TFNR - Separability
Separability is an extremely important concept due to its implications on the nature of InfoStructures, their dynamics, understanding the weird world of quantum, etc.
In light of what has been said regarding the internal distribution of ISs, let's try to outline a definition of "separability".
Let us assume that two ISs are separable where the set of internal correlations of the two individual ISs "prevails" over the set of external correlations between (corresponding) points/portions of the two ISs. What can we mean by "prevail"? Perhaps the intensities of the correlations are greater. That the internal correlations constitute a "unitary" "group", which "identifies" an IS.
How can we say that two flocks of birds are separate? What if they pass into each other? What if some birds from one flock join another? Are they still separated? What if they both head in the same direction? What if instead of birds, we imagine two swarms of drones, spatially separated, but whose flight plan has been established a priori and coupled to each pair of two drones belonging to the two different swarms (which will be entangled, so to speak)? Are the two swarms actually separate or does their related dynamic bind them into a single entity? In short, it is not a simple question.
Let's imagine two ISs of the Elementary Vortex sub-class, each with its own correlation scheme, its own distribution profile of the Elementary Action, its own correlation map of the internal distributions.
If the two particles are not entangled (their quantum states are not correlated, bound), easy. There are no external correlations, internal correlations obviously prevail. If the two particles are not entangled and not interacting, they are separate and their individual dynamics are independent. we could say that their internal distribution profiles, their maps of internal correlations are stochastically independent.
If the two particles are entangled (their quantum states are correlated, linked), the situation becomes more complex. It is necessary to establish whether external correlations prevail over internal correlations. If the two particles are not interacting, despite being entangled, despite external correlations being present, we can say the two particles are separate and their individual dynamics are independent, even if their internal distribution profiles, their maps of internal correlations are not they are stochastically independent, as they are entangled. In fact, I could expose one or both particles to an event capable of producing decoherence, and their dynamics would evidently be independent. Even by keeping them in entangled states, we could still vary their direction of motion, or any other non-entangled characteristic, thus highlighting their separation / separability. Distinct entities, or rather, Processes, even if some aspects of their internal organization are connected. Attention, not "connected". As we will see in the next sections, we assume here that entanglement does not involve any physical connection between the two particles.
Even a different situation for a pair of particles (entangled or not) in interaction. There are interactions that profoundly modify the nature, shape and dynamics of the particles involved. Interactions that involve the disappearance of a separate, identified, individual particle by fusion in another particle (elementary or already composite). In these cases, it is really difficult to determine whether and for how long during the interaction the ISs are separated or not, separable or not. When external correlations prevail over internal correlations, deforming, destroying, incorporating particles into each other, Wave-like and Vortex-like Structures in close interaction characterized by very high turbulence (for example quarks and gluons confined within nucleons ), etc., here the Structures involved, in addition to losing "purity", also lose "separability", becoming less "parts" of a system, and more "portions" of an individual and separable unitary entity.
A few more thoughts on this topic.
Separability has to do with Relations (correlations), not with (Elementary) Events which all happen in the Elementary Field, are "of" the Field. Events (Action, Causality), Relations (or correlations, Information, Variationality). Spatial fluctuations of the Field whose temporal distributions constitute the "fundamental raw material" which, in the dynamic scheme of existing correlations that define the Forms, incessantly builds and reconstructs the evolving Universe.
When we talk about separability of Information Structures "in" the Elementary Field, we talk about separability of organized sets (schemas) of (internal) correlations that bind in dynamic forms attracted by ideal forms, time by time present portions (volumes) "of" Field. Portions "of" the Field that support Structures "in" the Field. Distributions of Events "in" the Field that support patterns of Relationships "in" the Field. Action "of" the Field that supports Information (Information Structures) "in" the Field.
Speaking of Events and Relations that are linked in the Processes that represent what we see in the world, from waves and particles to the Universe as a whole... Let's remember that the Elementary Field is one, unique, unitary. That, in this sense, nothing can be seen as separate. But given the conformation of the internal distribution, density profiles of the ISs, degrading with the square of the distance, and the ubiquitous presence of chaos and the indeterminacy of the elementary fluctuations of the Field, we can separate and identify individual Structures in the Field. So we can say that we have infinite separate Structures within a unitary Field. In other terms, where the intensity of the correlations between the distributions of the elementary fluctuations (Elementary Action in its Components) falls below the local average intensity of the spontaneous correlations (Uncertainty Principle), what in quantum physics is defined as the spontaneous dynamics of virtual particles, there we can see the boundaries of the IS.
Regarding the fundamental aspects in which the formation of Reality manifests itself, we can imagine a causal and a variational separability. Causal separability concerns Events, Action: Events and effects cannot be produced in space-time areas that are not causally connected, no remote Action without contact, no remote Events without propagation of the Action in a continuous Field. Variational separability concerns Relations, Information and Information Structures: the definition outlined above applies.
We can also imagine that the case of free, non-confined ISs could be different from that of two confined ISs, perhaps in more articulated and complex systems of structures (e.g. atoms, molecules, etc.). Here the definition of separability that we have outlined may need to be modified, refined.
At a given moment we can imagine Structures that are propagating in the same portion of the Elementary Field.
If we are talking about Wave-like InfoStructures, without Mass, bosons we could say, these Structures can interpenetrate and transit in the same portion of the Field, in the same volume of space-time, so to speak passing one inside the other. Let's think of different waves crossing on the surface of the water. They may interfere, but essentially they continue to propagate, literally passing into each other.
In the case of Vortex-like Structures, massive particles, their "internal structure" does not allow the same behavior. Or in any case the dynamics of the interaction depends on dimensional factors, scale, spatial extension, speed, angle of incidence, movement constraints, degrees of freedom, etc. In particular, without considering Electric Charge, Spin, other more complex physical quantities (weak and strong nuclear forces), etc. we can imagine two particles of different types, with different masses and spatial extensions, for example an electron (very large and not very dense) and a neutron (not very large and very dense). They can pass one (the neutron) through the other (the electron) almost without interacting, especially if the electron is at rest and bound for example in an atom. They are like two waves of very different wavelengths.
Like an iron marble passing through a cloud of smoke. If we try to do the same thing with two electrons, the result will be very different. It is impossible to fit two electrons in the same volume of space. They will collide, a collision that will produce scattering, or the production of a swarm of other particles, depending on their mutual energy / speed / angle / position, etc. involved. Pauli's Exclusion Principle essentially derives from the nature, shape, dynamics and "internal structure" of particles, which says that no two electrons in the same atom can have identical values for all four of their quantum numbers.
In other words, in terms of this System of Knowledge and the hypotheses we are formulating, two electrons, two equal or at least "similar" Vortex-like InfoStructures, cannot be in the same place at the same time, cannot be supported by the same portion of Elementary Camp. The force, the energy necessary to place two electrons in the same portion would be very great, so great as to destroy the two Structures and transform them into something else. Of course, it's not just brute force. It's also about the footprint. Try placing two vortices of water into each other. If they have the same charge, i.e. the same chirality, it is already almost impossible to bring them closer. Let alone making them coexist in the same space.
In terms similar to those used in the field of Quantum Mechanics, we can say that in Vortex-like Structures, especially the peripheral areas of the vortices, where the density and organization of the Elementary Action is lower, the correlations between the temporal distributions of spatial fluctuations of the Elemental Field are less intense, such structures behave more like waves than particles.
We will see later how in the Forms where the Structures are constrained, we think of the electronic cloud around the nucleus of an atom, the forms, the internal profiles, of the electrons, especially the outermost ones, farthest from the nucleus, those in the less energetic quantum states, by interacting with other homologues of other adjacent atoms, for example bonding electrons in crystalline lattices, I can form fluctuating or even oscillating correlation patterns that take the form of standing waves that can create real waveguides, producing particular optical properties. Same thing, but at much lower scales, with much higher intensities, they can make the more energetic electrons closer to the nuclei, and even the atomic nuclei themselves, creating diffraction effects that are not detectable by ordinary light, "but by X-rays, or electron beams.
Links to the tables of contents of TFNR Paper
