>For this experiment, you must consider that a relationship is not proof of existence, but is existence itself.

But this is not the fundamental notion that we must accept to go along with your experiment.

>To begin, imagine one particle and nothing else.

Materialism is the fundamental assumption of your experiment. You implicitly assume that the world is material. As I wrote here http://science1.wordpress.com/2011/04/06/the-world-is/ the world depends on your initial assumption. You assume that the world is material and there exists absolutely indivisible particles. Yet, not only there are no experimental evidence for this Newtonian atomic materialism, but all observations suggest that we are living in a matterless world. Even physicists themselves slowly coming to this conclusion in their pathetically tortuous ways.

I think, your experiment touches on some fundamental questions and facilitates discussion of fundamental questions. For instance, what is real is convention (relation); what is convention is real. What exists is defined to exist by giving it a name. In order to know something we need to measure it with a chosen unit.

Maybe you can explain more what you mean by “existence is not a state” and “existence is a measure of relationships.” For instance, "There are no solids. There are no things. There are only interfering and noninterfering patterns operative in pure principle . . . (B. Fuller): http://science1.wordpress.com/2008/10/22/physical-semantics/

"The more particles in a system the more complex the relationships for particles, space and time become."

With this sentence, suddenly you are equating, with no justification, particle==matter; distance==space; and period==time. What is measurable is distance and period or an interval of time. It is typical of scholastic physics to confuse measurement of something with that something; this is the reification of labels (or the reification of coordinate axes, a standard practice in physics); and you might explain how you justify this assumption in your thought experiment. You might want to state in the beginning if you propose to understand (or define) the world by measurement. http://science1.wordpress.com/2010/10/18/what-is-our-worldvi... Because it is possible to define the world in many different ways.