To the extent I have anything resembling a reputation here, it is associated with longwinded, overly convoluted posts and threads. This is not without reason. However, recently I was informed that an email address I had would no longer be available to me and I should save whatever emails I wished to keep. So I skimmed through my email conversations to determine if anything was worth saving, and happened upon a conversation with a post-doc in neuroscience asking about the relevance of a particular topic in physics to consciousness.
Initially, I thought it might be good to reformulate my responses into a single, simplified version as they addressed issues that I and others have discussed here more times than I care to remember. But then I said to myself "Self, why not use these exchanges to make yourself look better?" Of course, I responded "How might I do that" to which I was informed "Self, everybody who has bothered to read your posts considers you a long-winded fool. Use this as an example to show how much your posts are actually excellent explanations and simplifications compared to what you are used to writing and what you write most of the time!" I, of course, being more reasonable than myself, thought to myself "but why on earth would anybody bother to read such an example, and even if they did, what would they learn?"
In reply, I was beaten continuously for some time, and then told "Self, who cares? The point is to demonstrate how much worse you could be than that you are. God's bodykins, man! You've written yourself into this corner, do SOMETHING to justify your pathetic compositions!"
Usually, I refuse to listen to myself, exactly for this reason. But this time, I decided it was easier to do this than try to re-write several responses to make them relevant, self-contained, and obviously just as boring and pointless as this thread. So here goes:
"You mentioned, if only in passing, the formalisms of physics in your latest contribution as well as in your first. For many reasons, I think that the issue of how we formally represent the properties, dynamics, states, etc., of physical systems merits a more focal treatment and one superior to any I have hitherto provided. The importance is not limited to the obvious matters, but also more nuanced, subtle considerations. The first is how much we much we take for granted simply because we are so accustomed to representing “real” things, from price to protons, using formal (symbolic) languages. Even in a majority of historical accounts of mathematics one is likely to find modern notation that did not exist during the period in question. Those like Leibniz were in a perfect position to appreciate how much the possession of formal apparati facilitated the development of the sciences, let alone mathematics. As a simple example, one has only to look to Greek mathematicians like Euclid who had to depend upon awkward use of grammatical constructions (e.g., verbs regularly used irregularly including common verbs, a technical vocabulary that was technical only in context, the uncommon 3rd person imperative, and the use of the same verb but differing in tense/aspect to distinguish the statement of a proposition/theorem vs. declaration of proof). It required a fair amount of ingenuity to for the Greeks (among others) to use normal language for relatively simple mathematics, and without symbolic notation much of modern mathematics could never develop. Furthermore, long after such notation existed lacked uniformity in use and the systematic nature of a rich formal language, ensuring that even great minds struggled with symbols that they could not relate to sensory-perceptual experience (such as complex numbers, most of algebra, foundational concepts of analysis like limits, etc.). Leibniz and his contemporaries were used to symbolic notation but still lacked, for the most part, formal systems/languages. Today, 12-year-olds around the world are as likely to ask what “3” or “+” REALLY means as they are to ask what a preposition does, but the lack of widespread formal systems made difficult such ready acceptance of symbols lacking concrete relations to real-world experience.
This has at least two relevant consequences for us. The first is how an early exposure to years of mathematics with little apparent application, not to mention the very the notion of “applied math”, has so thoroughly indoctrinated us that we are inclined to think of mathematical notations as meaningless symbols that acquire some abstract meaning through use. After years of using functions, manipulating algebraic expressions, the use of math to represent the properties, states, etc., of physical systems is just a more relatable use of mathematical representation. The second is how we approach modelling. Whereas for over millennia mathematicians struggled to express abstract operations, we have computers: physical ‘models’ of an abstract algebra. Few mathematical symbols in physics unique to physics, and for e.g, the Dirac notation the uniqueness is in form only; the richer, more powerful language of linear/matrix algebra could replace it entirely. For Leibniz, how mathematics related to physics (and both of these to metaphysics) was of vital import: “to miscast his mathematics…is to misunderstand Leibniz, for in fact his "philosophical system" is positively awash in the consequences of an interplay between mathematics and metaphysics that occurs at the very center of his thought and produces several of its most defining features" (Levey, S. (1998). "Leibniz on mathematics and the actually infinite division of matter." The Philosophical Review). While this was not exactly unique, only Leibniz went so far as to attempt formalizing language with his “algebra of concepts” (formally equivalent to Boole’s algebraic set theory) and proto-predicate calculus. At the heart of all of this discussion of mathematics, formalism, representation, and so on, is one issue that remains at the heart of the sciences but is nowhere more vital than the application of quantum physics to models of consciousness and theories of the mind.
To illustrate more concretely, let us examine phonons. That they are “real” in some sense is not in doubt. The question for our purposes is whether they are real the way that e.g., speed and velocity are, or the way liquids are (a grossly simplified ontological distinction, I know). Simply put, phonons are siblings of photons. One finds them discussed and used mostly in condensed matter physics represented using the algebraic structure of lattices, as crystalline structures are everywhere in solid state physics and lattices are ideal mathematical representations of these. You quite rightly compare phonons to electrons, but I think you weaken the analogy by referring to “mass-bearing modes like electron orbitals”. First, phonons are quintessentially “mass-bearing” (if I understand your meaning). They are “units” of motion caused by sound waves. They are basically matter waves that propagate through a crystalline structure causing the “wave-like” (non-local) lattice vibration. More importantly, the representation of photons in QFT can be equivalent to the mathematical representation phononic excitation (i.e., a quantum harmonic oscillator), and like photons it is often necessary to treat phonons as “particle-like” by using the superposition principle (for e.g., thermodynamic excitation rather than acoustic). Second, in a field theory phonons are not “like” electron orbitals at all, but like any EM quanta: “We now throw away the mechanical props and embrace the unadorned quantum field theory! We do not ask what is waving, we simply postulate a field—such as φ—and quantize it. Its quanta of excitation are what we call particles—for example, photons in the electromagnetic case.” (Aitchison & Hey (2003). Gauge Theories in Particle Physics (Vol. I). IOP Publishing).
In other words, phonons are “wave packets” that, quantum mechanically, are as “real” as electrons, photons, magnons, plasmons, etc., and not particularly interesting (outside of nanotechnology, solid state or condensed matter physics, and similar more applied physics). It is also important to note that the number of phonons is both different from phonon types and almost unrelated to the uncertainty principle. However, you have mainly pointed to Goldstone modes, which are interesting for a few reasons. In condensed matter physics such “massless modes” are called “soft modes”. Here again the issue of mathematical representation arises. Representing crystalline dynamics using lattices is intuitive as the mathematical structure is easily related to the physical. The conceptual leap is barely a step. Not all algebras have so intuitive a structure as those found in graph theory or ready analogues as does a lattice (and those that do are not limited to intuitive or relatable structures). Worse still, the language of modern physics is misleading here. There are exceptions, however, my favorite describing the dynamics of a Goldstone mode as a gauge boson fattened by eating a ghost. The reason for the description is the mathematical solution to the mathematical impetus for such an entity existing in a complex coset space to begin with. But before I get to that I’d like to give an example of what I mean by “misleading” language: “In principle it is indeed possible, though technically not so advantageous, to construct a quantum mechanical description of a spontaneously broken symmetry using a symmetric ground state. SSB [spontaneous symmetry breaking] is then manifested by long range correlations rather than nonzero vacuum expectation values” (Brauner, T. (2010). "Spontaneous symmetry breaking and Nambu–Goldstone bosons in quantum many-body systems." Symmetry.).
The “long range correlations” are characteristic of the kind of collective, unitary Goldstone mode you have referred to, but how do they suddenly “exist” if one is “to construct a quantum mechanical description” of SSB? For that matter, how is it “gauged away” (locally or globally) as the “ghost” the fattened gauge field “swallows”? First, note that even were we using some algebraic structure with clear physical analogues to describe Goldstone modes that are “global” we lose any intuitive pictures simply by virtue of the dimensions necessary. Goldstone modes cannot be produced (mathematically or otherwise) except in higher dimensions. As we live in a 3+1 dimensional world, we cannot possibly “observe” a boson that exists in n-dimensional space where n > 3.
Second, it is important to realize that Goldstone modes of the “unitary, collective”-type you describe are not just produced mathematically but exist as mathematical problems in a field theory: “Anomalies are of two types, anomalous global symmetries and anomalous gauge symmetries. In the case of anomalous global symmetries, the symmetry is not realized in the quantum theory…Quantum theoretically, since there is no symmetry, there is no Goldstone boson. In fact the quantum corrections generate a mass for the potential Goldstone boson.
Anomalies for a gauge symmetry can lead to unphysical results….Thus in a consistent physical theory there should be no anomaly for the gauge symmetries”
(Nair, V. P. (2005). Quantum field theory: A modern perspective. (Graduate Texts in Contemporary Physics). Springer.
Third, they are “fixed” mathematically as well: “a question may arise as to why people obtained the massless [Goldstone] boson in the [Nambu and Jona-Lasinio model] model. Not only Nambu and Jona-Lasinio but also quite a few physicists found a massless boson in their boson mass calculation. Surprisingly, the reason why they found a massless boson is simple. They calculated the boson mass by summing up one loop Feynman diagrams, but their calculation is based on the perturbative vacuum state. However, after the spontaneous symmetry breaking, one finds the new vacuum which has the lower energy than the perturbative vacuum state. Therefore, the physical vacuum state is of course the new vacuum that breaks the chiral symmetry, and thus if one wishes to calculate any physical observables in field theory, then one must employ the formulation which is based on the physical vacuum state” (Fujita, Hiramoto, & Takahashi (2009). Bosons after Symmetry Breaking in Quantum Field Theory. Nova Science.)
There are several important points here. One is why a physical theory is made better by the existence of something “unphysical” (note that unphysical does not mean massless). Another is why one should be able to, let alone wish to, “calculate…observables in field theory.” We “observe”, whether through some sophisticated measurements or by sight, the “observables” of systems in classical physics. In quantum physics, we calculate them. For Goldstone modes, including those that act as a unified, collective entity the way you describe, we don’t even do that. We derive them using: Let g be a group element g on a symmetry broken ground state ψ, and let g =exp(SUMs{ φT}) suitably close to group identity where φ & T are understood has having indices a (φsub-a as being some set of expansion coefficients, and Tsub-a being our set of generators living in the Lie group). If φsub-a has a suitable profile (weakly spatially fluctuating), then the functional S gives us S[φ] /= 0 and the expansion of the S in terms of φ yields a soft mode. Fantastic. What does this mean? Well, for one S (or whatever one uses to denote the functionals in a field theory) is a functional in the functional analysis sense. In other words, the space in which a Goldstone boson resides is a “function space”- an abstract space in which functions rather than familiar coordinates are the “points” in that space suitably endowed with some sort of overall scheme or structure and typically infinite dimensional (it is VITAL to realize that infinite dimensional DOES NOT mean that the space is infinite, as the real number line R is an infinite space but is 1-dimensional; infinite dimensional may be regarded as a space that extends infinitely in infinite directions).
I believe at this point Leibniz would have a coronary. It’s one thing to represent a system in some phase space with dimensions greater than 3 because of a dynamical systems degrees of freedom and the ways in which multiple variables of interest can increase the phase space dimensionality. It’s another to have the space be non-Euclidean and the system not “represented” in that space but “living” in that space. How the dynamics you refer to describe anything that happens to a physical system is unknown and probably unknowable to the extent they exist/happen at all. Algebraic QFT was designed to try to rid QFT of infinities that were unacceptable in that the mathematical structures and descriptions could not be considered complete. However, as any quantum field theory in modern physics is an extension of quantum mechanics, and quantum mechanics is “complete” yet describes systems that also dwell in a function space H as well as systems with infinitely many states out of which the application of an observable FUNCTION tells us how our initial transcribed preparation yielded a retroactively applied “state”, completeness is at least as mathematical as it is descriptive of the physical reality that “physics” ostensibly deals with.
Alas, we are not done with roadblocks yet. This is because the Goldstone modes that are unitary, collective modes are acausal. In fact, the entire framework that describes such modes is acausal, and thus even if we weren’t describing entities in function spaces derived mostly via mathematical manipulations, we would not get any classical or quantum mode that acts as a “dynamic unit” causally “involved in relations” in any sense: “in causal theories the vanishing of the surface term is guaranteed as long as the operator Φ is localized to a finite domain of spacetime. (In practice, it is often even strictly local.) In acausal theories such as some nonrelativistic models with instantaneous interaction, the surface integral tends to zero in the infinite volume limit when the interaction is of finite range or decreases exponentially with distance. In case of long-range interactions, however, the disappearance of the surface term must be checked case by case.” (Brauner, T. (2010). "Spontaneous symmetry breaking and Nambu–Goldstone bosons in quantum many-body systems." Symmetry.)
Having gone over the issues of the formalism and its relation to anything real, as well as additional problems, how should we proceed if we wish to apply a quantum field theory involving Goldstone modes of a particular sort to the brain? It’s true that, as you say, there are classical (or at least mainly classical) phonons. The problem is that these are local vibrations of matter and are no more “real” than sound waves (which are mechanical vibrations of matter). Quantum mechanical phonons, on the other hand, are simply one among many quasiparticles and field particles that “act” in a unified, collective manner on or as a system that has no relation to any known physical reality but rather exists in a mathematical space that, at least for Goldstone modes, is necessarily impossible to reconcile with any classical description as it cannot exist in the space the brain does and we all do. So we are left with the concept that localized vibrations of quantized as units of mechanical vibration of particles (parts) of dendrites somehow are relevant for mental/conscious processes. Only that is less unified than weak synchrony and has no relation to the fundamental and universally agreed method of information transfer the brain uses (action potentials). It is also not the kind of mechanism you have described (so far as I can tell). Like path integration, nonlocality, superposition, etc., we have progressed in our understanding such that it seems no longer possible to describe such processes as merely statistical rather than reflecting actual non-classical dynamics, but we remain without any capacity to relate the “representation” of a quantum system with any physical system.
This, then, is perhaps the key point. The descriptions of “modes” (phononic, photonic, bosonic, whatever) in quantum physics, and in particular the way global, unified, collective “modes” are linguistically described along with the formal representation, do not exist in any known sense outside of a mathematical space we cannot relate to the brain. In fact, it is in general a truism of all quantum physics that however apparently simple the mathematical representation of a system it is not representing any physical system in any known way. This makes extremely problematic any application of such a system’s “dynamics” to any neuronal processes because we cannot say how the representation of physical systems without known physical correspondences apply to physical systems without any known quantum dynamics. Meanwhile, the classical counterparts of phononic excitations are localized and cannot produce the kind of dynamics you describe without clear violations of known physics. Just as importantly, the capacity for a dynamical systems approach to unified neuronal activity is not only better grounded in physics but also capable of explaining a more unified, collective brain state than any effects of acoustic waves. This does not mean, as you rightly note, that we can connect such collective behavior with “phenomenal binding”. That said, I do not understand how the fact that nonlocal nearly ZLS is an enigma relates to Dr. Boly’s work. She is not only the lead author of at least one (fairly) recently published paper on the difficulties in assessing neuronal states but has contributed to the literature on the kind of dynamics I have referred, so I am unsure what you mean or what study/studies you refer to. More importantly, feature binding is an extremely complex problem and the only way we can make it relatively simple is by making is something it is not (i.e., comparing feature extraction algorithms that presuppose conceptual processing humans are able to “put into” and interpret the results “out of” some computational intelligence model/paradigm). In fact, the entirety of the “computational brain” is riddled with problematic assumptions based on metaphors from computer science even before computers that have consistently and wholly failed to reproduce the basic functions of brains. ). Also, empirical and formal models of dynamical properties of neural networks already go well beyond any mere integrate and fire model. The Hudkin-Huxley model of the 40s was a resonator not an integrator. I highly recommend (even if it is remedial for you) Dynamical Systems in Neuroscience by Izhikevich. The approach is very similar to Strogatz’ Nonlinear Dynamics and Chaos (an undergraduate level book that assumes a minimal amount of multivariate calculus and little else), but applied solely to neuroscience. Chapters 1, 8, and 10 are available online on his site.
Finally, I think it is a mistake to suppose that classical physics was definitively shown to be a some complete system that is entirely local, deterministic, and reductive (on this there is an interesting and pretty simple book Inconsistency, Asymmetry, and Non-locality: A philosophical investigation of classical electrodynamics by Mathias Frisch). I have no problem with a reductive model of a computational brain other than that after 60 years we have produced more of the same while we have empirically found that most of the nexus of different fields into the framework underlying the classical cognitive (neuro)sciences is without support. In that same period, the tremendous advances in nanotechnology, materials sciences, molecular chemistry, and a host of natural sciences have nothing close to comparable advancements in the life sciences. Schrödinger’s What is Life? is not far removed from Rosen’s work and the issue over the computability of living systems has no parallel in the natural/physical sciences. Yet even the study of non-living systems have revealed a complexity never imagined. “The athermal nature of granular media implies in turn that granular configurations cannot relax spontaneously in the absence of external perturbations. This leads typically to the generation of a large number of metastable configurations; it also results in hysteresis, since the sandpile carries forward a memory of its initial conditions.” (Mehta, A. (2007). Granular physics. Cambridge University Press). How do sandpiles carry “forward a memory” of their initial conditions? They don’t. It’s a way of saying that self-organized criticality and self-organization in general of properties of complex systems that we are, in non-living systems, able to describe in terms of known physical laws but cannot determine other than via some set of possible configuration states. The self-determination of living systems presents challenges that are unmatched by nonlinear systems in general. Let us also not forget that our fundamental approach to nonlinearity is to treat it as lines (which, locally, all curvature approximates; however, the higher the dimensional space the more arbitrarily small distances from an infinitesimal “point” make such approximations poor). You advised me against dogmatic or ideological dismissal of explanations, models, etc. I don’t dismiss quantum models, I simply prefer to not to assume that 19th century deterministic assumptions characterizes physics everywhere other than the quantum level and that we understand enough of complex systems to know we should look elsewhere to explain mental/conscious experiences."
Initially, I thought it might be good to reformulate my responses into a single, simplified version as they addressed issues that I and others have discussed here more times than I care to remember. But then I said to myself "Self, why not use these exchanges to make yourself look better?" Of course, I responded "How might I do that" to which I was informed "Self, everybody who has bothered to read your posts considers you a long-winded fool. Use this as an example to show how much your posts are actually excellent explanations and simplifications compared to what you are used to writing and what you write most of the time!" I, of course, being more reasonable than myself, thought to myself "but why on earth would anybody bother to read such an example, and even if they did, what would they learn?"
In reply, I was beaten continuously for some time, and then told "Self, who cares? The point is to demonstrate how much worse you could be than that you are. God's bodykins, man! You've written yourself into this corner, do SOMETHING to justify your pathetic compositions!"
Usually, I refuse to listen to myself, exactly for this reason. But this time, I decided it was easier to do this than try to re-write several responses to make them relevant, self-contained, and obviously just as boring and pointless as this thread. So here goes:
"You mentioned, if only in passing, the formalisms of physics in your latest contribution as well as in your first. For many reasons, I think that the issue of how we formally represent the properties, dynamics, states, etc., of physical systems merits a more focal treatment and one superior to any I have hitherto provided. The importance is not limited to the obvious matters, but also more nuanced, subtle considerations. The first is how much we much we take for granted simply because we are so accustomed to representing “real” things, from price to protons, using formal (symbolic) languages. Even in a majority of historical accounts of mathematics one is likely to find modern notation that did not exist during the period in question. Those like Leibniz were in a perfect position to appreciate how much the possession of formal apparati facilitated the development of the sciences, let alone mathematics. As a simple example, one has only to look to Greek mathematicians like Euclid who had to depend upon awkward use of grammatical constructions (e.g., verbs regularly used irregularly including common verbs, a technical vocabulary that was technical only in context, the uncommon 3rd person imperative, and the use of the same verb but differing in tense/aspect to distinguish the statement of a proposition/theorem vs. declaration of proof). It required a fair amount of ingenuity to for the Greeks (among others) to use normal language for relatively simple mathematics, and without symbolic notation much of modern mathematics could never develop. Furthermore, long after such notation existed lacked uniformity in use and the systematic nature of a rich formal language, ensuring that even great minds struggled with symbols that they could not relate to sensory-perceptual experience (such as complex numbers, most of algebra, foundational concepts of analysis like limits, etc.). Leibniz and his contemporaries were used to symbolic notation but still lacked, for the most part, formal systems/languages. Today, 12-year-olds around the world are as likely to ask what “3” or “+” REALLY means as they are to ask what a preposition does, but the lack of widespread formal systems made difficult such ready acceptance of symbols lacking concrete relations to real-world experience.
This has at least two relevant consequences for us. The first is how an early exposure to years of mathematics with little apparent application, not to mention the very the notion of “applied math”, has so thoroughly indoctrinated us that we are inclined to think of mathematical notations as meaningless symbols that acquire some abstract meaning through use. After years of using functions, manipulating algebraic expressions, the use of math to represent the properties, states, etc., of physical systems is just a more relatable use of mathematical representation. The second is how we approach modelling. Whereas for over millennia mathematicians struggled to express abstract operations, we have computers: physical ‘models’ of an abstract algebra. Few mathematical symbols in physics unique to physics, and for e.g, the Dirac notation the uniqueness is in form only; the richer, more powerful language of linear/matrix algebra could replace it entirely. For Leibniz, how mathematics related to physics (and both of these to metaphysics) was of vital import: “to miscast his mathematics…is to misunderstand Leibniz, for in fact his "philosophical system" is positively awash in the consequences of an interplay between mathematics and metaphysics that occurs at the very center of his thought and produces several of its most defining features" (Levey, S. (1998). "Leibniz on mathematics and the actually infinite division of matter." The Philosophical Review). While this was not exactly unique, only Leibniz went so far as to attempt formalizing language with his “algebra of concepts” (formally equivalent to Boole’s algebraic set theory) and proto-predicate calculus. At the heart of all of this discussion of mathematics, formalism, representation, and so on, is one issue that remains at the heart of the sciences but is nowhere more vital than the application of quantum physics to models of consciousness and theories of the mind.
To illustrate more concretely, let us examine phonons. That they are “real” in some sense is not in doubt. The question for our purposes is whether they are real the way that e.g., speed and velocity are, or the way liquids are (a grossly simplified ontological distinction, I know). Simply put, phonons are siblings of photons. One finds them discussed and used mostly in condensed matter physics represented using the algebraic structure of lattices, as crystalline structures are everywhere in solid state physics and lattices are ideal mathematical representations of these. You quite rightly compare phonons to electrons, but I think you weaken the analogy by referring to “mass-bearing modes like electron orbitals”. First, phonons are quintessentially “mass-bearing” (if I understand your meaning). They are “units” of motion caused by sound waves. They are basically matter waves that propagate through a crystalline structure causing the “wave-like” (non-local) lattice vibration. More importantly, the representation of photons in QFT can be equivalent to the mathematical representation phononic excitation (i.e., a quantum harmonic oscillator), and like photons it is often necessary to treat phonons as “particle-like” by using the superposition principle (for e.g., thermodynamic excitation rather than acoustic). Second, in a field theory phonons are not “like” electron orbitals at all, but like any EM quanta: “We now throw away the mechanical props and embrace the unadorned quantum field theory! We do not ask what is waving, we simply postulate a field—such as φ—and quantize it. Its quanta of excitation are what we call particles—for example, photons in the electromagnetic case.” (Aitchison & Hey (2003). Gauge Theories in Particle Physics (Vol. I). IOP Publishing).
In other words, phonons are “wave packets” that, quantum mechanically, are as “real” as electrons, photons, magnons, plasmons, etc., and not particularly interesting (outside of nanotechnology, solid state or condensed matter physics, and similar more applied physics). It is also important to note that the number of phonons is both different from phonon types and almost unrelated to the uncertainty principle. However, you have mainly pointed to Goldstone modes, which are interesting for a few reasons. In condensed matter physics such “massless modes” are called “soft modes”. Here again the issue of mathematical representation arises. Representing crystalline dynamics using lattices is intuitive as the mathematical structure is easily related to the physical. The conceptual leap is barely a step. Not all algebras have so intuitive a structure as those found in graph theory or ready analogues as does a lattice (and those that do are not limited to intuitive or relatable structures). Worse still, the language of modern physics is misleading here. There are exceptions, however, my favorite describing the dynamics of a Goldstone mode as a gauge boson fattened by eating a ghost. The reason for the description is the mathematical solution to the mathematical impetus for such an entity existing in a complex coset space to begin with. But before I get to that I’d like to give an example of what I mean by “misleading” language: “In principle it is indeed possible, though technically not so advantageous, to construct a quantum mechanical description of a spontaneously broken symmetry using a symmetric ground state. SSB [spontaneous symmetry breaking] is then manifested by long range correlations rather than nonzero vacuum expectation values” (Brauner, T. (2010). "Spontaneous symmetry breaking and Nambu–Goldstone bosons in quantum many-body systems." Symmetry.).
The “long range correlations” are characteristic of the kind of collective, unitary Goldstone mode you have referred to, but how do they suddenly “exist” if one is “to construct a quantum mechanical description” of SSB? For that matter, how is it “gauged away” (locally or globally) as the “ghost” the fattened gauge field “swallows”? First, note that even were we using some algebraic structure with clear physical analogues to describe Goldstone modes that are “global” we lose any intuitive pictures simply by virtue of the dimensions necessary. Goldstone modes cannot be produced (mathematically or otherwise) except in higher dimensions. As we live in a 3+1 dimensional world, we cannot possibly “observe” a boson that exists in n-dimensional space where n > 3.
Second, it is important to realize that Goldstone modes of the “unitary, collective”-type you describe are not just produced mathematically but exist as mathematical problems in a field theory: “Anomalies are of two types, anomalous global symmetries and anomalous gauge symmetries. In the case of anomalous global symmetries, the symmetry is not realized in the quantum theory…Quantum theoretically, since there is no symmetry, there is no Goldstone boson. In fact the quantum corrections generate a mass for the potential Goldstone boson.
Anomalies for a gauge symmetry can lead to unphysical results….Thus in a consistent physical theory there should be no anomaly for the gauge symmetries”
(Nair, V. P. (2005). Quantum field theory: A modern perspective. (Graduate Texts in Contemporary Physics). Springer.
Third, they are “fixed” mathematically as well: “a question may arise as to why people obtained the massless [Goldstone] boson in the [Nambu and Jona-Lasinio model] model. Not only Nambu and Jona-Lasinio but also quite a few physicists found a massless boson in their boson mass calculation. Surprisingly, the reason why they found a massless boson is simple. They calculated the boson mass by summing up one loop Feynman diagrams, but their calculation is based on the perturbative vacuum state. However, after the spontaneous symmetry breaking, one finds the new vacuum which has the lower energy than the perturbative vacuum state. Therefore, the physical vacuum state is of course the new vacuum that breaks the chiral symmetry, and thus if one wishes to calculate any physical observables in field theory, then one must employ the formulation which is based on the physical vacuum state” (Fujita, Hiramoto, & Takahashi (2009). Bosons after Symmetry Breaking in Quantum Field Theory. Nova Science.)
There are several important points here. One is why a physical theory is made better by the existence of something “unphysical” (note that unphysical does not mean massless). Another is why one should be able to, let alone wish to, “calculate…observables in field theory.” We “observe”, whether through some sophisticated measurements or by sight, the “observables” of systems in classical physics. In quantum physics, we calculate them. For Goldstone modes, including those that act as a unified, collective entity the way you describe, we don’t even do that. We derive them using: Let g be a group element g on a symmetry broken ground state ψ, and let g =exp(SUMs{ φT}) suitably close to group identity where φ & T are understood has having indices a (φsub-a as being some set of expansion coefficients, and Tsub-a being our set of generators living in the Lie group). If φsub-a has a suitable profile (weakly spatially fluctuating), then the functional S gives us S[φ] /= 0 and the expansion of the S in terms of φ yields a soft mode. Fantastic. What does this mean? Well, for one S (or whatever one uses to denote the functionals in a field theory) is a functional in the functional analysis sense. In other words, the space in which a Goldstone boson resides is a “function space”- an abstract space in which functions rather than familiar coordinates are the “points” in that space suitably endowed with some sort of overall scheme or structure and typically infinite dimensional (it is VITAL to realize that infinite dimensional DOES NOT mean that the space is infinite, as the real number line R is an infinite space but is 1-dimensional; infinite dimensional may be regarded as a space that extends infinitely in infinite directions).
I believe at this point Leibniz would have a coronary. It’s one thing to represent a system in some phase space with dimensions greater than 3 because of a dynamical systems degrees of freedom and the ways in which multiple variables of interest can increase the phase space dimensionality. It’s another to have the space be non-Euclidean and the system not “represented” in that space but “living” in that space. How the dynamics you refer to describe anything that happens to a physical system is unknown and probably unknowable to the extent they exist/happen at all. Algebraic QFT was designed to try to rid QFT of infinities that were unacceptable in that the mathematical structures and descriptions could not be considered complete. However, as any quantum field theory in modern physics is an extension of quantum mechanics, and quantum mechanics is “complete” yet describes systems that also dwell in a function space H as well as systems with infinitely many states out of which the application of an observable FUNCTION tells us how our initial transcribed preparation yielded a retroactively applied “state”, completeness is at least as mathematical as it is descriptive of the physical reality that “physics” ostensibly deals with.
Alas, we are not done with roadblocks yet. This is because the Goldstone modes that are unitary, collective modes are acausal. In fact, the entire framework that describes such modes is acausal, and thus even if we weren’t describing entities in function spaces derived mostly via mathematical manipulations, we would not get any classical or quantum mode that acts as a “dynamic unit” causally “involved in relations” in any sense: “in causal theories the vanishing of the surface term is guaranteed as long as the operator Φ is localized to a finite domain of spacetime. (In practice, it is often even strictly local.) In acausal theories such as some nonrelativistic models with instantaneous interaction, the surface integral tends to zero in the infinite volume limit when the interaction is of finite range or decreases exponentially with distance. In case of long-range interactions, however, the disappearance of the surface term must be checked case by case.” (Brauner, T. (2010). "Spontaneous symmetry breaking and Nambu–Goldstone bosons in quantum many-body systems." Symmetry.)
Having gone over the issues of the formalism and its relation to anything real, as well as additional problems, how should we proceed if we wish to apply a quantum field theory involving Goldstone modes of a particular sort to the brain? It’s true that, as you say, there are classical (or at least mainly classical) phonons. The problem is that these are local vibrations of matter and are no more “real” than sound waves (which are mechanical vibrations of matter). Quantum mechanical phonons, on the other hand, are simply one among many quasiparticles and field particles that “act” in a unified, collective manner on or as a system that has no relation to any known physical reality but rather exists in a mathematical space that, at least for Goldstone modes, is necessarily impossible to reconcile with any classical description as it cannot exist in the space the brain does and we all do. So we are left with the concept that localized vibrations of quantized as units of mechanical vibration of particles (parts) of dendrites somehow are relevant for mental/conscious processes. Only that is less unified than weak synchrony and has no relation to the fundamental and universally agreed method of information transfer the brain uses (action potentials). It is also not the kind of mechanism you have described (so far as I can tell). Like path integration, nonlocality, superposition, etc., we have progressed in our understanding such that it seems no longer possible to describe such processes as merely statistical rather than reflecting actual non-classical dynamics, but we remain without any capacity to relate the “representation” of a quantum system with any physical system.
This, then, is perhaps the key point. The descriptions of “modes” (phononic, photonic, bosonic, whatever) in quantum physics, and in particular the way global, unified, collective “modes” are linguistically described along with the formal representation, do not exist in any known sense outside of a mathematical space we cannot relate to the brain. In fact, it is in general a truism of all quantum physics that however apparently simple the mathematical representation of a system it is not representing any physical system in any known way. This makes extremely problematic any application of such a system’s “dynamics” to any neuronal processes because we cannot say how the representation of physical systems without known physical correspondences apply to physical systems without any known quantum dynamics. Meanwhile, the classical counterparts of phononic excitations are localized and cannot produce the kind of dynamics you describe without clear violations of known physics. Just as importantly, the capacity for a dynamical systems approach to unified neuronal activity is not only better grounded in physics but also capable of explaining a more unified, collective brain state than any effects of acoustic waves. This does not mean, as you rightly note, that we can connect such collective behavior with “phenomenal binding”. That said, I do not understand how the fact that nonlocal nearly ZLS is an enigma relates to Dr. Boly’s work. She is not only the lead author of at least one (fairly) recently published paper on the difficulties in assessing neuronal states but has contributed to the literature on the kind of dynamics I have referred, so I am unsure what you mean or what study/studies you refer to. More importantly, feature binding is an extremely complex problem and the only way we can make it relatively simple is by making is something it is not (i.e., comparing feature extraction algorithms that presuppose conceptual processing humans are able to “put into” and interpret the results “out of” some computational intelligence model/paradigm). In fact, the entirety of the “computational brain” is riddled with problematic assumptions based on metaphors from computer science even before computers that have consistently and wholly failed to reproduce the basic functions of brains. ). Also, empirical and formal models of dynamical properties of neural networks already go well beyond any mere integrate and fire model. The Hudkin-Huxley model of the 40s was a resonator not an integrator. I highly recommend (even if it is remedial for you) Dynamical Systems in Neuroscience by Izhikevich. The approach is very similar to Strogatz’ Nonlinear Dynamics and Chaos (an undergraduate level book that assumes a minimal amount of multivariate calculus and little else), but applied solely to neuroscience. Chapters 1, 8, and 10 are available online on his site.
Finally, I think it is a mistake to suppose that classical physics was definitively shown to be a some complete system that is entirely local, deterministic, and reductive (on this there is an interesting and pretty simple book Inconsistency, Asymmetry, and Non-locality: A philosophical investigation of classical electrodynamics by Mathias Frisch). I have no problem with a reductive model of a computational brain other than that after 60 years we have produced more of the same while we have empirically found that most of the nexus of different fields into the framework underlying the classical cognitive (neuro)sciences is without support. In that same period, the tremendous advances in nanotechnology, materials sciences, molecular chemistry, and a host of natural sciences have nothing close to comparable advancements in the life sciences. Schrödinger’s What is Life? is not far removed from Rosen’s work and the issue over the computability of living systems has no parallel in the natural/physical sciences. Yet even the study of non-living systems have revealed a complexity never imagined. “The athermal nature of granular media implies in turn that granular configurations cannot relax spontaneously in the absence of external perturbations. This leads typically to the generation of a large number of metastable configurations; it also results in hysteresis, since the sandpile carries forward a memory of its initial conditions.” (Mehta, A. (2007). Granular physics. Cambridge University Press). How do sandpiles carry “forward a memory” of their initial conditions? They don’t. It’s a way of saying that self-organized criticality and self-organization in general of properties of complex systems that we are, in non-living systems, able to describe in terms of known physical laws but cannot determine other than via some set of possible configuration states. The self-determination of living systems presents challenges that are unmatched by nonlinear systems in general. Let us also not forget that our fundamental approach to nonlinearity is to treat it as lines (which, locally, all curvature approximates; however, the higher the dimensional space the more arbitrarily small distances from an infinitesimal “point” make such approximations poor). You advised me against dogmatic or ideological dismissal of explanations, models, etc. I don’t dismiss quantum models, I simply prefer to not to assume that 19th century deterministic assumptions characterizes physics everywhere other than the quantum level and that we understand enough of complex systems to know we should look elsewhere to explain mental/conscious experiences."
