Harlan,

Thanks for the detailed answers. I also responded to your remarks on my thread, without remembering at the time that you were the same person who wrote this essay.

I see that your definition and treatment of "objective reality" is based on aspects of the history of science that you are more familiar with than I am. I have a reasonably good physics education, but the history is something that tends to be neglected.

Regarding path integrals, I am not sure how general the duality you mention is. I tend to doubt the ultimate relevance of the continuum, as you know from reading my essay. I know how to derive an analogue of the canonical formulation very generally from the sum-over-histories approach, but I am not sure about the converse. Take care,

Ben

Dean, thanks for the kind words!

Before getting started, I want to make sure I clarify that locality is a critical feature of quantum mechanics. On the face of it the choice expressed by Coleman of classical mechanics or non locality is directed at those who talk about quantum mechanics being non local in order to highlight that they are thinking about the problem wrong. It points out that that no form of classical theory could be correct, quantum mechanics, with space filling component wave functions, uses local operations to produce observations. It is therefor fundamentally different. What makes it possible to *think* of it in terms of local *objects* is that the fundamental space filling waves have a dual representation as oscillators moving in time in some abstract space. Collection of oscillators define discrete particles that we represent in spacetime.

What is interesting, in Boltzmann's paper "Reply to a Lecture On Happiness Given by Professer Ostwald" Boltzmann expresses admiration for Mach even while admitting differences. He also gives Mach's view of the world:

"Mach pointed out that we are given only the law-like course of our impressions and ideas, whereas all physical magnitudes, atoms, molecules, forces, energies and so on are mere concepts for the economical representation and illustration of these law-like relations of our impressions and ideas. These last are thus the only thing that exists in the first instance, physical concepts being merely mental additions of our own."

Two things are interesting here.

1) Referencing Einstein's meeting with Mach in my response to Ben Dribus above, Mach never actually moved from his position. Einstein and others may have interpretted it that way when he said atomism was economical, but he never wavered (this view is also reinforced by ref [1] in the paper)

2) We have evidence of the thought process that what we consider as objective reality in Boltzmann's view is an emergent phenomena. Referencing the response to Ben Dribus again, if we start with objective reality everything that defines ourselves does not emerge. Classical mechanics completely fails.

So its not so much of an all or nothing choice between classical mechanics or non locality, it really is a nothing or everything choice between classical mechanics or quantum reality.

Hal

I would agree with your start point that we have to dispense with the notion that the 'basic constituent is a billiard ball', but...

In attempting to identify what constitutes the 'bottom line' of physical reality, think on this. If one asserts that the elementary state is 'something' (be it different types and/or like a 'billiard ball' or whatever), then the question becomes: what constitutes physical reality as at any given point in time? Because that 'something' alters in its physical state (which might be manifest as spin, or some other changing attribute). Similarly, in respect of the notion of 'wave', the question is what physically constitutes this, and then the same conundrum applies? And furthermore, whatever exists (ie is fundamental), definitely does so. There is no form of 'vagueness' about it, physical existence cannot occur that way.

So the elementary physical state which constitutes physical reality cannot be the 'things' of themselves. It must relate to the physical state of the properties of the elementary 'things'. The principle here being, as Joe says above, there can only be one physically existent state in any given sequence at a time.

Apologies for the non-technical language.

Paul

    Hi Paul!

    Thanks for the comment!

    This gets into a very interesting discussion on what we mean by wave function. Definitions are sometimes fluid, which is why the particular definition of objective realism appeared in the essay. When we cross into physics we need something that can translate into definite concepts. What is interesting about the wave function is that in the traditional Copenhagen Interpretation, the wave function is understood to be the "state of knowledge" an observer has of the larger system. In quantum mechanics, states can be combined linearly, and any state can be decomposed into component basis states. This is understood as the principle of superposition.

    I don't want to be ambiguous, I agree that at any instant there is only one observed state that an observer can be in, and there is only one state that has any *emergent* property that one would normally associate with what we see. In other words, I do not subscribe to the Many World Interpretation (MWI) that has become the favorite in popular shows on physics. However, a proper understanding of the theory tells us that any state can be decomposed into component basis states. This is general understood in terms of Fourier expansion of a given wave function.

    Hal

    "This gets into a very interesting discussion on what we mean by wave function". Indeed it does, a question I have asked several times in the past year. But that is just a sub-set of a wider question, which is: whenever any concept is referred to, what is the corresponding physical reality?

    "the wave function is understood to be the "state of knowledge" an observer has of the larger system". If this is so, then it is incorrect. What existed (ie was physical reality) as at any given point in time, did so. It also did so in a definite state. Physical existence does not occur with some form of indefiniteness. Any form of knowledge of that physically existent state is seperate, and probably inaccuate/incomplete for a whole range of practical reasons.

    "any state can be decomposed into component basis states. This is understood as the principle of superposition". If a 'state' can be decomposed, then it is not a physically existent state, but a combination thereof. If anything is deemed to be physically existent, then it can only be in one physical form. That is, if alteration is involved then, by definition, what is being described involves more than one physically existent state. One needs to differentiate what occurs until one identifies what existed as at a point in time. Which is easy to say, but probably impossible to achieve.

    "I agree that at any instant there is only one observed state that an observer can be in". It is not a case of the observer. It is a function of how physical reality occurs. Indeed, any form of sensing (observation being the most prominent) involves the receipt of physically existent phenomena which exist as a result of an interaction with what existed. Though I agree with your subsequent position.

    Paul

    Thanks for your insight Paul!

    If we first agree on the definition of concept I think we can get through some of these points. From wikipedia for concept:

    "A concept is a general idea, or something conceived in the mind"

    So I interpret your first question as: Whenever anything is conceived in the mind, what is the corresponding physical reality? This is very similar to questions Einstein was trying to address in his paper, and this is where the first mistake is made. Einstein asserts the following:

    "Any serious consideration of a physical theory must take into account the distinction between the objective reality, which is independent of any theory, and the physical concepts with which the theory operates. These concepts are intended to correspond with the objective reality, and by means of these concepts we picture this reality to ourselves."

    Here we see the formation of a logical fallacy. It happens when there is an assertion of there being an objective reality. Once this premise is accepted then one begins to fall down the slippery slope. However, lets take a look at the rest of this statement. Using our definition of concepts, Einstein is saying that the theory is working with an idea conceived in the mind. So he is saying that elements of the mind are to correspond to objective reality. However, the premise of there being an objective reality is something that Einstein asserts as existing, whereas it can only be understood by humans as a concept that is another idea of the mind. So Einstein is really saying that ideas of the mind should correspond to ideas of the mind, which is obviously tautological.

    So the measure of completeness is then whether a theory can accurately capture all the ideas of the mind. Ultimately the analysis boils down to whether quantum mechanics can capture the ideas of the mind, and also whether hidden variables can capture ideas do mind. As stated before, the wave function was designed to represent a "state of knowledge" so any concept and idea in principle could be a component of the wave function. Hidden variables on the other hand is limited only to inanimate objects and the properties thereof. It should be intuitive to see that whether I am thinking red or blue has no meaning in classical physics, but can in fact be represented as two separate states in quantum mechanics. In fact that is exactly the point made when we say that Dirac's kets can have arbitrary labels.

    Getting to your other points, I think the best way to address these is to go directly to Dirac's The Principles of Quantum Mechanics 4th ed page 12. To paraphrase, Dirac discussion superpositions of states, and how whenever a system is definitely in one state it should also be considered as partly in two or more other states. The original state must be considered as a result of the superposition of other states which is foreign to classical mechanics. Quoting Dirac directly:

    "Any state may be considered as the result of a superposition of two or more other states, and indeed in an infinite number of ways"

    To summarize, the question of "whenever any concept is referred to, what is the corresponding physical reality?" is that any concept that can be conceived inside the mind can be represented as a state in quantum mechanics, physical reality is a concept of the mind, and can also be represented as a state in quantum mechanics. So essentially the theory does offer a complete description of "reality". Its the question then that is tautological.

    Hal

    "Whenever anything is conceived in the mind, what is the corresponding physical reality?"

    Yes(ish). My word 'concept' did not have any specific meaning, it was just a mechanism to refer to anything. For any representational device, whether it be words, graphics or maths, which purports to define physical reality, there must be corresponding physical existence. Now, we (and all sentient organisms) are aware of reality (of which we are a part) through the evolution of sensory detection systems (ie sight, hearing, etc). This is a closed system, ie no organism can transcend its own existence, but physical existence is independent of it. So we have an objective basis (assuming we eradicate any 'interference' that occurs in the processing of received physical phenomena!-but this is physics not psychology or sociology). The main problem with this is that for a number of known practical reasons we cannot always effect direct experience. So hypothesis is necessary (ie indirect experience), but that should be based on direct experience. The danger is that one can 'drift' too far with combinations of hypotheses, or, say, the development of a mathematical model which takes on a 'life of its own', ie is driven by the intrinsic logic of the system, rather than extrinsic validity. And since these are references to phenomena which cannot be directly experienced, disproof becomes problematic.

    "It happens when there is an assertion of there being an objective reality"

    As above, this is not the problem, as such. Because there is an objective reality. Or at least to be precise, within the confines of our existence, there is one. And since anything else is only a logical possibility and we can never know it anyway, it is irrelevant. Scientifically, we must confine ourselves to explaining what is manifest to us (which includes that which would appear to exist but for demonstrable practical reasons we cannot directly experience). The problem is when hypotheses become 'self-fulfilling', ie they incorporate assertions as to what constitutes reality, and then create a depiction which has no extrinsic validity, although intrinsically the hypothesis 'works'. Validity/completeness/whatever is subservient to validated experience (or proven potential thereof), not, inherently, correctness of the model in itself.

    Another important point here is what we, or any sentient organism thinks, etc, is irrelevant. Physical reality occurs independently of this. The problem is we only have individual perceptions as a start point from which to ultimately infer what physically existed.

    I found a copy of the Dirac pages you refer to. He attributes a state, which can be measured in all aspects as at any given point in time, to a presumption of classical mechanics. Whereas it is a function of the nature of physical reality. By definition, to physically exist, whatever is existing can only be in one physically existent state at a time. Otherwise 'it' cannot exist, neither can there be alteration (apart from asking, 'what was 'it', one then asks 'what changed to what'). And physical existence must involve definiteness, the question being what constitutes a state of physical existence, not whether it involves some attribute which is contrary to the very essence of existence. Whether or not we can measure/observe it is irrelevant. Our deficiencies do not affect physical reality. After all, sensory detection evolved to give sentient organisms, as against rocks, an advantage in terms of survival, not a system which is capable of decomposing reality in its entirety. Furthermore, it is irrelevant what physical phenomena one is referring to, ie the same principles still apply. Because any phenomena deemed to have physical existence must conform to the principles of a physical sequence.

    The essential point here is that one should start with what is known about physical reality, hence what that implies about how it occurs, and then establish what is occurring, given those generic rules. Not make observations, which are bound to involve deficiencies, and then try and make sense of them.

    Paul

    Hal,

    Thank you for the clarification. If I understand clearly (and I am slightly sleep deprived, so confusion is eminently still possible), then 'classical mechanics' and 'objective reality' based on the viewpoint of a human observer both fail and that what we experience are emergent phenomena arising from local operations (what I might call inter-actions) on oscillators that do not have a grit-like particle existence, but are wavefunctions spread out in space and have an existence in an abstract space (Hilbert space).

    I still find myself falling down conceptual rabbit holes if I'm not careful!

    The abstract space seems so important and 'real' in its own right to me. I may wrongly have come to conceptualize/visualize this abstract space as largely not space-like at all, except in the narrow realm of it participating in local operations. I know people sometimes say "you can't visualize quantum mechanics," but I have found it incredibly useful to try!

    Though thoroughly 'entangled' and un-billiard ball like as a whole, it seems unwise to minimalize the importance of the abstract space just because we have experimental methods and 'normalization' that, as Penrose says, 'can largely safely ignore' most of the more bothersome random, entangled or superposed aspects, at least in cases which can be handled in a largely linear, statistical or highly local fashion. Don't get me wrong ... I am in awe of how high-functioning quantum mechanics is, and what *can* be handled by it is anything but *simple*, but I am bothered by the mystical thinking around the edges!

    As you may be able to tell, the main focus of my somewhat haphazard studies has been on constructing a coherent and consistent conceptual model that embraces the -- for lack of better phrases -- non-local or entangled aspects of wavefunctions in a way that conveys the entangled-ket nature of quantum theory without destroying causality or the possiblity of an emergent 'reality'. I wrote my essay in the hopes that I'm either closer to a workable 'functional myth', or someone can show me the error of my ways more quickly than I usually can do on my own!

    In any case, I hope I haven't made an even bigger mess of your ideas. I appreciate your careful clarification and I should probably sleep before I make a real mess of things!

    Dean

      Paul,

      Thanks again for your insights!

      I think I didn't make myself plain enough. Remember, the issue here is that Einstein asserted the existence of an objective reality, which is an assertion he makes without any proof. The point is that once one recognizes that one can ultimately only view objective reality as a derived concept within the mind. In your response you reassert that there is an objective reality.

      "Because there is an objective reality."

      Again this is an assertion, or an assumption. The key point in the Bell experiments and GHZ is that there is no way this assumption could be valid. One must accept either quantum mechanics or non-locality, and since accepting non-locality contradicts the evidence of relativity in classical theories, then one is forced to accept quantum mechanics, and the assumption of objective reality is no longer valid, so it can not be asserted as fact.

      This debate is old, one could make certain statements that it dates back several thousands of years in various forms. People who are absorbed into metaphysics and philosophy might see the argument in light of body versus soul, or the material world vs. the spiritual world, but such discussions and comparisons are not particularly helpful.

      However, if one looks at dialogues with Einstein one sees these conversation in the context of his discussion about god not playing dice with the universe (see page 58 of Einstein and the Poet: In Search of the Cosmic Man By William Hermanns, Albert Einstein.

      http://books.google.com/books?id=QXCyjj6T5ZUC&lpg=PP1&pg=PA58#v=onepage&q&f=false

      Here ome gets that proper sense that Einstein again was arguing about the independence of the objective world. In his mind the objective world was god, this explains his philosophical view that he did not believe in a personal god. His point was that he felt observers were merely looking at some larger corporeal object whose actions were completely independent. This is what is being challenged in quantum mechanics. Observers in quantum mechanics play a key role, they can not be left out of the picture. This does not necessarily mean that observers need to be particularly advanced creatures, or creatures at all, only that we can not ultimately separate them from the surrounding environment without changing the environment.

      Hopefully that helps you on your thoughts about this problem, thanks again for the post!

      Hi Dean, thanks!

      I think the definitions of reality is fine by itself, if we pull up wikipedia for reality, the way the way its described is:

      "reality is the state of things as they actually exist, rather than as they may appear or might be imagined"

      The key point is the issue of what we call objective. There are different definitions for the word objective and some of those are not incompatible with quantum physics in any way. The key one though is how the words "objective reality" relates to physics and its alignment with classical approaches to theory.

      What most people associate with "reality" in the physical sense are actually collections of observations. The assumption people make is that observations are associate with classical objects (in the sense of Boltzmann's particles) that have independent existence and that theory a complicated interaction, certain other relationships emerge. So that ultimately, everything can be reduced to pure interactions driven by forces between the inanimate classical objects (billiard balls). This is also the approach of classical computer theory and the associated mathematics. In essence, the idea is that the observations are the result of mixing of properties associated with an independent "thing".

      Where quantum theory diverges first is that it is a theory of observations, it really isn't a theory about classical particles. Although certain types of observations can be grouped in such way we can characterize them as being associated with different types of particles, what the theory is trying to predict is the possible outcome of an observation.

      One of the current divergences occurring in the physics community hits directly on this question about whether the wave function is real in the sense that it is classical object itself, spread out in space. This the type of concept that led to pilot wave theory (http://en.wikipedia.org/wiki/Pilot_wave). Pilot wave theory is another sort of hidden variables theory that has been shown to be incompatible with the outcomes of Bell's experiments and GHZ.

      What this means is that one way we can really think about the problem is that there are observations that can be made that can be grouped in such a way that they can be associated with some more fundamental entities. That we still call them particles is a matter of convenience, but ultimately what we are interested in the outcomes of observations. The wave function controls the evolution of the possible outcomes and it can be viewed as no more real than the idea that there is some function that tells us the possible outcomes of throwing a pair of dice, or what cards might come up in a game of poker. Certainly no one would argue that the relationships that control the outcomes of a poker game are "objectively real" even if they accept the definition of reality as provided by wikipedia.

      Hal

      But it is not an assertion. Leaving aside beliefs, which science is not concerned with, what is manifest to us (and all organisms), via the sensory systems, physically exists. There is 'something there' (which includes us). And it occurs independently of the sensory systems which enable sentient organisms to be aware of it, because the physically existent results (eg light, noise, etc) of physical interactions with it, are physically received by these sensory systems. That is, the subsequent processing into meaningful perceptions cannot alter physical existence, ie there is an objective physical reality.

      So, for the science of physics, we have two knowns: a) there is an independent physical existence, b) there is alteration. Which means that it is sequence, etc, etc, etc.

      It is not a case of: "one can ultimately only view objective reality as a derived concept within the mind". Individual perceptions are just the only available start point, they are not reality. But, by understanding the physical processes involved, it is then possible to reverse-engineer them, and eradicate individualism, thereby establishing what originally occurred (existed). Remember, not only do individuals 'interfere' with what is received when creating their perceptions, they do not receive the reality under consideration anyway, but the results of interaction with it. And furthermore, what they do receive may not be a complete and/or accurate representation of that reality for a number of practical reasons.

      "The key point in the Bell experiments and GHZ is that there is no way this assumption could be valid". As with Julian Barbour, who referred to some theory, the point here is: which comes first? And the answer is, the way in which physical reality must occur in order to correspond with what we directly experience and know. This is rather like ignoring the known physical qualities of wood, and asserting they are something else, then turning up at a woodworking class with a hairbrush and nail clippers and expecting to get results. The inherent nature of what is being investigated takes precedence over models purporting to represent it. And if those models contradict fundamental characteristics of physical reality, then they are, in effect, belief systems.

      For example, if a theory involves the presumption that 'observers play a key role', then it has a problem, because any form of sensing cannot affect what existed. Since a) the senses do not receive reality, b) reality occurred before the senses received what they did receive, c) reality cannot exist in some form of 'incomplete' physical state, neither can it be in more than one such state at a time, otherwise physical existence would not occur.

      Paul

      Paul,

      Thanks again, but unfortunately you are still wrong on this matter

      "So, for the science of physics, we have two knowns: a) there is an independent physical existence, b) there is alteration. Which means that it is sequence, etc, etc, etc"

      On the second point of alteration, one might actually call it recursion, and I have no real difficulties with this point if its in the proper context. However, still with the first point, independent physical existence is purely an assumption, and now virtually a certainty that its not a valid one.

      You really should read the book Einstein and the Poet, it really does get into the discussion and the mindset of Einstein on this topic. Did you know that he was a very religious person?!

      There is a great quote on page 90:

      "I think I am a religious man," said Einstein, "and no one will convince me that the world can survive with Jewish-Christian ethics."

      Kind of interesting isn't it?

      On page 94:

      "Religion and science go together," said Einstein. "As I've said before, science without religion is lame and religion without science is blind. They are interdependent and have a common goal - the search for truth. Hence it is absurd for religion to proscribe Galileo or Darwin or other scientists." Einstein grinned, "And it is equally absurd when scientists say that there is no God. The real scientist has faith, which does not mean," he looked at the minister, "that he must subscribe to a creed. Without religion there is no charity. The soul given to each of us is moved by the same living spirit that moves the universe."

      However, Einstein is clear about one additional fact, on page 108:

      "Do I have to repeat that I don't believe in a personal God who rewards and punishes His creatures? He did not create cosmic laws in order to override them when man asked Him to do so."

      and on page 72:

      "The world consists of real objects, and there are consistent laws underlying them. If we want to honor God, then let us use our reason and intellect to grasp these laws, which form the basis of a perfect mechanism."

      This last point is important because it is exactly this point that is proven wrong. If although there may be consistent laws (quantum theory), the world does not consist of real objects (classical mechanics). It is absolutely fundamental to understand this point.

      The problem Einstein had in finding unification is that he couldn't see past this point. For him it was a moral imperative that the world consist of objects, and this was a bias that was introduced by hardships associated with the events leading up to the holocaust, an event where Einstein states on page 96:

      "I lost most of my family."

      So we can begin to see that Einstein's refusal to accept quantum mechanics was likely influenced by horrible personal tragedy.

      What is more interesting, is that even Einstein ultimately relents and says that objective reality is a mere assumption. On page 143 we see Einstein a young physicist who is depressed about life:

      "Pat pointed to a tree. 'Can I truthfully say that that is a tree and, if so, what it means?'

      'This could all be a dream,' replied Einstein, matter-of-factly. 'You may not be seeing it at all. But you have to assume something. Be proud of being the mean between macrocosm and microcosm. Stand still and marvel. Try not to become a many of success, but a man of value. Look around at how people want to get more out of life than they put in. A man of value will give more than he receives. Be creative, but make sure that what you create is not a curse for mankind.'"

      Here we have from the man himself that there is a contradiction in his insistence of the material world. This is further reinforced on page 108:

      "Dear Reverend, it is not a religion that teaches that man is made in the image of God - that is anthropomorphic. Man has infinite dimensions and finds God in his conscience."

      So if the objective world represents Einstein's God, has not Einstein just refuted this position?

      Again, there is no basis other than personal assertion that there is an objective reality. Experimentation has even validated this point, and the lead proponent of the objective world has even capitulated.

      apologies...

      "I think I am a religious man," said Einstein, "and no one will convince me that the world can survive with Jewish-Christian ethics."

      should be: (verified)

      "I think I am a religious man," said Einstein, "and no one will convince me that the world can survive without Jewish-Christian ethics."

      Hal

      "with the first point, independent physical existence is purely an assumption"

      I suggest you do not test this assertion by standing below an avalanche! Noise, light, vibration, etc, are received by sentient organisms, ie they are not created by them. And noise, etc, are physically existent. Furthermore, they are the physical results of an interaction with other physical phenomena. Beyond that, we cannot know, because we cannot transcend our existence. Or put the other way around, one can assert anything, and it cannot be disproved, which is not science. The point is that we can only know of physical existence via the sensory systems and subsequent processing thereof, but this is not creating reality, it is enabling awareness of it. If something is there, it is there, irrespective of whether any sentient organism is aware of it, or indeed what meanings are attributed to the physical input received from it.

      "On the second point of alteration, one might actually call it recursion"

      There is never any form of 'repeat'. Even if the exactly the same physically existent state occurred again, it is different, because it occurred at a different point in time, at a different point in the sequence order.

      On the subject of religion (or indeed any form of belief/assertion), I will say this. Our physical existence invokes the logical possibility of 'something else' (ie if A there is the logical possibility of 'not-A'). It is always only a logical possibility; by definition it cannot be known, because it is not part of the existence available. So, objectively, there is a logical possibility of anything anybody wants to assert. But that is it. Unless there is some experience based evidence, or at least a demonstrable possibility thereof based on experience, one can go no further with that assertion, from the objective perspective.

      Paul

      Paul,

      Thanks again!

      "I suggest you do not test this assertion by standing below an avalanche!"

      No need to worry, these probabilities of events are relatively easy to calculate, of course if we accept physical reality and classical determinism, there is little I could do if the universe had plans for me to be under the avalanche.

      Since I reject objective reality and can compute the probability of interaction relatively easy (which is a problem significantly decreased because of decoherence), then it is relatively easy to assure that I can avoid such avalanche...first of all by not doing silly things in snow covered mountainous areas.

      Again, I want to revisit a point I made earlier, the world we call objective is an emergent entity. You have to understand information theory in order to get this point.

      Quantum mutual information (http://en.wikipedia.org/wiki/Quantum_mutual_information) is defined as:

      [math]I(\rho^{ab}) = S(\rho^{a}) S(\rho^{b}) - S(\rho^{ab})[/math]

      which in terms of relative entropy is:

      [math]I(\rho^{ab}) = S(\rho^{ab}|| \rho^{a} \otimes \rho^{b})[/math]

      As the article states:

      "if we assume the two variables x and y to be uncorrelated, mutual information is the discrepancy in uncertainty resulting from this (possibly erroneous) assumption."

      It is easy to assume that when we are talking about classical variables, such as position and momentum, uncertainty does not scale with the number of systems, so as more and more systems are added, mutual information increases, so the uncertainty in larger systems decreases and the system becomes more classical...e.g. the classical world emerges as we scale up with more systems.

      I might even be tempted to declare it a law, but that would be an easy way out.

      In any case, this is sufficient to begin discussions about how the objective world of Einstein is a world dependent all the component density matrices, and the world as we know it is an emergent property in the limit of vanishing uncertainty.

      This is also best explained by understanding the relationship of Wigner's function and the Moyal equation to Liouville's equation (http://en.wikipedia.org/wiki/Density_matrix#.22Quantum_Liouville.22.2C_Moyal.27s_equation)

      As mutual information increases with the number of systems, the uncertainty decreases, this would appear as a decrease of the uncertainty (represented with h) in the equivalent classical phase space. So the classical world eventually starts to emerge in the limit of large systems. However, a priori it does not exist.

      Thanks Ben,

      No doubt that I tend to place a high value on the human component of physics, which leads one to want to understand physics in with its historical aspects. Einstein believed there are simple equations that can describe all of what we see in the physical world, and we have certain theories that are sufficiently abstract that show there are consistent ways to connect all of physics. The problem still comes down to one of arbitrary variables, which I believe is a result of the interplay between our concepts of discrete and continuous numbers and the nature of conservative systems.

      Dualities play an important role because the lead to comparative connections. I will think on your points on generality though, thanks.

      Harlan

      One last comment on the alteration and recursion thing. I would agree that there are circumstances were one is not the other, especially depending on defintions, so I was perhaps hasty in my thoughts on this.

      I would however argue that recursion can be a very broad concept and frequently misused because of people's narrow understanding of the idea. Recursion is fundamental to our conceptualization of QFT in the sense that we are looking at the evolution of states from one plane at infinity to another. Alteration could be interpreted as perturbation, and the interaction Hamiltonian is a perturbation of the non interaction Hamiltonian. Since most of the problems in QFT are associated with the interaction hamiltonian, and its components are associated with this notion of evolution from infinity to infinity, one can understand the relationship with recursion and the obvious self mapping.

      Hal

      The point is not about what recursion or any other concept means, or what theories assert, it is about what must be the fundamental nature of physical reality. The trick is to recognise that the very nature of physical existence means that only one physically existent state can occur at a time, and it must be definitive (physical existence cannot involve some form of lack of definition, that is in our inability to identify it). Then another occurs, which when compared manifests differences, ie there has been alteration. There is no future, only that which occurs next in the sequence as a function of what occurred immediately previously. There is no past, because what immediately previously existed must cease so that the successor can exist. The present (ie what exists as at any given point in time) is like the still frame in a film. It is the ultimate physical state where no alteration occurs, because if there is change, then by definition, there must be more than one physically existent state, ie it can be further differentiated.

      Now, having established that, and the logical consequences, then, and only then, does one consider theories about physical reality. Not the other way around. The innate nature of physical reality determines how, and on what basis, a theory of it can be properly constructed.

      Paul