What Does the Wave Function Truly Represent?

[apeiron]

In MWI and the original version of GRW, it was claimed that anything beyond the wave function itself is kind of superfluous, unlike in Bohm's where you have both spaces (3-space and 3-N space). If one takes this view that the wave function is everything then, there's a problem:

Your core question seems to be about the reality of particles and wavefunctions, and hence about the reality of the two difference spaces they inhabit.

There would seem to be three general stances on the question of realism.

1) Something is real - it actually exists in the ontic sense.

2) Reality is an illusion - it is a picture we invent as a result of our instrumental models.

3) Reality is emergent - in this view, things don't "exist" in some brute a-causal fashion. Instead they are the emergent results of some causal process, so at best can be said to be "real persistent features".

Our instrumental models are mostly reductionist, so describe the emergent in terms of the actual. In terms of their limit states.
The upshot of this is that our models are "illusory", but only very slightly when a system is in a high state of development. A process is close enough to being crisply real when it is asymptotically close to its limits.

I of course have been defending (3), the process philosophy and systems science view.

When it comes to particles, I say they are real in the sense of solitons. They are knots locked into spacetime by a fabric of constraint. Which in turn throws the burden of realism onto spacetime itself. The 3D vacuum, or what Wilczek calls condensates, is what has to be explained first. The N particles are further definite degrees of freedom it is true - but ones that "exist" at a logically higher level of the hierarchy of "existence". They are not part of the fundamental degrees of freedom that define naked spacetime condensates.

When it comes to wavefunctions, these now are just instrumental descriptions (though they refer to something real about the world of course). Every so-called particle - and even point of spacetime - has an irreducible fuzziness. At least under the right "viewing conditions".

The vacuum and its trapped knots look strongly like a void populated by particles (with inertial spins and boosts) when spacetime is large and cold. The process that produces 3-space is asymptotically close to its limit. But change the scale of observation to the small/hot and both the particles inhabiting the vacuum, and even the vacuum itself, have their constraints relaxed, so gaining (or re-gaining) extra degrees of freedom. The wavefunction then measures these regained freedoms against the "fictional" metric of configuration space.

For configuration space to be real, we would have to have a world entirely without constraints. In Peircean terms, that would be a state of vagueness. And indeed, vagueness is populated by an infinity of degrees of freedom. The difference is that they would not be organised into "particles". So this would be much larger than a 3N space. And in fact a completely diffuse realm in which nothing could be described as actually located to a point in a realistic sense.

In practice then, wavefunctions seemed anchored to individual locations or paths in spacetime. They are evolving "loosenings" of emergent objects in an emergent 3-space. There is no fully realized configuration space inhabited by wavefunctions that exist in a non-collapsed way as envisaged by, say, MWI. Configuration space is just a concept of a general metric for measuring all these localised, passing, "loosening of constraints" against.

I think this paper from Lewis is a good analysis of the difficulties of treating configuration space as real.

http://philsci-archive.pitt.edu/1272/

Note that as far as classical mechanics goes, it doesn’t matter which conception of dimension one uses; one obtains the same answer either way. But quantum mechanically the two conceptions come apart; the configuration space in which the wavefunction lives can be taken as 3N-dimensional or as three-dimensional, depending on the conception one chooses. The wavefunction is a function of 3N parameters, and in this sense it lives in a 3N-dimensional space just as a classical object lives in a three-dimensional space. In both cases, the parameters are independent; the value of each parameter can be chosen without regard to the values of the others. But the analogy here is not perfect, since the three parameters of the classical space are independent in an additional sense not shared by the 3N parameters of the configuration space. Each parameter of the classical space refers to a different spatial direction, so there are three separate choices to be made in specifying the coordinate axes. But it is not the case that there are 3N separate choices to be made in specifying the coordinate axes for the configuration space; again, there are three. Even though the values taken by the 3N parameters are independent of each other, the directions referred to by the parameters are not all independent; every third parameter refers to the same direction.
My contention, then, is that there is an important ambiguity in the term “dimension” when it is applied to the quantum mechanical wavefunction...

 

[bohm2]

I think this paper from Lewis is a good analysis of the difficulties of treating configuration space as real.

I read over the Lewis-Monton debate on this topic and found it pretty interesting. Monton goes as far to suggest that QT is a false theory because it can never be reconciled with general relativity. He is critical of both Albert's ultra-realist notion of configuration space and even Lewi's attempts to defend some aspects of wave function ontology (by trying to interpret "dimension" in non-spatial way). Monton is also not sympathetic to any attempts to try to get emergence of 3-D space from 3N-D space as suggested by Wallace and Timpson (2009). What's surprising is that even among Bohmians there are 3 different interpretations of Bohm's theory with respect to interpretations of the configuration and 3-D space:

1. Albert: Bohmian physical objects are represented by wave function consisting of a particle and its field evolving in 3N-D space.

2. Allori, Durr, Goldstein, Zanghi: physical objects are described by particles evolving in 3-D space while the wave function is an abstract entity that serves a nominalist function (a law of nature) that specifies how the objects in 3-D space evolve.

3. Bohm and Hiley: There are 2 different physical substances: particles in 3-D space and an abstract informational field that lives in configuration space (dualism at the primitive level).

And the Orthodox (Copenhagen) has arguably similar, if not greater problems:

It is interesting to note that even the orthodox quantum theory (OQT, the theory originally proposed by Bohr in which there are two separate worlds: a classical and a quantum one) involves such a dual structure: what might be regarded as its primitive ontology is the classical description of macroscopic objects, including in particular pointer orientations, while the wave function serves to determine the probability relations between the successive states of these objects. In this way, also in the case of OQT, the wave function governs the behavior of the primitive ontology. An important difference, however, between OQT on the one hand and the other theories on the other is that in the latter the primitive ontology is microscopic while in the former it is macroscopic. This makes OQT rather vague, even noncommittal, since the notion of 'macroscopic' is intrinsically vague: of how many atoms need an object consist in order to be macroscopic? And, what exactly constitutes a 'classical description' of a macroscopic object?

This stuff is really confusing the hell out of me.

http://www.niu.edu/~vallori/Allori-OnTheMetaphysicsOfQuantumMechanics.pdf

 

[bohm2]

I thought some might find this interesting. Maudlin writes:

The fact that the wave-function exists in configuration space rather than physical space is often overlooked because for a single particle, configuration space is isomorphic to physical space (one specifies the complete ‘configuration’ of a one-particle system by saying where it is in space). One-particle problems, such as the infamous two-slit experiment, can therefore be analyzed as if the wave-function were a classical field in space. But as soon as more than one particle is involved this analogy becomes untenable. In general, a system consisting in n particles inhabiting an m-dimensional space will have a wave-function defined over an (n * m)-dimensional configuration space. (Maudlin in Quantum Relativity & Relativity, p. 197)

On this topic, Monton traces Schrodinger’s attempt to try to reconcile the difficulty of mapping the 3N-dimensional space of the wave function with our experienced 3-dimensional space. He wants to treat the wave-function as physically “real” in order to explain interference effects but encounters difficulties when going beyond one-particle systems:

And Schrödinger does explicitly consider the possibility that the ontology for quantum mechanics involves a 3N-dimensional space. In fact, one might think that he is endorsing that ontology in a 1926 article, when he writes:

The true mechanical process is realized or represented in a fitting way by the wave processes in q-space [where “q-space” is Schrödinger’s terminology for “configuration-space”

But Schrödinger makes this claim in the context of a discussion of one-particle systems, where configuration space is just three-dimensional space. So what would he say about a multiparticle system? Schrödinger considers a two-particle system late in the paper, but has only one sentence about the physical representation of the six-dimensional wave function:

The direct interpretation of this wave function of six variables in three-dimensional space meets, at any rate initially, with difficulties of an abstract nature.

Schrödinger kept trying to develop an ontology for the wave function – there’s a long and interesting story here, but to present it all would be outside the scope of this paper. The short version of the story is that Schrödinger was looking for a way of having the wave function be a mathematical representation of physical processes in three-dimensional space. For example, Schrödinger wrote a letter in response to Lorentz’s, in which the first point he addresses is the issue of the multi-particle wave function. He writes:

I have been very sensitive to this difficulty for a long time but believe that I have now overcome it.

Schrödinger kept working on this project for a while, but by 1935 he had given up. He wrote:

I am long past the stage where I thought that one can consider the wave-function as somehow a direct description of reality.

For the record, it’s unclear to me to what extent Schrödinger gave up on the project of considering the wave function as a direct description of reality because of the measurement problem, and to what extent he gave up on the project because of the issues of interpreting the 3N-dimensional wave function as representing something existing in real, three-dimensional space. It’s clear though that Schrödinger was not willing to endorse the view that the space of reality is 3N-dimensional. (Monton in against 3N-Dimensional Space).

http://spot.colorado.edu/~monton/BradleyMonton/Articles.html

 

[apeiron]

Schroedinger was certainly a good systems thinker.

“But when you come to the ultimate particles constituting matter, there seems to be no point in thinking of them again as consisting of some material. They are as it were, pure shape, nothing but shape; what turns up again and again in successive observations is this shape, not an individual speck of material.

Erwin Schroedinger, 1952, Science and Humanism, New York, Cambridge University Press, pp. 18.

On the 3-space vs q-space issue, isn't it simply that 3-space is our map of actuality (even if it is an emergent actuality) and q-space is our map of possibility (the ground from which actuality emerges)?

The ontic issue you seem to be banging your head against is the question of which is fundamental. But a systems approach says the dichotomy is what is fundamental - the fact reality is bounded by its two limits of the actual and the possible. From an emergence point of view, you need both to have anything.

And more generally, the whole QM interpretation game seems to be centred around two equally bad motivations here.

1) The urge to recover "primitive ontology". A strong belief that reality is composed of material objects and is ruled by locality, determinism, etc, leads to all sorts of contortions of thought to recover this view through an interpretation such Bohmian mechanics.

2) The urge to assume the least ontology. The other route is embrace the interpretation "with the least extra bits". Which leads to ontological idiocies like MWI. Or epistemic hairshirt positivism like Copenhagen.

The third response, as I see it, is to first accept reality is going to be radically different from the "primitive ontology" of mechanics. So quit trying to fix QM to make it look completely local, material and deterministic. And then also accept that a new ontology is going to be quite complex, with a lot of subsidiary bits (at least until it becomes so familiar that the supporting notions "go without saying").

The interpretation problem is far bigger. A new ontology of reality has to unite QM, GR and thermodynamics (and note that Schroedinger did blaze the trail here). Tackling just one arm, like QM, in isolation is a wasted effort.

I suppose the focus is on QM because that is seen as the fundamental theory. But that again is just a presumption of "primitive ontology" thinking, which likes to privilege the "smallest scale" of action in any causal discussion.

 

[bohm2]

But a systems approach says the dichotomy is what is fundamental - the fact reality is bounded by its two limits of the actual and the possible...

The urge to recover "primitive ontology". A strong belief that reality is composed of material objects and is ruled completely by locality, determinism, etc, leads to all sorts of contortions of thought to recover this view through an interpretation such Bohmian mechanics.

I don't agree with your assessment of Bohm's interpretation. Non-locality plays a prominent role in Bohm's interpretation. The dichotomy you mention is also fundamental in Bohm's interpetation (although it's set out somewhat differently). Furthermore, the "wholeness" and bi-directional causality (between global and micro) also plays a prominent role in Bohm's interpretation (hence the title of their book "Undivided Universe"). As Maudlin writes, in assessing Bohm's interpretation:

It is not just that the whole is more than the sum of the parts but that the parts can't even be defined apart from the whole.

But even with these inclusions difficulties arise in Bohm's scheme from my understanding of it. A kind of mind-body interaction problem at the micro level re-appears. How can an abstract information field that seems to represent hypothetical trajectories (potentialities) push around particles? The only option they argue, is to treat the wave function as some kind of "real" object but exactly what that means is unclear? Furthermore:

Such a wave-function can’t be broken down into individual three-dimensional wave-functions, corresponding to what we think of as particles in three-dimensional space. That would leave out information about correlations among different parts of the system, correlations that are experimentally observed. Only the entire wave-function, defined over the entire high-dimensional space, contains all the information that factors into the future evolution of quantum mechanical systems

.

http://courses.cit.cornell.edu/north/QM_for_volume.pdf

 

[apeiron]

The dichotomy you mention is also fundamental in Bohm's interpetation (although it's set out somewhat differently). Furthermore, the "wholeness" and bi-directional causality (between global and micro) also plays a prominent role in Bohm's interpretation (hence the title of their book "Undivided Universe").

There are actually many critical differences here.

A key one in the systems perspective is precisely that wholeness is built on a micro~macro (or rather, local~global) divide. So the fundamental dichotomy is not the implicate realm (the as-yet undivided bit). It is what gets made crisply explicit. The holism lies in the local~global relationship that emerges as a result of a broken symmetry, not the underlying ground of potential.

The logic can sound similar, but it is very different. Bohm says the information organising the world is hidden at a more fundamental level. The systems view is that the information organising the world emerges in the form of its developing global constraints. The information is explicit (which is why there is no problem of how there is an interaction).

And then there is Bohm's desire to find "mind" at the fundamental level. Consciousness is a complexly emergent thing and has nothing at all to do with fundamental physical reality (at least IMO, though I agree there are systems scientists and many others who still want to somehow wrap the mysteries of mind into the mysteries of fundamental existence).

So a systems/semiotic approach focuses not on "information stored at a hidden implicate level" but instead on the information that is explicit in a system as a product of its developmental and evolutionary history. The information encoded by genes, words, membranes, synapses and other such biological machinery. Information that has nothing to do with QM levels of description.

 

[bohm2]

The information encoded by genes, words, membranes, synapses and other such biological machinery. Information that has nothing to do with QM levels of description.

I'm having trouble understanding this. Doesn't that go against your point that "the wholeness is built on a micro~macro (or rather, local~global) divide"? Doesn't bi-directional causality imply that the QM levels of description are also important on the global level? I mean, is there no trace of the micro level at the global scale? I still don't understand how specifically the systems approach explains the results of the two-slit experiment? More generally, how does possibility become actuality in your system?

 

[apeiron]

I'm having trouble understanding this. Doesn't that go against your point that "the wholeness is built on a micro~macro (or rather, local~global) divide"? Doesn't bi-directional causality imply that the QM levels of description are also important on the global level? I mean, is there no trace of the micro level at the global scale? I still don't understand how specifically the systems approach explains the results of the two-slit experiment? More generally, how does possibility become actuality in your system?

As was discussed previously, a dichotomy is defined by being mutually exclusive, jointly exhaustive. So that is a very particular logical claim. It means there should be "no trace of the other" at the complementary poles of description.

Take any standard metaphysical dichotomy such as discrete~continuous, to be discrete is not to be continuous, and vice versa.

So the usual reductionist notion of a hierarchy is that it is composed of "more of the same". The macro is just a whole bunch of the micro glued together.

But the systems view - well, at least my view of it based on Anaximander, Hegel, Peirce, etc - is that the local and global levels have this dichotomous logic. The global scale is not more of the same, a bunch of locales glued together. Instead it is the antithesis - everything that the local is not. The wholeness then comes in the resulting synthesis of course. When the complementary interacts.

So taking discrete~continuous as an illustrative example again, reality would be a synthesis of these two opposing, but complementary, poles of possibility. And indeed, what do we find? On the micro-scale, reality becomes quantum - it breaks up into discreteness. While on the global scale, it instead smooths over to become GR-style continuous.

You have a situation that the logic of dichotomies actually predicts. A model of the local in QM. A model of the global in GR. And a big problem mashing one into the other to create a quantum field theory of gravity.

So the ontically complementary nature of the local and global - in the manner of Hegelian thesis and antithesis - is one key point here. It is a principle that there will be an absolute separation, as with for instance local degrees of freedom and global constraints when we are talking in terms of causality.

In a system, two things are going on! Both the differentiation (the dichotomous repulsion) and the integration (the holistic equilibrating) are happening together. Again, this maps to reality. The universe both expands (differentiates) and cools (integrates) at the same time. There is interaction between local and global, but it is a complex interaction with two faces itself.

Then there is another vital aspect of systems ontology. That is the development from vague potential to crisply developed hierarchical organisation. Or from raw possibility to definite actuality.

This introduces an ontic category that is entirely missing from reductionism. And possibility becomes actuality by dichotomisation. Local and global are not just labels for the way things are. It is the universal process by which things become definite.

Peirce talks about this in terms of firstness, secondness and thirdness - or synechism - if you want to read up on it.

I'll have a go at applying this to twin slit experiments - the quantum eraser version in particular - in another post.

 

[bohm2]

Here’s a very interesting suggestion of combining Bohm's and the GRW model (referred to as BM-GRW in the paper)so that one gets the benefits of both GRW and Bohm’s while removing some of the problems inherent in each model. At the least, it may give one some hints of what is required in a more elegant, "realist" interpretation of QM:

From this point of view the BM-GRW theory acts as a stepping stone between the two. From BM-GRW we can either move to BM by removing the noisy information process and its effect on the wavefunction, or, move to GRW by dropping the hidden particle trajectories and regarding the wavefunction on its own. This helps to clarify the relationship between the two underlying theories. However, we will argue that the advantages of BM-GRW make it worth considering as a theory in its own right.

A common criticism of BM is that, whereas the wavefunction has an influence on the set of particles, the particles have no influence over the wavefunction. Not only does this conflict with the universal principle for laws of physics stating that any action is matched by a reaction, it also leads to a lot of redundancy in the wavefunction. For every branch of the wavefunction containing the actual particle trajectories, there are countless other branches corresponding to every other potential ‘world’ which would have been realized had the particle positions been different. The effects of decoherence soon disable the influence of other branches on the particle trajectories, leaving much of the wavefunction redundant. Nonetheless these redundant branches are an essential element of BM...

This criticism of BM has led several authors to argue that BM is little more than a version of the many-worlds interpretation in which the particle trajectories are a way to select one particular world...It has also led Durr, Goldstein, and Zanghi to suggest that the wavefunction should be regarded as nomological, with a role analogous to the Hamiltonian in classical mechanics.

In the BM-GRW theory the particle positions do influence the wavefunction. This comes from identifying the noise in the GRW equations for the wavefunction with the innovations process which represents information about the signal process (the particle positions). The influence of particles on the wavefunction is unusual in the sense that it does not result from a direct interaction between particles and wavefunction (as can be said for the particle guiding equation). Rather it results from a transfer of information from particles to wavefunction. The outcome is that the complete wavefunction continually reflects the true particle trajectories and the redundant branches find themselves diminished.

http://arxiv.org/PS_cache/arxiv/pdf/1104/1104.1938v1.pdf

The author is the same one who has recently (with others) developed a Lorentz invariant matter density "realist" model:

http://arxiv.org/PS_cache/arxiv/pdf/1111/1111.1425v1.pdf

 

[bohm2]

3. T. Maudlin:3N-dimensional space is a mathematical tool but the wave function is "real" (in a unique way)
There are two distinct fundamental spaces (3-dimensional and 3N-dimensional), each with its own structure. What’s more, each space must possesses additional structure beyond what is normally attributed to it. Further structure is needed to ground the connections between the two fundamental spaces, saying which parts and dimensions of the high-dimensional space correspond to which parts and dimensions of ordinary space, and which axes of configuration space correspond to which particle.

I thought this was another interesting perspective (to the scheme suggested above) by Antony Valentini (lecture from Perimeter Institute). He basically suggests that configuration space is "real" (like Albert, it seems) and argues that the quantum wave is a new type of "causal" agent that may take some time for us to understand it, in the same way scientists had difficulties accepting the concept of "fields" when they were first introduced. So he sees an evolution (see slides) from forces to fields to this non-local quantum wave (which does not vary with distance and appears to be completely unaffected by matter in between). So in his scheme, the configuration space is always there where the pilot wave (a radically new kind of causal agent that is more abstract than conventional forces or fields in 3-D space) propagates. He seems critical of treating the wave function as nomological (law of nature) as Goldstein/Durr and even Maudlin do. What is interesting is during the questioning (1:11) an audience member questions him about the action-reaction principle violated in this pilot-wave scheme. His answer doesn't appear very satisfying but he suggests that we must get used to thinking of QM as a non-mechanical theory. If you want to get to the nitty gritty in the video just check these times: (17:30, 32:00, 39:00, 1:11):


http://streamer.perimeterinstitute.ca/Flash/3f521d41-f0a9-4e47-a8c7-e1fd3a4c63c8/viewer.html

 

[bohm2]

I'm not sure if this can be done but I thought these quotes by Einstein regarding trying to reconcile the 2 spaces (configuration and our familiar 3-D space/4-D space-time) as some of the authors(e.g. Monton, Lewis, etc.) above seem to be trying to do is interesting:

For instance, in order to describe multiparticle systems, Schrodinger had replaced de Broglie’s waves in 3-space with waves in configuration space, and had abandoned the notion of particle trajectories...But Einstein was dubious of this move: "The field in a many-dimensional coordinate space does not smell like something real", and "If only the undulatory fields introduced there could be transplanted from the n-dimensional coordinate space to the 3 or 4 dimensional!"

http://arxiv.org/PS_cache/arxiv/pdf/0706/0706.2661v1.pdf

 

[ThomasT]

I'm not sure if this can be done but I thought these quotes by Einstein regarding trying to reconcile the 2 spaces (configuration and our familiar 3-D space/4-D space-time) as some of the authors(e.g. Monton, Lewis, etc.) above seem to be trying to do is interesting:
http://arxiv.org/PS_cache/arxiv/pdf/0706/0706.2661v1.pdf

bohm2, as I mentioned before, I think you might get more replies (and anyway I'm interested to see how more qm knowledgeable PFer's might respond to your queries) if you post your considerations in the quantum theory forum.

 

[bohm2]

bohm2, as I mentioned before, I think you might get more replies (and anyway I'm interested to see how more qm knowledgeable PFer's might respond to your queries) if you post your considerations in the quantum theory forum.

I thought it was more philosophy than physics but, I'll try to post something on "The ontology of configuration space" in the QM forum and summarize in more organized form some of the papers that I posted here. I've been kind messed up the past few weeks (e.g more university, work, bills, etc.) and my medication seems to be less effective(no focus, anxiety, etc) so I hope I don't write stuff that makes no sense. Because I've noticed I'm pretty lost, the past few weeks.