For this thought experiment, you must appreciate the notion that existence is a measure of relationships. The idea of existence without relationship, that existence precedes relationship, is philosophical, and by definition, there can be no evidence of it. For this experiment, you must consider that a relationship is not proof of existence, but is existence itself. Existence is not a state; it is a measure of relationships. If you don't appreciate this, there's not much point in reading on.
To begin, imagine one particle and nothing else. Of course, you can quickly recognize that this is an impossible scenario. We are working with the premise that existence is relationship, and the particle has nothing to relate to. The particle has no reference for position, and cannot be compared to anything else. The particle cannot exist.
Now, imagine two identical particles and nothing else (Fig. 1A). Existence is a measure of relationships. Therefore the particles might be said to exist, but only in terms of the relationship they share. Except for their position, the particles are identical; therefore the distance between them is their only relationship. However, distance has a problem in this system. There is only one distance: the distance between the two particles. How is this distance defined? Are the particles close to each other? Are they far apart? Close and far are comparisons between distances, and this system only has one distance. Similar to the situation in the one-particle system, the distance between the two particles does not exist as there are no other distances to compare it to. There is no distance between the two particles, there are not two particles. The particles cannot exist.
Now, imagine three identical particles and nothing else (Fig. 1B). In this system, there are three distances. Each distance exists insofar as it compares to the other two distances. In this system, two particles can be closer to each other than they are to the third. Also, in this system, there can be a very simple evolution of state. One distance could be the shortest of the three, and then it could be the longest of the three. It could be considered that time could pass in the simplest manner. However, it can’t be said how long it took for these distances to change. We can compare the positions of particles by comparative lengths of the distances, but the shortening of one distance is the lengthening of another.
Now, imagine a four identical particles and nothing else (Fig. 1C). You see where this is going. The more particles in a system the more complex the relationships for particles, space and time become.
Now, imagine a system with several more particles (Fig. 2A). There are a numerous distances, positions, and even comparative evolutions of relationships in this system. Time, particles, and space are fairly complex, as each component of the system has several relationships. Existence for each component is multi-faceted. Even relationships have comparative relationships in this system.
Now, imagine that one particle of a multi-particle system becomes relatively distant from the others (Fig. 2B,C). What is the consequence?
As the relative distance between this particle and the distances between the others grows, this particle begins to have a relationship with the other particles that resembles the two-particle system. The particle, and time and space relative to it, become less defined as the distance in-between it and the other particles becomes relatively large. The particle exists less and less as the relative distance between it and the others grows. Also, existence in the multi-particle system becomes less complex, but much less so.
That’s the end of the thought-experiment. However, here is something that I think is worth thinking on: Matter has a gravitational field that describes how it alters space and time. Time is relatively slowed as a gravitational field increases in strength. For something traveling at a constant speed into a gravitational field, it takes relatively more time to travel the same distance as a gravitational field increases.
In a future post, I’ll talk about how I think the ideas in this thought-experiment, and gravity might be related.
I do appreciate this but wonder what happened to identity? Minus this, this will reduce to 'just' [g] geometry... You mention distance, but your system is incomplete without the analog of proximity. I would encourage you to inject that notion into your thought experiment: 2 classes of particles exists: class 'F' occupies space exclusively; class 'B' particles do not ... [edit: I posted immediately after reading the OP; and this critique was apparently mentioned earlier by other members. Nevertheless hope this has added to the discussion.]
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.
>For this experiment, you must consider that a relationship is not proof of existence, but is existence itself. Existence is not a state; it is a measure of relationships. If you don't appreciate this, there's not much point in reading on. I tried. :)
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.
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/
What I meant by "existence is not a state", is akin to what Buckminster Fuller was getting at, I think. However, what I want to then move to address, is rooted in what bothers me about BF's statement: 'non-interfering' and 'pure principle'. Are these just turtles below the turtle we have dispelled? I only have a moment, but I'll get back to this and provide a more in-depth answer to your question in a day or two. It's a good question, and I want to. Thanks!
I think this reasoning is flawed. The distance between the two particles is not only the relationship between the particles. The particles itself define a relationship with respect to the distance. Not only does the distance define the particles, the particles define the distance. What you are effectively trying to postulate is that sets of two items cannot exist. The premise that there are two particles implies that there exists some kind of distance, otherwise there would be only one particle.
Another problem with these 'systems', is that I don't define exactly what constitutes a relationship. I am working on a follow-up essay where instead of relationships, these characteristics are defined only in terms of interaction; In this, relationship is past and possible future interaction. It's not an easy thing to do however, and I decided to start in the most clear and concise manner I could. That said, your point is the one that has been raised most to me, and I think I am going to have to draft this introduction again where I address the nature of particles to some degree. Thanks, I appreciate the feedback.