Something is bothering me at the boundary of physics and metaphysics. It seems very likely that a successful theory of quantum gravity will entail that our actual universe is finite. This follows from two considerations. First, in the new theory, the singularities of general relativity will be banished, and the universe will be seen to be grained at the Planck scale. Second, it seems to me that the observable universe can be identified with the actual universe: in what sense should we consider a putative region of the universe beyond the reach of any possible causal contact to be actual? So, it follows that the actual universe is finite.
Now in reading metaphysical papers recently by Ross Cameron and Jonathan Schaffer, (see posts here and here), I was introduced to the argument for the conceivability of “gunk”. Gunk is stuff every part of which has proper parts -- that is, it is infinitely divisible. Now is a world made of gunk conceivable? It seems so. Now, since I have embraced the general stance that conceivability implies possibility, I would have to concede that if the actual world is finite, this is a contingent rather than necessary fact about the world.
For some reason, this just rubs me the wrong way. I don’t like thinking that something as fundamental as the conclusion that our world is finite in extent is just a contingent fact. But given that we are (famously) adept at conceiving infinities, and the strength of my opinion regarding the modal rationalist link between conceivability and possibility, I’m stuck.
The only strategy which I think might work is as follows. I could assert that the conceivability of infinity is grounded by the whole space of possible worlds, and its application to a single possible world is a mistake. The gunky world would itself have to comprise all possible worlds by virtue of its infinite extent. It would itself necessarily constitute the entire modal space, so it couldn’t also be one of the constituents of modal space. Individual possible worlds themselves would be necessarily finite in this scheme.
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11 comments:
If the observable universe is identical to the actual universe, then conservation of energy is violated each time a new star enters our light cone. (Unless you have a further provision whereby not all energy in the universe is "actual" but becomes actual upon entering our light cone. But that seems an odd stance.)
Thank you for the comment. I'll have to think about the implications of my "observable universe" statement. In terms of energy conservation, though, I'm not sure current cosmological models have much of a commitment to global energy conservation -- but I'm not well read on this. I will look into it. - Steve
Out of curiosity, you say, "the observable universe can be identified with the actual universe: in what sense should we consider a putative region of the universe beyond the reach of any possible causal contact to be actual?"
Are you rejecting the brane theories?
Interestingly there is a new paper (www.arxiv.org/abs/0704.3473) that argues for measurable implications of a multiverse where universes collide - perhaps with our own.
I just don't know enough of the relavant physics (yet) to follow all the details. And it's not as if there are a shortage of completely different multiverse theories. But certainly there are several that don't have each universe completely causally independent.
Regarding global energy conservation it's a tricky issue. The old, oft made, claim that Noether's theorem entails no global energy conservation isn't completely true. It ends up being that figuring out conservation and what it means is a very non-trivial undertaking. Add in cosmologies that have to include more than GR and things get even trickier.
Thank you for the link, Clark, and for your comments on energy conservation. I will check out that paper. In terms of branes and bubble universes – if they have measurable effects and help explain phenomena in our universe, I’ll have to get with the program. On my mind when I wrote the post were the eternal inflation models where we are conjectured to be part of a particular style of infinite universe without any expectation of measurable consequences.
Just to note, I'm not sure I buy brane theories myself. String theory is something I just don't have the math or theoretical physics background to understand sufficiently. I strongly feel from the physics I do know that you can't really understand until you've carefully done the math. Which means most folks pontificating on string theory really can't say much. However I tend to find the anthropic reasoning and it's explanation of too much troubling.
However there are so many multiverse theories that I don't think we can discount them. More to the point it isn't clear to me why we should assume this is the only universe unless there's a good reason to think that. The fact it's all we observe seems insufficient to justify the claim that it is all there is.
From a metaphysical point of view, I'd say that if you're going to put that much weight on conceivability, you need a stronger test. It's not enough to check whether you seem to be able to hold the idea in mind without running into problems, I think: I can do that with many things which are actually impossible or even absurd.
There are, moreover, at least vague reasons to think gook might be inconceivable. You might feel that if there's no bottom level, there remains an element of indeterminacy in reality (Is there a particle of x in this solution? We can only say there aren't any larger than s), and you might find that offends your metaphysical principles. I think it was something broadly along those lines that led people like Democritus to adopt the idea of the atom in the first place, long before there were any good empirical scientific reasons to do so.
Clark - let me try to clarify somthing. I don't want to discount all multiverse theories, but I question treating these proposed extensions of reality as part of the actual world absent contact. The out-of-contact parts would constitute possibily existing worlds or world regions, rather than actual. I'm engaging in potentially confusing terminology here, since I don't equate "actual" with "existing". I'm trying to use the terms in the same way as I use them in the metaphysics of modal realism. (It may be a mistake to try to bring together the multiverses of physics with the possible worlds of philosophers, but that's what I have in mind.)
Thanks for your comment, Peter. It is controversial whether we can conceive of actual infinities. In conceding the conceivability of gunk I was influenced by the ease with which we conceive of infinite sets in mathematics. But it may be a mistake to conflate this conceivability of an abstract entity with that of an actual one.
Hi Steve, here are a few comments. You say:
"Second, it seems to me that the observable universe can be identified with the actual universe: in what sense should we consider a putative region of the universe beyond the reach of any possible causal contact to be actual?"
Are you a realist or an instrumentalist with regard to physical entities? If you are a realist and accept that the spacetime metric, or whatever entity replaces it in a complete quantum gravity, is really "out there", then it would be extremely odd if it had a boundary beyond which it was not defined, just at the boundary of the causally connected region of some evolved primates on a tiny planet! A rather extreme form of anti-Copernicanism. Problems with energy conservation are among the least of the multiple problems this has, from a physics point of view.
If you are an instrumentalist/positivist, on the other hand, you can reject "reality" that we can't observe, but then you don't interpret the metric or any other physical entities as "real" when we can observe them either. They are just theoretical constructs to predict observations. Being a realist about physical entities but only within our causal region makes little sense to me.
A completely different problem with your general argument for finiteness of the universe, is that avoidance of singularites does not entail that. For example, in Loop Quantum Cosmology, if you evolve the equations of motion backwards in an expanding universe you can go "through" the Big Bang singularity, which is resolved with Planck scale discreteness, and find yourself in a collapsing previous universe, which could have existed since infinitely large previous times. And of course, it can be spatially infinite too, unless we accept your other arguement about unobservable regions which I have already rejected.
In a word: discreteness is not the same as finiteness. If the universe is discrete it is made of a countable number of elements instead of an uncountable one. But it can very well be a countable infinity (aleph-nought) instead of a finite number.
Thanks very much Alejandro. You may be right that it doesn’t make sense, but I must say first that I’m not happy with the realist/instrumentalist choice (this is true when I think about quantum foundations as well!). I want to say that we are part of a vast (but finite) concretely real causal network, but beyond this network there are events which exist but as possibilities or propensities, not actualities.
Now, this is all stemming from some intuitive discomfort I have with a concretely real infinite expanse. I understand that cosmological models can provide for an infinite extent even if reality is discrete, so that, if these models turn out to be true, there is no good reason not to acknowledge the full reality of this expanse. Perhaps I can get over my intuition problem.
I thought the Dennis Overbye essay in the last Science Times section was interesting: he muses on the contingency of our ability to even make the astronomical observations which form the basis of cosmological models.
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