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EPR/Bohm/Bell & Localism vs Universalism

  1. May 30, 2013 #1
    It is commonly understood that the progression from EPR to Bohmian mechanics to the Bell theorem relates to the idea that there is a common sense notion of the constitution of physical reality that is in need of being reevaluated. This notion is simply that the fundamental elements of physical reality are to be understood as causally isolated material points (ie particles). The name we can give to this notion is the principle of locality, or more simply, localism. It is further said that a thorough understanding of Bell -- especially in light of the experimental confirmations starting with Aspect -- leaves us with nothing other than a physical reality that is essentially "non-local".

    This is where I start to have issues. That is, even though we know what physical reality is *not*, we are no further along the line concerning what it *is*. My fundamental question here is simply this: besides localism, what else is there?

    From where I stand, the polar opposite of localism would have to be something called universalism.

    I guess we would then have to ask: does non-localism imply universalism? And does non-universalism imply localism?

    This is all just to ask if the concepts of semi-localism (or semi-universalism) can possibly have any rigorous sense.

    I think it much wiser to assert that the common sense notion of physical reality is not one of strict localism, but rather of a pragmatic, wishy-washy semi-localism that is crucially dependent on the context of the physical picture at hand. When thinking in terms of the objects of everyday experience, a single location will be on the order of meters. In terms of geography, it will be on the order of kilometers. Cosmologically, locations may be up to light years in extent.

    My thinking is that all notions of semi-localism are founded upon the empirical sciences. The objects of empirical science are always simply transparently given to us. This is just to say that the act of observation itself is never taken into account in any empirical science. Astronomy, chemistry, and biology are obvious examples of sciences whereby the act of observation is never at issue.

    But physics is different. While it is true that there may be many branches of physics that do indeed utilize transparently given objects, at the most fundamental level (ie Quantum Mechanics), physics is a science that has as its central question the nature of the act of observation, as such.

    My understanding is that QM is the first rigorous effort to finally come to terms with the origin of all strict localism: Newton's reduction of empirically given, semi-local bodies to their centers of mass. It is only in this way that Newton was able to handle the phenomenon of gravity using [fairly simple] analytic mathematical techniques. But I think it is safe to assume that Newton did not think that material points could possibly have any place in a fundamental description of nature.

    Once it came time to give theoretical descriptions of the elementary constituents of physical reality, Newtonian-style reductionism was no longer in the theoretical physics community's bag of tricks. But the sh*t didn't finally hit the fan until de Broglie's thesis was hailed by Einstein, and used as a source of inspiration for Schrodinger's thinking. Bohm, of course eventually joined the party. Then Bell.

    I would strictly define semi-localism as any understanding of nature that utilizes a fundamental distinction between matter and space. That is, the "material location" is taken to be everything that is contained within a simply connected surface (eg, a spherical or boxlike boundary). I find it wise to immediately discard all semi-local fundamental theories of physical reality.

    So, there seems to be either localism or universalism. We know that reality is most definitely *not* local, right?

    I will leave with the following quote from de Broglie:

    "An electron is for us the archetype of [an] isolated parcel of energy, which we believe, perhaps incorrectly, to know well; but, by received wisdom, the energy of an electron is spread over all space with a strong concentration in a very small region, but otherwise whose properties are very poorly known. That which makes an electron an atom of energy is not its small volume that it occupies in space, I repeat: it occupies all space, but the fact that it is undividable, that it constitutes a unit."
     
    Last edited: May 30, 2013
  2. jcsd
  3. May 30, 2013 #2
    Localism is just a atribute, a characteristic, a property of reality, REALITY goes beyond properties.
     
    Last edited: May 30, 2013
  4. May 30, 2013 #3
    I would call localism a property of particular models of reality; especially those kinds of models that want to make use of a Newton-esque mathematical formalism (eg, analytic algebraic equations).

    I would call semi-localism a property of reality, as it is experienced.

    I would agree that reality-as-such is beyond properties, if we think of a property as an X that is theoretically understood as a subset of universal space.

    I just feel that the problem with QM is that it continues to use the term non-local in such a way that most people will simply think of a semi-local picture. But if we instead force an explicit choice between local and universal, then we can at least eliminate entire classes of theories that do not have universally defined objects as their elementary constituents.
     
  5. May 30, 2013 #4
    Why is it necessary to define locality as localism and nonlocality as universalism and why does one imply the other?


    What properties would semi-localism have?


    You lost me here.
     
  6. May 30, 2013 #5

    DrChinese

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    Hardly. It is true that "classical" Realism is not compatible with Locality post Bell. But there are a number of non-realistic interpretations of QM. Examples are Many Worlds, Time Symmetric/Retrocausal, and even orthodox QM in many respects. These generally do not feature influences which propagate faster than c.
     
  7. May 30, 2013 #6
    I am just arbitrarily equating the terms "principle of locality" and "localism".

    The question of what, precisely, the phrase "non-local" is supposed to positively denote is what I am asking. For instance, the phrase "non-green" stills leave an infinite number of options along the entire EM spectrum.

    The reason why I say "the one implies the other" is because the notion that reality fundamentally consists of arbitrary surfaces between matter and space is simply not theoretically pleasing to me. The precise nature of this kind of "theoretical displeasure" is not very easy for me to describe, which is why I wanted to post this thread! :)

    My definition of semi-local was as such:

    The main point is that most people would never think of QM as having any stake in questions about the *universe* if its understanding of non-localism is simply a kind of semi-localism. Using this as an assumption, the range of questions that are applicable to QM will never include the range of questions that apply to the universe as a whole (such as are applicable to GR).

    So... if, for instance, the wavefunction could be seen as being necessarily applicable to the entirety of universal space, then this provides a direct entry way for QM theorists to begin framing the kinds of questions that previously have only been available to astrophysicists/comologists.
     
  8. May 30, 2013 #7
    Haha... this is precisely what I was expecting you to say! In fact, it was my perusal of that Scholarpedia article on Bell's Theorem thread that caused me to start thinking about this question. I actually read through most of that article (sans math), and found it quite refreshing.

    My understanding of the various "interpretations" of QM can be categorized as follows:

    1) de Broglie/Bohm-like causal mechanisms
    2) Bare instrumentalism (pure mathematics)
    3) Abuses of language

    I enjoyed the Scholarpedia article so much because it made no bones about the fact that those other interpretations you mention simply fail to say anything at all rather than saying things that are simply "counter-intuitive" or "hard to imagine".

    I think it is quite appropriate to quote Wittgenstein in times like this:

    (Whereof one cannot speak, thereof one must be silent.)

    All I'm saying is that I'm not interested in debating the notion of "realism", if it is structurally embedded into our language, and is what makes meaningful discourse at all possible.

    In terms of the idea of whether there can be influences that propagate faster than c, this question already assumes that the fundamental elements of reality are essentially non-universal. If this means that the elements are strictly local (ie, they occur between material points), then my contention is that we are speaking along the lines of the "Newtonian reduction" that I mentioned above, which was never meant to be a framework to aid in the theoretical understanding of the fundamental constitution of nature. But if it means that they are merely semi-local, then I would say that we are just involving ourselves in a framework that is no longer using the question of the nature of the act of observation as its guiding theme. It's an either/or thing in my book...

    Either: We are reducing empirically given material bodies to their centers of mass, in which case we are simply evading the question.

    Or: We are transparently using "real world" measuring devices in order to describe the elements of nature, in which case we aren't even aware of the existence of the question.

    In terms of a framework whose elements are strictly universal, we can at once rid ourselves of the "ghost" of Newtonian reductionism, while at the same time developing reasonable theoretical models for practical signal propagation between sources and receivers. These kinds of models do not (in fact they cannot) include things like simple particles moving in void space. They can indeed include the kinds of intuitive wave propagation models that Maxwell himself would have found agreeable.
     
  9. May 30, 2013 #8
    i agree en masse, fully.

    the term "universal" says a lot too.
    local to me, is a primitive term.
     
  10. May 30, 2013 #9

    bhobba

    Staff: Mentor

    Errrr. Not quite - eg Many Worlds is not pure mathematics nor is it an abuse of the language. And that's just one example here is another - Consistent Histories:
    http://quantum.phys.cmu.edu/CHS/histories.html

    Can I ask where you got such an idea from?

    Thanks
    Bill
     
  11. May 31, 2013 #10

    DrChinese

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    Sadly, the Scholarpedia article has a explicitly Bohmian take on Bell. Travis Norsen and several others did a number on that, effectively mixing some good material with other which represents a bias not generally accepted in science. Your refusal to discuss the significance of Realism in Bell is probably influenced by that. Travis does not acknowledge Realism as a requirement to the Bell result. On the other hand, this is almost universally acknowledged by researchers in the area.

    Specifically, most physicists would say that the outcomes of experiments are observer dependent ("contextual"): there is no independent reality to non-commuting pairs of observables. I believe this is probably a viewpoint shared by most Bohmians, Travis being an exception. Once you acknowledge this, interpretations such as the MWI and Time Symmetric types seem to be reasonable options.
     
  12. May 31, 2013 #11
    Actually, Travis is not an exception to this rule. He agrees, as a matter of ideology, that you cannot have reality corresponding to two non-commuting observables. After all, Bohmian mechanics only ascribes reality to position. But, as you said, somehow he claims that realism isn't essential for Bell's theorem.

    For the benefit of others (you already understand all this), here is my post from the old Scholarpedia thread where I identify what I think is the problem with Travis' argument. Basically he's implicitly invoking counterfactual definiteness, AKA realism.
     
    Last edited: May 31, 2013
  13. May 31, 2013 #12

    really, you have to define locality/non-locality just like subsets of contextuality/noncontextuality,
    contextuality is broader, subsumes locality/nonlocality.
    that every state that is contextual with respect to the defined test of contextuality is nonlocal as per the CHSH (Clauser, Horne, Shimony, Holt test) but the converse is not true, or as i like to ask:

    Every state that is contextual is nonlocal.
    ...and the inverse, is every state that is nonlocal is contextual ?


    -----
    measured values (atributtes, characteristics, properties) in context, just is related to that, "context", be real goes beyond properties, the possibility of values requires pre-existent objects or process, without objects, there is no possibility of properties (values).
     
  14. May 31, 2013 #13


    Your language is confusing, e.g. you could have used the standard phraseology typical for such a topic and used - "Does non-locality imply holism?" instead of "does non-localism imply universalism?"








    I still fail to see what semi-localism is supposed to be and how it's expected to account for the perfectly local macro reality. But there is no contradiction between locality and the implied non-locality of qm as soon as you understand that the observed local macro reality is a subset of the wider quantum reality, experienced as it is due to your experiential interaction with it.


    "Dephasing in electron interference by a 'which-path' detector":

    http://www.nature.com/nature/journal/v391/n6670/full/391871a0.html


    Physics concerns itself with issues of practical purposes, so for all practical purposes locality can be considered to be intact. For the more philosophically-minded, 'observer' and 'observed' are hard to separate, hence locality and non-locality are equally 'real' and equally there and there is no issue between them. So if by 'universalism' you mean reality as it's experienced, I would say that non-localism hints at universalism.
     
    Last edited by a moderator: May 6, 2017
  15. May 31, 2013 #14

    DevilsAvocado

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    If you just could elaborate on what this epic transition from non-locality to universalism will do in terms of scientific values – I would be more than happy.

    (audioloop seems so universal epiphany happy, I’m jealous)
     
  16. Jun 1, 2013 #15
    What is universalism?

    Can you define it with a positive definition rather than, "...the polar opposite of localism would have to be something called universalism"?

    I think you jump too quickly into the semi-localism discussion before telling what universalism assumes, implies, infers, and entails...

    Let's pin that down first.
     
  17. Jun 1, 2013 #16
    I read the responses, and just decided to write one big free-flowing response to everyone at once...

    The entire reason anyone knows about Bell in the first place is just that he wanted to blow the lid off of von Neumann's crusade against an independently subsisting reality that is otherwise known as "hidden variables". Bohm was influenced by Einstein in terms of the idea that if the term "physics" is to have any meaning, then it must be referring to the causal mechanisms (ie, universally applicable principles) that determine how nature functions. And Bell was influenced by Bohm.

    The idea that Einstein really gave a hoot about SR-esque localism when it came to fundamental physical theory is just untrue. He cared deeply about the idea of causation. He absolutely despised the idea that a fundamental description of nature is necessarily probabilistic. And I would say that he despised it *not* because of some kind of arbitrary, innate prejudice. It is because statements of the form "X happened because it was probably going to happen" is not any kind of statement at all. It is simply an abuse of how we use the term "because".

    The reason why von Neumann wanted to dispense with discussions about an independent, objective reality in the first place is because its nature cannot possibly be finally verified through necessarily subjective experimentation. But this is precisely the reason why Einstein liked it so much. Einstein was an "imagineer" of the highest caliber. He most certainly had very little interest in experimental confirmation, although he certainly had to pay lipservice to it.

    Never before had physics tried to understand the mechanisms underlying the interface between light and matter. But light, as such, cannot possibly be "seen", and neither can "matter". For whatever reason, objects are presented to our intuition via the faculty of sensation (Kant's terminology). In order to develop foundational theories of light and matter, therefore, we are going to have to descend into a purely theoretical realm.

    But since science had never been purely theoretical (at least, not *modern* science), there was a natural resistance to the turn to pure theory. Given that all possible classical, observation-based theories had pretty much [arguably] already been done, the only thing left to do was to develop a "meta theory" about physics, as such. The new theorists were then tasked to develop a framework in which the irreducible elements of reality are "acts of observation", or "observables". In other words, rather than being a theory about the measures of independently subsisting constituents of nature, QM ultimately became a first order theory about measurement, in itself.

    So, let's think about this. The essential idea of canonical QM is just that there are categories of "observables", that are arranged by groups of "quantum numbers", such as charge and spin. But there is still the inevitable implicit assumption (due to the nature of language itself) that physical theory is about independently subsisting elements of nature. Because of this assumption, the names that we have given to certain classes of observables (electrons, photons, etc) are mistakenly thought by many to be references to elements of nature (ie, physical things).

    But observables are the irreducible elements of QM. There is no possibility of a mechanism to connect observables, if mechanisms are things that theorists invent after they have made their observations. Let me emphasize this point: QM, as we know it, is about the act of observation, and nothing else.

    In lieu of imaginatively devised causal mechanisms, the only way to speak about "why" certain observations are made is to invoke the spectre of probability. Furthermore, the probability for any particular observation can never be 1, because this would imply certainty, which would itself imply the need for some kind of deterministic, causal mechanism.

    Each of the preceding remarks must be fully appreciated before we start speaking about the non-Bohm-like interpretations of QM (assuming that keeping a purely mathematical relationship to the QM formalism is not truly an interpretation.) Anything that speaks not about *this* world, but "many worlds" violates the necessary definition of physics that it is an investigation of a singular, collectively experienced natural order (rather than of some number of imaginary, parallel natural orders). And anything that speaks about effects that precede causes violates how the concept of causation is structurally embedded into our language.

    So, we speak about physics being about the causal connections between things in a single universe *not* because we are making some kind of arbitrary choice based upon "personal taste", but because the very structure of language, as a reliable mechanism for communication, enforces it upon us. And since physics *is* about the causal connections between things, we have to start developing imaginative pictures about what constitutes a "thing", and the principles that govern their interactions in order to start making new headway.

    The ultimate point of the original post is that physical theory can either speak about the locations of things (ie, their centers of mass), or about the forms of things. We already have well-defined theoretical "pictures" of what fundamental elements of reality might look like, and those are the "atomic orbitals" that every Intro to Chemistry texbook shows. But rather than thinking of them, naively, as objects of microscopic proportions, I propose that the only reasonable thing to do is to think of them as being universally defined. This is just to say that the semi-local picture that chemistry students have of atoms is based purely on the idea that atoms can be definitively measured, just like the objects of the other empirical sciences. But they cannot be. Atoms are purely theoretical constructs that are meant to give reasonable models for how the material complexes (eg, gases, crystals, organic chains, etc.) of the higher level chemistry-based sciences form. But there is no a priori reason why they can't also be used as models for how, for instance, things like cosmic-scale gravity fields form. That, in a nutshell, is my whole point here.
     
    Last edited: Jun 1, 2013
  18. Jun 2, 2013 #17

    bhobba

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    Einsteins views of QM changed quite a bit over time. At one time he made comments like God doesn't play dice with the universe but that was not his primary concern during his later years. You can read it in the introduction to Bohm's book on QM - he wrote a well respected standard textbook prior to Bohmian Mechanics and Einstein wrote a forward to it explaining his view. He believed QM was correct - just incomplete. He did not believe in a world created by observation - for him it existed independent of whether it was observed or not - that was his main concern.

    Here is a good paper I found of what Einstein really thought:
    http://www.scientiaestudia.org.br/associac/paty/pdf/Paty,M_1995b-NatEinsObjQM.pdf
    'Later on, he would consider that quantum mechanics is free of inner contradictions but is incomplete. It is in trying to show this incompleteness by physical arguments that he made explicit the non-local character of physical systems as described by quantum mechanics. We notice, in such attempts, that incompleteness, in Einsteins's view, is not merely to be identified a priori with indeterminism and the statistical character of the description. We shall emphasize further that Einstein's motivation was not primarily to restore determinism against probabilistic description, but to point out non-locality as a defect of the formalism which lets us with only a statistical description.'

    I think anyone that has seen pictures of atoms using scanning tunneling microscopes or even being exposed to Brownian motion will likely hold a different view.

    I have a few more comments I could make, but personally I don't, and never have thought, philosophical analysis is the way forward on QM issues. For example in the last few decades decoherence has been much better understood and has has a lot to say on interpretations. IMHO it is fully working out the consequences of this very rich, interesting, and mathematically very beautiful theory (as an aside, and I dont quite know why it is, we don't see a lot of posts about just how mathematically beautiful this theory is eg symmetries determine dynamics - that's really mind blowing when you think about it) theory that is the way forward. There have been some hints that string theory for example may have something to say on fundamental issues in QM - but it really is early stages.

    One thing that I never have been able to get out of my mind is maybe there is a connection at a very deep level between the MWI and Eternal Inflation.

    Thanks
    Bill
     
    Last edited: Jun 2, 2013
  19. Jun 2, 2013 #18
    Was this quote meant to be an example of abuse of language? Clearly the uncommunicable object of the quote is being communicated about in the very quote itself. The abstraction is yet a contradiction.

    The proper form for this type of statement must truly be a blank line (written silence)?
     
  20. Jun 2, 2013 #19

    DevilsAvocado

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    glengarry, it’s always great to think ‘out of the box’, and at the same time it’s sometimes easy to get blinded by your own ‘splendid ideas’. Perhaps I could help you see things that maybe aren’t ‘enlightened’ enough in your reasoning.

    As bhobba points out, Einsteins views changed over time, and it isn’t always easy to sort it all out. Recommended reading (beside bhobba’s):


    Okay, so if I toss a coin for left/right, it’s an “abuse” to say – “We are going to the right because we got heads”...?

    Forget words like ”finally” etc, science is not about the final ultimate truth. That’s for the priests in the Vatican.

    Well, “lipservice”... when Einstein heard of Hubble's discovery, he said that changing his equations was "the biggest blunder of his life"...

    Courtesy of the Archives, California Institute of Technology

    Isn’t this is a bit ‘dramatized’? Are you saying that when Newton in 1717 studied the interference pattern in “Newton's rings” – and came to conclusion that light is composed of particles or corpuscles – this is “classical, observation-based theories”, and when Richard Feynman et.al. formulated QED looking at exactly the same problem – this is a “purely theoretical realm”?

    420px-Newton_rings.jpg

    The funny thing is that QM theory says absolutely nothing about what happens at measurement... interpretations yes, but that’s a completely different story. And besides, not one Nobel Prize in Physics has been given without empirical evidence, not one (ask Stephen Hawking).

    I agree that the “language of QM” is not the peak of precision with words as “system, apparatus, environment, microscopic, macroscopic, reversible, irreversible, observable, information, measurement” etc. and J.S. Bell had a lot of intelligent remarks on this. But how could QM only be about “the act of observation” when it’s not specified in the theory = The Measurement Problem...

    Sure it can, two polarizers set aligned or orthogonal will give probability 1 or 0 every time, guaranteed. Work for QM & Classical.

    I agree the interpretations are not exactly “The Jewel of Physics”... some are just crazy. But at the same time – who says that nature is made to make us happy (about the logic)? I don’t like MWI, but what is “*this* world”? We know we aren’t the center of universe, and we’re restricted to our “observable bubble”, which means there must be other “*this* world” out there that we will never ever get in contact with, right?

    I agree to some extent, with the caveat that it’s not guaranteed that nature is ‘the way we wish for’. It’ could be ‘weird’, and if so – we just have to accept it.

    I don’t agree. If you bombard gold atoms with gazillions of electrons in a modern scanning tunneling microscope, this is the picture you get:

    Atomic_resolution_Au100.JPG

    Is this fake? Is it false?? Of course not, it’s the classical state of the QM world, right there. To me the next ‘paradigm’ in physics might be to exactly find and define (what Bell calls) “the shifty split” – that is, the division between “the quantum part” and “the classical part.

    When we do that, we will get rid of most of the terrible interpretations, and get a much better understanding on what’s really going on... I think...

    Hum... gravity, well that’s TOE... that’s a BIG jump for Bell’s theorem, but who knows, who knows...
     
    Last edited by a moderator: Apr 15, 2017
  21. Jun 2, 2013 #20

    DevilsAvocado

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    Thanks bhobba, very nice.
     
  22. Jun 2, 2013 #21
    I think this is misleading. The issue is not if there are point-like particles or not. The problem remains unchanged if we consider it from point of view of a field theory.

    I think the whole notion "local realism" is misleading in the context of violations of Bell's inequality. The question is not at all if reality consists of things which have a location.

    The issue is the speed of causal influences.

    You can have local causal influences. You make a free decision, and this decision-making process is somewhere localized inside your body. It does not matter at all if your body is an excitation of a continuous field which describes some property of an ether or if it consists of atoms or other elementary particles - all what matters is that your body is localized, and that you are able to make a decision.

    And this decision can have influences on various part of the future. This influence needs some time to influence things far away. So there is a speed of causal influence.

    Relativity assumes that this speed has an upper bound c. If it appears to be 2c, or 100000c, nothing conceptually changes. Your decision is localized in your body, the causal influence is restricted - you cannot influence the past, and can influence only some part of the future, you cannot influence anything out of your reach if the maximal speed is 100000c. These is another value for the maximal speed, but the basic principle remains unchanged.

    But in the modern jargon this is named "nonlocal". Instead of naming it "non-Einstein-causal". So there is no nonlocality in the modern notion of nonlocality.
     
  23. Jun 2, 2013 #22

    he mean "holism"
     
  24. Jun 2, 2013 #23

    bhobba

    Staff: Mentor

    Thanks

    Einsteins actual relation to QM is a very very interesting thing.

    For example did you know Einstein used to keep a copy of Dirac's Foundations of QM beside his bed and when he came across a particularly hard problem would say - Where is My Dirac?

    He understood QM very well. And in his later years believed it true. For example in the preface of Bohm's textbook on QM commended QM's ideas to all physicists as something they must know - the only negative he could muster was he thought physics was going through some sort of intermediate phase and it would eventually be replaced by something deeper.

    The truth is always a bit stranger and more interesting than what popularization's spew forth. They are full of how he fought against it to his dying day, never accepted it etc etc. He never accepted it as the final theory - that's it - that's all. And even today we have highly eminent people like Wienberg and Penrose that agree with him so he is hardly the odd man out cut off from the rest of the scientific community some portray him as.

    My issue with Einstein in his later years is not his views on QM - they were quite reasonable IMHO - but that he let it interfere with making contributions at the frontiers of science. He became obsessed with a TOE rather than participate in the slow but steady progress of mainstream science. But I believe he even commented he had earned the right to do that - which was true but still such a pity.

    Thanks
    Bill
     
  25. Jun 3, 2013 #24
    In this post, I will finally attempt to explicitly answer the question "What is meant by the term universalism?" by way of a theoretical construction of a Bohm-like universe residing in classical spacetime. This thing took me a long time to write, so please do me the honor of giving me your complete attention!

    Most people will tend to have issues with the idea of universalism because it is contains much more philosophical baggage than that of localism. We are dealing with localism every day in every way whenever we speak about particular points in space (places), time (times), or spacetime (events). These points are thoroughly integrated into Newtonian mechanics, through the usage of Cartesian coordinate systems on Euclidean spaces. So we see that the question of the location of a material body is one thing, and is handled by its own ontological framework. But the question of its form is another thing entirely, and requires an ontology of its own. When we are asking of the form of a body, we are interested in the way in which it occupies space.

    The way to begin thinking about this is that a "body" must be represented as some kind of a field, such that all of the values of the field are necessarily related to one another. The idea of "necessary relations" between the values of a field is satisfactorily given by some kind of mathematical function. A function can give us a form like this:

    Code (Text):

    y2-->         _________
                 |         |
                 |         |
    y1-->  ------           ------
           ^                     ^
           |                     |
           x1                    x2
     
    We can see that there is a definite domain (x1->x2) and range (y1->y2) within which the function operates. It just so happens that this function includes sudden jumps between minimum and maximum values. But we tend to think of nature in terms of continuous functions. If the above picture were instead smoothed out, then we could call it a wavefunction.

    The two necessary conditions that must be fulfilled if a wavefunction is to represent a physical body are as follows:

    1) It must have a definite domain. That is, it must be bounded in terms of the magnitude of the field that it occupies. If it were unbounded, then it could not be said to be a body.

    2) It must have a definite range. If the field could contain infinite values, then there is no way the body could possibly relate to any other body in a reliable way. This just means that the laws of physics always break down whenever there are infinite values.

    The way in which we can understand the concept of universalism is just through the idea that all bodies in a given physical reality must necessarily be represented by functions over the very same domain. Furthermore, if this physical reality is to be taken as "natural", then all of these functions must be continuous -- ie, they must be wavefunctions.

    But there is another, more subtle issue at play. If we think of physical bodies as wavefunctions over a singular domain (a "universe"), then in what way can we understand the idea that they have translational degrees of freedom relative to one another?

    To illustrate the urgency of this question, let us think about the simplest case of a one-dimensional universe. All of the wavefunctions in this universe will look like the harmonic standing waves of a vibrating string. But there is no way we can speak of motion, given that the waveforms are essentially "trapped" by the boundaries of the string. A two-dimensional universe is different in that waveforms defined by a circular boundary are capable of rotations about their common center points. But still, there is no possiblity of translational motion! The same problem holds for three-dimensional waveforms that are defined by a single spherical boundary.

    The only solution to the problem of translational motion is to think of the domain as self-connected. That is, the one-dimensional case turns from a linear field into a circular one, the two-dimensional case turns from a disc-like field to a spherical one, and the three-dimensional case turns from a ball-like field to a hyperspherical one. In this way, all of the waveforms can be functions over the very same domain, with the caveat that they will all have their own distinct boundaries.

    We can still define each waveform in its own native, flat "configuration space", but then contort it into shape so that it conforms to the "mold" of the radial universal domain. That is, we must do a kind of reverse map projection of each original waveform, so that its distorted manifestation on the universal domain is the one that is seen by the universe's inhabitants.

    Our picture of the universe now includes arbitrary numbers of waveforms that are capable of relating to each other via translational means. Given that the universal domain now has a self-connected radial form (ie, circle, sphere, or hypersphere), we can speak of the possible translations of each body as consisting of angular displacements. But given a large enough universe, its degree of curvature will be effectively zero at any sufficiently small subset of locations, allowing the inhabitants to instead think in terms of measurements within a flat space.

    It is within this context of waveforms that are defined fully within their own boundaries but are nevertheless residents of the very same circular (or [hyper]spherical) universal domain that the idea of Bohm-style Quantum Mechanics can be given an explicit formulation. It is crucially important to understand that there is no concept of "physical interaction" between waveforms, if we think of such interactions in terms of mutually exclusive objects (like cars or billiard balls) colliding into one another, thereby altering each other's intrinsic properties. Each of the waveforms in the universe instead serves as an immediate context for every other waveform. And given that waves can be trivially added to each other by the superpostion principle, we can think of a composite universal waveform that serves as the complete context that -- given an appropriate universal "law of motion" -- determines how any given single waveform must behave.

    The inability for any previous notion of wave mechanics to gain any traction within the theoretical physics community is simply due to the failure to, in principle, understand physical bodies precisely as functions of an explicit, self-connected universal domain. For, once we see that we must contort each flat waveform into a radial shape in order for it to become an element of a singular physical reality in which translational degrees of freedom become possible, then the idea of localized matter (eg, atoms and subatomic particles) naturally emerges. That is, in the 2- and 3-dimensional cases, the contortion process causes the elemental configuration space to become compressed the closer that we approach the boundary point. In the 2-dimensional case, the single latitudinal dimension eventually gets squeezed into a point. And in the 3-dimensional case, there are two shrinking dimensions. In all cases, we can see that the amplitude of a given wavefunction will decrease roughly linearly as we move toward its fully compressed boundary along a longitude. But in the 3-dimensional case, given that two dimensions are disappearing, its elemental spatial density will actually increase in a squarewise fashion. As a foundational principle, we can assert the following of a three-dimensional universe: since elemental spatial density increases faster than the wavefunction diminishes, the particulate nature of physical reality within universal space is given a precise logical basis.

    Another important aspect of this picture is that the boundary of a wavefunction always represents a node -- that is, its value is by definition guaranteed to always be zero. In terms of field theory, a crucial logical inconsistency has always been the idea that the "source material" of a field is infinitely concentrated at its central location. We therefore get the problem of infinite energy values at this location. But in terms of the wave picture, even though the spatial density is always increasing as we approach the boundary point, the actual amplitude values of a given waveform are still decreasing predictably towards zero. This in fact gives us a very good model of the kind of potential gradient that we see occuring everywhere in nature; namely in the form of gravity fields.

    The fundamental elements of this Bohm-like picture of physical reality are universally defined waveforms. Since the harmonic solutions to the wavefunction can be any of an infinite variety of "shapes" (see http://en.wikipedia.org/wiki/Atomic_orbital) there is no shortage of geometric novelty available to us, when considering the chemistry-based sciences. But since we can also arbitrarily adjust parameters like maximum amplitude and frequency (remembering that we are dealing with dynamically oscillating standing waves), we can thus see that it is totally within our power to determine precisely how particulate vs. spacelike we want these elements to be.

    To the extent that we want to model the objects of QM (atoms, electrons, etc), we can use very feeble and fast oscillators that only practically affect a very limited space around the nodal boundary point. But when the oscillators are powerful and slow (they may have frequencies on the order of billions of years, or more), we can begin to model the objects of GR (the gravity fields of planets, stars, galaxies, superclusters, etc).

    The final result is that while elementary physical bodies are, in their theoretical mathematical description, universally defined, they can indeed have an effective (experimentally determined) size of any extent. They can be practically pointlike or they can serve as bridges across expanses of space that dwarf the dimensions of the observable universe.
     
  26. Jun 4, 2013 #25
    Concerning the distinction between locations of material bodies and their "forms" (wave-functions of finite range and domain within a common field) with respect to translation; can you touch on some clarifying treatment regarding group velocity and phase velocity, just to make clear what it is that is translating?

    Hyper-spherical space is interesting because a rotation in 4D is a hyperbolic radial expansion in 3D which suggests the appearance of an instantaneous non-physical interaction without exchange.
     
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