First off, it’s important to note that I’m dealing with the *logic* of boundaries between sets of rules. It’s *not* necessary to know the content of a single Law of Physics, or for any of our Laws of Physics as currently understood to be correct.

So what happens to anything trying to transit the boundary?

- There is a rule, or metarule, that governs the transition. But for this to be the case the metarule must apply on both sides of the boundary, and be consistent with both sets. This means that the “local rules” on either side of the boundary are just manifestations of the metarule, and that we are dealing with what physicists call a “phase transition”, (the sort of thing that happens when ice melts) and not a genuine rule change at all.
- There is no rule, and what happens on one side of the boundary has no bearing on what happens on the other side. In which case “nothing” crosses over, and what we have is a place in “our” space where things happen at random. Noether’s Theorem – If the Laws of Physics are symmetric through all possible rotations (ie if they are universal) then the existence of the universe must be underpinned by a universal constant (ie energy) – has implications here since it means there can’t be such a boundary – a reaon for thinking that the universe is unbounded.

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I remember when you first mentioned this to me, I can’t remember where specifically on hootoo. So I gets me thinking about Lisa Randall’s book on current understanding of particle/higher-dimensional physics – and spacetime being important here.

What strikes me is the similarity between case 1 above, and Randall’s description of our 3-dimensional world (universe?) being a “local sinkhole” over lower dimensionality, embedded in a higher dimensional “multi-verse”. The fundamental particles we know (electrons, etc.) are unqique to our 3D world, and do not communicate with anything outside. However, gravity particles (gravitons/gravity waves) can actually travel between the higher dimensional multiverse, and our local 3D sinkhole.

I’m guessing that hypothetically there could exist other types of particles in the “outer” multiverse which can’t interact directly with us. In this case, the metarule – the fundamental element/structure of the universe is based on (related to? derived from?) the graviton

I’m not really up on the science, but it seems to me that there is noreason why the “shape” of space shouln’t be complicated in this way – there would still be no boundary to space.

The philosopher Kant reached the conclusion that human beings couldn’t think of space as either infinite or bounded over 200 years ago, but couldn’t resolve the conundrum with the Newtonian view of space that existed then. That had to wait for the new geometries (Reimann etc) in the following century.

by the non-infinite, non-bounded, to you mean periodic, eg. “wrap-around”

Basically yes (I think – I’m not a scientist), but with the possibility that the wrap-around(s) are n-dimensional.

My (probably oversimplistic) thought is that “space” is the sum total of all the cause and effect connections that there are, and that its shape is determined by the distance (measured in time?) between various locations.

yes, I agree completely. The n-dimensional wrap-around is impossible for me to picture, but I understand it “mathematically”, and I think that might be the possibility.

It was reading about how closely intertwined matter,energy and space are that made the light bulb go on, and made me really understand that space is “cartesian” it doesn’t exist in a vacuum independent of everything else. And that points to the idea then that space, energy, matter are all inter-related – (expressins of a meta-rule?). My simplistic view is that one way to think about it is that it takes energy to move matter over space. But it was the realization that it is equally valid to think that space is merely the manifestation of the fact that in the past energy was applied to matter thus creating space. The equivalence of these two descriptions really blew me away.

I’m not sure about “energy was applied to matter”, as the two are generally considered equivalent.

The mathematical descriptions of space, time and energy are interrelated in a way that isn’t true of our ordinary everyday perception, but which can be related to them (confirmed by observation).

“My simplistic view is that one way to think about it is that it takes energy to move matter over space.”

This might be better expressed as energy changes as it moves around in spacetime, but we do have the problem that we can’t really visualise all this very well.

Presumably the “shape” of space at our perceptual level is dictated by the gravitational connections. It’s interesting that various string theories propose a larger number of dimensions, with the remainder being wrapped around on the scale of particles.

It gets to be quite a complicated picture.

Right, I expressed that badly. I guess what I was trying to say about the matter-energy-space thing was that I perceive it to be a case similar to particle-wave duality in quantum mechanics. Thinking of it as either a particle or a wave is wrong. Understanding that either representation is incomplete is the only understanding I have. The same holds true for matter-energy-space. The “traditional” view energy moves matter through space works sometimes, but is wrong. The idea of matter=energy(?=space?) is “correct” but impossible to wrap my head around…

I’m not sure how much it’s like particle-wave duality.

My own personal route wasn’t really scientific, but started with a rather throwaway remark I once made – Descartes, in trying to show the existence of God, once said that a cause must be at least as great as its effect, and it occurred to me that the effect must also be as great as the cause (or you wouldn’t be able to see the excess cause), pointing to a conservation law for cause and effect. The analogy with the conservation law for energy is obvious. The universe simply is a system of cause and effect, of rules. In the abstract, stuff can be regarded as rules, and space and time are properties of the rules.

I understand the concepts here, but if I’m going to master them I’ll need to experiment a little.

Let’s say that there are objects called “solos,” which obey a set of rules denoted “Single”. There are also objects called “partners” which obey another, distinct set of rules, denoted “Coupled”. Now, there is a boundary condition governing transition between solos and partners called “compatibility”; if any two solos meet the condition of compatibility, they become members of the set of partners, and are no longer subject to the Single rules; instead, they now obey the Coupled rules.

If you want a mathematical analogy: solos are represented by integers, while partners are sets containing two integers. The Single and Coupled rules are a set of functions with the same domain and co-domain, while the compatibility condition is that the integers must not be equal and must have a GCD > 1 (so obviously, prime integers cannot become partners).

Which of your two scenarios applies in this case? Is this even a properly constructed example of a boundary transition problem?

“It’s interesting that various string theories propose a larger number of dimensions, with the remainder being wrapped around on the scale of particles.”

Smaller than particles, IIRC…

(Incidentally, and somewhat related: http://tenthdimension.com/ is one of my favourite websites explaining how to wrap one’s head around multiple dimensions.)

Hi Jordan.

It’s quite interesting that you find my explanation, couched in philosophical language, difficult to “get your head around”, while I find your clarification, couched in mathematical language, equally difficult to follow.

But this is indisputably one of those areas where scientific, mathematical, and philosophical disciplines overlap. I’ll be back again shortly with an attempt to clarify what I was saying.