Preface
First of all, thank you for reading this. I am, by any definition of the term, an amateur in the fields of physics, mathematics, philosophy, information theory, complex systems analysis, to name but a few of the subjects I have attempted to grapple with in this work. As such, I experience doubt and anxiety regarding my credibility and intelligence; my right to contribute to this (or any) field of study. I expect dismissal and/or humiliation at every turn; and have found that this expectation in no way diminishes the accompanying disappointment, and the crushing effect on my confidence, when I am inevitably dismissed.
However, whilst I am not a “scientist” in any official sense, I am possessed of a curious mind, and an ability to indulge and analyse logic quite deeply and rigorously. Having taken refuge in imagination for most of my life, I find I am now able to systematically explore complex, even esoteric, concepts and their implications from the relative comfort of my own brain, even if I lack the technical vocabulary to articulate my observations as effectively as I would like. This is not to say that I am gifted in this way; far from it. I fear I make many mistakes and assumptions which would be avoided by dedicated education.
I do, however, feel a bizarre drive to explore this line of reasoning further - the likes of which I have never experienced in any other area of my life, and which I still struggle to describe or define; I am compelled to see where these threads of logic lead, and what they may unravel when tugged upon.
Ultimately, I consider this a work of natural philosophy (read: speculation) more than anything; whilst it may eventually offer some testable predictions, and I am attempting mathematical formalisation, it is an exploration of logic first and foremost; a thought experiment.
To some readers, aspects of this work may be remedial, to others; opaque. The intention has been to explain as much as possible so that a variety of readers may understand, but given the highly technical and interdisciplinary nature of the work, there are bound to be some assumptions made about the reader’s grasp of complex, dynamic systems, mathematics, philosophy, thermodynamics, computer science, cosmology, quantum physics, and presumably other areas not listed here. I can only apologise, and ask you to persevere through my ramblings as best you can, and please keep an open mind.
Introduction
The term “System” generally refers to a set of units or elements, each of which possesses particular parameters and behaviours, which are determined by the rules of operation for the system, and its initial state. Depending on their rules, systems may exhibit dynamic and/or emergent behaviour as elements interact and change each other, and potentially even alter the system’s rules as well, if the initial rules permit.
The “state” of a system refers to a static snapshot of the values and configurations of every element in that system. We can also refer to the states of individuals and/or subsets of elements within a system. In either case, we are referring to all data regarding all properties and relationships of one or more elements.
Closed and isolated systems are variants which do not, or barely, interact with their surroundings; little or nothing escapes or enters. However these systems can (and usually do) make use of predefined spatial or temporal coordinate systems, or other externally derived metrics. Whilst convenient and intuitive, these systems are insufficient for our purposes, hence the more stringent Sealed System.
Characteristics
The Sealed System is one outside of which absolutely nothing exists, originates, or terminates (in fact it is misleading to refer to an “outside" at all). The sealed system has no surroundings; it does not exist on, or interact with, some predefined coordinate or dimensional system, and it does not possess any voids. The only way such a system can be described is in strictly self-referential terms. What follows is an introduction to the characteristics and peculiarities of the sealed system, which will be explored and justified further throughout the text, and the work as a whole.
There is only one sealed system. It would be meaningless to model multiple concurrent sealed systems since by definition they will never interact in any way; it would be functionally identical to modelling them independently. Whilst a sealed system could theoretically contain multiple subsystems which barely interact at all, no such subsystem will ever be truly isolated - they may be closed, but not sealed; even existing on the same coordinate system precludes such systems from being sealed. Since there can be only one sealed system, we primarily refer to it as “the sealed system”.
The sealed system is a conservationist system. Just as there are no external influences, interactions, or metrics, there is no capacity for elements to be created, destroyed, or entirely isolated from the whole, though they can be divided, combined, and transformed in other ways.
Time in the sealed system is inseparable from the progression of the system's state. If the system does not progress in state, it does not progress in Time. If any element in the system changes in any way, the system's state has changed - time has progressed at the system scale (i.e. the system has progressed), but only the changed element has progressed in time locally. If a change in an element's state causes some other element(s) to change state as a result, then both change and time propagate throughout the system. If any such changes are irreversible, then Time is also irreversible. If these propagations form feedback loops and thus reverberate indefinitely around the system, then Time is continuous, though not necessarily uniformly distributed throughout the system. In computer science terms, the sealed system is event-driven; some element updates, intrinsically causing other elements to update, each of which causes further updates, et cetera ad infinitum.
We cannot describe an overall system state as lasting for some duration; we can only describe the frequency of state changes in subsets of elements, relative to each other. The system's minimum increment of time is therefore partly defined by whichever element has the highest ratio of state changes compared with all other elements.
All descriptions and measurements within the sealed system are relative to other elements within the system. The lack of externality means there is no absolute frame of reference, and all properties are defined by their relationships to other properties within the system. The possible exception is the total quantity of the system (perhaps mass-energy or total information); but even this can only ever meaningfully be defined as 1 - any other value is ultimately arbitrary and/or subjectively derived from within the system. The only way to delineate quantity in a way which is effectively objective is to do so relative to this total; i.e. the mass of a body being denoted as a percentage of all mass-energy in the universe, which must be considered equal to 1.
All rules and laws governing a sealed system must originate from within the system itself. This means that any laws of physics, logic, or computation that apply will be internally consistent and will not depend on any external frameworks; they will be grounded in the functionality of the system's most basic unit(s) of logic, the parameters of the initial system state, and the sequence of states which necessarily follow. These rules may evolve, but such evolution must be a consequence of the system's internal dynamics and initial state. The sealed system therefore operates entirely autonomously. There are no external or random influences or interventions, and all changes occur due to deterministic internal processes.
The sealed system is deterministic, but impossible to predict from within. Perfect prediction would require the availability of total information regarding every component of the system, plus additional information to encode relationships, referencing this data historically for the entire lifespan of the system, and encoding additional information about how the relationships interact; a complete causal map of the system. Since any predictor entity must also be part of the sealed system, this requires that it predicts its own predictions, leading to an infinite regress of computation. Furthermore, it would either need to obtain this information without influencing the system, implying externality, or else would need to account for the effects of its observation, leading again to the necessity of self-prediction. This is related to Gödel's incompleteness theorem, and, to a lesser extent, Turing's halting problem.
Whilst approximate, and even highly accurate, predictions are possible through the acquisition and cross-analysis of vast information, these will always be necessarily probabilistic, in order to account for their incomplete resolution.
It is theoretically possible to simulate a sealed system from within a sealed system, but it is impossible for the simulation to ever approach the complexity of the host system, and thus it could never serve as a tool for perfect prediction of the host system.
We can analyse the sealed system in the abstract because we can break its rules. We can observe a hypothetical or simulated sealed system without interacting with it. We can take on the impossible role of non-interactive observers, external and separate from the system, but with access to total information regarding its behaviour. As mentioned, limited computational ability means we can only do this for relatively simple system configurations, but nonetheless it is a valuable tool for discussing and exploring this concept, provided we adhere to its self-referential structure in our analysis. We may, occasionally, compare certain system configurations to more familiar structures, or superimpose certain concepts as a way of illustrating similarities and contrasts between them (for example, visualising a one-dimensional structure as a line in three-dimensional space, or imagining the system in stasis), but these are only ever to be employed as tools for aiding in comprehension, and are not conditions actually present in the system; there is no external or absolute view.
Self-Referential System Modelling
We have already briefly discussed the self-referential definition of Time (state changes), but the self-referential definitions of speed and distance are more complicated. Here is an introduction to how the sealed system can be modelled using concepts from relational geometry, tensor calculus, vector space, and field theory. Reader beware: this is not only hard to explain, but can be very challenging conceptually. Also note that these explanations are expanded upon in part two of this work.
Each point in sealed system space is composed of (or “contains”) a quantity of energy-mass. The sum of all these values across the set of all points is the total Energy of the system, and is constant. Each point’s energy-mass is normalised to the total energy of the system (i.e. it is given as a percentage of all energy) leading to the aforementioned conclusion that the total energy of the system can only be considered as 1. Contextualising the energy-mass of each point in space to the total of all energy-mass in the system is as close as it is possible to get to absolute quantification of mass-energy within this framework. The quantity of energy contained in each point, and the total number of points can both vary (though primarily the former decreases when the latter increases).
Each point in space can be represented by a tensor, the length of which is equal to the point's energy-mass quantity. The rank of these tensors is partially determined by the total number of distinct points to which the point in question is directly connected; meaning that energy can pass from one point to the other without going via any intermediary points.
Each component of a point’s tensor represents, essentially, the weight or motion of energy flow between that point and each of its neighbours. We can refer to this tensor as the tension distribution of a point; encapsulating both the quantity of energy contained in (or represented by) that point, and the bias of energy flow through that point, simultaneously. When referring to these values for a set of points, we may refer to the mass-energy landscape of that set.
To assess the distance from A to Z we need total information regarding the intervening mass-energy landscape (points B-Y), which requires a recursive approach; similar in overall principle to pathfinding algorithms. The state of each point in the landscape must be known, and those points must be evaluated in terms of the effect each would have on a signal which is intended to travel towards Z. This can be accomplished using a modified arctangent function (an n-dimensional angular comparison), to determine the angle between the overall directional bias (average or maybe normal?) of a given point, and the direction of the intended final destination of the signal.
However, the signal also alters the tension distribution of each point it passes through, and does so variably depending upon the strength and angle of the signal relative to the point; the signal essentially curves the tension distribution of each point it passes through towards its trajectory, but the signal is in turn diffused and its trajectory altered by the dynamics of each of those points.
More specifically, a signal entering a point is a state change; an event. During this event, the point has the characteristics of the signal, as modified by its own state. This causes state changes in all of its connected points, which respond to this sudden change in the tension distribution of one of their neighbours, triggering further state changes, as discussed in the section of self-referential time. This leads to noise (discussed more in a moment).
All of this means that we would need to compute the effects of every possible interaction at every step of every version of the journey from A to Z in order to precisely calculate the effective distance at the scale of points in space. We could then select the path which involves the fewest steps, and/or which reaches the destination with the signal closest to its original strength (i.e. least diffusion or diversion of the signal).
This is already very computationally complex, and yet there are still more challenges; the above example assumes a simple and, other than the signal we are concerned with, a static system. In reality there are any number of other signals present within the system at any time; diffusion echoes from other signals. Each time our measurement signal propagates, the energy landscape ahead of it will have changed, potentially in ways which radically alter the projected trajectory of our signal. The system is dynamic and noisy, and only with total information regarding every point in the space could we perfectly compute / predict trajectories; this level of information is unattainable from within the system, as has been discussed, leading to functional randomness from the perspective of any internal observer.
Another key aspect of an energy landscape is via the sensitivity/rigidity of the points which define it. Sensitivity and rigidity are oppositional measures of the uniformity and magnitude of a point's tension distribution. Points which are being pulled evenly across their connections, and which contain little energy, are more easily altered by the signals which pass through them constantly to and from their neighbouring points (background noise), and they alter those signals less in return; they are more sensitive, and less rigid.
The more interconnected a set of elements are, and the greater and more balanced their tension distributions are to each other, the more they resist external influences, due to the energy equalising very quickly throughout the integrated structure. The more a point, or set of points, resists incoming signals, the more those signals are changed instead. Resistance can be directional (or dimensional, in tensor terms), meaning that a collection of points forming a structure can be highly resistant to some types of signals and highly responsive to others.
One result of all this is that we can define a form of self-referential distance between two points in space as a function of how much energy loss occurs in the transit of a fixed-strength signal from one to the other. Spacetime points, when modelled in this way, can be connected in ways which produce some familiar behaviours; for example, it is possible for A and B to be close, or even directly connected, but to behave as though they were (perhaps infinitely) distant for certain forms of interaction, which is reminiscent of the phenomena of entanglement (correlation in specific aspects of physical state despite apparent spatial distance) and dark matter (physical interaction through gravitational effects, but not electromagnetic ones). It is possible for energy to flow more easily from B to A than from A to B, reflecting a wide array of interactions, but particularly gravitational phenomena, such as black holes.
To Be Continued…
The best way to explain and demonstrate these principles is by examining them in action via the step-by-step evolution of a sealed system from an initial singularity into a diverse and intricate system governed by identifiable and familiar principles. This will form the main body of the experiment, and will be its own document.
