Philosopher JB Manchak discusses. Curious whether other philosophers of science concur?
I never met Alan, sadly, but his work leading the charge in making philosophy of sex “a thing” in contemporary…
5 responses to “The universe is unknowable”
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These theorems about General Relativity have been known since the 80s. Of course, they are mathematically accurate, but to say that "we can't know the structure of the universe" on the basis of them puts such a high demand on "knowing" that the result is trivial, and does not require anything fancy to prove. The demand is that "to know" something about the universe, you must have some set of observations that, together with the theory you are using, admit of only one solution to the fundamental equations. Otherwise, one can say one "doesn't know" (even granting the correctness of the theory) what the structure of the universe is, because your observations are *logically consistent* with different models.
But that is just not what we ever mean by "know" in empirical science, so the result is just the sort of universal skepticism (like universal skepticism about induction) that science rightly ignores. Here's a much simpler example. Can you "know" that you were born and grew up, or even that you actually ever read the first part of this comment? Well, in a Cartesian skeptical mode you can say you can't know: all the *evidence* that you are relying on to draw that conclusion depends on at least trusting your (apparent) memories. But consider the hypothesis that the entire physical universe just came into existence three seconds ago, in whatever physical state it happened to have been in three seconds ago. On that hypothesis, you were not born, did not grow up, and never read the start of this post. But (obviously) the hypothesis is logically and physically consistent with all your present apparent memories being what they are (although they would be false) and also with whatever observations will be made in the future. So the skeptical hypothesis cannot be empirically refuted, at least not by you or even all of humanity to the future. Well, sure. All that shows is that what we consider to be empirical knowledge is not, and cannot be, only things logically entailed by the "observational evidence" we have (or even will have). If you insist on that high a bar for "knowledge", then we just don't have any, which is basically what Descartes gets at the end of Meditation 1 for the physical world. (And since the proof of God's existence in Mediation 3 fails, Descartes never gets back any knowledge of the physical world, despite his attempt to.) But that's garden variety radical skepticism, and you don't need anything like General Relativity to get to it.
On the other hand, anyone who seriously doubts, on the basis of the foregoing, that they were born and grew up is basically unhinged. One should adopt a moderate skepticism—in the form of acknowledging that any particular empirical claim could in principle be false—without descending into Pyrrhonian skepticism (see: Hume). That's the rational position.
These funny GR constructions were (I think) originally made by Clark Glymour and John Earman, or at least they first reported them to the philosophical community. As I said, his has been around for over 40 years. It's not anything new.
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Hi Tim. A couple of points: (1) Building on the work of Clark Glymour, the weaker version of the theorem was conjectured in 1977 by David Malament (with a proof sketch). It wasn’t proven until 2009. So I agree that the result is not new. But I disagree that this has been known since the 80s. (2) When the conjecture was proven, it was strengthened considerably: the result goes through even under any type of local induction. One is free to assume that the normal physical laws we determine in our spacetime vicinity are applicable at all other spacetime points. This isn’t just about logically consistency. So I would push back on the claim that “All that shows is that what we consider to be empirical knowledge is not, and cannot be, only things logically entailed by the "observational evidence" we have (or even will have).” In order to break the underdetermination, one necessarily has to start assuming that the universe has certain global properties. But what justifies such assumptions? Given the theorem, we know this justification cannot be due to any observational data we have collected — even after allowing for any local induction on such data.
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As the previous comment notes, this is a powerful result: one must supplement the theory of general relativity in the background with some global property that spoils the chain spacetime construction, for any local induction to break the underdetermination result. Assuming for the sake of argument that it is uninteresting to break the underdetermination in this way (breaking it "by hand"), one might also be interested in whether underdetermination can instead be broken by helping oneself to a more ambitious, *quasi-local* induction scheme. Specifically, might some global properties be forced on us by the structure of an inductive argument that counts over whole spacetime regions — the causal pasts of points — instead of over points themselves? The version of the Copernican principle that underwrites moving from local property p being observed to be true about all points in my past lightcone to p being true about all points in spacetime (the version that says we are free to assume the normal physical laws in the vicinity are applicable elsewhere) admits a close cousin: what is observed to be true about the observable part of the universe — the whole region that is my past lightcone — is true about all like parts of the universe — i.e., all past lightcones of points in the spacetime.
What I know about my causal past is more than just what is true, locally, about each of the points within that region (such as: they all satisfy p). This is the sense in which counting over past lightcones of points instead of counting over points themselves yields a more ambitious induction scheme. For instance, I know that my causal past is consistent with its being properly embedded in the standard model of cosmology, given general relativity (equally: consistent with its being properly embedded in a chain spacetime construction). This raises the question: is there some physically salient global property G such that the following holds.
> Suppose that for every point q in (M,g), G is true of the causal past of q. Then G is also true of (M,g).
As far as I know, this is an open question. It would be interesting, for instance, if the observable universe admitting a twist-free foliation into isotropic spatial slices (such that we know it is consistent with its being embedded in the standard model) could force us, by this quasi-local induction, into the conclusion that the larger spacetime admits such a foliation/is precisely the standard model (or is it possible that stitching together all of the foliations in all of the overlapping causal pasts eventually leads to a kink somewhere in the larger spacetime?). Likewise, can the observable universe being hole free (by some definition) force us into the conclusion that the larger spacetime is hole free ("because the hole can't show up in anyone's past lightcone")?
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Hi Mike. It’s a really nice idea to try to come up with something in between local induction (which is not enough to break the underdetermination) and global induction (where one unjustifiably breaks the underdetermation “by hand”). Your project has two steps: (1) Define “quasi-local” spacetime properties and figure out which spacetime properties are quasi-local. (2) Investigate to see if any of the identified quasi-local properties are enough to break the underdetermination result. Here are some thoughts on each:
(1) Following your idea, let’s say that a spacetime property Q is *quasi-local* if, for every spacetime (M,g), if each point q in M is such that its past light cone (i.e. the open region I^-(q)) has property P when taken as a spacetime in its own right, then the entire spacetime (M,g) has property Q. As one would expect, any local property (e.g. “being a vacuum solution” or “satisfying an energy condition”) counts as quasi-local. But some global properties also count as quasi-local. Chronology (i.e. no “time travel”) is one such property. One wonders about other causal properties, e.g. global hyperbolicity. Another global property that counts as quasi-local is the Heraclitus asymmetry property (i.e. no distinct points share the same local structure). You mentioned hole-freeness as a possible quasi-local property but I’m not seeing that one. The t<0 region of Minkowski spacetime will be such that every past light cone is hole free but the entire spacetime is not. I’m not sure about your isotropy question.
(2) We now seek a quasi local property Q such that the following is true: If any spacetime (M, g) with property Q is observationally indistinguishable from another spacetime (M’,g’) with property Q, then the two spacetimes are the same, i.e. isometric. This captures a (universal) sense of broken underdetermination under the assumption quasi-local property Q. It’s not hard to see that the two quasi-local properties identified above (chronology and Heraclitus) are not strong enough to break the underdetermination. What about other possibilities? Perhaps global hyperbolicity and isotropy will wind up being quasi-local properties. For the sake of argument, suppose they are. What is a bit mind blowing is that even these incredibly strong properties are not enough to break the underdetermination. Just consider the simple example discussed by Glymour and Malament that that kicked off this whole literature: two-dimensional de Sitter spacetime (with non-trivial observational horizons) and its universal covering space. Both such spacetimes are globally hyperbolic and isotropic and they are observationally indistinguishable. But fail to be isometric, i.e. the underdetermination is not broken. (See Gordon Belot’s new book for more on de Sitter spacetime in this context.) The example shows how frustrating it can be to try and break underdetermination *even if* one were to buy into the quasi-local induction game and *even if* one were able to show that various incredibly strong global properties like global hyperbolicity and isotropy also count as quasi-local.
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Thanks, JB. That is a really nice way of setting things up!
Just to add to your comment (1): it'll pay to be specific about what notion of spatial isotropy is desired. If the definition takes for granted that the four-dimensional spacetime admits a foliation of time-ordered spacelike hypersurfaces — each one then being isotropic — then I believe we have a quick example below shows that the property fails to be quasi-local. (Should spatial isotropy be defined that way? It's definitely not an intuitive definition from a pure geometry perspective, but maybe from a cosmology perspective it seems more reasonable that we'd be after a definition that gets us almost all the way to the standard model in a single property.)
Consider the four-dimensional spacetime constructed by identifying antipodes in de Sitter spacetime. This spacetime is not time orientable, so does not admit a foliation that is suitable. But it is observationally indistinguishable from de Sitter spacetime (its universal covering space) because of similar sorts of troubles with observational horizons that plague the two-dimensional case you mention. And the chronological past of each point in de Sitter spacetime admits a foliation of time-ordered spacelike hypersurfaces (e.g. constant values of t in the global coordinates in de Sitter spacetime).
It's a cheap example because the only work done by the time function is to cause trouble. Still, I think it's a helpful example to keep in mind as an illustration for one way intuitions about "stitching together" the causal pasts that each satisfy the property can go wrong in ensuring the property obtains in aggregate. (As for the question of whether global hyperbolicity is quasi-local: unfortunately, as the pasts of points in de Sitter spacetime are not themselves globally hyperbolic, this challenge construction doesn't apply.)
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