«Once Upon a Spacetime by Bradford Skow A dissertation submitted in partial fulﬁllment of the requirements for the degree of Doctor of Philosophy ...»
We might give up mereological essentialism for regions of space, and say that one and the same region can include diﬀerent points at diﬀerent times. Then even if the distance between any two points of space is the same at all times, the distances between regions can change. Or we might accept mereological essentialism, deny that particles really move, and try to explain away appearances to the contrary. Diﬀerent regions are particle-like (by instantiating mass properties and so on) at diﬀerent times; since the pattern of mass-instantiation changes continuously, it looks like one persisting thing is moving around, but this is an illusion.20 Luckily, we can avoid having to say either of these things by denying that space and time are separately exiting things. Believe instead in a four-dimensional spacetime that uniﬁes them. In this context dualists explain what it is for a particle to move by citing features of its worldline. So, for example, a particle accelerates just in case its wordline is not straight. Supersubstantivalists who identify a particle with its worldline can say the same thing.
So much for particles. What about ﬁelds? The case for identifying the parts of physical ﬁelds (like the electromagnetic ﬁeld) with regions of spacetime is even better than the case for identifying particles with regions of spacetime. In this case we don’t have to worry about motion: whether and how the electromagnetic ﬁeld moves is of no importance to the theory of electromagnetism.
Of course this was not always so. According to classical electromagnetism, light is a wave in the electromagnetic ﬁeld. And many in the 19th century assumed that if there is a wave then something must be waving: something must be changing its shape, as the water in the pond changes shape when a rock falls in it. So there had to be some physical stuﬀ that carried electromagnetic waves: the ether.
I think that even this theory can be given a supersubstantivalist interpretation:
identify each part of the ether with its worldline in four-dimensional spacetime, and This is analogous to what mereological essentialists who aren’t supersubstantivalists say: strictly speaking, there are no persisting tables, but it looks like there are because diﬀerent things are momentarily table-like in the same place at diﬀerent times.
explain its motion in the same way the motions of particles are explained. But the ether interpretation of electromagnetism has been discredited. We no longer think that there can be a wave only if something physical is changing shape, and so we no longer need a moving ether.
8 The Modal Argument Against Supersubstantivalism As I said in the last section, supersubstantivalism is best combined with a belief in four-dimensional spacetime, rather than in space and time separately. This version of supersubstantivalism entails the doctrine of temporal parts: every persisting thing is composed of instantaneous temporal parts. Arguments against the doctrine of temporal parts, then, are also arguments against supersubstantivalism. But I have nothing to add here to the debates over the doctrine of temporal parts.
The most serious remaining argument against supersubstantivalism is the
(1) I could have been three feet to the left of where I actually am right now.
(2) No region of spacetime could have been three feet to the left of where it actually is right now.
(3) So I am not a region of spacetime.
This argument should look familiar: it is structurally similar to the problem of motion for supersubstantivalists that I discussed above. There the problem is accounting for the apparent fact that one and the same material object can be in diﬀerent places at diﬀerent times; here the problem is accounting for the apparent fact that one and the same material object can be in diﬀerent places in diﬀerent possible worlds. For this reason, parts of my reply to the modal argument will resemble parts of my discussion of the problem of motion.
Supersubstantivalists could deny the ﬁrst premise and try to explain away our tendency to accept it. They could say: a region three feet to the left of me could have been intrinsically just like I am right now. Maybe we are confusing this possibility with the possibility according to which I am three feet to the left.
This move doesn’t look very plausible. What, then, about denying the second premise? Before looking at how to deny it, we need to clarify its meaning. What does talk of where a region of spacetime actually is mean? Supersubstantivalists should insist it means something relational: for it to be possible that a region of spacetime be three feet from where it actually is at some time, there must be a possible world in which its distances from other regions at that time are diﬀerent from what they actually are. So if region A is actually one foot to the left of region B at that time, then in the other possible world A must be four feet to the left of B, and so on.
Is this really possible? There are two ways in which this possibility might be realized. First, the points in A might be diﬀerent distances from the points in B in the two possible worlds. Second, while all points of spacetime stand in the same geometrical relations to each other in both possible worlds, the points that compose A and B diﬀer in the two worlds. So to deny (2) supersubstantivalists must give up one of two doctrines. They must either reject (some version of) geometrical essentialism, the doctrine that points of spacetime have their geometrical properties essentially; or reject compositional essentialism for spacetime regions, the doctrine that regions of spacetime cannot contain diﬀerent points in diﬀerent possible worlds.21 I am happy to give up geometrical essentialism, for reasons I discussed in 2: it does not sit well with general relativity. To supersubstantivalists who do accept both of the above doctrines I oﬀer the following reply to the argument. They should say that our modal talk is context dependent. In some context the essentialist doctrines are true; in some context they are false. In the ﬁrst kind of context, then, (1) is false and (2) is true. In the second kind, (1) is true and (2) is false. In no context are both premises true: when we are led to think both are true, it is because the context is shifting back and forth.
One way to explain this context dependence is to give a counterpart-theoretic analysis of these de re modal claims. In some contexts (contexts in which we are This is the doctrine that deserves the name ‘mereological essentialism for spacetime regions;’ but this name is already widely used for the claim that regions cannot contain diﬀerent points at diﬀerent times.
thinking about regions of spacetime as regions of spacetime) we use a counterpart relation that values geometrical similarity and makes these essentialist claims true. In other contexts (contexts in which we are thinking about regions of spacetime as material objects) we use a counterpart relation that values other kinds of similarity—like similarity with regard to mass and charge distribution—over geometrical similarity, and makes the essentialist claims false.22 By ‘values geometrical similarity’ I mean more than that counterparts are geometrical duplicates; I mean also that counterparts of two regions stand in the same geometrical relations as the regions do.
Chapter 4 What Makes Time Diﬀerent From Space?
1 Introduction No one denies that time and space are diﬀerent; and it is easy to catalog diﬀerences between them. I can point my ﬁnger toward the west, but I can’t point my ﬁnger toward the future. If I choose, I can now move to the left, but I cannot now choose to move toward the past. And (as D. C. Williams points out) for many of us, our attitudes toward time diﬀer from our attitudes toward space. We want to maximize our temporal extent and minimize our spatial extent: we want to live as long as possible but we want to be thin.1 But these diﬀerences are not very deep, and don’t get at the essence of the diﬀerence between time and space. That’s what I want to understand: I want to know what makes time diﬀerent from space. I want to know which diﬀerence is the fundamental diﬀerence between them.
I will argue for the claim that (roughly) time is that dimension that plays a certain role in the geometry of spacetime and the laws of nature. (In this paper, then, I focus on what is distinctive about time, and say little about what is distinctive about space.) But before giving the argument I want to put my question in slightly diﬀerent terms. Instead of asking, ‘what makes time diﬀerent from space?,’ (Williams 1951, page 468). Williams actually says that we care how long we live but do not care how fat we are.
I want to ask, ‘what makes temporal directions in spacetime temporal, rather than spatial?’2 After rejecting some bad answers to this question I’ll present my view.
2 Spacetime Diagrams and Directions in Spacetime It is often helpful, when approaching problems in physics and in metaphysics, to draw a spacetime diagram. Spacetime diagrams represent the careers in space and time of some material objects. Traditionally in a two-dimensional spacetime diagram (the easiest kind to draw on paper) the horizontal axis represents space and the
vertical axis represents time. So suppose I’m conﬁned to one dimension in space:
I can only move to the left or to the right. Then the diagram in ﬁgure 2 might represent part of my career. The zig-zag line represents me; it’s my worldline. (I’m incorrectly represented as point-sized, but that’s not important.) According to the diagram I stand still for a while; then I walk to the left, stop, stand still for a little while longer, and then walk back to the right.
I said I wanted to ask what makes temporal directions in spacetime temporal, rather than spatial. So what is a direction in spacetime? We can use spacetime diagrams to get a sense for what directions in spacetime are. To represent a direction in spacetime (at some spacetime point) on the diagram we can draw an arrow, or vector, on the diagram at the point that represents that point of spacetime. So in ﬁgure 2 the arrow labeled ‘A’ points in the leftward direction in space and the arrow labeled ‘B’ points in the future direction in time. There are in this diagram, then, at least two temporal directions: toward the future and toward the past; and two spatial directions: toward the left and toward the right.
Two arrows may point in the same direction while being of diﬀerent lengths.
A direction then is an equivalence class of vectors—the set of all vectors that point It is important to distinguish this question from another commonly discussed question. Many philosophers want to know what makes the future diﬀerent from the past. But that is not what I am asking. Toward the future and toward the past are both temporal directions, and I am not asking what makes one temporal direction the direction toward the future and the other, the direction toward the past. Instead I’m asking, what makes either of them a temporal, rather than spatial, direction in the ﬁrst place?
in the same direction and diﬀer only in their length. Following standard usage, I will sometimes call a vector that points in a temporal direction a ‘timelike vector,’ and a vector that points in a spatial direction a ‘spacelike vector.’ What about the arrows labeled ‘C’ and ‘D’? They don’t seem to point in either a temporal or a spatial direction. What to say about arrows like C and D really depends on what geometrical structure the spacetime represented by the diagram has. In (two-dimensional) neo-Newtonian spacetime every arrow that does not point either to the left or the right points in a temporal direction, while in Minkowski spacetime (the spacetime of the special theory of relativity) arrows that are less
than 45◦ from the vertical (like C) point in a temporal direction, while arrows that are more than 45◦ (like D) from the vertical point in a spacelike direction.
Why frame the discussion in terms of spatial and temporal directions, rather than space and time? Modern physical theories are formulated in terms of a fourdimensional spacetime, instead of in terms of three-dimensional space and onedimensional time separately. In some older theories (Newtonian mechanics, in particular) there is a way to identify certain regions of spacetime as points of space and other regions as instants of time. But in more recently theories, especially the Figure 4.3: Newtonian Spacetime
instant of time point of space
general theory of relativity, this cannot always be done.
We can identify points of space and instants of time with certain regions of Newtonian spacetime because Newtonian spacetime has certain special geometrical features (see ﬁgure 4.3). There is a unique and geometrically preferred way to divide up this four-dimensional spacetime manifold into a sequence of threedimensional Euclidean submanifolds. Each of these Euclidean submanifolds is well-suited to play the role we want instants of time to play: events that occur on the same submanifold occur simultaneously. So these submanifolds are instants of time. A point of space, then, is a line in spacetime perpendicular to each time.
(Events located on the same line, whether simultaneous or not, occur in the same place.) Facts about which regions are points of space, and which are instants of time, are absolute: not relative to any observer or frame of reference.
In Newtonian spacetime the distinction between time and space and between temporal and spatial directions coincide. A vector that points in a spatial direction is one that points along (is tangent to) a time, and so points toward other points of space. A vector that points in a temporal direction is one that points at an angle to a time, and so points in the direction of future or past times.