Wednesday, March 21, 2007

Merriam's Quantum Relativity

Paul Merriam posted a paper called Quantum Relativity: Physical Laws Must be Invariant Over Quantum Systems in which he puts forth a conceptual strategy for understanding how a relational interpretation addresses the foundational issues of quantum mechanics. Please see this prior post for more background. What follows is a summary and attempted interpretation of what I found to be key aspects of the paper. The usual caveats are in place: my summaries may be not only incomplete (including omission of formalisms) but also misleading due to errors in interpretation. Please read the paper to judge.

The paper starts with a section which discusses why decoherence does not solve the foundational issues of QM. Since I believe this is generally acknowledged (see this recent blog post from Matt Leifer; an old blog post of mine is here), I’ll just focus on the most important part of this discussion. Recall that one of the perceived shortcomings of the relational interpretation of QM revolves around the question of how two or more interacting systems come to “choose” the same basis. Merriam says that decoherence has a “change of basis” problem of its own.

To see this, Merriam returns to the “Wigner’s friend” framework and replaces "Wigner" with the "environment" to create a decoherence version of the scenario. Relative to the environment E, the experimenter (called A) and the system he or she is measuring (S) are in superposition and evolve according the Schrödinger picture. Decoherence would lead to the selection of relatively stable “classical” appearances of the observable which is the basis of the measurement. But suppose A decides to measure a different observable of S (change of basis). Decoherence takes place over a period of time (decoherence time); this time depends on many factors, but the “change of basis” is a problem for the time between zero and the decoherence time. (Decoherence is not measurement).

Next Merriam discusses (repeating the arguments of his older paper) the issues highlighted by the Wigner’s friend setup, arguing again that the quantum state describes a system relative to another system. Quantum mechanics is an intransitive theory.

The next section is titled “Quantum Relativity”. So having acknowledged the perspectivist nature of QM, what’s the next step? When considering two quantum systems: “The essential point of this paper is that since both systems physically exist they are both valid coordinate frames from which the laws of physics must hold. Quantum mechanics is as valid in S as it is in A.” If A describes S in terms of a superposition across some measurement basis, then S will describe A as starting out in a corresponding superposition. When A observes (measures) S to be in some eigenstate, “S must also observe A to be in some corresponding eigenstate…”

The key point is brought out by the word “must” here and in the title of the paper. The conceptual hurdle we are jumping here is as follows: if QM is valid from the point of view of all “quantum systems” (including everything from electrons to physicists), then when they interact they necessarily select the consistent basis for interaction. The basis problem is solved by asserting that basis choices must match if QM is to be valid from all points of view.

Merriam believes this conceptual leap has consequences analogous to special relativity. The next passage (see p. 6) looks at the formalism of the Schrödinger equation from A’s and S’s perspective and wonders how they can be consistent if the mass is so different in the two cases. But he notes the values for length or distance between the two quantum observations do not have to have the same numeral values in both systems. If distance is scaled to the relationship of the masses, then it is possible to create a transformation from the superposition of S as described by A to that of A described by S. There can be a group of such transformations for any number of systems. Merriam derives a transformation constant in analogy to the role the speed of light c plays in relativistic transformation.

Merriam also speculates about that one could extend the idea to include gravity by taking the equivalence of gravitational force and acceleration to be relative to the local quantum reference system. He suggests the shape a quantum version of Einstein’s equation would take. I will skip for now further discussion of this idea and a section on how gauge invariance might be impacted, since I think the key concept is in place with the analogue to special relativity.

Key to special relativity is the postulate that physical laws valid from one reference frame should be form-invariant when translated to another frame. To review, we assume that QM gives a valid physical description from the point of view of a system, and each quantum system forms a physically valid coordinate frame. Note that systems only share a reference frame when they interact. We should be able to translate the state of a system S which is in superposition relative to system A to the state of A relative to S. Again, this only works if we stipulate that if an interaction takes place, the “basis choice” is necessarily consistent from both perspectives.

Friday, March 16, 2007

Exploring the Borderlands

Recent books on atheism and religion have been the focus of much debate recently, which I think is a good thing. It’s no surprise that the debate is dominated by traditional religious believers on the one hand, and those who hold to a traditional materialist strain of atheism on the other. Of course, there is a wide, if seemingly less populated, territory between these views. I think the truth lies in the border regions.

If one is a realist, as I am, about first-person experience and the existence of some degree of freedom, then materialism is inadequate. On the other hand, one’s worldview must be shaped by valid inferences from the success of science. Because of this, I find traditional supernatural entities and interventions highly implausible, and have in the past characterized my own worldview has an enriched or expanded version of naturalism.

My more recent ruminations on modal realism and abstract entities have led me to consider that my realist commitments may actually require a necessary ground of possibilities underlying and penetrating our contingent concrete world. While at the end of the day labels aren't important, it seems as if a commitment to the idea that reality extends beyond our world in this way may get me expelled from the naturalist club.

I’m very reluctant to name this necessary existent “God”, since that unavoidably summons up a cluster of attributes and associations which go far beyond my commitments. But there is no getting around the fact that I may be moving into the vicinity of theism.

Monday, March 12, 2007

Priority Monism

[UPDATE: 25 Sept.2009: Links fixed, but note the post refers to an earlier draft of the paper]

As a follow-up to the last post, I want to very briefly take note of Jonathan Schaffer’s noble attempt to argue that the fundamental (ontologically prior) level is the whole rather than the parts – “priority monism”.

The draft paper “Monism: the Priority of the Whole” includes a fairly lengthy discussion of a historical context in which the case for monism has mostly gone unappreciated (it is often caricatured and dismissed as the position that there exists exactly one thing). He takes some time explicating the idea that both the whole and the parts exist, one of these must be prior, and the choice of either the whole or the parts is an exclusive and exhaustive list of options. Then it is “game on” to see which prevails.

There are four sections to the argument over priority. Two of these I consider a tie: the argument over which comports best with common sense, and which option better explains the apparent heterogeneity of the world (he’s right to say that saying pluralism explains heterogeneity begs the question).

The next section asks what fits best with science. Here, I think Schaffer makes a mistake. He invokes the idea of entanglement from quantum mechanics and infers that the whole world is entangled, making reference to a wave function for the entire universe. In my opinion, this is wrong. The entire world would be entangled only from a perspective standing outside the universe. There is no wave function for the entire universe. The interactions (measurements) between the many quantum systems in the world constitute concrete reality, and the whole of the concrete world is the relational network of these many interactions.

The last section asks which view on priority best deals with the possibility of the world being made of “gunk”, which is stuff with no proper parts (or to put it another way, stuff which is infinitely divisible). Schaffer references a couple of scientific theories and speculations that physical entities might be infinitely divisible. Here I think the existence of the Planck scale is actually good evidence of a limit to divisibility, so again his attempt to invoke science doesn't succeed.

I think that if we’re speaking of our concrete world, then the parts are prior to the whole. The possibility is open, however, that there is a holistic non-concrete ground of possibilia which supports the parts, but this would be a different discussion.

Monday, March 05, 2007

Must there be a Ground-Floor Turtle?

I have a strong intuition that there is a fundamental level of reality which ultimately grounds the phenomena of the world. This intuition forms a basis for preferring certain philosophical arguments over others. For instance, take the cosmological argument. In one traditional formulation, the argument goes something like this: every effect has a cause, and if you follow the chain backwards in time, there must be a first cause. I’ve never felt this argument was very forceful – what’s wrong with an infinite chain of causes? Now, however, if you recast the argument as saying that the contingent facts of the world ultimately and necessarily depend on a fundamental fact or collection of facts, then suddenly I start nodding my head affirmatively. There can’t be an infinite chain of contingent facts depending on other contingent facts, can there? Ontological priority seems to need a starting point more urgently than temporal priority. In the famous expression invoked by Ross P Cameron in his recent paper on this topic (found via OPP): it can’t be turtles all the way down, right?

Our desire for explanations seems to drive the intuition. If an entity is shown to depend on something else, it is thought to be explained. We want this search for explanation to find an ending point in terms of ultimate constituents. In our world, we seem indisputably to encounter composite things which seem comprised of parts; this drives our search for reductionist explanations. I guess it is possible to think that perhaps the “ceiling” rather than the “floor” is fundamental; perhaps the whole of the universe is the fundamental thing and the parts ontologically depend on the whole. Now, this seems counterintuitive to me: if we start with a whole, why should there be any parts? In any case, the direction of dependence is probably less important for this discussion than the idea that there is some fundamental level.

In his paper, Cameron asks whether there is a good argument for the truth of this intuition that there cannot be an unending chain of ontological dependence. Can we, for instance, argue that if there were no fundamental level grounding other entities, then nothing would be real? Cameron concludes that this would essentially be restating the intuition, rather than providing an argument. He considers a couple of other strategies in the paper and finds no satisfactory argument. On the other hand, he doesn’t see any good arguments against the intuition either. In fact the search for a metaphysical argument for the intuition may be seen to parallel the search for a deeper and deeper ontological level: you have to start somewhere, don’t you? Why not with an intuition? He notes as an example that Leibniz never argues for the Principle of Sufficient Reason, it’s just his starting point. Now, one can’t thereby defeat a skeptic who doesn’t share the intuition, but at the end of the day I don't find that the skeptics and deflationists of the world provide very good metaphysical explanations themselves.

Cameron says we can justify the intuition against infinitely descending chains of dependence by appeal to theoretical utility. We can give better explanations for entities if we identify an ultimate ontological basis in a collection of independent entities. This may be reason enough. He notes that this won’t convince someone who thinks the search for metaphysical explanation is misguided to begin with. On the other hand he says: ”…if you believe in metaphysical explanation you should believe it bottoms out somewhere.” He ends the paper by noting that given the pragmatic way the use of the principle is being justified, we should be modest about holding forth about the necessity of its truth.

Also interesting in this context is David Chalmers' recent paper: Ontological Anti-Realism (see blog post with links). His support for anti-realism in the paper (most of which is devoted to a mapping out of the terrain of meta-ontological stances) holds out the possibility of an exception for realism about the fundamental level. Jonathan Schaffer, in his commentary on the paper argues that Chalmers’ framework actually requires realism about the fundamental level. If Schaffer’s arguments are right, it seems to help to bolster the case that if you want to pursue metaphysical explanations, you need to be a realist about the fundamental level.