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## Main Question or Discussion Point

Someone suggested to me that this stuff may be more appropriate in the QM section (I’m not sure?). I think others on here have brought this up before but I thought I’d post some stuff I’ve come across that may be useful to some as a kind of an introductory reading on the ontology of configuration space. These authors have tried to present an ontology of configuration space (and the wave function). I thought these skeptical quotes by Einstein regarding this topic is an interesting introductory quote on the topic:

If QM is supposed to be more “fundamental” than classical physics, does this suggest that configuration space is more "fundamental" than normal 3-space or (4 dimensional space-time)? If it’s more fundamental, why does the world appear to evolve in 3-space or (4 dimensional space-time)? What is the nature of this configuration space where the wave function lives in? Goldstein writes:

http://philsci-archive.pitt.edu/8470/1/rrwf01.pdf

On the Metaphysics of Quantum Mechanics

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

I’ve been reading over the various models and trying to better understand them and here is a brief summary of my basic understanding. If I messed up please correct them because I’m no expert on these views!

The space we live in, the space in which any realistic understanding of quantum mechanics is necessarily going to depict the history of the world as playing itself out...is configuration-space. And whatever impression we have, to the contrary (whatever impression we have, say, of living in a three-dimensional space, or in a four-dimensional space-time) is somehow flatly illusory... In reality, there is just a single 3N-dimensional wavefunction, and the division of reality into separate three-dimensional objects, including organisms, is just the product of our internal representation. Thus, for Albert objects exist as single points, evolving one way or another in this very high-dimensional space.

Wave function Ontology

http://www.princeton.edu/~hhalvors/teaching/phi538_f2004/montonwfo.pdf

While their arguments are somewhat different, both claim that the world really is 3-dimensional and the 3N-dimensional space is a kind of an illusion for different reasons. While Monton flatly rejects the reality of 3-N space ("the wave function is no more real than the numbers-such as 2 or p"), Lewis rules out the reality of configuration space by arguing that the "dimensionality" of configuration space defining the wavefunction is not really "spatial".

QM and 3-N Dimensional Space

http://spot.colorado.edu/~monton/BradleyMonton/Articles_files/qm 3n d space final.pdf

Against 3-N Dimensional space

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

Dimension and Illusion

http://philsci-archive.pitt.edu/8345/1/dimensions.pdf

Life in Configuration space

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

There are two distinct fundamental spaces (3-dimensional and 3N-dimensional), each with its own structure. What’s more, each space must possess 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.

Maudlin argues, that's fine, because such structure is needed to make an informationally complete description, from which "every physical fact about the situation can be recovered". With respect to the wavefunction structure, Maudlin doesn't make a commitment but suggests that it may be unlike anything else (sorta "physical"/real but in a unique/different way), kind of "in its own metaphysical category". These authors appear (if I understand them) to regard configuration space as only a mathematical tool and the wave function as nomological (a law of nature). Thus, they seem to regard the wave function as more than just a probability wave. And even though we don't have direct “access” to it, this doesn't bother them as Maudlin writes: "If our only access to the wavefunction is via its effect on the particles, and if the connection to the lived world is primarily through the particles, then we are not constrained about the physical nature of the wavefunction."

Maudlin video-Can the world be only wave-function?

http://vimeo.com/4607553

Reallity and the role of the wave function in QT

http://arxiv.org/PS_cache/arxiv/pdf/1101/1101.4575v1.pdf

So, 3-N space is an abstract multi-dimensional "informational space" that guides a particle evolving in 3-dimensional space.

http://www.mindmatter.de/resources/pdf/hileywww.pdf

Meaning and Information

http://www.implicity.org/Downloads/Bohm_meaning+information.pdf

From the Heisenberg Picture to Bohm: a New Perspective on Active Information and its relation to Shannon Information

http://www.bbk.ac.uk/tpru/BasilHiley/Vexjo2001W.pdf

He accepts reality of configuration space but not Bohm's/Hiley's 'quantum potential'. He disagrees with Goldstein and thinks the wave function is not just nomonological (a law of nature). Valentini 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 in video) 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.

Valentini video- from Perimeter Institute The nature of the wave function in deBroglie’s pilot wave theory

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

http://arxiv.org/PS_cache/arxiv/pdf/0706/0706.2661v1.pdfIn 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!”

If QM is supposed to be more “fundamental” than classical physics, does this suggest that configuration space is more "fundamental" than normal 3-space or (4 dimensional space-time)? If it’s more fundamental, why does the world appear to evolve in 3-space or (4 dimensional space-time)? What is the nature of this configuration space where the wave function lives in? Goldstein writes:

Reality and the Role of the Wavefunction in Quantum TheoryA second point is that for a multi-particle system the wave function (q) = (q1 ,..., qN ) is not a weird field on physical space, it’s a weird field on configuration space, the set of all hypothetical configurations of the system. For a system of more than one particle that space is not physical space. What kind of thing is this field on that space?

http://philsci-archive.pitt.edu/8470/1/rrwf01.pdf

On the Metaphysics of Quantum Mechanics

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

I’ve been reading over the various models and trying to better understand them and here is a brief summary of my basic understanding. If I messed up please correct them because I’m no expert on these views!

**1. David Albert: Configuration (3N-dimensional) space realism.**The space we live in, the space in which any realistic understanding of quantum mechanics is necessarily going to depict the history of the world as playing itself out...is configuration-space. And whatever impression we have, to the contrary (whatever impression we have, say, of living in a three-dimensional space, or in a four-dimensional space-time) is somehow flatly illusory... In reality, there is just a single 3N-dimensional wavefunction, and the division of reality into separate three-dimensional objects, including organisms, is just the product of our internal representation. Thus, for Albert objects exist as single points, evolving one way or another in this very high-dimensional space.

Wave function Ontology

http://www.princeton.edu/~hhalvors/teaching/phi538_f2004/montonwfo.pdf

**Problems:**Why does the world appear 3-dimensional (or 4-dimensional if space-time) to us? What does N represent in 3N space (what is the space a configuration of, if not the particles)? Maudlin finds this view hard to swallow because he finds it "obscure how something happening at a point (such as a particle occupying a point or a field being concentrated near a point) could have complexly structured physical state of affairs...it is not easy to understand how those physical structures could constitute cats, or chairs, or people."**2. Monton/Lewis: 3-dimensional space is fundamental. The 3N-dimensional space is an illusion/false and wave function is only a mathematical tool.**While their arguments are somewhat different, both claim that the world really is 3-dimensional and the 3N-dimensional space is a kind of an illusion for different reasons. While Monton flatly rejects the reality of 3-N space ("the wave function is no more real than the numbers-such as 2 or p"), Lewis rules out the reality of configuration space by arguing that the "dimensionality" of configuration space defining the wavefunction is not really "spatial".

**Problem:**Predictions of QM depend on the 3N-dimensional space that get lost in the 3-dimensional representation (e.g. information about correlations among different parts of the system, that are experimentally observed are left out).QM and 3-N Dimensional Space

http://spot.colorado.edu/~monton/BradleyMonton/Articles_files/qm 3n d space final.pdf

Against 3-N Dimensional space

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

Dimension and Illusion

http://philsci-archive.pitt.edu/8345/1/dimensions.pdf

Life in Configuration space

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

**3. T. Maudlin/Goldstein: While 3N-dimensional space is a mathematical tool 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 possess 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.

**Problem:**Adds additional fundamental structure, making it less elegant/far more complex.Maudlin argues, that's fine, because such structure is needed to make an informationally complete description, from which "every physical fact about the situation can be recovered". With respect to the wavefunction structure, Maudlin doesn't make a commitment but suggests that it may be unlike anything else (sorta "physical"/real but in a unique/different way), kind of "in its own metaphysical category". These authors appear (if I understand them) to regard configuration space as only a mathematical tool and the wave function as nomological (a law of nature). Thus, they seem to regard the wave function as more than just a probability wave. And even though we don't have direct “access” to it, this doesn't bother them as Maudlin writes: "If our only access to the wavefunction is via its effect on the particles, and if the connection to the lived world is primarily through the particles, then we are not constrained about the physical nature of the wavefunction."

Maudlin video-Can the world be only wave-function?

http://vimeo.com/4607553

Reallity and the role of the wave function in QT

http://arxiv.org/PS_cache/arxiv/pdf/1101/1101.4575v1.pdf

**4. Bohm/Hiley: The 3N-dimensional space is a "real" objective information space.**So, 3-N space is an abstract multi-dimensional "informational space" that guides a particle evolving in 3-dimensional space.

**Problem:**How can an "informational field" guide the particle? How does it interact with it to inform it? The field acts on the particles but particle doesn't act on the field. Brown has argued that this goes against Einstein's action-reaction principle. Einstein wrote it is "contrary to the mode of scientific thinking...to conceive of a thing...which acts itself, but which cannot be acted upon." Regardless this ontology requires far greater intrinsic complexity to be given to particles like electrons, etc. This leads to russian dolls and problem of infinite regress at. Bohm writes:Can Mind Affect Matter Via Active Information?This would imply firstly that the information represented by the Schrodinger wave field is being 'carried' by a finer and subtler level of matter that has not yet been revealed more directly. But even more important, it also implies that there may be a finer and more subtle level of information that guides the Schrodinger field, as the information on the Schrodinger field guides the particles. But this in turn is a yet more subtle 'somatic' form, which is acted on by a still more subtle kind of information, and so on. Such a hierarchy could in principle go on indefinitely. This means, of course, that the current quantum mechanical laws are only simplifications and abstractions from a vast totality, of which we are only 'scratching the surface'. That is to say, in physical experiments and observations carried out thus far, deeper levels of this totality have not yet revealed themselves.

http://www.mindmatter.de/resources/pdf/hileywww.pdf

Meaning and Information

http://www.implicity.org/Downloads/Bohm_meaning+information.pdf

From the Heisenberg Picture to Bohm: a New Perspective on Active Information and its relation to Shannon Information

http://www.bbk.ac.uk/tpru/BasilHiley/Vexjo2001W.pdf

**5. Antony Valentini: Configuration space is "real" where wave function, a new causal agent, evolves. (his position seems somewhere in between Albert’s, Bohm's and Maudlin/Goldstein?)**He accepts reality of configuration space but not Bohm's/Hiley's 'quantum potential'. He disagrees with Goldstein and thinks the wave function is not just nomonological (a law of nature). Valentini 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 in video) 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.

**Problem:**Mixture of above ones.Valentini video- from Perimeter Institute The nature of the wave function in deBroglie’s pilot wave theory

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

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