Suppose that spacetime really exists. Name our world's spacetime "Spacey". Now, we have some very interesting question of which properties of Spacey are essential to it. Consider a possible but non-actual world whose spacetime is curved differently, say because some star (or just some cat) is in a different place. If that world were actual instead of ours, would Spacey still exist, but just be curved differently, or would a numerically different spacetime, say Smiley, exist in Spacey's place?
There are three different views one could have about some kind K of potential properties of a spacetime:
- All the properties in K that Spacey has are essential to Spacey.
- None of the properties in K are essential to Spacey.
- Some but not all the properties in K that Spacey has are essential to Spacey.
Suppose K is the geometric properties. It's plausible that at least the dimensionality is essential to Spacey: if Spacey is four-dimensional, it is essentially four-dimensional. Any world with a different number of dimensions doesn't have our friend Spacey as its spacetime. If so, we need only to decide between (1) and (3).
Here is an argument for (3). Spacey's properties can be divided into earlier and later ones, since one of the four (or more) dimensions of Spacey is time. Further, according to General Relativity, some of Spacey's later geometric properties are causally explained at least in part by Spacey's own earlier causal influences. But if (1) were true, then Spacey would not have existed had the later geometric properties been different from how they are, and a part of the explanation of why it is Spacey that exists lies in the exercise of Spacey's own causal influences. But nothing can even partly causally explain its own existence. (Interesting consequence: If Newtonian physics were right, we might think that view (1) was true with respect to geometric properties. But this is implausible given General Relativity.)
Similar arguments go for the wavefunction of the universe, if it's a fundamental entity.
I would think that there are modal truths like "I might have been in Bermuda right now." But if I might have been in Bermuda, then Spacey might have been (very slightly) curved differently. So, not all of Spacey's properties are essential to it.
ReplyDeleteOf course, you could insist that the location of every object with mass is an essential property of that object. You could also insist that, had I been in Bermuda, I would not be living in Spacey but in some other space-time, e.g. Curvey. But I don't know what would motivate those views.
I think that but for my explanatory argument and its relatives the Curvey hypothesis would be worth taking seriously. Suppose we think spacetimes are akin to their mathematical models. Well, the models have all their properties essentially.
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