Do preceding events cause subsequent ones in a four-dimensionalist world?

Question

I feel like this question has a good chance of having been asked here before, but the first ten-odd "similar questions" listed by the site when I composed the title didn't cover what I'm aiming for, so I'm not sure. Will delete if it turns out to be a duplicate, anyway.

Also, the only SEP article I refreshed my memory of before composing this question is one about time in general. Could easily be addressed in e.g. the article about the metaphysics of causation. For now, my incomplete memory of the latter does not testify on behalf of said address, however.

So "caveat emptor," so to say...

Definition of causal determination at issue. Assume that the past and "half" the present function as constants relative to a variable future. The past/part of the present determine the future mathematically in the sense of "solving for" the variable of the future.

The four-dimensionalism consideration. Imagine a world consisting in a single tesseract whose fourth coordinate slot is timelike. Without supposing an absolute past, present, or future, we have all facets of the tesseract "given" in atemporal simultaneity.

It seems as if no facet, taken to be pastwise, "solves for" other facets as variables, since no facet is a variable as such. All facets are determined "at once" by whatever function projects the whole tesseract "at a glance." We can't step outside the tesseract (if we're inside of it) to say that the unit cause of the entire structure is itself an effect of a prior cause, etc. Perhaps this is possible in general, but for reasons of local empirical-causal closure, this fact transcends our possible empirical knowledge. And logically, it is impossible to predetermine the content of an information powerset from prior information sets; there is always underdeterminately more in an indefinite powerset than is in its base. So there is no a priori guarantee of determination either.

Question: so what use is the concept of causal determination in a four-dimensionalist closed world? A unit circle could be determined from x² + y² = 1 but no infinitesimal side of the circle "causes" the other sides to be so. And we have no knowledge that the formula for the unit circle must be an effect, so to say, of another formula, and so on "backwards in time." So is the notion of temporal determination, as A-series determination, required at all to interpret four-dimensionalism as such? Because it seems, here, not to be required at all.

Answer 1

As Conifold helpfully explained here

McTaggart was an objective idealist, all subject bound constructs were "unreal" to him. ... He is asking for a tenseless explanation of tenses

McTaggart's B series is the tenseless 4D tesseract; a deterministic map of events, separate from living agency in which the present is perceived/reified. So there is no actual present in the tesseract. You can pick a time, any time.

In contrast there is the A series, where the present is the moment of living existence — the nunc stans — demarcating the tenses.

So is the notion of temporal determination, as A-series determination, required at all to interpret four-dimensionalism as such? Because it seems, here, not to be required at all.

There should still be considerations of entropy in a B series tesseract, so it is not a matter of indifference whether a chemical reaction, such as combustion, runs forwards or backwards. However the tesseract map/model is indifferent to tenses; it is meaningless to say the reaction has happened, is happening or will happen.

So in the 4D tesseract there is "temporal determination" in regard to the arrow of time, but not in regard to tenses.

Answer 2

You might consider How does biological evolution work in the block universe/b-theory of time?

And on causation in general Is the idea of a causal chain physical (or even scientific)?

Hume's Problem of Induction already points at causation as suspect. We have continuous symmetries under transformation in physics, and they give us false confidence in the idea the simple principles can account for regularities in change. As you say, mathematics is a whole area of logical rather than causal relationships.

In modern physics, in order to find a theory of quantum gravity, it is widely expected that space and time will be emergent. Such as in Loop Quantum Gravity. The Holographic Principle can help give insight into how this might work, with a way of talking that sees a surface between objects, then something like the AdS-CFT correspondence linking a surface to a way of talking that looks like a 'bulk'; but actually they are different ways of talking about the same thing.

Answer 3

One way to deal with this is to replace the notions of "cause and effect" with the notion of pattern. There are clearly patterns in the world. All cats have certain characteristics in common, for example. Apples are usually good to eat. All of the round, hard things you find in a streambed tend to be the sorts of things that you don't want to get hit in the head with.

This notion of patterns can be extended to patterns of events. There is a pattern associated with a stone flying through the air. It will continue to fly through the air in a mostly-predictable trajectory until it collides with something such as the ground or somebody's head. If it hits somebody's head, there is an additional pattern involving blood and skull fractures.

Rather than thinking of nature as a collection of causes and effects then, we can think of nature as a collection of patterns extended in time and space. This model of nature is fully compatible with scientific investigation, and is also compatible with a four dimensional view of spacetime.

Answer 4

I cannot tell from your question whether your 4-d world is an imaginary concept or is intended to mean the actual spacetime we inhabit. If the former, then it will be subject to whatever rules you imagine. If the latter, then the concept of causal determination most definitely has a use- indeed, it underpins virtually every aspect of our understanding of reality.

There are certain dubious ideas baked into your question. You talk of the 4-d space being given in 'atemporal simultaneity'- I cannot quite fathom what you mean by that, especially since atemporal simultaneity seems to be an oxymoron of sorts. If you mean that it is possible to conceptualise the entire 4-d block without considering which 3-d surface within it might correspond to a particular 'present', then I agree with you, it is possible to think of it in that way in the abstract, but so what? It does not follow that the 4-d block has a material existence. Most branches of physics successfully model reality by assuming that all matter exists in the present. More specifically, if a particle exists at a location of spacetime with a time coordinate t (in whichever reference frame you wish), it does not exist at any point with a time coordinate of t plus or minus n, where n is any non-zero number you like. Particles are point like objects that move along worldlines in directions of increasing time- they are not 4-d shapes extending backwards and forwards through time. The equations of physics tell us how the configuration of matter and energy at time t will evolve with time, and we take that evolution to be causal, in the sense that interactions at one time lead to configurations at later times.