Research Imprints in Time: a Moderately Robust Past

Imprints in Time: a Moderately Robust Past

Editors note: Because of a major snowfall in Savannah, GA during the Eastern APA, the Blog of the APA has been hosting papers by people who missed the opportunity to present or who would like a larger audience for their work. This is the final post in the series.

By Michael Longenecker

There are two intuitions that we should hope that our theory of time can accommodate. These can be roughly stated as: (i) tensed truths must be grounded and (ii) there is genuine change. The challenge in accommodating these intuitions is that they seem to push in opposite directions: the grounding intuition pushes us to incorporate past objects with features robust enough to ground past tensed truths, yet the objective change intuition pushes us to keep past objects from having features that are too robust. I don’t think extant views of time balance these intuitions in a satisfying way.

My aim is to present a view that does a better job. My proposed view uses the resources of Einstein’s theory of General Relativity, which tells us, roughly, that the presence of mass and energy determines the curvature of spacetime. The view I develop on this basis essentially tells us this: the past consists of curved spacetime regions devoid of mass and energy. This allows us to say that what exists—such as dinosaurs—genuinely changes, nevertheless the truth of “dinosaurs existed” is grounded in the curvature of the past. The curvature of the past is the imprint mass and energy leaves on time.

1 First intuition: past-tensed truths are grounded

As Sider (2001, 36) notes, there are two ways of cashing out the intuition that past-tensed truths must be grounded. The first is the truth-maker principle that for every truth, there’s an entity whose existence suffices for its truth. The second is the supervenience claim that truth supervenes on the existence and properties of objects and the relations they stand in with one another. Many find one or the other of these grounding principles gripping (Bigelow (1996), Lewis (2001), Sider (2001), Mozersky (2011), Cameron (2015), McDaniel (2017)). Others, such as Trenton Merricks (2007) and Kierland and Monton (2007), deny them. But I will assume that something like them captures what we want from a theory of time. Though I prefer to be neutral between the two principles, for simplicity I will talk in terms of supervenience rather than truth-making.

The supervenience claim seems to rule out Presentism—the view that only present objects exist. (I will assume that there’s a timeless sense of “exist” on which Presentism neither turns out trivially true or trivially false). Presentism has no past objects around (in this timeless sense) for the truth of “there were dinosaurs” to supervene on. Nor does the truth supervene on any present objects. For consider a world, W, where the present is just like ours—complete with paleontologists and fossils (that are intrinsic duplicates of the fossils we have) in the ground—but where dinosaurs never existed. Perhaps we can imagine this as a world that came into existence only five minutes previously. If so, then the actual world (at present) and W (also at present) seem to have all the same objects with the same properties and relations between those objects, yet they differ in the truth of “there were dinosaurs”. There’s a strong sense that the truth of this claim can’t just ‘float free’ from the world in this way; it must supervene on the way the world is.

John Bigelow (1996, 46) has tried to preserve Presentism in the face of this charge by pointing out that objects can have properties like previously containing dinosaurs. Assuming Presentism, “there were dinosaurs” can be true in the actual world but not W since only the universe in the actual world has the property of previously containing dinosaurs. But there’s a general sense of dissatisfaction with this solution (shared by Sider (2001), Merricks (2007), Cameron (2015), McDaniel (2017) among others). For this response seems to be cheating. Even if objects do instantiate such past-directed properties, the properties themselves shouldn’t belong in the supervenience base. Since they ‘point beyond’ their instances, they should supervene on something further.

It might be helpful to spell out what makes past-directed properties a cheat a bit more precisely as:

Cheating Properties: If property p (i) is instantiated at t, (ii) entails that some (non-trivial) intrinsic property was instantiated before t and (iii) is in the supervenience base, then p is a cheat.

We should note that we ordinarily infer all sorts of truths about the past just by looking at the present. Given that Spot is a dog, I infer that there once were two other dogs that copulated and eventually gave birth to Spot. Given the conservation of mass and energy, I infer that the total amount of mass and energy that existed in the universe yesterday is the same as it is now. And it doesn’t seem like cheating to include the instantiation of being a dog, having a total amount of mass and energy m, in the supervenience base. But even though they make it reasonable to assume that there were dog parents of Spot, the amount of mass and energy was the same, there’s no guarantee that these were the case—that it, they don’t entail such things. The instantiation of such properties is compatible with the entire universe coming into existence at the moment before their instantiation.

I have explained why Presentism fails to respect the grounding intuition and the ban against cheaters. On the other hand, views that respect it generally include merely past objects with robust features in their ontology. Take, for example, The Block view on which now is a temporal location much like the spatial location here in two important resects. First, times earlier and later than now are as real as now just as spatial locations other than here are as real as here. Second, just as there is no spatial location that is the privileged or objective here location, so there is no temporal location that is the privileged or objective now location. Another view is The Growing Block, which is much like The Block view, except the spatiotemporal block ‘grows’ in the future direction—new times are constantly added to the side of the block pointing to the future—and the present is the time on the ‘cutting edge’. Both views can treat “there were dinosaurs” as supervenient on the existence of dinosaurs at some time earlier than the present (however “the present” is spelled out). So all the properties in the supervenience base are non-cheaty; and any past-directed properties supervene on them.

The Block and Growing Block theory do well with the grounding intuition. But how well they handle the genuine change intuition is what we turn to next.

2 Second intuition: there’s genuine change

Things change. We start out as fetuses and grow larger and stronger. The day changes to night and back to day. But how do we understand this change? On The Block view, this change is just like the sort of difference we see in spatial location: currently this part of the street is well lit, but that part of the street is dark. So we can say that America changes from bright to dark in the same sort of sense that the street (spatially) changes from light to dark. But many object that this sort of change isn’t genuine change. As A. N. Prior puts it, “I believe that what we see as a progress of events is a progress of events, a coming to pass of one thing after another, and not just a timeless tapestry with everything stuck there for good and all.” (1996, p. 47) Yet The Block view doesn’t give us this. Though it tells us that America has “changed” from being bright to now being dark, the bright part is still there and bright! This doesn’t seem to capture the sort of change we want. It is, however, controversial whether there is an intelligible sense of ‘genuine change’ over and above the sort of change The Block view has (see especially Skow (2015)). But I will assume that there is such an intelligible sense and it’s something we should want our theory of time to have.

In order to account for the change, it looks like we need to move to some form of A-Theory—where ‘A-theoretic’ views can be understood, roughly, as views on which there is a ‘privileged present’ (see Cameron (2015) for further explication). But not just any A-Theory will do. For example, we might try adopting the Classical Moving Spotlight view (“The Spotlight” for short) instead. This view is much like The Block, except it posits a primitive monadic property of ‘presentness’ that moves through the block—the ‘moving spotlight’—which is the objective present. But the addition of this property is too little of a difference from The Block view to really do justice to the genuine change intuition. As Sider puts the point:

the only reason for invoking [the monadic property of presentness] at all is to be able to say that there is genuine change in which moment is present. But notice that the spotlight theorist does not admit genuine change for anything else! For her there is no genuine change in whether I am sitting, or in whether there are dinosaurs, or in whether a war is occurring, since her account of these matters is identical to [The Block theorist’s]. All that genuinely changes is which moment has presentness. Is securing this smidgen of genuine change worth the postulation of primitive tense? (2011, 260).

The idea is that even though we can deny that there are dinosaurs that presently exist, there nevertheless still are (in the timeless sense) dinosaurs. So even though The Spotlight gets us some change, it doesn’t seem to get us the degree of change that we’re after.

In order to avoid dinosaurs being located in the block, we need a more drastic alteration of The Block view than The Spotlight gives us. I think the right way to accommodate the genuine change intuition is to start ‘deleting’ characteristics from past objects. Peter Forrest’s Growing Block view (2006) employs the deleting strategy to a small degree: on his view nothing in the past has consciousness. This allows us to say that there is genuine change in what things have pain and other experiences—only present things! But it doesn’t make for genuine change in the existence of dinosaurs, tables, etc.

I think the lesson is that we need to use the deleting strategy more aggressively to account for this. Of course the danger of applying it too aggressively is that past objects won’t be robust enough to ground past-tensed truths—thus falling prey to the first intuition. So my aim is to find a sweet spot that balances the two intuitions: thin out the features of past objects to the point that we don’t have dinosaurs and tables in the past, but keep them thick enough to ground past-tensed truths.

3 A moderately robust past

I think the way to balance the intuitions better is to have a past that only includes empty past regions of spacetime—all that exists in the past is the fabric of spacetime. By deleting all mass and energy from the past, we are able to preserve the idea that the dinosaurs have gone out of existence. But can we ground the truth of “dinosaurs existed” in a non-cheaty way? Aren’t empty regions too bare to do such a thing? But I think a promising way of getting the required grounding going is to treat such regions as having curvature.

According to general relativity, the Moon orbits the Earth because the spacetime around the Earth is curved; this prevents the Moon from moving in a straight line, instead moving in an orbit. And the Einstein Field Equations tell us, roughly, that there is a direct correlation between the curvature of spacetime on the one hand and the mass and energy contained within it on the other. Not only can we determine the curvature of spacetime from the characteristics and distribution of mass and energy, but the reverse holds true as well: we can determine the characteristics and distribution of the mass and energy by the curvature of spacetime. This is much like looking under a trampoline, observing its curvature and determining the properties of the objects on top. And since even the smallest particles have gravitational effects, even their characteristics can be determined by the curvature of spacetime. These curvatures would be far too miniscule for us to detect. But from a God’s-eye point-of-view, the curvature is enough to tell us all about the accompanying mass and energy.

My proposal, then, is that not only do these spacetime regions have a curvature when they are filled, but the curvature remains even when they are empty. Just as a snake leaves its imprints in the sand as it moves through it, so material objects leave curvature imprints in spacetime. The Einstein Field Equations, I suggest, tell us the relation between the curvature of spacetime and mass and energy only in the present—that is, all and only presently curved spatial regions are filled with mass and energy. No past curved spacetime is filled; such curvature is only the trace of the mass and energy that moved through it.

We might worry that this account is at odds with General Relativity. General Relativity is supposed to be true everywhere and always. Yet doesn’t the proposal deny this? Not quite. The proposal says that General Relativity doesn’t hold for, say, Jan. 1 2000; nevertheless General Relativity did hold for that time. It held for that time when it was present. So General Relativity still holds for every time when those times are present. And I think this captures what physicists have in mind when they claim that General Relativity is always true. After all, physicists are interested in positing theories that capture observable phenomena. And we can only observe times when they are present. I think it’s the metaphysician’s job to figure out if General Relativity holds for times when they aren’t present—the claim here is that it does not.

4 Objections

There are a few objections to the view that are also attacks on prominent A-Theoretic views. For example, these are objections that A-theories can’t ground the truth of <t was present> for some time t, Smart’s (1949) objection concerning the rate of time, McTaggart’s (1908) objection, and objections from relativity (see Putnam (1967) and Sider (2001)). I shall leave these objections aside since they aren’t specifically aimed at my view, and they have been much discussed elsewhere.

Let’s now turn to some objections directed more specifically at the view. The first is that the view makes General Relativity necessarily true; that is, for any world in which there’s mass and energy, the view requires that there be a curvature in spacetime. Yet, surely this is only a contingent truth. We can conceive of a world where there’s mass and energy but no spacetime curvature at all. But I agree with Kripke (1980) that there can be a posteriori necessary truths. Even though we had to discover that water is H2O, it’s nevertheless necessarily true that water is H2O. We can likewise say: even though we had to discover that the presence of mass and energy requires a curvature of space, that link is a necessary one.

There is a real worry, however, that General Relativity isn’t even actually true. The incompatibility of General Relativity with quantum mechanics requires substantial revision to our understanding to at least one of the two. And it could very well be General Relativity that loses out. So there’s a real risk that the view will go down as our physics advances. But if Karl Popper (1959) is right that falsifiability is a virtue of theories, then this should in fact be seen as a positive aspect of the view! Of course, we should reject the view if it’s falsified; but merely being falsifiable isn’t a mark against it.

Instead we might wonder how the view could deal with past-tensed singular propositions such as <Delilah the dinosaur existed>. There are numerous ways of addressing this issue that can be straightforwardly adopted (cf. Markosian (2003)). To name a couple: we might deny that there are singular propositions concerning objects that no longer exist; or, we might think that there are such propositions, but they now have “blanks” where they once had individuals. Apart from these suggestions, we could, however, ground such singular propositions by treating objects as identical to regions of spacetime. For example, there is some region R that The Eiffel Tower occupies. But on the current suggestion, The Eiffel Tower isn’t some object distinct from R; rather The Eiffel Tower just is R. And its properties, such as having mass m, are directly ‘pinned’ to the region rather than some distinct object that occupies it (see Schaffer’s (2009) for further explication). We could thus ground <Delilah the dinosaur existed> in the fact that Delilah is identical to some past region of spacetime.

One might instead object that the view doesn’t get us enough of the change we want since there wouldn’t be genuine change in whether spacetime regions exist. But I find a commitment to past regions of spacetime time a far less troubling than a commitment to past dinosaurs and tables. This is because the sort of spacetime posited by General Relativity is a highly theoretical one—one that isn’t posited as an item of commonsense, but because of its role in accounting for various physical phenomena. Even if spatial regions themselves aren’t so foreign to commonsense (we do ordinarily talk about space, even empty space), regions that warp and bend in the way General Relativity requires are very much foreign to commonsense. That is, though commonsense seems to tell us about dinosaurs (and that they don’t exist), it doesn’t seem to tell us that such regions no longer exist. In any case, it seems that we need something to exist in the past to respect the grounding intuition (complete with its ban against cheating).  And including empty spacetime regions seems to be the most conservative way of doing so.


Michael Longenecker is a graduate student at the University of Notre Dame. He recently completed his dissertation under the direction of Peter van Inwagen. His website is


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