.
Subsequently I found the 1994 MIT PhD thesis by Mark Andrew Smith on Cellular Automata Methods in Mathematical Physics which plows similar ground. However, as with Ostoma and Trushyck, publishing on this topic appears to be a career-killing move, as I can find no subsequent trace of this author. Smith bylined briefly in 2001 as a member of the Harvard Department of Molecular and Cellular Biology, and after that I can truly find no trace of him on the web. So, a seven year gap between publications, and then nothing. One fears the worst, especially as he mentions in his thesis that
My first years at MIT were ones of great academic isolation, and I would have dropped out long ago if it were not for the fellowship of friends that I got to know at the Thursday night coffee hour in Ashdown House.
Or are the missing cellularautomatophysicists here, one wonders:
The idea of physical space quantized into cellular automated seemed satisfying until I looked through the window. My eyes could see a lot of visual information coming to me from a distance. That’s not counting a lot of non-visual information such as radio waves and magnetism and so on. Presumably everything I am seeing at a distance is propagated to me and summarized on a cell by cell level by a complex of information representing all of this information that is arriving to the cell from all of these sources at the same time. It doesn’t seem like it can be summarized in a single bit. So, how many bits are needed to represent the information being received by a single cell? If one posits an “operating system” or collection of common rules that is replicated in every cell, what are the implications for the size of that rule set to manage and store the amount of information being received from each neighboring cell?
Dear readers, do you know of any other credible published work on cellular automata models for relativity which are concrete enough to be programmed as simulations? What are your thoughts on the bits-per-cell problem and how we perceive, at a single point, light arriving from a distance from many sources?