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What is the wave function about? 
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#91
Oct2211, 04:02 PM

PF Gold
P: 691

With respect to the "space" in which the wave function evolves, am I understanding these 4 positions accurately? If you favour one, which one do you favour and why?
1. David Albert:3Ndimensional space realism. The space in which any realistic interpretation of quantum mechanics is necessarily going to depict the history of the world as playing itself out … is configurationspace. And whatever impression we have to the contrary (whatever impression we have, say, of living in a 3dimensional space, or in a 4dimensional spacetime) is somehow flatly illusory...In reality, there is just a single 3Ndimensional wavefunction, and the division of reality into separate threedimensional objects, including organisms, is just the product of our internal representation. Problem: Why does the world appear 3dimensional (or 4dimensional if spacetime) to us? What does N represent in 3N space (what is the space a configuration of, if not the particles)? (For Albert all that exists is a single particle, evolving one way or another in a very highdimensional space). 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 be a 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:3dimensional space is fundamental. The 3Ndimensional space is an illusion/false as wave function is only a mathematical tool While their arguments are somewhat different, both claim that the world really is 3dimensional and the 3Ndimensional space is a kind of an illusion for different reasons. While Monton flatly rejects the reality of 3N space ("the wave function is no more real than the numberssuch as 2 or p"), Lewis rules it out by arguing that the "dimensionality" of configuration space defining the wavefunction is not really "spatial". Both seem to deny the reality of the wave function. Problem: Predictions of QM depend on the 3Ndimensional space that get lost in the 3dimensional representation (e.g. information about correlations among different parts of the system, that are experimentally observed are left out). 3. T. Maudlin:3Ndimensional space is a mathematical tool but the wave function is "real" (in a unique way) There are two distinct fundamental spaces (3dimensional and 3Ndimensional), 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 highdimensional 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/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". He does appear (if I understand him and those that discuss his views) to regard configuration space as only a mathematical tool; however, he also regards the wave function as more than just a probability wave, even though we don't have direct access to it. This doesn't bother him as he 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." 4. Bohm:3Ndimensional space is a "real" information field represented in a "mindlike" entity represented by the wave function. 3N space is an abstract multidimensional "informational space" that guides a particle evolving in 3dimensional 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 actionreaction 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. Bohm writes: In analogy to what has been said about human experiences, the particles constituting matter in general may be considered to represent a more gross (explicate) somatic level of activity, while the Schrodinger wave field corresponds to a finer, subtler, more implicate and 'mindlike' level. In human experience however, it has been proposed that each 'mindlike' level can be regarded as a somatic bearer of form when seen from a yet finer and more subtle level. 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 this far, deeper levels of this totality have not yet revealed themselves. http://www.implicity.org/Downloads/B...nformation.pdf http://philsciarchive.pitt.edu/8345/1/dimensions.pdf http://users.ox.ac.uk/~sfop0257/papers/Finding.pdf http://courses.cit.cornell.edu/north/QM_for_volume.pdf http://spot.colorado.edu/~monton/Bra...ce%20final.pdf http://vimeo.com/4607553 (Maudlin videoCan the world be only wavefunction?) 


#92
Oct2311, 10:44 PM

PF Gold
P: 691

I found the debate on the reality of the "quantum potential" between Bohm/Hiley versus some "Bohmians", interesting. Hiley writes:
I think this adjective takes its meaning from a particular view strongly advocated by Dürr, Goldstein and Zengi (DGZ), who have actually coined the phrase "Bohmian mechanics". Their take on the Bohm formalism is what I call mechanistic minimalism. That is they take a position that attempts to keep as many of the traditional features of a mechanistic view of physics as possible, introducing the minimum number of assumptions that seem necessary to generate the formalism...The choice of the term "Bohmian mechanics" is rather unfortunate because Bohm himself did not think the quantum formalism suggested a mechanistic interpretation. In his classic book Quantum Theory, Bohm wrote under the section entitled 'The Need for a Nonmechanical Description' "This means that the term quantum mechanics is very much a misnomer. It should, perhaps, be called quantum nonmechanics" To summarise this section then, let me emphasise that the differences between the advocates of Bohmian mechanics and our own approach is not about the need to have a account of the actual, but about what form this account should take. Clearly such a choice is largely decided by what each group regards as an acceptable physical explanation. There is no dispute about the form of the equations. Where Bohm and I differ from many advocates of Bohmian mechanics is the attitude we adopted to the formalism. Our long period of working with the formalism and reflecting on how it works has led us to believe that rather than a simple return to a mechanistic picture something much more subtle is involved. We tried to bring this out in our book but clearly we have not got across our message! Some Bohmians question the concept of "quantum potential" partly because of it's "bizarre properties" which include some of the following: 1. The quantum potential has no external source so that there is nothing for the particle to 'push against'. The energy is internal so it's role “it is more like the role the gravitational field plays in general relativity where the gravitational energy curves spacetime itself.” 2. The quantum potential does not arise directly from the Hamiltonian and therefore does not appear explicitly in the algebraic equations (8) and (9). (see links for equations) The quantum potential only appears when we project equation (9) into a particular representation space. This is even more like gravitation where the 'force' appears only when we project the geodesics into a Euclidean space. It is only in this space that we see the deflected trajectories revealing the presence of the gravitational force. 3. The quantum potential is not changed by multiplying the field, ψ by a constant. This can be seen by examining the mathematical form of the quantum potential given by equation... This means that the quantum potential is independent of the magnitude of ψ and so is independent of the field intensity. This in turn means that its effect can be very large even when the amplitude of the field is very small. Because of this, the effect of the potential need not fall off as the distance increases and this is just the property required for an explanation of the EPR correlations. 4. Because there is nothing to push against we should not regard the quantum potential as giving rise to an efficient cause, ('pushing and pulling') but it should be regarded more in the spirit of providing an example of Aristotle’s formative cause...The form is provided from within but it is, of course, shaped by the environment...The quantum potential carries information about the environment in which the particle finds itself. For example, in the electron twoslit experiment, the quantum potential carries information about the two slits, their size, shape and distance apart. Thus it carries information about the whole experimental arrangement. Thus the quantum potential reflects the experimental conditions...it is important to emphasise once again that our concept of information is not 'information for us' but objective information for the particle.... http://www.bbk.ac.uk/tpru/BasilHiley/Vexjo2001W.pdf http://www.bbk.ac.uk/tpru/BasilHiley...foTeleWein.pdf 


#93
Oct2411, 02:46 AM

P: 1,414

@ bohm2,
I think your scholarship deserves some replies from people more knowledgeable than me, but in lieu of that I'll throw in my two cents again. (By the way, I think your questions would be ok in the quantum physics forum, and you might get more replies there.) Wrt your post #91, I prefer the view (2.) that 3D space is fundamental, ie., nature/reality is 3 dimensional wrt any and all scales of behavior. I think that the development of QM is conceptually based on this view, but that imaginary 'spaces' are required for calculation purposes. Wrt 1., I've never liked (understood) the way Albert interpreted QM. Wrt 3., I don't see (understand) the reason for assuming that reality consists of 2 distinct fundamental spaces. Wrt 4., it makes sense to me to think of reality in terms of hierarchy of wave fields (ie., as far as we can be concerned, a hierarchy of particulate media), the more fundamental of which emerged from disturbances in a seamless fundamental medium. It might be, as Bohm states, that " ... in physical experiments and observations carried out this far, deeper levels of this totality have not yet revealed themselves", however if reality is 3D, and if there is at least one fundamental wave dynamic, then it seems to me that this would be more or less evident wrt all scales. And this does seem to me to be the case, which presents a problem, imo, for the Bohmian view, or anyway its theoretical realization, insofar as the nonmechanical actionatadistance of BM is concerned.  Wrt your post #92 and the quantum potential: While the wave equation and wave function of standard QM do contribute to some very reasonable inferences regarding the deep nature of reality, I find it difficult to associate the quantum potential with a fundamental physical concept. That is, I don't have any good ideas about what it might mean. Have you made any progress in developing your own interpretation of it? 


#94
Oct2511, 12:11 AM

PF Gold
P: 691

Interpreting quantum nonlocality as platonic information The "hidden variables" or "guiding equation" explanation for the measurement of quantum nonlocality (entanglement) effects can be interpreted as instantiation of Platonic information. Because these BohmdeBroglie principles are already external to the material objects that they theoretically affect, interpreting them as Platonic is feasible. Taking an approach partially suggested by Quantum Information Theory which views quantum phenomena as sometimes observablemeasurable information, this thesis defines hidden variables/guiding equation as information. http://scholarworks.sjsu.edu/cgi/vie...20potential%22 


#95
Oct2511, 05:05 AM

P: 1,414

The term "quantum nonlocality" has a couple of connotations wrt standard QM, neither of which refer to or imply actionatadistance or FTL transmissions between the entangled entities. Imho, this "Platonic information" approach is the wrong approach to understanding the essence of quantum entanglement. Bohm's general view, as I currently understand it, is based on the idea that reality is a seamless whole, perhaps arising from a fundamentally seamless medium, involving both particulate (ie., bounded but nonetheless possibly highly complex) structures and wave mechanical principles/laws applicable wrt any medium (particulate or not). This also makes sense, and is thereby attractive, to me. There's no necessary, fundamental differentiation between physical and mental wrt this as far as I can tell. But I do believe that you'll finish it, and understand it, before I'm able to. If minds and mental activity are traceable to physical phenomena, then, while ascertaining the precise mechanics of their emergence might be somewhat problematic, the mechanism of their emergence isn't necessarily an unsolvable mystery. Anyway, I'm hoping that the relative heavyweights (apeiron, Demystifier, Pythagorean, Ken G, Hurkyl, et al.  if I left any worthy contributors out I apologize, but they can indelibly etch their names in my memory by contributing some insightful comments here) will present their opinions on your latest considerations. And also please record here any further insights that you might have gotten in contemplating this stuff. 


#96
Oct2511, 02:05 PM

PF Gold
P: 691

It may be added, with Russell and others, that although physics appears to tell us a great deal about certain of the general structural or mathematical characteristics of the physical, it fails to give us any real insight into the nature of whatever it is that has these characteristicsapart from making it plain that it is utterly bizarre relative to our ordinary conception of it. It is unclear exactly what this last remark amounts to (is it being suggested that physics is failing to do something it could do?) But it already amounts to something very important when it comes to what is known as the "mindbody problem." For many take this to be the problem of how mental phenomena can be physical phenomena given what we already know about the nature of the physical. And this is the great mistake of our time. The truth is that we have no good reason to think that we know anything about the physical that gives us any reason to find any problem in the idea that mental or experiential phenomena are physical phenomena...How can consciousness be physical, given what we know about what matter is like?" If one thinks this then one is, in Russell's words, "guilty, unconsciously and in spite of explicit disavowals, of a confusion in one's imaginative picture of matter". One thinks one knows more about the nature of matterof the nonexperientialthan one does. This is the fundamental error. Of course all of them reach different conclusions with respect to what this means regarding the nature of metaphysics/philosophy of mind/body, etc. I think all of them recognize the difficulty of trying to unify consciousness/the mental with presentday physics but hold the view that perhaps as physics/science progresses it will all make sense in the future (assuming it lies within our intellectual ability). That is, the gaps are real but they will progressively be "filled" in as science progresses. One other point I've been thinking as I'm reading this paper is that some (many?) linguists and cognitive scientists view mathematical objects as essentially mental objects so they don't subscribe to the view that such objects exist independent of minds. Chomsky writes: In its most elementary form, a generative system is based on an operation that takes structures already formed and combines them into a new structure. Call it Merge. Operating without bounds, Merge yields a discrete infinity of structured expressions. Hence Merge, and the condition that it can apply without bound, fall within UG (Universal Grammar)...The conclusion that Merge falls within UG holds whether such recursive generation is unique to the faculty of language or is appropriated from other systems. If the latter, there still must be a genetic instruction to use Merge to form structured linguistic expressions satisfying the interface conditions. Nonetheless, it is interesting to ask whether this operation is languagespecific. We know that it is not. The classic illustration is “the mathematical capacity,” which troubled Alfred Russel Wallace 125 years ago because it “is wholly unexplained by the theory of natural selection, and must be due to some altogether distinct cause,” if only because it remained unused. One possibility is that it is derivative from language. If the lexicon is reduced to a single element, then Merge can yield arithmetic in various ways. Speculations about the origin of the mathematical capacity as an abstraction from linguistic operations are familiar, as are criticisms, including apparent dissociation with lesions and diversity of localization. The significance of such phenomena, however, is far from clear. They relate to use of the capacity, not its possession; to performance, not competence. For similar reasons, dissociations do not show that the capacity to read is not parasitic on the language faculty, as Luigi Rizzi points out. http://www.punksinscience.org/kleant...Chomsky_UG.pdf Edit: I read, "Interpreting quantum nonlocality as platonic information". I was hoping it would be interesting. I didn't find it interesting or useful. 


#97
Oct2711, 07:48 PM

P: 1,414




#98
Oct2811, 05:00 PM

PF Gold
P: 2,432

So an object = substance + form. Or in more modern terminology, object = local degrees of freedom + global constraints. In our minds, we tend to think imagistically of maths in terms of objects  constraints in some embodied form. A circle or triangle is thought of not as a generalised relationship but pictured as some concrete and particular example of a circle of triangle. That is some expanse of something enclosed by a limiting geometry. But the actual maths itself is not these mental images. It is the formal description of the shapes in terms of various definite constants and relations. It is the apparatus we use to reconstruct(!) a constraint of nature as part of our modelling of nature. Out in the real world, that constraint simply exists as a limit on the material organisation of local degrees of freedom. This is the key to understanding the wavefunction too I believe. The temptation is to think of both the particle and its wavefunctions as objects. Concrete, material, particular, definite and localised emboddied forms. So you have two things that actually exist, but which then also seem to require their own set of dimension in order to be located. One needs its 3space. The other needs its configuration space. And as separate objects, it is unclear how the two interact  what their relation is. Or what relation this duo have to all the other concrete particle/wavefunction pairings. But if you instead understand the compound nature of objects  the division into bottomup or constructive degrees of freedom (Aristotle's material and efficient causes) and topdown or global constraints (Aristotle's formal and final causes)  then you can interpret the duality differently. There is no actual located and material particle. That is just a figment of our "objectprojecting" imagination. All that exists in reality at a location are some collection of degrees of freedom. And then there are all the constraints that bear on these degrees of freedom to limit them to have some concrete form or organisation. The wavefunction represents those constraints  their evolution over time. So the wavefunction "exists" as something physical. But not in the sense of an object. It is part of the constraints that in interaction with local degrees of freedom create the compound event or action we call "a material object". The collapse of a wavefunction is then nothing more than an increase in those constraints. Decoherence steps up the constraints on some set of degrees of freedom so as to limit them much more strictly. So talking about 3D vs configuration space, the classical three dimensional space of material objects is a maximally constrained state. Configuration space is a loosening of all possible constraints to describe the same place in terms of maximised local freedoms. The actual world out there is of course pretty much completely classical. Having grown large and cold, it exists as a highly constrained realm as close as possible to the classical limit. It only looks quantum when returned locally to a very hot or very small scale of existence. This loosens the prevailing state of constraint and reveals the greater degrees of freedom that can exist as limits are relaxed. Configuration space is then our map of that greater realm of the possible which grounds our (cold and expanded) classical actual. Configuration space did perhaps once exist (around the moment of the big bang when the universe was hot and small and so lacking sharp boundaries to its degrees of freedom). But now it represents a space of the possible more than a space of the actual. 3D seems the more real  it is what we concretely experience. We can only glimpse that greater realm of possibility represented by configuration space when we make observations at the quantum scale. So yes, our minds wants to think about things in terms of objects. But objects are compounds of local degrees of freedom and global constraints. Even atoms are not real in the sense of being irreducible particles of matter  little actual lumps of stuff. They are the product of an interaction, a localised blend. The same goes too for the void. Spacetime is not an object but again a dynamical interaction, the evolution from possibility to some actuality. This is the process philosophy view, the systems science view. And it requires a far more abstract notion of what "physically exists". Both global constraints and local degrees of freedom are far more abstract concepts than the "embodied objects" that our minds are so used to picturing. 


#99
Oct2911, 10:57 PM

PF Gold
P: 691




#100
Oct3011, 12:40 AM

PF Gold
P: 2,432

There does not have to be a fundamental stuff in the sense of a substance possessing irreducible properties. Constraint can create "stuff" by organising local degrees of freedom. 


#101
Oct3011, 04:38 PM

PF Gold
P: 691

1. The output is the the position of particles in 3space. 2. The algorithm that generates the output is the wave function in configuration space. What is your output? Is there any room for anything beyond the wave function, itself, in your model; that is, is there anything beyond the wave function that makes direct contact with the world of our experience? If there is, what is it's ontology? 


#102
Oct3011, 05:05 PM

PF Gold
P: 2,432

What I was arguing for was a definite separation of "objects" into local degrees of freedom and global constraints. And even a wavefunction seems a rather objectlike notion  a probablistic view of a particle's uncertainty, the stilltobe determined aspects of its state. So my interpretation of the wavefunction would be that it is the sum of all the constraints that impinge on "a particle". To even have a wavefunction means that much has already been pinned down already due to a history of constraints on a locale. But there are still degrees of freedom to be determined by "observation". 


#103
Oct3011, 05:51 PM

PF Gold
P: 691




#104
Oct3011, 06:43 PM

PF Gold
P: 2,432

Personally, I don't hold to some single interpretation of QM. I don't think we are there yet. But I most like a consistent histories approach mixed with elements of decoherence and transactional interpretations. And as I say, the more general systems view of "particles" that would derive from an analogy with the solitons or quasiparticles of condensed matter physics. So cats and tables are constructed of particles which are pretty definite objects  degrees of freedom trapped early in the big bang by the rapid cooling/expansion of spacetime. Electrons and protons don't seem likely to decay at current ambient cosmic temperatures and scales. There is a history of constraint that locks these particles into place. But then there is still a finegrain quantum uncertainty concerning their identity and interactions. At the level of cats and tables, this fuzziness is pretty irrelevant. But at the fine scale of observation, it is still part of reality. So the division of particle vs wavefunction seems only to distinguish the aspects of a locale that are strongly determined by prior history and the aspects that remain faintly indeterminate. The "surprise" is that this allows in "retrocausality" (as in quantum eraser experiments) and other kinds of nonlocal weirdness. This implies that spacetime and causal locality/determinism are in fact emergent features, not fundamental. But clearly, that is the ontology I have been arguing for all along. So yes, we live in a classical 3+1D world in which a void is populated by particles. But that is the emergent view. The deeper view is the systems one which describes emergent objects (and the vacuum is also such an object) as the product of local degrees of freedom in interaction with global constraints. 


#105
Oct3011, 07:53 PM

PF Gold
P: 691

Since the proposal is to take the wave function to represent physical objects, it seem natural to take configuration space as the true physical space. But clearly, we do not seem to live in confguration space. Rather, it seems obvious to us that we live in 3 dimensions. Therefore, a proponent of this view has to provide an account of why it seems as if we live in a 3dimensional space even though we do not. Connected to that problem, we should explain how to "recover the appearances" of macroscopic objects in terms of the wave function. Primitive Ontology and the Structure of Fundamental Physical Theories http://www.niu.edu/~vallori/AlloriWfoPaperJul19.pdf 


#106
Oct3111, 06:15 PM

PF Gold
P: 2,432

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 acausal 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 socalled 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 3space 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 regaining) 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 3space. There is no fully realised configuration space inhabited by wavefunctions that exist in a noncollapsed 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. 


#107
Nov111, 12:11 AM

PF Gold
P: 691

1. Albert: Bohmian physical objects are represented by wave function consisting of a particle and its field evolving in 3ND space. 2. Allori, Durr, Goldstein, Zanghi: physical objects are described by particles evolving in 3D space while the wave function is an abstract entity that serves a nominalist function (a law of nature) that specifies how the objects in 3D space evolve. 3. Bohm and Hiley: There are 2 different physical substances: particles in 3D 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/AlloriO...mMechanics.pdf 


#108
Nov111, 03:07 PM

PF Gold
P: 691

I thought some might find this interesting. Maudlin writes:
And Schrödinger does explicitly consider the possibility that the ontology for quantum mechanics involves a 3Ndimensional space. In fact, one might think that he is endorsing that ontology in a 1926 article, when he writes: http://spot.colorado.edu/~monton/Bra.../Articles.html 


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