Manifold Questions: Particle Interaction vs Element Separation

[frankinstein]

Is there a difference between a manifold that is a result of particle interactions and say a system of elements where there is no interactions? E.g. Two particles interact with one another by exchanging force carriers and as a result they create a manifold in the form of a sphere. Isn't this different from say two particles separated by trillion of light years where there is no interaction between them and in fact the space between them is flat, where as the space in the first example is curved since trajectories are constrained to a sphere?

 

[frankinstein]

I guess I should have rephrased this question: What I'm really asking is the concept of a manifold more than just a geometric construct and that it is in fact a mathematical abstraction? Without the resultant composition realized by something that can emulate a manifold's features there is no manifold? So it doesn't matter if the abstraction is done by a binary machine, or human being drawing on a piece of paper or even a set of particles that interact and realize a geometric form. With that said then is a manifold spontaenously created when particles interact with one another?

Frank

 

[Hurkyl]

"Manifold" is a mathematical abstraction. So are things like "integer", "real number", and "ket".

Math doesn't care what something "really is" -- just what properties it has. The word "manifold" means "something that has a particular collection of properties". So if something does have those properties, then it is a manifold.




It sounds like you're trying to describe some physical hypothesis that doesn't really resemble anything I'm familiar with, so I'm going to kick this over to the general physics forum, and maybe they can help you out.

 

[frankinstein]

I ran into some information that points to where I'm thinking which is a form of digital physics but more distinctly generalized to information processing by abstraction layers. Does anyone know of any papers written on "gage" phenomena as a product of a system's IQ or swarm intelligence?

I've seen a paper using swarm intelligence to search Ising ground states but very little else, any help would be much appreciated.

Frank

 

[frankinstein]

The closes't thing to swarming I could find is "Monte Carlo swarm experiments", which isn't quite what I'm looking from. I just hate starting for scratch...

Frank