A Quantization isn't fundamental

[Twodogs]

Your question and the matter is naturally fuzzy and easy to misinterpret, but given that disclaimer i can make sense of what you write, and the answer to your question from my perspective is loosely this:

I am grateful for your tentative reply. I was about ready to post an apology for my question thinking it was inappropriate due to lack of clarity, excessive speculation or simple naivete. Perhaps it was a bit of all these things. In any case, your reply gives me perspectives to consider.

 

[Andrea Panza]

Hi,
My understanding of physics it is probably not deep enough to fully appreciate all this thread, but I think the link below of 'cell emergence' from a simple rule might be relevant for the discussion.



This is the link to the Nature paper:

https://www.nature.com/articles/srep37969

Regards

 

[Twodogs]

the confinement does not refer to 3D space as space does not yet exist in this level of the vision. Instead spacetime and the dimensionality must be emergent as evolved self-organised relations between the interacting encoding structures.

This seems to be a relevant insight.

 

[KipIngram]

Suffice to say, this paper is a must-read. Many thanks to @mitchell porter for linking it and to Sir Michael Atiyah for reigniting the entire discussion in the first place.

Wow - that is a pretty interesting paper. I want to find some of the counter-arguments to it as well, but thanks for bringing this one to my attention. Surely there must be some testable things here that can be checked...

 

[mitchell porter]

I have been wanting to make a comment or two about the prospects for Manasson's proposal... Consider figure 1a in his 2008 paper. That's a binary tree with sixteen leaves, the leaves being the 16 fixed points of a limit cycle in some unknown dynamical system, which are also supposed to be 16 particle states from the first generation of the standard model.

There are other ways you might want to assign particle states to the fixed points of the bifurcation diagram. For example, he doesn't include quark color, which would multiply the number of quark states by three. But that would just bring the total number of states per generation to 32, which is the number of fixed points after the next bifurcation.

Also, he implicitly treats these particles as 4-state Dirac fermions, whereas we now understand the phenomenological Dirac fermions to arise from a Higgs mechanism that pairs up two 2-state Weyl fermions. Again, this is just a change in the details, it doesn't inherently affect the viability of the concept.

But however you make the assignment, ultimately you want to mimic the standard model. We know the lagrangian of the standard model, it contains many interaction terms that involve these fermionic states. So given a particular assignment of states to the tree, you can directly translate the lagrangian into the dynamical systems language.

The lagrangian will contain terms like "electron couples to charged weak boson and becomes neutrino", or "left-handed fermion couples to right-handed fermion via Higgs". These should translate directly to statements like "third fixed point on level 4 couples to charged weak boson and becomes seventh fixed point on level 4", etc.

Recall that, on the dynamical-systems side of this correspondence, the 16 states correspond to fixed points of a limit cycle in an iterated dynamical system. So the seventh fixed point is what you get after applying some mapping four times to the third fixed point.

There is another way to get there, and that is to change levels within the tree, rather than move along the same level. But either way, once you make a specific assignment of fermion states to the tree, this implies a large number of highly specific claims about how the bosons of the standard model (whatever they are) interact with the different states of the fundamental self-organizing system described by the bifurcation diagram.

So I want to propose a rather concrete way to explore the difficulties of implementing Manasson's vision. It's partly inspired by quantum computing, where there are concepts of a "physical qubit" and a "logical qubit". A physical qubit is a concrete quantum system - a nuclear spin, an electron spin, whatever. A logical qubit is a qubit at the level of quantum algorithms. A logical qubit is typically made of some number of physical qubits with an error correction scheme applied.

Anyway, what Manasson has done is to take a type of universal dynamical behavior, and propose that some version of it underlies particle physics. To judge the viability of this idea, we need a way to explore it in generality, or at least without already knowing the details of the fundamental self-organizing system. But we also need something concrete enough that we can try to make it work, and learn from the difficulties.

I think a quantum version of the logistic map can provide a concrete starting point. The logistic map, maps one value of x to another value of x, and has a parameter r. So the first step that I suggest, is to think of these as quantum states... |x>. There can be technical problems with having a continuum of quantum states, but they are familiar from ordinary quantum mechanics and we can use ordinary methods should they prove necessary.

So then the logistic map is actually an operator on a Hilbert space, or rather a family of operators parametrized by r. These states are then analogous to the states of the "physical qubit". Then, for specific values of r, there are fixed points and basins of attraction. These are analogous to the "logical qubit" states. Note that if a particular range of x-values belong to the basin of attraction for a single fixed point, there will be a subspace of the overall Hilbert space, whose basis vectors are the |x>s in that range.

So now we have a kind of concrete model for the fundamental self-organizing system. When we say "left-handed electron is third fixed point on level 4", that refers to a particular subspace of our Hilbert space. And this also gives a new concreteness to the propositions like "third fixed point on level 4 couples to charged weak boson and becomes seventh fixed point on level 4"; that is now a statement about how certain quantum systems interact.

I know that Manasson (and also @Auto-Didact) hope to derive quantum mechanics itself from something more fundamental, but whatever the foundations, the standard model is quantum-mechanical and e.g. obeys the principle of superposition, so some version of the scheme has to make sense as a quantum theory.

Nonetheless, for those seeking something beneath quantum mechanics, I would point out a recent paper by Tejinder Singh, which takes as its subquantum theory a version of Stephen Adler's trace dynamics. It's a relatively sophisticated approach.

 

[arivero]

. Consider figure 1a in his 2008 paper.

Hey, he cites P. Cvitanovic's "Universality in chaos", a nice book. He is, I think, the same person who calculated the g-2 parameter at sixth order. Then he started to notice patterns in the calculations and went to explore other, er, branchs of physics. Before transitioning to chaos, he did some articles on "Parton Branching", this sounds as a good candidate to the "unknown dynamical system". But if Cvitanovic failed to find such system, I doubt it exists.

 

[Twodogs]

5) If by axiomatic approach you mean purely formally i.e. giving proofs based on axioms, then I urge you to read this.

I don’t know if it is interesting or fruitful, but here are two foundational axioms to consider.

Axiom One: The universe of one piece, an undivided whole.


Axiom Two: The universe is divided, one part distinct from another, and etc.

If we accept that both are still true, I am curious as to know what would follow.

 

[Auto-Didact]

I don’t know if it is interesting or fruitful, but here are two foundational axioms to consider.

Axiom One: The universe of one piece, an undivided whole.


Axiom Two: The universe is divided, one part distinct from another, and etc.

If we accept that both are still true, I am curious as to know what would follow.

The problem with axioms is that they usually are pretty shallow ideas from a fundamental exploratory perspective i.e. a careful analysis doesn't lead to any deeper understanding, only to logically possible reductionist explanations of higher level concepts. Moreover, axioms also often end up being intrinsically somewhat vague and therefore often unfalsifiable as well; if the vagueness can be removed, the deduced consequences on the basis of the axioms have the risk of changing completely.

One can often tell the difference between an axiom and a principle by how they were first comstructed, namely axioms are a priori interpretations i.e. usually non-empirical definitions tied up in some particular conventions, while principles are a posteriori descriptions i.e. hypotheses that have managed to survive repeated attempts at falsification, and so eventually end up exposing some core concept. This just shows that axioms and principles have fundamentally different aims, i.e. empirical versus rational explanation; e.g. a complete logical proof can only be based on axioms, yet the axioms may turn out to be incorrect, directly rendering some proof irrelevant and the conclusions based on it obsolete.

For example, contrast the axioms you stated with known principles, such as the principle that being at rest is a form of motion, the principle that everything the animals do result from the motion of atoms or the principle that all life springs from a common mechanism. In each of these cases, the principles are so broad that they tend to naturally apply far beyond what they were specifically aiming to describe; this is where unification comes from in the practice of physics.

In other words, far more comes out of the idea than what is originally put in, not merely in an empirical sense but also conceptually, often directly leading to novel purely mathematical constructions; Feynman liked to say 'the idea turns out to actually be simpler than it was before'. This openness of the applicability domain of a principle is the hallmark of a good principle. On the other hand, the hallmark of a good axiom is that it has a precisely delineated boundary, making long range deductions possible.

 

[Twodogs]

We are discussing the foundational substrate within which self-organized dissipative dynamics would arise as a natural consequence. Your cautionary comments on the pitfalls of axiomatic arguments are mostly understood – here my limitation rather than your lack of clarity. Granted, a hard-won, empirical principle would weigh more heavily than an axiomatic premise made for purpose of discussion.

The problem with axioms is that they usually are pretty shallow ideas from a fundamental exploratory perspective i.e. a careful analysis doesn't lead to any deeper understanding,

Moreover, axioms also often end up being intrinsically somewhat vague and therefore often unfalsifiable as well; if the vagueness can be removed, the deduced consequences on the basis of the axioms have the risk of changing completely.

Clear enough. I don’t wish to waste your time, but moving from general case to particular example, may we consider the two given axioms with the understanding that are propositions for sake of argument. The first proposition, “The universe is of one piece, an undivided whole,” is not readily apparent. It is far from, “that which commends itself as evident.” However, it was David Bohm’s often stated view and the conclusion of at least a couple of spiritual disciplines. Neither of which makes it true, but it does make it proposition worthy. It may not be sufficiently explicit, but it is a briefly stated proposition of fundamental continuity.

The second proposition, “The universe is divided, one part distinct from another, and etc.,” is readily evident, actually hard of avoid. The advance of science has regularly occurred through lifting the veil of unnecessary detail and finding beneath the unifying principle. This is the proposition of discreteness.

Considering both of these antithetical propositions as true would reflect Niels Bohr’s proclivity as outlined by Edward Teller, “…every important issue has an opposite side that appears as mutually exclusive with the other. The understanding of the question becomes possible only if the existence of both sides is recognized.”

Be that as it may, the goal of such a process is your “deeper understanding” and here I see at least one significant consequence: If we accept both propositions as valid, then all distinctions are fundamentally topological in nature.

Is that the case? Is it useful?

And once again, I appreciate your willingness to engage here. Given the subject matter, such opportunities don’t often occur.

 

[Auto-Didact]

Be that as it may, the goal of such a process is your “deeper understanding” and here I see at least one significant consequence: If we accept both propositions as valid, then all distinctions are fundamentally topological in nature.

Please elaborate.

 

[arivero]

If we accept that both are still true, I am curious as to know what would follow.

Connes's tangent groupoid.

You have separate states, but also arrows joining them, with an algebra associated to describe the topology, and an operator to describe the notion of distance.

 

[Twodogs]

Please elaborate.

The notion that all distinctions are fundamentally topological arises from the perhaps naive assumption that, if the universe is both one and two, then the two must be topological transforms of the one. This is perhaps a narrow view of the possibilities.

I believe it to be true, but I come to it via a general systems world view governed more by metaphor, analogy and rules-of-thumb than a disciplined mathematical framework. Within this world view I find that a very useful and perhaps overarching rule-of-thumb is the observation that:

Path is emergent between the traveler and the terrain.

It is emergent because its pattern is not solely determined by either traveler or terrain, but rather by their mutual dynamical interface. This is an empirically useful description on the macro level and likely to have translatable relevance on the micro level. If our complexity metric reflects long range correlation, then complexity of path is directly related to and arises from the complexity of both traveler and terrain and is maximal within some intrinsic energy regimen.

I have come to suspect that it is useful to consider that the universe is a construct of traveler and terrain dynamics ‘all the way down.’ Here we are piloted by a systems view first expressed by da Vinci and paraphrased by David Bohm: “Movement gives shape to all forms and structure gives order to movement, and a deeper a more extensive inner movement creates, maintains, and ultimately dissolves structure". This notion is sketched out here in seven-hundred words and one ‘equation.’

First, probing deeper we find a striking affinity between traveler and terrain. They are both hybrids – composite, dynamical constructs arising as sustained paths between their own intrinsic ‘travelers’ and ‘terrains.’ We find the traveler is always part terrain, the terrain is always part traveler and both share elements of a larger whole.

With a leap of soft logic, we can further devolve this pattern of nested dynamics, step by step, to a foundational level. Here, as an imprecise, qualitative ansatz and with the expectation that there is a more precise underlying, mathematical description, we will characterize traveler and terrain by two qualitative, verbal placeholders using ‘change’ for traveler and ‘constraint’ for terrain.

The benefit of this exercise is a very rudimentary equation governing the fitting together of these two antithetical qualities:

Change + Constraint = O

Wherein “O” represents any of the species of cyclical or wavelike dynamics and the properties of both addends are conserved in the sum. That is, cyclical, wavelike dynamics arise as a means of integrating these two antithetical properties into a path in which change is ongoing and yet constrained to a certain dynamical regimen. Here we note that cyclical and wavelike dynamics are ubiquitous in the universe over spatiotemporal scales varying by many orders of magnitude and, though they manifest in a myriad of distinct mechanisms, they may be similarly driven at a foundational level.

Further, on this level of first things, it is expected that:

1) “O” is the first element of time volume and the first stele in a space geometry. It is the dynamical knot that binds phenomena into being, “gives to airy nothing a local habitation and a name.”

2) ‘Change’ and ‘constraint’ represent two orthogonally opposed transforms of a single topology and may be mathematically described and developed inductively from complementarity relations and conserved properties.

3) The physical universe is the path emergent between these two topologies.

4) The “orthogonally opposed transforms” are both proto-physical and trans-physical, that is, both genesis and sustainer of the physical universe and are “present at any moment” (as in Bohm’s characterization of the implicate order). Their mutual effect is evident in the exacting dynamic translations between kinetic and potential energies. They manifest only in relation to each other and are endlessly complected (PIE root "to plait, braid") into dynamical structures.

5) The existence of “orthogonally opposed transforms” may be confirmed by measurement of the angle formed at the intersection a mason’s plum line and his(her) spirit level. It is simply a matter of interpretation. ;>)

6) This foundational schema would serve as a substrate for the emergence of iterative, self-organizing dissipative systems.

I have no idea if this will have any traction with you. Be that as it may, several years ago sonar engineers discovered that adding a little noise to a source might push its weak signal over the threshold of detection. Nice when that happens. Thanks.

 

[Auto-Didact]

The notion that all distinctions are fundamentally topological arises from the perhaps naive assumption that, if the universe is both one and two, then the two must be topological transforms of the one. This is perhaps a narrow view of the possibilities.

I believe it to be true, but I come to it via a general systems world view governed more by metaphor, analogy and rules-of-thumb than a disciplined mathematical framework. Within this world view I find that a very useful and perhaps overarching rule-of-thumb is the observation that:

Path is emergent between the traveler and the terrain.

It is emergent because its pattern is not solely determined by either traveler or terrain, but rather by their mutual dynamical interface. This is an empirically useful description on the macro level and likely to have translatable relevance on the micro level. If our complexity metric reflects long range correlation, then complexity of path is directly related to and arises from the complexity of both traveler and terrain and is maximal within some intrinsic energy regimen.

I have come to suspect that it is useful to consider that the universe is a construct of traveler and terrain dynamics ‘all the way down.’ Here we are piloted by a systems view first expressed by da Vinci and paraphrased by David Bohm: “Movement gives shape to all forms and structure gives order to movement, and a deeper a more extensive inner movement creates, maintains, and ultimately dissolves structure". This notion is sketched out here in seven-hundred words and one ‘equation.’

First, probing deeper we find a striking affinity between traveler and terrain. They are both hybrids – composite, dynamical constructs arising as sustained paths between their own intrinsic ‘travelers’ and ‘terrains.’ We find the traveler is always part terrain, the terrain is always part traveler and both share elements of a larger whole.

With a leap of soft logic, we can further devolve this pattern of nested dynamics, step by step, to a foundational level. Here, as an imprecise, qualitative ansatz and with the expectation that there is a more precise underlying, mathematical description, we will characterize traveler and terrain by two qualitative, verbal placeholders using ‘change’ for traveler and ‘constraint’ for terrain.

The benefit of this exercise is a very rudimentary equation governing the fitting together of these two antithetical qualities:

Change + Constraint = O

Wherein “O” represents any of the species of cyclical or wavelike dynamics and the properties of both addends are conserved in the sum. That is, cyclical, wavelike dynamics arise as a means of integrating these two antithetical properties into a path in which change is ongoing and yet constrained to a certain dynamical regimen. Here we note that cyclical and wavelike dynamics are ubiquitous in the universe over spatiotemporal scales varying by many orders of magnitude and, though they manifest in a myriad of distinct mechanisms, they may be similarly driven at a foundational level.

Further, on this level of first things, it is expected that:

1) “O” is the first element of time volume and the first stele in a space geometry. It is the dynamical knot that binds phenomena into being, “gives to airy nothing a local habitation and a name.”

2) ‘Change’ and ‘constraint’ represent two orthogonally opposed transforms of a single topology and may be mathematically described and developed inductively from complementarity relations and conserved properties.

3) The physical universe is the path emergent between these two topologies.

4) The “orthogonally opposed transforms” are both proto-physical and trans-physical, that is, both genesis and sustainer of the physical universe and are “present at any moment” (as in Bohm’s characterization of the implicate order). Their mutual effect is evident in the exacting dynamic translations between kinetic and potential energies. They manifest only in relation to each other and are endlessly complected (PIE root "to plait, braid") into dynamical structures.

5) The existence of “orthogonally opposed transforms” may be confirmed by measurement of the angle formed at the intersection a mason’s plum line and his(her) spirit level. It is simply a matter of interpretation. ;>)

6) This foundational schema would serve as a substrate for the emergence of iterative, self-organizing dissipative systems.

I have no idea if this will have any traction with you. Be that as it may, several years ago sonar engineers discovered that adding a little noise to a source might push its weak signal over the threshold of detection. Nice when that happens. Thanks.

I can partially see what you are trying to say, but I would like to see it worked out mathematically, before passing judgment. If you have trouble doing so yourself, I would suggest collaborating with a mathematician or programmer/computer scientist with the relevant conceptual background.

 

[Twodogs]

I appreciate your looking it over. I realize it is a bit of a popsicle stick construct and would certainly like to dialogue with someone who felt an interest in at least clarifying the ideas. It seems like it would be a real challenge to turn it into an effective mathematical statement and someone would have to want to take it on out of personal curiosity. Regards