Quantum physics and relative truth

There has been some discussion recently about whether propositions are true or false absolutely, or only relative to a possible world, or relative to a world and a time. What hasn't been considered, to my knowledge, is whether propositions are true or false only relative to a branch of the wave function of the universe.

For example, suppose we shoot a photon at a half-silvered mirror. It then enters into a superposition of passing through and getting reflected: these are the two "branches" of the superposition. More precisely, it is not the photon that enters into the superposition, but the entire setup, and there are actually many more branches, corresponding to various precise paths the photon can take. Moreover, these branches are only the position branches of the superposition -- there are other branches of the same superposition, corresponding to resolutions of other properties.

Nevermind the details, it seems like ordinary propositions such as

(1) The photon got reflected

can only be evaluated for truth or falsehood relative to particular branches of the setup's state. On some branches, the photon got reflected, on others it didn't. Semantically, on some branches looks much like a modal operator, except that there may be no determinate "actual" branch relative to which non-modal sentences are evaluated. (That's why non-modal sentences are neither true nor false.)

One might say that (1) is simply false, because what's true is that the photon is in a superposition of passing through and being reflected, which is not at all the same as simply being reflected. OK, perhaps. But then it's still also true that on some branches the photon got reflected and on others it didn't get reflected -- so the allegedly false proposition (1) is still true relative to certain branches. So it looks like propositions are still true or false relative to branches.

Another problem with this suggestion is that arguably, superpositions don't only happen at the level of microphysics. If not, then a lot of ordinary proposition like

(2) Gottlob Frege is the author of the Begriffsschrift

are also true only relative to certain branches of the state of the universe. So on the suggestion that (1) is (absolutely) false, (2) would also have to count as false. But surely quantum physics doesn't tell us that Frege is not the author of the Begriffsschrift!

Comments

# on 29 November 2010, 15:43

Suppose we set aside quantum physics for a moment. Suppose, with the philosophical mainstream, that propositions have truth values only relative to possible worlds. What will we say about your (1)?

(1) The photon got reflected

We don't say that it's true or false simpliciter; (1) is true at some worlds, and false in others. Whether, in a given context, we're happy to say that (1) is true will depend on which world we're talking about. But when the context is provided, we're happy to say that (1) is, say, true -- what we mean when we say that is that it's true relative to, say, the actual world.

So suppose that quantum physics shows that propositions are only true relative to branches. Then we should say the same thing. Even after we've made it clear which world we're talking about, either implicitly or by affixing, say, an 'actually', we'll still want to say that (1) is true relative to some branches and false relative to others. If we've settled on a branch, then we can just say that (1) is true, by which we'll mean it's true in the relevant branch.

I don't see a case to be made for just saying that the unqualified (1) is false on grounds like these. We wouldn't be tempted to say that for the worlds case. It's not like it's false that p just because p is false in some possible worlds.

# on 30 November 2010, 07:33

Hey wolfgang, I am not sure if you had this in mind but the structure here is very much like the motivation for MacFarlane's relativistic semantics from the open future.

For him "There will be a sea battle tomorrow" uttered at t is not true or false absolutely -- but is true relative to an assessment point. The assessment point establishes a "branch". So, roughly speaking, future contingents only have a truth-value relative to a branch.

In both MacFarlane's relativistic semantics and the picture you sketch above there is no determinate branch on which an utterance takes place. This, I take it, is the reply to Ickikawa's suggestion: the context of utterance does not determine a branch but it does determine a world. So in the quantum case, like the future contingents case, there is no such thing as truth-at-a-context (unless we supervaluate or something).

# on 01 December 2010, 06:55

Jonathan: if you're suggesting that we should say that propositions are ultimately true or false only relative to a branch, but that we may sometimes omit mentioning the relevant branch if it's clear from context, then I agree -- that's the most straightforward way of dealing with the issue. But it seems to me that this would not please people like Cappelen and Hawthorne and Soames, who deny that propositions are only true relative to something. Nor would it please all those people (e.g. Jeff King) who claim that propositions are only true relative to worlds, and not e.g. times. Superpositions present a challenge to these views which I haven't seen discussed yet. You're right that it does not present a special challenge to views according to which propositions are anyway true only relative to a shopping list of indices.

Brian: yes, the fact that there's often no "utterance branch" is one of the interesting aspects here. It depends a bit on whether there is collapse. Suppose not. Then if we measure the photon's position, we become entangled in the superposition -- on one branch, we see that it got reflected, on another that it passed through. On the first branch, we say "it got reflected", on the second we don't. So then there is an utterance branch, and what we said is true on that branch. I guess this is how the Frege sentence would come out as true in every context we can encounter. However, this only works if our utterances are suitably entangled with the relevant properties. E.g. if we haven't yet measured the photon's position and utter "the photon got reflected", then the photon is in a superposition relative to the utterance branch, so the proposition seems neither true nor false relative to that branch.

# on 02 December 2010, 11:13

I think relativization-of-truth-to-branch strategies of this sort have indeed been considered in various places.

Many people read Everett's original work like this. He called his theory a 'relative state' interpretation and insisted that macroscopic objects only had states relative to a branch. Given some fairly uncontentious assumptions about truth, that gets you relative truth.

Simon Saunders was a bit more explicit about it. In some papers in the mid nineties (I think 'Naturalizing Metaphysics', in The Monist, is a good example - but see also the 'time, quantum mechanics and X' trilogy in Synthese) he pushed the line that Everett relativized 'value-definiteness' to branches. A doctoral student of Jeff Barrett's at UC Irvine called Christina Conroy has just written a PHD thesis defending this sort of line.

More recently 'branching-time semantics', Belnap-style, has been applied to the case of EQM. That's effectively a truth-relativization strategy as well. A few people have written on this, but it might be worth going straight to Belnap & Muller 2010 in the BJPS.

Having learned the trade in the shadow of Williamson and Hawthorne it's maybe not surprising that I don't have much time for truth-relativization strategies like this. In fact I've just written a paper arguing against it. I think I'll send you a copy. :)

# on 02 December 2010, 20:41

Alastair, thanks for the pointers! I wonder if my talk of "branches" was a bit misleading: by a "branch" of a superposition I simply mean a projection, e.g. a determinate photon position. Whether or not time branches, or whether the "many worlds" have a branching structure, is an entirely different matter.

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