What is the 'atom' of a process, its smallest existent? (I don't wanna say smallest particle, because this implies substance.) Does this question even make sense in pp'ical terms? — rachMiel
It makes sense to me to think of it in terms of smallest form or structure. So you could follow the condensed matter view that a particle is a quasiparticle or soliton. That is, it is like a knot or frustration in the fabric of existence.
https://en.wikipedia.org/wiki/Quasiparticle
https://en.wikipedia.org/wiki/Soliton
1. If time is a process, any slice of it (duration) would have a beginning, middle, and end. Likewise, each of these would have a beginning, middle, and end. And so on, fractal-like, ad infinitum. Yes? — rachMiel
Space and time are ways in our modelling to give change a static backdrop against which it can be measured ... as change. So we have to have something that stands still as the way we make it clear that something else is moving or evolving.
Thus in process thinking, we have to realise the nature of the trick we are playing. We invent a notion of a fixed spacetime backdrop so as to dramatise the fact that there are then energetic changes taking place within that steady reference frame.
That non-process approach works really well. But ultimately, it is a physical fiction. As general relativity and quantum physics eventually show. What is fixed and unchanging is simply a point of view.
The next step after that - which gets you into a proper process story - then generalise the (semiotic) notion of a point of view so that change is basic, but a recognisable structure of reality still emerges.
At root, this is just relativity - the light-cone holographic structure of the universe. All action is scaled by c. And so two points in space share the same moment in time only if they are in communication and are integrated or coherent in the sense of being in a cause and effect relation to each other.
If the Sun went supernova now, you wouldn't know about it for another 8.5 minutes. There would be no disturbance in the light or gravity you think it is pumping out until news of that arrived at lightspeed.
So c sets a basic scale of integration when it comes to the physical definition of a temporal duration or moment. Nothing has really changed until two points in space have had enough time to be energetically connected ... in a way that could cause a difference.
Lightspeed is the very fastest rate of temporal integration. But the relaxation times of more complex physical processes could be much slower. How long does it take for a mountain range to be thrust up by the collision of tectonic plates? Geology would have its own really slow scale at which the network of forces and masses involved reached system-wide state of equilibration after any perturbation. A moment of geological time would take forever to unfold compared to the simplest level of universal equilibration - the establishing of regions of space coherently connected in terms of photons and gravity.
So a process view would see temporal duration as being about the time it takes for a spatially distributed action to unfold and arrive at some coherent balance. And with relativity, a fundamental rate for this integrative action was established by saying nothing can happen faster than c. And then we know that any process involving mass happens at sub-light integration rates. So the "cogent moment" for material systems can be way slower in terms of the rates at which a process of equilibration unfolds, and much smaller in the distances that are being integrated over.
So it is all kind of fractal. It has scale symmetry. But there is a fundamental relativistic baseline set by c.
In terms of your question, there would be a thinnest kind of slice - the c-scaled slice, or the lightcone story. Then in terms of other material processes, they would all have much fatter "moments". They take longer, and span less distance, to achieve the cogency that defines a duration - the time it takes to achieve a stable change, a change stable enough to be fixed as a fact of history, a constraint on future freedoms.
2. If time is a process, does it imply that space is also a process? — rachMiel
Space, time and energy together make up the process. So space is an aspect of the process. We want to get away from the simple Newtonian separation of the three, even if the three are quite separated seeming in our current state of the Universe - where it is so cold and expanded that it is pretty close to its static Heat Death condition.
One way to think about space then would be as the opposite of time. And if time is how we think of integration, then space is how we think of differentiation. If two points are distinct and at a distance from each other, then that is why it is going to take time for them to become connected and in touch with each other in an energetic or communicative sense.
For there to be an issue with integration, then there has to be differentiation. And vice versa. So really the two are the two sides of the same coin. That is why relativity can speak of spacetime.
Time then gains a direction once we stir thermodynamics into the pot. Entropy breaks the symmetry of relativistic spacetime and so gives us a direction that points to the past and a direction that points to the future. The past is all the spatial extent that is now temporally integrated. The future is all that extent yet to be integrated.
So a process view would understand reality as a web of relations not a collection of bits. And then we would see structure arise as the result of fundamental contrasts in those relations. You would have action going in two directions at the same time - integration and differentiation. And that in turn would map to what the "collection of bits" ontology has been calling temporal duration and spatial separation.
A process view would have to change its very jargon to escape the familiar clutches of the mechanical view of nature. So asking what "space" or "time" are, is still to be thinking that the holism of the process view ought to reduce to the mechanicalism of classical physics.
Now mechanics is great. It is a really efficient for calculating the state of the world - in the near Heat Death state that defines our particular moment in Cosmic history.
But a process view is about a metaphysics of relations. It is about seeing nature in terms of its coherent structuring forms rather than as an atomistic collection of parts ... floating in a supposedly a-causal void.