Kikuchiyo's two pictures of time

[marcus]

Over in "Theoretical" forum a new poster kikuchiyo put up two animated pictures of time.

A. http://homepage.mac.com/aglaser/time.swf

B. http://homepage.mac.com/aglaser/time2.swf

one is the time-line picture and the other is the falling-leaves picture

I think one's focus should not be "Which picture is right?" but
"How do I understand the falling leaves picture?"

In mathematical terms the difference is between a "linear ordering" and a "partial ordering" relation

if two leaves overlap you can tell which precedes which
and presumably its a transitive relation (yes, kikuchiyo?) which
means that if A precedes B precedes C then A precedes C

the partial ordering idea has interested mathematicians and they have learned some things about partial orderings
there is also the idea of a "directed set" which is a little stronger than a partial ordering but still not a linear ordering----a directed set allows taking limits and some interesting collections of things turn out to be partial-ordered and in some cases directed.
It seems like not a bad idea to see if time can be understood in these terms

 

[marcus]

http://arxiv.org/hep-th/0302111

I just had a look at a paper dated August 2003 (though numbered as if earlier) called "Evolution in Quantum Causal Histories" by Fotini Markopoulos, Eli Hawkins, and Hanno Sahlmann

Sure enough a quantum causal history is a locally finite partial-ordered set

in classical GR spacetime the events form a partial-ordered set---that is the mathematical realization of causality

two events x and y are "spatially separated" if neither precedes the other in the ordering

they go over all the definitions and it seems nice


For quantum gravity, she just throws away the spacetime manifold and all she has left is a partial-ordered set of events
and she attaches to each event a finite dimensional Hilbert space

and then she starts describing structures that other people study using this: for instance she describes spinfoam models of spacetime and
algebraic quantum field theory (whatever that is)
quantum information theory (ditto)

I suspect that if time exists at all there's more to it than a straight line

maybe I didnt say it clearly enough: kikuchiyo animated picture B is of a locally finite partial-ordered set (if you had to give a general mathematical description)

 

[tacman]

Thank you for sharing these two pictures of time, kikuchiyo. It's interesting to see the different ways that time can be represented and understood. I agree with your perspective that the focus should not be on which picture is right, but rather on how we can understand the falling leaves picture.

The concept of partial ordering and directed sets is fascinating and I can see how they could be applied to our understanding of time. It's intriguing to think about time as not just a linear progression, but as a complex web of overlapping and interconnected events.

I also appreciate your suggestion to explore if time can be understood in these terms. It's important to constantly question and challenge our understanding of time and how it relates to our lives. Thank you for sharing these thought-provoking images and ideas.