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«Once Upon a Spacetime by Bradford Skow A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy ...»

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One might refuse to answer this question. But then I am not sure why I should take seriously the claim that there are possible worlds like those described in the examples. Or, one might answer this question by proposing an alternative theory of what makes time different from space. I’ll criticize a few such theories in the next section. Or, one might say: we can imagine the worlds described, and it is part of the content of our imagining that the directions called ‘spacelike’ are spacelike. And since imagination is a guide to possibility, that gives us reason to believe that these worlds are possible.

How does this act of imagination work? Maybe like this: we imagine watching the history of the world in question unfolding, as if we were watching a movie.

We can tell which directions are timelike and which spacelike when watching a movie (without needing any theory of the difference to help us); in the same way, we can tell which directions are timelike and which spacelike in these worlds.

But imagining watching the history of the world unfold as if watching a movie is only a legitimate way to learn which directions in that world are timelike if those are the experiences an observer who existed in the world would have. But if the worlds described in these examples contain conscious observers, then there must be many more laws than the ones mentioned. Once all these laws are also taken into account, I doubt it will be so clear that the laws govern the evolution of the For example, in (Carroll 1994).

world in a spacelike, not a timelike, direction.

Example 3: In this world, the laws are those of Newtonian mechanics and Newton’s law of universal gravitation. This law governs in a spacelike direction: if I know that there is a particle here of a certain mass now, I know something about the value the gravitational field now has at every other point.

This example is not convincing. First, it is not clear that on a correct interpretation, Newtonian gravitational theory say that there really is any such thing as the gravitational field. And even if it does, knowing that there is now a particle here of a certain mass doesn’t tell me the value of the field at any other point; to know that I’d have to know how many particles there were in total, and what their masses and positions are right now. If I know anything about what is going on elsewhere, it is only how the particle here contributes to the value of the gravitational field elsewhere; but since this is consistent with the field’s actual value being anything at all, and since we get no information of the kind we’re really looking for (namely, information about which other regions of space are occupied by material objects), these laws are not really governing the world in a spacelike direction.

Example 4: In this world, the laws of quantum mechanics govern the world. In an EPR-type experiment, there are two particles some distance apart, and if we measure the spin on one of them in some direction, we know with certainty the outcome of a measurement of the spin of the other particle in that same direction, even if the measurement events are spacelike-separated. So these laws govern the evolution of the world in a spacelike direction.

This example is not convincing, for two reasons. First, I want to complain that, as in examples 1 and 2, the determination by laws in a spacelike direction here is not the robust kind needed to refute my view. But there is a second, more important, problem. For laws to govern the evolution of the world in a spacelike direction, it must at least be the case that given information about what is going on in one place (say, right here), the laws give information about what is going on at other places that are spacelike separated from it. But if all we know is that (after being measured) some particle right here has spin-up in some direction, the laws don’t tell us anything about what is going on elsewhere. They only give us information if we also know that there is another particle somewhere else, and that the ‘system’ comprising the two particles is in an entangled state. But this information is not just information about what is going on right here.

9 Alternative Views Finally, I will review some alternative views about what makes time different from space, and say why I reject them. My goal is not to give these theories detailed formulations and refutations; I aim only to suggest why I think they go in the wrong direction from the start.

–  –  –

According to this view, a direction is timelike just in case it is a possible direction of causation. This theory was inspired, I think, by a certain way of thinking about Minkowski spacetime. There is a synthetic axiomatization of this spacetime’s geometry using just one two-place predicate that can be taken to mean ‘x and y are causally connectible.’ Perhaps this axiomatization is getting the metaphysics right: the spatiotemporal relations in Minkowski spacetime, and so facts about which events occur before which other events, are derived from a more fundamental relation of causal connectibility.17 I reject this theory for two reasons. The first, and less important reason, is that it precludes the possibility of instantaneous causation. It looks like Newtonian mechanics involves instantaneous causation—according to that theory the sun’s being a certain distance from the earth instantaneously causes the earth to experience a certain force—and I accept that Newtonian worlds are metaphysically possible.





But I place more importance on a second reason. I just don’t think that facts about causation are more fundamental than the difference between space and time. But they have to be, for this theory to be right.

See (Sklar 1974).

(My theory, of course, requires that the laws be more fundamental than the difference between space and time. One might wonder why I am comfortable with this and uncomfortable with the causal theory of time. I won’t give a detailed answer to this question; I will just point out that many contemporary philosophers share the feeling that causation is less fundamental than lawhood.18 )

9.2 Three-Dimensionalism

Three-Dimensionalism is the view that material objects persist through time without having temporal parts. Since it is commonly admitted that material objects are extended in space by having spatial parts, there is an asymmetry here between space and time. One might try to distinguish space from time using this asymmetry: time is that dimension in which material objects are extended without being made up of parts.

Three-Dimensionalism is controversial, so insofar as I am not a three-dimensionalist I am not tempted by this proposal. But I do not think three-dimensionalists should be either. One standard argument that material objects that persist through time must have temporal parts is the argument from temporary intrinsics: if something is spherical at a time, then it must have a temporal part that is spherical simpliciter, on pain of making sphericality a relation to times, and not an intrinsic property at all.19 Three-dimensionalists think they can resist this argument. But if they can, then they can also resist the parallel argument that material objects that are spatially extended must have spatial parts, the argument from local intrinsics: if something is red in one place and green in another, then it must have a spatial part that is red simpliciter, on pain of making redness a relation to places. (Maybe redness and greenness are not the best examples, but there are others.) So three-dimensionalists ought to admit the possibility of material objects that are spatially extended without David Lewis (1986a) is one example: he analyzes causation in terms of counterfactuals, and his truth-conditions for counterfactuals appeal to laws. But even philosophers who reject counterfactual analyses of causation, like Maudlin (2004), believe that laws are more fundamental than causation.

This argument is much discussed; it is presented, among other places, in (Lewis 1986b) and (Sider 2001).

having any spatial parts. But once that possibility is granted, there is no longer an asymmetry between the way material objects are (or can be) extended in space and the way they are (or can be) extended in time.

9.3 The Brute Fact View According to the brute fact view, there is no need to appeal to geometry or the laws to distinguish spacelike from timelike directions. Instead, there is no way to distinguish spacetime from timelike directions in other terms. There is no informative answer to the question, ‘what makes timelike directions timelike?’ One way to put this view is to say that there is a fundamental property, the property of being a timelike direction. But it might seem odd to believe that things like directions could have fundamental properties. If we confine our attention to Newtonian spacetime we can avoid this oddness by avoiding talk of directions.

Some regions of this spacetime are times, and others are not. The ones that are times have some fundamental intrinsic property that the others do not: the property of being a time. End of theory.

This theory is not plausible. Certainly the regions that have this special property must also play the appropriate role in the geometry. (Supposing we characterize Newtonian spacetime using two distance functions, the role is as follows: each region contains all and only the points that are zero distance from any point in that region, according to one of those distance functions.) But why is there this necessary connection between this special property and a certain geometrical role? The brute fact view gives no answer. My view does better: since it does not postulate the special property, it has no necessary connection to explain.

But maybe that is just a caricature of the brute fact view. Here is a closely related view one might have. Do not postulate a special non-geometrical fundamental property of being a time. Instead, pick out one of the geometrical relations that gives spacetime its structure, and make it special. Sticking to my focus on Newtonian spacetime, one way to put the view is as follows: this spacetime get its structure, let us suppose, from two distance functions. One of these is the temporal distance function, and the other is the spatial distance function.20 Times are regions containing all and only the points that are zero distance from any point in them, according to the temporal distance function. What makes one function the temporal distance function, rather than the spatial distance function? There is no answer. It is just a brute fact.

This view I take more seriously as a competitor to my own than the others I have considered. But I do think it is wrong. The reason appeals, again, to twodimensional Newtonian spacetime.

Take a world w with two-dimensional Newtonian spacetime, and ‘rotate’ all the matter in that world ‘90 degrees’21 to produce a new world w∗. I can describe this world in a bit more detail, but I don’t want to beg any questions by calling certain regions of spacetime in w∗ ‘times’ or ‘points of space.’ So I will have to pick out regions of spacetime in w∗ using features those regions have in w. The description ‘regions of spacetime that are points of space in w’ picks out a definite set of regions of spacetime in w∗, while leaving it open whether those regions are also points of space in w∗. In more detail, then, w∗ looks like this: events that are simultaneous in w occur (in w∗ ) in regions that (in w) lie on different times but are in the same place. The laws of w∗ are also obtained from the laws of w by ‘rotation’: the w∗ -laws treat regions that are points of space in w as the w-laws treat the regions that are instants of time in w. I think w∗ is qualitatively indiscernible from w. But the brute fact view cannot say this. According to the brute fact view, two-dimensional Newtonian spacetime is not symmetric in this way. So the brute fact view entails that either the ‘rotation’ operations cannot be performed (that is, there is no such ‘rotated’ world), or, if they can, they result in a world that is very very different, qualitatively, from w. So I reject this view.

Both versions of the brute fact view are similar to the view that what makes the future different from the past is that the future direction in time has some special There are analogous ways to formulate the view on other accounts of the fundamental spatiotemporal relations that characterize Newtonian spacetime.

Of course, this doesn’t really make sense in the geometry of Newtonian spacetime. What I really mean is: consider this world represented on a two-dimensional Euclidean plane, like a piece of paper; then rotate everything 90 degrees on this Euclidean plane; now consider the world this new diagram represents.

intrinsic property that the past direction in time lacks.22 I reject the brute fact view for the same reason many reject this view about the difference between the past and the future.23 In the later case, it seems that a world in which the distribution of matter were ‘mirror reversed’ around a given time (the laws, being time-reverse invariant (we may suppose), would be the same) would not be a world in which everything were ‘going backwards,’ but a world in which the direction that is actually the future direction is the past direction. Many who hold this view identify the future direction with the direction in which entropy increases;24 so it is not intrinsic to the future direction that it be the future direction. I accept this view about the difference between the future and the past. And my view about the difference between space and time is analogous.

(Maudlin 2002) seems to defend this view, as does (Earman 1974).

(Price 1996) is an example.

(Reichenbach 1956) is one example.

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