Questions About Time and Space

The last post presented a version of causal process theory as a framework for ontology. The world is fundamentally a causal network, made up of persisting causal processes that participate in change-producing interaction events. As I mentioned, many details would need to be filled in to have a more complete picture. Below, I tackle a subset of the questions about this picture: specifically, some of those relating to time and space. Compared to past posts, this one is speculative and I don’t always know the relevant literature very well—comments are very welcome as always.

1. How Should We Interpret Relativistic Spacetime?

I separate this question from the one below it, about time’s passage and directionality, so I must briefly say why I do not think the second question is determined by the first.  Some folks assert that relativity theory, which replaced the classical picture of absolute space and time with 4-dimensional spacetime, implies that the passage of time must be illusory. They conclude we live (somehow) in a static, four-dimensional “block universe.” This conclusion does not follow, however. The theory of Special Relativity (SR) does indeed contradict the notion of absolute simultaneity. This conflicts with the intuition that the “now” associated with our sense of time passage is something that is shared across the universe. And while the move to General Relativity (GR) opens up some room for proposals that introduce a preferred cosmic time-direction, it is unclear that any of these are workable models for the actual cosmos. Further, they rely on assumptions about global matter-energy distribution that probably are not relevant to understanding how humans experience time passage. Despite these considerations, however, nothing in SR or GR rules out the notions of becoming or passage if they considered as local phenomena that respect the relativity of simultaneity. Recent work by a number of philosophers (See Aames 2022, Arthur 2019, Savitt, 2015, Balaguer 2021) clarifies this point: while authors may disagree about how to define locally appropriate notions of the “present” and its passage, they agree there is no necessary conflict with relativity theory.¹

With that said, we can return to the question of the how to interpret spacetime in light of our causal theory. As a caveat to this discussion, I must note that GR, despite its outstanding success in predicting gravitational effects, is limited by its incompatibility with quantum theory. My hope is that a successor theory can be found that provides a unified account of large and small-scale physics. I think it is promising that some nascent approaches to quantum gravity (QG) use some kind of causal structure as a foundation. Causal set theory is probably the most well-known of these – see this article for an overview (my old blog was replete with excited posts about various QG ideas—see this one for instance, which also includes links to other such posts).

Getting to the point: I don’t see that my particular causal ontology offers much insight for interpreting the spacetime of GR (as opposed to its implications for time passage/direction—see below). As things stand, GR’s conceptual separation of matter-energy from spacetime presents unsatisfactory options. The first option is to say that causal interaction events take place in a spacetime that has a distinct existence; in this case we might posit that these events are represented by the matter-energy side of GR models. But, in this case, spacetime itself is just a brute addition to ontology. The other option is to insist there is nothing real other than the bare causal network, and spacetime represents some aspects of the behavior of the causal web, while matter-energy physics represents other apects (keeping in mind that we must take the continuous manifold of GR models to be an idealization—the underlying causal framework is discrete). This second option is the one I prefer, but a problem arises in that it seems to run against the grain of existing GR-based critiques of so-called relational interpretations of spacetime. In such an interpretation, spacetime would be a non-fundamental consequence of relations among physical systems. However, matter-energy distributions do not completely determine spacetime structure in GR, and we can readily model various spacetimes in the absence of any matter-energy at all. While there is an active and complex debate about these issues, a preponderance of theorists maintain that GR implies (to some degree) a “substantivalist” rather than relational notion of spacetime (the SEP has a nice article in two parts about the history of this debate). In other words, GR seems resistant to theorizing about about a monistic reality underlying both spacetime and matter-energy physics. But, returning to my initial caveat above, I hold out hope that a successor theory to GR will dissolve the debate by providing a more unified framework for physics which has a clearer representational relationship to the world’s causal foundation.

2. Does time pass or flow?  What accounts for its apparent direction? Is time fundamental or derived from causation?

As a starting point, I note that the causal theory already includes a minimal notion of passage/becoming. Every change in a causal process involves the passage from a possibility to its actualization—a disposition possessed by the process becomes manifest in an altered dispositional profile. This new profile then sets the stage for the becoming of additional actualization events. I think this basic template plausibly provides the raw material for understanding our experience (as composite causal processes ourselves) of time’s flow or passage. In other words, the phenomena we associate with time (its flow and directionality) are derived from this causal foundation. On the other hand, more needs to be said. For instance, the becoming associated with a single, isolated causal event couldn’t be said to have a direction in the absence of some larger context. What accounts for our subjective experience of directional passage in time, invariably proceeding from past to future? Well, since this experience arises from the perspective of a composite system that is embedded in a complex, macro-scale environment, an explanation will need to appeal to features of this broader context.

A first suggestion would be to embrace a popular explanation for time’s apparent direction: increasing entropy in keeping with the second law of thermodynamics (a prominent early discussion is due to Reichenbach). The idea is that our macroscopic, psychological/biological sense of both the passage of time and its consistent directionality is due to the entropy gradient in the universe (or region of the universe) in which we find ourselves. This idea has been fleshed out in a number of ways by a variety of physicists and philosophers of science over the years. I won’t review the details, but whichever is the most promising version, one would adapt it to the present discussion by positing that the causal patterns that constitute ourselves and our environment are consistent with this physical explanation of time’s directionality. So, to clarify: while causal production is indeed “directed” in the sense of creating new events out of the set of possibilities, the pattern at the macro level need not have been so neatly organized into the uniform direction we experience.  That is due to the entropy gradient. Whether there is, in fact, some deeper explanation of the universe’s seemingly contingent thermodynamic character (“why was entropy so low in the past?”) is a distinct and difficult question.  But with the entropy gradient framework in mind we can draw a couple of conclusions about the relationship between causation and time:

• Causation is independent of and prior to time passage and time direction. Certainly, the becoming of events is a necessary ontological ingredient for passage to occur.
• However, the mere existence of causation does not fully determine the human experience of passage, and in particular, its strong directionality. These are due to the entropy gradient that characterizes the large-scale causal patterns that constitute and surround us.

Upon reflection, however, I think there is merit to a different explanation, where temporal direction is fully explained by the causal metaphysics without the appeal to entropy. The key motivation for this alternative lies in the holistic character of the dispositions possessed by the plenitude of causal processes. Because all dispositions are for mutual manifestations with one or more partner processes, there is a coordinated aspect to all the events that occur. This is not to say they are determined. They should, in fact, be seen as irreducibly indeterministic (in keeping with quantum mechanics). However, for causal production to take place, the possibilities inherent in the dispositions of the participating causal processes must be compatible with one another, and this must continue to be the case as new interactions follow. This would seem to enforce a common directionality in the collective interaction pattern of any large causal network (either in its entirety or in a region large enough to seem like the whole picture to us). If this wasn’t the case, it would seem to open the door to causal/temporal disorder incompatible with our experience.

A recent preprint by Emily Adlam contains an argument relevant to this discussion (“The Inaccessibility of the Past is Not Statistical”). She argues that a potential problem with relying on entropy considerations to explain our experience of time’s directionality is that it is merely delivers a statistical bias toward the future, not an absolute rule. Exceptions, perhaps only rare and microscopic, would be possible. Even if we wouldn’t normally observe these, it seems that, in principle, a skilled experimental physicist might be able to exploit this fact in order to intervene, say, to affect the past state of a particle. However, if this were possible, then it would be possible to create a contradictory scenario involving a particle’s present state being determined differently by past and future influences.  In order to rule out such contradictions, it seems we must have a stronger, loophole-free, basis for temporal direction.

Adlam goes on to formalize this argument using a definition of processes as classes of experiments with characteristic inputs and outputs (this can be adapted for classical or quantum physical operations). These processes can themselves be linked in longer chains. She shows that a requirement of non-contradiction enforces a strict partial order for processes – in other words, a causal ordering (using “causal” here in a common technical sense as in, for instance, causal set theory; also, chains must not loop—in other words they must correspond to a directed acyclic graph). In the context of relativistic spacetime, this order is simply the temporal order of the experiments in a given reference frame (as long as there are no closed timelike curves—CTCs—in spacetime). An agent embedded in this matrix of process chains would be expected to experience a consistent, exception-free direction in time.

The causal theory I favor shows how causal production occurs, but does not contain additional laws enforcing order in the resulting causal web.  I suggested above that the source of the order is implicit: it arises from the holistic or coordinated nature of the dispositions possessed by the participating processes. When considering Adlam’s model, we can view this ontology as providing a more metaphysical backdrop for the kind of ordered structure that she concludes must prevail to rule out contradictions. To summarize:

• We are embedded in a causal network that is large relative to its component elementary processes. Long, patterned chains of events comprise the large-scale features relevant to our experience.
• Both everyday experience and our scientific investigations are inconsistent with the existence of anything other than a strict partial ordering of events.
• The fact that dispositions toward interaction events are always for reciprocal manifestations (with two or more partners) rules out “rogue” retrograde chains of processes among the members of a family of possibly connected process chains.
• This enforces the large-scale order which underwrites our experience of the direction of time.

Note that the thermodynamic arrow is undoubtedly still very important when it comes to understanding the nature of the particular processes that comprise our world. But we don’t need the 2^nd law to explain the direction of time.

Now let’s finish with a few quick bonus questions.

3. Do (elementary) interaction events contribute to temporal duration, or are they instantaneous?

The notion of an instantaneous event, like that of an infinitesimal point, I take to be an abstraction.  It represents the importing of a mathematical notion into metaphysics. Elementary causal interaction events—the becoming of which is the raw material of our experience of the world—make a contribution to our impression of time passage. This contribution may be small but not zero. Reminder: abstract physical models often feature continuous manifolds, but in this ontology the concrete world they seek to represent is actually discrete.

4. Does realism about causal production imply presentism?

The reality of becoming and time passage is inconsistent with eternalism: the view that past, present and future events all exist in an even-handed way. If time’s flow is real (founded on causal production), then there is something special about the present. However, one can choose between two alternatives: the first is presentism (where only present events are real), keeping in mind we need a version that respects the absence of global simultaneity; the second is a growing-block model, where the present builds on a past which is also real. Since new events are causally produced by processes that propagate from previous events, there is an asymmetry between past and future in the causal picture that seems absent in presentism. The evolving causal network appears to conform to the growing block view.

5. Going back to a point from the last post: Isn’t it weird that causal processes are not locatable between interactions?

Interactions between causal processes are the concrete events of our world. Elementary processes, when not interacting, possess dispositions toward these interactions. While we can envision them as the “edges” of a causal graph (or “arrows” on a directed graph), while the events are the “nodes”, this is a somewhat misleading picture, since it makes them seem classically local. Given the need to be compatible with quantum theory, they must be non-local in a way that events are not. Given this, it isn’t clear whether these dispositions make any contribution to our theoretical notions of spacetime and its (locatable) contents. But they play a role in our reality: for instance, as proposed above, the process of dispositions becoming manifest is the raw material for our experience of time passage. On the other hand, unmanifested dispositions seem to have a different mode of existence (as “possibilia”) compared to the actual reality of manifested events. So, the view seems committed to an ontology that includes these two ways of being.

References

Aames, J. (2022). Temporal becoming in a relativistic universe: causal diamonds and Gödel’s philosophy of time. European Journal for Philosophy of Science. 12:44, DOI: 10.1007/s13194-022-00471-z.

Adlam, E. (2022). The Inaccessibility of the Past is Not Statistical. PhilSci-Archive. http://philsci-archive.pitt.edu/20539/

Arthur, R. (2019). The Reality of Time Flow: Local Becoming in Modern Physics. Switzerland: Springer Nature.

Balaguer, M. (2021). How to Make Presentism Consistent with Special Relativity. PhilSci-Archive. http://philsci-archive.pitt.edu/19820/

Dowker, F. (2008). Causal Sets and the Deep Structure of Spacetime. arXiv. https://arxiv.org/abs/gr-qc/0508109

Reichenbach, H. (1971). The Direction of Time. Berkeley: University of California Press.

Savitt, S. (2015). I ♥♦ s. Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics, 50, 19–24.

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¹ There is a pattern here which recurs across various topics. Scientific discoveries frequently reveal that our common-sense ideas (or “folk intuitions”) are flawed. Sometimes, scientists and philosophers will extrapolate the evidence further than warranted to assert that our experience is profoundly illusory. Other examples: it is said that the fact that subatomic experiments have particular outcomes is an illusion (many-worlds interpretation of quantum mechanics); and some philosophers of mind have claimed that the qualitative character of consciousness itself is an illusion (“illusionism”). A scientific worldview need not imply any of these things, and in fact such claims tend to undermine themselves: our subjective, qualitative, temporally organized experiences are the empirical foundation for the sciences.