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Originally Posted By: Adib Ben Jebara
...space and time are defined as sets of urelements...
Hi, Adib. You should be always prepared to assign a number of dimensions and/or space-time metric to these sets. Is it principally possible? If not, then the set of "elements" cannot serve as a model of space or time, because it cannot comprehend all physical attributes of these concepts, assigned so far by another theories. By another words, you should use the definitions of space and time, which are backward compatible with existing concepts/definitions, so they can be reconciled with them on the background of correspondence principle.

What the urelements are supposed to be from physical point of view? Can we derive something testable from such assignation?

From Aether Wave Theory perspective the definition of space and time is very simple. The causal energy spreading can occur only along surfaces of Aether density gradients in transversal waves. After then the space dimensions are the directions, along which energy spreading occurs. And the time dimensions are the rest directions, which are perpendicular to space dimensions.



For example, the water surface can be considered as a local space-time for mechanical wave spreading. After then the space dimensions are the directions plan-parallel with water surface and the time dimension is the direction perpendicular (normal) to these directions, i.e. the direction of water surface gradient itself. It's easy to comprehend definition and it brings surprisingly high number of testable insight/predictions into Aether model. You can try to explain your definition of space/time on background of my definition, as I suppose, the physically relevant definitions should be always compatible.

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There are at least two posssinilities for dimensions, I am still
thinking about if we should have U1xU2 for space and time or
U1xU2xU3xU4.
As for urelements, they are "objects" which do not contain anything and which are undistinguishable, which fits space and time.
As for the lack of compatibiliity with other theories, it would be seen by critics.
May be you can help.
Adib Ben Jebara.

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Originally Posted By: Adib Ben Jebara
...as for elements, they are "objects" which do not contain anything and which are indistinguishable, which fits space and time...
I can see nothing very useful in this concept. The Aether Wave Theory (AWT) is using so called the "unparticle concept", which was proposed independently here. But the Unparticle physics is still nothing, what cannot be derived from common particle physics directly - it's just another view to it.

The AWT is using a following trivial insight: everything what we can see from the gas aren't the particle itself, but a density fluctuations of it. It means, during condensation of dense gas, we couldn't never see its particle itself, just a density fluctuations. And the AWT idea is: WHAT IF every particle, which we can see is just a density fluctuation of another particles, i.e. without any exception? It means - here's no upper or lower limit of particle size, every particle can be considered as a dense cluster of another particles: from gravitons to whole observable Universe itself. It means, here are no "fundamental particles" - simply because here's no meaningful physical reason to have some. Everything can be explained at the scope a few adjacent particle generations, which we are living in and it has no mean to ask about limits of such structure - simply because we would be required to explain them, after then.

Only practical limits (for example the speed of energy spreading) limits the size and the fractal dimension of the observable structures. Here are another limits given by curvature of the space-time, mediated by such structure: after some number of generation the space perceived would become formed by its own distant fluctuations (a sort of Uroboros or Klein bottle model) by the similar way, like the space formed by nested foam (i.e. foam, where each bubble is formed by another bubbles, recursively). But these small bubbles aren't small, in fact - they're just a very distant one.

In this model the observable structures are of limited size and they're created by itself. A practical realization of such system can appear like interior of black hole, which contains another black holes, recursively.

Motto: "if you don't about reason of reasons, don't ask about them".

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Particles theory is the challenge not unparticle theory which does not explain well particles and is not even clear enough.
Adib Ben Jebara.

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Originally Posted By: Adib Ben Jebara
..unparticle theory which does not explain well particles and is not even clear enough...
The unparticle physics was "guessed" as an ad-hoc theory by the same way, like LQG or string theory, but from AWT perspective they're all steps by correct direction, because the scale invariant density fluctuations in heavily compressed particle matter are both spin loops, strings and unparticles at the same moment.

The AWT is based on the assumption, the Universe is completely random, but the number of states is limited due the limited speed of information (transversal wave spreading), so that the randomness of the directly observable system is always violated due the finite number of states in it.

It's like the observation of set of infinite many numbers - we have no chance to observe some regularity in it. But at the moment, the number of states in the set is limited, we can observe a multinomial distribution between similar members. It's like the throw of dice: if the dice would be of infinite wall number, we cannot detect any regularity between individual throws. But when the the number of walls will be limited by polyhedra, we cen observe a sequences of multinomial distribution: ...1101011010100011010111... We can observe "something".



For example, the system of colored points, where the colors are limited by finite set can be never fully homogeneous: it exhibits a colored spots: a fluctuations of color density. And these fluctuations are scale invariant, they're behaving like "unparticles". It doesn't matter, in which scope these colors spots will be averaged: they'll always exhibit the color spots of the same distribution,

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