Introduction to causal dynamics

[Ralph Alexander Bariz <ralph.bariz@pm.me>]

Hi all,

My name is Ralph Alexander Bariz. I've written a, I think quite usable, proof of concept for a runtime which should introduce a new kind of algorithmic dedicated to the graph oriented modeling and execution of complex non-linear systems.

Please see https://gitlab.ralph.or.at/causal-rt/wiki/-/blob/ralph/debconf/debconf.odp

Please see the C++ POC Implementation https://gitlab.ralph.or.at/causal-rt/causal-cpp

I request to move over the whole project group to salsa https://gitlab.ralph.or.at/causal-rt

My salsa username is "udet".

Below I've written, for people interested in the why and probably a way to some kind of new discrete and, error-resistant discretely, executable physics, the thesis. I would also like this post to be seen as an official pre-publication of this thesis.

Thanks.

Preface:

I'm system analytics and architect, no mathematician. So this wont contain a lot of numerical math what probably also is not necessary but instead the results of a structural analysis of what Germans call "Wirklichkeit".

While this journey begun with working out a methodology to model and execute symmetric interaction simulations on GPU's utilizing definite integrals I was not convinced it could allow to model and execute the aimed complex systems observed to be real.

It continued passing by actor model systems which were more what I seek for but still very data oriented while lacking for a definition of "the how".

At that time I came into contact with Werner Heisenberg's and Hans-Peter Dürr's "last assumption" defining a virtual entity they called "Wirks". This, for me, was the key to understand what we seem to have missed all the time. Here a discrepancy between the German and the English language got very obvious. While a certain understanding of "the how" seems to be deeply integrated into German language, the English language seems to completely lack it. This discrepancy gets most obvious when thinking about the classic definition of causality in both languages. While the English language defines causality as the implication cause -> effect, while cause and effect are both about the "what", the German definition is "Ursache"(cause) -> "Wirkung" while "Wirkung" is not about the "what" but about the "how". Also one might note, the English "reality" covers the German "Realität" but not the German "Wirklichkeit" while the reality is about the set of all being and the "Wirklichkeit" is the set of all happening.

When trying to model this thought of a "Wirks" there came up a few implications which made such a model very attractive not only in context of Max Planck's assumption of a discrete energy and spacetime but also seems to connect the strings in context of thermodynamics and the simple question, why there is entropy but also allows to neatly and exactly define a model of time and why density(mass and extent) of a system influences the flow of time within this system in relation to another system of another density. Also it seems, that such a model allows to understand certain effects observed in quantum-mechanics and why space is not a that certain thing as we use to treat it as. Causal dynamics has implications to the concept of "calculus" and neatly defines the symmetric corner-cases where it is useful but clearly points out why in "real" asymmetric/complex and not dominated(like domination of suns mass where error can but cut as negligible) cases it cannot be applied.

In the following lines I will not handle the concrete "proof of concept" implementation for classic computing I have done but use one of its example's to support some of previously broached claims. Still it has to be clear, this POC implementation is NOT complete neither correct. Also please mind, here I define causal dynamics as the thesis observed and deduced but not as the thesis making philosophical sense. There is an extended thesis assuming that all systems are continuous in their nature and its aspects are discretising on interaction but since there, for me, is no hint available yet, that this could be the case, but even seemingly one that this might not be the case(entropy) I will not touch this thought at this point.

Definitions:

• A "Processor" is an environment allowing the execution of a causal systems
  
• An "Aspect" is a piece of Information in context of a system
  
• A "Wirks" is the necessity of information to change
  
• A "Tick" is a pattern allowing a processor to process a certain "Wirks" within a causal system
  
• A "Wirkung" is a branch of "Wirks" implying each other
• A "Wirklichkeit" is an integral set of "Wirkung" influencing each other

Axioms:

• Principle of "demand": nothing happens without triggering interaction as it is required in sum interaction
  
• Principle of "inertia": nothing happens without a sufficient cause (investment of energy by trigger of interaction)
  
• Principle of "exclusivity": no concurrent involvements of a single "aspect" can happen
  

Deductions:

In our view "time" seems to be something passing by as a whole. We do not naturally understand why time can be "slower" or "faster" in relation to observers "time" and why it seems to be connected with "space" even both seem to be very different. Principle of "exclusivity" brings up an understanding of "time" as a causal order influenced by the amount of interactions happening on an aspect and "space" being just the consequence of this order. While this might at first glance make sense for dense systems it seems not to explain the observed dilatation for accelerated systems. When thinking about "speed" in such a context, we need to see what speed does. So it seems naturally to me, when an object of a certain speed is moving its interaction partners are changing due to that directed quantity of speed when assuming a homogeneous density distribution of whats in front and whats behind. But when closely thinking about the problem I have to acknowledge the amount of interaction of an accelerated system might increase on acceleration and there fore lead to an inverted effect as on unaccelerated moving away from lesser dense systems towards more dense systems. This assumption allows to understand the speed of light as the point where a system is interacting with everything available what leads to observed wave behavior of light and other particles accelerated to near light speed. Also this allows to understand why there cannot be a "higher" speed. There is no more than "everything" available. As there is no spatial but only causal direction any more. The requirement to invest more and more energy for gaining higher and higher speeds is due to the principle of "inertia" in context of every single interaction. A system requiring to interact with "everything" also requires the energy for doing so. However propagating(what I'm not necessarily doing), that unlimited energy is required to accelerate a system of mass to speed of light would, in this context, imply an unlimited amount of possible available interaction partners what conflicts with the thought of a finite reality, a begin and an end.

Due to "demand" everything is uncertain unless information is required in interaction, at that point overall demand defines probability.

We tend to see things in an absolute way wondering about effects observed in quantum mechanics. In a system perfectly isolated from any interaction partner which is not interacting with observer, however it seems natural to measure what is expected by observer why observed system might seem to be certain before measurement. So the assumption making quantum mechanics that unintuitive is the assumption uncertainty would be the exception and observer is unrelated to observation. But at this point it seems, uncertainty is the default and probability is strongly defined by requirements of the sum of all observers but when all other observers are interacting with observer looked at it seems certain all the time.

Here space gets really messy. It seems that there is nothing like a "space". No framework stuff is existing within but just a mesh of demands for causal interaction. So assuming space gets bent inside a star would imply it is the same "space" which somehow gets altered. But, to me, it seems more, that there is nothing in common between our "Wirklichkeit" and those within some star like our sun except the interfacing surface of it. We are not part of the inner mesh of "demand" within a star and there fore could only tell properties observable from the outside. The inner of a star however stays uncertain to us and might, if there is no demand playing a role unknown to us, fit the expectation of outside observer basing on happened observations until intrusion and direct measurement but never will violate made observations. One could say, the "Wirklichkeit" will come up with a way to ensure consistency across all observations and if its not possible to ensure then observation wont be possible.

Example of an oscillating system:

When imaging a system consisting of oscillators in a matrix interconnected by springs, one could also speak of a granular membrane, we can apply exactly such a causality. This causality would be defined by an oscillator passing it's impulse to their neighborhood using Hooke's law implying them to also pass their impulse to their neighborhood. When applying some impulse to one of those oscillators this leads to a wave which, under the assumption of system being symmetric, is as perfectly circular as granularity of systems allows while, for obvious reasons, it gets more and more circular towards radius getting infinite. This example has two possible manifestation. The one is discrete and there fore limits the smallest size of impulse by (overall difference in impulse)/(number of neighbours) > 0 and there fore leads to impulse getting lost(entropy/heat) when ΔI/Nn = 0. The other is continuous and does not know entropy what seems not to be real. The probably most interesting observation would be certain effects known from quantum mechanics like interference's without requiring any real or even transcendent constants and purely using integer domains for parameters and result.