Spacetime in Everettian QM

(some of this is adapted from a comment I posted at Theories ‘n Things)

How should we think about spacetime in Everettian quantum mechanics? If we adopt the Saunders-Wallace multiple-utterance proposal as a way of accounting for uncertainty (and hence probability) in EQM, we still have a choice. Either we treat spacetime the same way as we treat material objects (in which case spacetime doesn’t literally fission, and there is exactly one object in each spatio-temporal location even counting by identity) or we treat it as a common background to all the branches (in which case it literally fissions, and material objects are literally collocated on a grand scale). This choice is exactly the choice of whether spacetimes diverge or branch.

If we go the latter way, we need to count by world-indexed identity if we want to say that there is exactly one object in a particular spatio-temporal region. But we don’t need to count by world-indexed identity to say (for example) that there is only one cat on the mat, or only one table in this room: the cat, mat, table and room are all branch-bound objects. So then the semantics of ‘there is one table in this room’ and ‘there is one table in this spatio-temporal region’ would be structurally different. This seems good reason to consider the alternative route.

If we go the former way, what remains of the notion that reality is branching? The answer is simply that branches branch. But this can all get very confusing. I’ll try to clear this up a bit by reiterating how everything’s supposed to fit together. This is my current preferred take on things, which presupposes supersubstantivalism, for reasons I’ll discuss below.

1) At the fundamental level, there is just the universal state.
2) Decoherence picks out an approximate basis to decompose the universal state, approximately defining an emergent branching structure.
3) Pick out big-bang-to-heat-death histories from this emergent branching structure and call them branches.
4) Pick out parts of branches and call them branch segments. Branch segments are common to multiple branches.
5) Ordered pairs [branch segment,branch] are identified with spacetime regions. A special case of this is when the branch segment is the whole branch; the spacetime region [branch x, branch x] just is the spacetime of branch x.
6) Via supersubstantivalism, subregions of a spacetime are identified with objects and agents.

So on this account spacetime and ordinary objects do not branch, but the underlying emergent branching structure does. This is my preferred set-up at the moment; but I imagine many people will baulk at the supersubstantivalism. Why is it needed? Consider another way of setting it up which appeals to a more orthodox view of spacetime:

1-4) unchanged
5) Ordered pairs [branch segment,branch] are identified with spacetime regions. A special case of this is when the branch segment in question is the whole branch; the region [branch x, branch x] is the spacetime of branch x.
6) For some spacetime regions there is a material object occupying that region.

The problem I have with this is that material objects only come in at the final stage. What we have in stages 2-5) is a new kind of entity being extracted from an already-accepted layer of ontology. But in stage 6 a new kind of entity is introduced in a different way; material objects are just stipulated to occupy particular regions of spacetime. But the hypothesis made in 1) is that the quantum state is the only fundamental existent, so these material objects must be emergent from it somehow. But the non-supersubstantivalist story doesn’t give us any picture of how this works.

We could switch things around as follows:

1-4) unchanged
5) Ordered pairs [branch segment,branch] are identified with material objects. A special case of this is when the branch segment in question is the whole branch; the material object [branch x, branch x] is the mereological sum of all objects realized by branch x.
6) For every material object there is a spacetime region which that material object occupies.

But this looks even less good. Not only do spacetime regions now seem to float free from the underlying ontology just as material objects did in the previous version, this version doesn’t even seem to get us unoccupied spacetime regions.

Perhaps all this isn’t so much of an argument as a restatement of the intuition motivating supersubstantivalism. Accepting two different kinds of entity (objects and regions) related by a primitive ‘occupation’ relation doesn’t add any extra explanatory power to supersubstantivalism, rather it makes things more mysterious. We are faced either with the problem of explaining where material objects come from, given a spacetime, or the problem of explaining where spacetime comes from, given material objects. Just calling the relation between the two ‘occupation’ won’t cut any ice in a naturalistic picture.

Spacetime in Everettian QM

Easy possibility

Tim Williamson has made use of a notion of ‘easy possibility’ in his modal account of knowledge – some event is an easy possibility if it could easily have happened. Where did this notion come from? It seems plausible that ‘event x could easily have happened’ is an anthropomorphic generalization from ‘person p could easily have performed action a’. I’m going to briefly explore the consequences of this.

Easiness is at least a partially normative concept; as well as circumstances, competence plays a role in deciding whether a is easy for p. So consider an exceptionally competent archer – if a clear path to a target at 20 metres distance is available, he will always be able to easily hit it. An incompetent archer in exactly the same circumstances would not find it easy to hit the target. So easiness of an action is (obviously) agent-relative. But when we use the phrase ‘could easily have happened’, which agent is it relativized to?

It’s easy (apologies for the pun!) to see that it can’t be any contingent agent. We can apply the notion of easy possibility to particle-interactions well before any life existed: it could easily have been that more interactions occurred in the first nanosecond of the universe than actually did occur in the first nanosecond. An idealized human agent won’t do either. If an idealized human agent were around in the early universe, they would die before having the chance to tweak any particles. It looks like we’re going to have to wheel in God.

If God was the relevant agent, it would give a pretty satisfying reductive account of easy possibility. Something could easily have happened if it would not have required much effort for God to change things so that it happened. Maybe the idea is that God would only have had to alter the position of a particle one millionth of a micro-metre, and more interactions would have occurred in the first nanosecond than actually did occur.

Why not take this as a conceptual analysis of the notion of easy possibility? Event e could easily have occurred iff it would have been easy for God to change things so that e occurs. Obviously ‘easy’ is a vague term, but then so plausibly is the extension of easy possibility; no problems there. I think this looks like the bare bones of a good analysis. Indeed, I think it’s a worryingly good analysis for the friend of easy possibility; through the association with an idealized agent, it casts doubt on whether easy possibility has a place in naturalistic modal metaphysics.

Easy possibility

Grades of nomic necessitarianism

Some have claimed recently that the laws of nature are necessary truths. What does this claim amount to? It can’t just mean that they hold in any naturally possible world, if natural possibility is analysed a la Lewis in terms of a restricted space of metaphysically possible worlds – otherwise, it would be trivial. This is what I think Kit Fine is getting at in his paper ‘The Varieties of Necessity’ (Fine 2002). (See this post for my objection to the way that Fine uses this point.)

Another approach is called for. Plausibly, the necessity of laws of nature involves at least the claim that Bird in Nature’s Metaphysics calls ‘weak nomic necessitarianism’ (WNN) – the claim that fundamental natural properties have their nomological role essentially, and obey the same laws of nature in every world in which they exist.

Bird describes the thesis of strong nomic necessitarianism (SNN), which goes beyong WNN by adding the further proviso that all fundamental natural properties exist at all worlds (call this claim APAW). To a lot of people this looks too strong. Bird intends APAW to rule out an objection to the necessitarian position which alleges that, while it might be that gravity is necessarily (approximately) an inverse-square law and necessarily acts between masses, there is another possible force, fravitation, just like gravitation in every way except for being an inverse-cube law and acting between schmasses. An acceptance of the possibility of such alien properties (and of alien laws of nature which the alien properties necessarily obey) seems to vindicate the contingentist intuition. But then APAW starts to look like an ad-hoc move to preserve necessitarianism as an interesting and substantive position.

Compare the situation with the debate about alien fundamental natural properties in connection with modal realism. The argument that Lewis finds compelling for the existence of alien natural properties is that it seems parochial to assume that our world is maximal in terms of its inventory of fundamental natural properties. If (as appears intuitively possible) some worlds lack some of the properties found in the actual world, why might the actual world not lack some of the properties found in other worlds? This line of objection tells against the principle APAW which makes SNN stronger than WNN. A more direct line of objection against APAW is the possibility of subtraction itself – it is judged intuitively possible that there could have been no mass, but APAW entails that mass exists at all worlds.

One response to these worries would be to distinguish between existence of a property at a world and instantiation of a property at a world. We could say that mass exists at some worlds but is not instantiated there, and that there are might or might not be unknown properties which exist at the actual world but are uninstantiated here. The problem with this response is that it once again seems to give up on the core of the necessitarian view. Nothing in the picture rules out schmass and fravitation as existent but uninstantiated, and the contingentist can reasonably point to this as vindication of their view. Given that the distinction between instantiation and existence doesn’t help us find a stable form of nomic necessitarianism, I will henceforth assume that they are co-extensive to simplify the rest of the presentation.

Given the problems with APAW mentioned above, it is not surprising that SNN is treated with suspicion by most metaphysicians. But I think that there are ways to uphold necessitarian principles in a non-trivial form without being forced to assert the speculative-looking claim APAW that all natural properties exist in all worlds. One claim we could use to bolster WNN would be the claim that there are a finite number of possible fundamental natural properties. Call this claim FP. While FP is still compatible with our world being maximal in terms of fundamental natural properties, it does not entail this conclusion, avoiding the parochialism objection which afflicts APAW. Indeed, it is compatible with FP that no world be maximal in the sense of containing all natural properties. Maybe two fundamental natural properties exclude one another, for example.

Call the conjunction of WNN and FP Finite Nomic Necessitarianism, or FNN. FNN entails that the actual laws of nature are necessary in that they necessarily apply to the natural kinds which actually exist but it allows for a further sense in which they are necessary – that no world contains any law which is closely similar but still distinct from a given actual law. The actual law may be the only possible law of its type, relating properties of particular types.

This characterization of FNN is obviously very general – but I think it shows there is conceptual room for a brand of nomic necessitarianism in between Bird’s WNN and his SNN. Indeed, there could be many different strengths of this in-between necessitarianism, depending on the details of structural similarities within the set of possible laws. From this perspective, SNN and WNN are different ends of a spectrum, rather than exhaustive exclusive alternatives.

Grades of nomic necessitarianism

McKitrick on manifestations

Another talk at the powers conference which grabbed my interest was by Jennifer McKitrick, on the metaphysical status of disposition-manifestations. The central debate is about which of two kinds of thing we should take the manifestation of a disposition to consist in. Are manifestations particular events, the ‘net results’ of the activation of dispositions, or are they instead partial contributions to the ‘net result’? McKitrick was defending the line that manifestations should be thought of as events; Mumford is the main author to have taken the opposing view.

A couple of examples are useful here. Consider the case of a boat pulled along a canal by two horses. Each horse exerts a force at an angle to the canal, but the direction in which the boat accelerates is along the canal. Each horse has the disposition to accelerate the boat, but what are the manifestations of these dispositions? Is the boat’s actual acceleration along the canal the manifestation of each disposition, or is each disposition manifested separately in some contribution to the boats actual acceleration? McKitrick was arguing for the former conclusion, which involves making the relation between particular disposition and particular manifestation many-one, rather than the one-one relation envisaged by Mumford.

One strand of McKitrick’s argument was epistemological. We cannot in general directly observe the individual contributions made by particular dispositions to the net result of a transition, but we want to say that we individuate dispositions by their manifestations. This leads to a tension; unless manifestations are events, either dispositions are individuated by something other than their manifestations, or we have problems individuating dispositions.

Another line of argument was metaphysical. Mumford gives us no clear general account of what the manifestation of a disposition consists in. In the case of the two horses towing a boat, it looks like he would say that the manifestations of the two individual dispositions to accelerate the boat are two individual ‘virtual’ acceleration vectors, which sum to the actual acceleration vector.

In discussion, Kit Fine emphasized some interesting properties of these virtual effects: only in combination with other virtual effects do they condense into a real, observable event. He was very inclined to recognise these virtual vectors as genuine (albeit peculiar) entities, admitted into our ontology for their explanatory power. If we’re prepared to be as ontologically generous as Fine, I think McKitrick’s arguments can be resisted. The manifestations of dispositions on this view are sui generis virtual effects; their postulation is justified in the same way as the postulation of unobservable theoretical entities like quarks.

A variant on this view would be to say that in certain scenarios, virtual effects can be directly observed. We certainly feel the push of the wind when we walk in a gale, even though we can resist this push and not fall over. It could be said that what we are feeling is a virtual effect, and hence that such effects can after all be observed; the line of thought is similar to the idea that we can observe singular causation directly. I think some delicate issues in philosophy of mind and action are likely to be raised here, so I’d like to try and skirt this debate by focussing on fundamental natural properties. I don’t think anyone is likely to say that we can observe directly the gravitational forces exerted on one proton by a distant pair of protons; but this kind of interaction is a paradigm of combination of virtual effects. If we have to accept virtual effects into our ontology at all, we will have to accept fundamental unobservable virtual effects as well as the more homely and potentially observable macroscopic virtual effects that feature in the common examples.

So it looks like the friend of virtual effects can postulate an inferential route to knowledge of them, perhaps combined with non-inferential knowledge of a macroscopic subset, defusing McKitrick’s epistemological objection. But a metaphysical strand of objection remains; perhaps these virtual effects are simply too strange to be admitted into our ontology. McKitrick pressed this line by challenging the audience to produce a clear account of what the virtual effects amount to, for example in the case of the boat pulled by the horses.

I thought I’d have a go at explaining virtual effects a little. A helpful example is the case of a train which is moving through a station. At the same time, I’m walking along the train with an equal and opposite velocity, so that I remain stationary relative to the platform.

McKitrick’s way of explaining this is that I have a disposition to change position* relative to the platform when I walk, but also a disposition to change position relative to the platform (in the opposite direction) when the train moves. These two dispositions cancel out, such that each of them is manifested in the same result; me remaining stationary.

On the virtual effect picture, there is a clear sense that can be given to the virtual effects. One virtual effect is my change of position relative to the train; the other virtual effect is the train’s change of position relative to the platform. The dispositions that both the train and I have are manifested directly in these virtual effects. In special relativity, change of position relative to an inertial reference frame is a genuine physical quantity, so in this case at least physical meaning can be assigned to virtual effects. The case obviously generalizes straightforwardly from macroscopic trains to microscopic particles.

However, to give an account of virtual effects applicable to the boat case, we have to complicate matters a bit. If we replace motion in the train case with acceleration, so that the train starts to pull out of the station just as I start to walk along it, then the virtual effects end up being accelerations relative to an accelerating frame. Arguably, in special relativity accelerations relative to accelerating frames are not genuine physical quantities, since accelerating frames are non-inertial.

Here however we can appeal to general relativity; an acceleration relative to an arbitrary frame of reference is a genuine physical quantity in general relativity. Here’s how I would then suggest explaining the boat case. In a frame of reference accelerating in the direction of one of the net forces applied by one of the horses, the boat really is accelerating in the direction of the force applied by the other horse. When we move to the correct non-inertial frame, we can see what was a virtual effect in another reference frame. Virtual effects in one reference frame are genuine physical effects in other frames.

McKitrick’s defence of manifestations as effects amounts to a pair of arguments against the virtual effect picture, and it looks like these arguments are inconclusive. We can get epistemological access to virtual effects through standard scientific inferential procedures, and we can identify them with genuine physical quantities by making use of varying frames of reference. The upshot is that both accounts of manifestations are still on the table. One traditionalist at the conference was overheard to remark that it looked like this was a thoroughly boring debate about terminology – that we have a stable conception of manifestations as effects, and another stable conception of manifestations as virtual effects, and that we use sometimes one conception and sometimes the other. I’m not sure whether this is right, but it’s food for thought.

* In combination, Jennifer said she didn’t like thinking of motion as a disposition to change position. But this is just the introductory case; skip to the acceleration case if you like.

McKitrick on manifestations

Does dispositional essentialism need natural necessity?

I’ve been lucky enough to have a world-class conference on my doorstep over the last three days – Anna Marmodoro organized everything really well, and it was great to hear Alexander Bird, Kit Fine, EJ Lowe, Stephen Mumford, Ernest Sosa and others in full flow. Over the next week or so I’ll be discussing a few of the suggestions raised there in this blog. Let’s begin with natural necessity.

On Tuesday afternoon, Markus Schrenk and Stephen Mumford gave two parts of a very interesting ‘Nottingham paper’ on the relation between power and necessary connection. The written version of Markus’ paper is here. Very briefly, they argued that necessary connections between (token local) events should be carefully distinguished from powers, and that we should believe in the latter but not the former.

The master argument is based on the idea that any causal chain can be interfered with, so no episode of singular causation or disposition-manifestation occurs with natural necessity. The way the conclusion was stated was that they were denying natural necessity, although rescuing powers, causation, natural possibility, forces, tendencies, and so on.

What does their denial of natural necessity amount to? Their target notion of necessary connection is a relation between events – so it looks like all it takes for there to be no naturally necessary connections in the world is that for each actual transition from cause to effect or from disposition to manifestation, that transition could have (naturally) possibly not occurred. A token cause, considered by itself, does not necessitate any particular effect, since the intrinsic specification of the cause does not exclude the possibility of interfering environmental factors. This claim seems plausible – so maybe there is indeed no natural necessity to the relation between local token events. This, I think, is interpreted as a partial vindication of the Humean denial of necessary connections.

A different candidate sort of natural necessity is the conservation of charge. In conversation afterwards, Mumford suggested that he wanted to take this form of necessity as a Kripkean metaphysical necessity. The idea would be that electromagnetic interactions form a natural kind, and that it is part of the constitution of this kind that all such interactions conserve charge. So although there is metaphysical necessity in the picture, we still haven’t found any non-trivial natural necessity (unless, of course, we follow Bird and Edgington in identifying natural necessity and metaphysical necessity).

However, natural necessity does re-enter the picture when we look beyond particular pairs of localised events, at the bigger picture. Consider ‘maximally conditional’ natural necessity – specify a past light cone, and the effect follows with necessity if the underlying physics is deterministic. If the underlying physics is indeterministic, instead we get probabilities for effects following with necessity. Either way, there is at least one non-trivial form of natural necessity. This point was raised a few times in discussion, by Jennifer McKitrick and then by John Heil and Galen Strawson. Mumford’s reply, which seemed to appeal to Anscombe’s heterodox view of determinism, wasn’t enough to leave me satisfied.

So although Schrenk’s and Mumford’s rejection of necessary connections between token local events is plausible, and their distinction between necessary connections and powers is attractive, I think the dispositional essentialist should resist their headline claim that natural necessity is non-existent.

Does dispositional essentialism need natural necessity?