More specifically, here is a review paper of an experimentally falsifiable phenomenological proposal:This might help, can you give an example?
A measurable set, to be honest it needn't even be a space (i.e. have a topology). In the ontic case it has the additional constraint that it can be decomposed as a Cartesian product with one element the Hilbert space. It doesn't have to be a fiber bundle or a symplectic manifold.This ##\Lambda## seems to be a very particular kind of fiber bundle or symplectic manifold. You are calling it a state space, but can you elaborate on what kind of mathematical space this is exactly?
Doesn't sound conceptually right as a foundation at all. This is because all state spaces in the canon of physics - definitely all I have ever seen in physics and applied mathematics w.r.t. other sciences - are always most naturally formulated as symplectic manifolds, fibre bundles or some other analogous highly structured mathematical object.A measurable set, to be honest it needn't even be a space (i.e. have a topology). In the ontic case it has the additional constraint that it can be decomposed as a Cartesian product with one element the Hilbert space. It doesn't have to be a fiber bundle or a symplectic manifold.
I see absolutely no reason to exclude such spaces a priori, especially given Manasson's model's mathematical basis in non-linear dynamical systems. One only need recall that practically all objects from non-linear dynamical systems were just a few decades ago universally regarded by mathematicians as nothing more than 'pathological' mathematical notions which were meant to be excluded by hand.The only way you would escape this is if there were additional variables beyond the wavefunction that had a non-measurable state space.
It includes those as special cases, so anything proven for the general ##\Lambda## holds for them.Doesn't sound conceptually right as a foundation at all. This is because all state spaces in the canon of physics - definitely all I have ever seen in physics and applied mathematics w.r.t. other sciences - are always most naturally formulated as symplectic manifolds, fibre bundles or some other analogous highly structured mathematical object.
I don't follow this to be honest. It only being required to be a measurable set is simply to make it very general. It also includes symplectic manifolds, fiber bundles, etc as special cases. I don't really see how that makes it secretly epistemic, otherwise anything supporting integration is secretly epistemic.It seems to me that the exact same thing is going on here, since it is as you say a measurable set i.e. an axiomatic probability-esque object. Practically all mathematical objects with such properties are (or tend to be) purely epistemological in nature, directly implying that ##\psi## is actually being treated epistemologically instead of ontologically, the epistemic nature carefully hidden behind axiomatic gymnastics.
There's no a priori reason to exclude them and I think this is where the point is being missed.I see absolutely no reason to exclude such spaces a priori, especially given Manasson's model's mathematical basis in non-linear dynamical systems. One only need recall that practically all objects from non-linear dynamical systems were just a few decades ago universally regarded by mathematicians as nothing more than 'pathological' mathematical notions which were meant to be excluded by hand.
It would be like somebody setting out to see what constraints apply to discrete models of some theory and then objecting to their use of ##\mathbb{Z}^{d}##
(a) I don't think so, I know what the terms mean, they're fairly simpleIn my view, you seem to be a) frequently confusing (psi-)ontology with (psi-)epistemology, b) interpreting certain extremely subtle arguments at face value and therefore incorrectly (e.g. Valentini's argument for BM, on the face of it goes against accepted wisdom in contemporary physics, this in no way invalidates his argument, his argument is a logically valid argument), c) interpreting no-go theorems possibly based on shaky assumptions as actual definitive demonstrations and d) attributing concepts deemed impossible within contemporary physics (e.g. superdeterminism, superluminality, retrocausation) as effects of fine-tuning based arguments in the form of c).
Again where have I done this? I know the ontological framework axioms, so I know where they apply and don't.This is made clearer when you automatically generalize the validity of proofs using concepts defined in a certain context as if the proof covers all contexts - seemingly purely because it is a theorem - something you have no doubt learned to trust from your experience of using/learning mathematics.
Well the ontological models framework show certain such models have pathologies in a rigorous way, one can easily say something is "expected" according to your personal intuition, quite another to actually prove it.In a way, i reject the "ontic space model" on generic grounds, simply because its for the above reason doomed to fail. I would even think its irrational to try to model general uncertainty by means of ignorance in this sense. This can be expectated from the logic i think, even without bothering with theorems. That is, give or take nonlocality or superdeterminism etc. I find it pathological to start with.
I understand that that is the intention, but it is actually a quite subtle point I am trying to make. I understand that the goal is to make scientific progress, my point is that axiomatics isn't a proper basis for reasoning in (the foundations of) physics: research in foundations needs to lead to experimentally falsifiable statements, not axiomatic theorems. There is simply too much uncertainty regarding the actual range of validity of the known laws of physics, way too much uncertainty in order that one can make definitive axiomatic statements (theorems) without deluding oneself.It includes those as special cases, so anything proven for the general ##\Lambda## holds for them.
The problem with reification of some mathematics as an actual physical concept, especially w.r.t. an overt generalization such as the measurable set - a mathematical construction, which just like ZFC and other standard foundations of mathematics, was purely constructed a posteriori in order to do axiomatics - is that the underlying physical concept originally under research can become divorced from its conceptual properties and so lost during this abstraction process; I am arguing that the ontology vanishes as well leaving one with nothing but epistemology.I don't follow this to be honest. It only being required to be a measurable set is simply to make it very general. It also includes symplectic manifolds, fiber bundles, etc as special cases. I don't really see how that makes it secretly epistemic, otherwise anything supporting integration is secretly epistemic.
I understand that and I am glad that you realize that, however I'm not so sure other physicists who read and cite foundations literature do realize this as well. In my experience they tend to take statements - especially theorems - at face value as either non-empirical evidence or definitive mathematical proof; this goes for physicists at all levels, from (under)grad students up to professors.There's no a priori reason to exclude them and I think this is where the point is being missed.
The goal of foundations is to provide exactly such definitive statements; the problem is that axiomatic statements such as the no-go theorems, and in fact axiomatic reasoning itself, has historically never belonged to the toolbox of foundations of physics, but instead to the toolbox of mathematical physics. It is paramount to understand axiomatics, being essentially a form of deductive logic, cannot go beyond what is defined. As Poincaré said:I think both you and @Fra are taking the ontological foundations framework as some kind of claim of a "final argument" or something. For example thinking they are "rejecting the possibility of non-measurable spaces". Nobody is doing that, it's simply a very general framework so one can analyse a broad class of theories, nobody is arguing that the truth "must" lie within the framework. It's just that we have no-go results for anything that does, which is useful to have. It has allowed us to see what list of things you have to reject in order to get a decent theory that explains quantum phenomena and what set of theories are either hopeless or will end up with unnatural fine-tunings.
As I said to @Fra :
Historically, the goal of foundations of physics has always been to challenge accepted concepts which are deemed fundamental, by looking for mathematical reformulations which enable a natural synthesis (NB: not natural in the sense of naturalness but in the classical sense, i.e. 'spontaneous' or the opposite of artificial) between conflicting concepts often directly paired with novel experimental predictions.Poincaré said:We have confined ourselves to bringing together one or other of two purely conventional definitions, and we have verified their identity; nothing new has been learned. Verification differs from proof precisely because it is analytical, and because it leads to nothing. It leads to nothing because the conclusion is nothing but the premisses translated into another language. A real proof, on the other hand, is fruitful, because the conclusion is in a sense more general than the premisses.
Apart from a) which I have elaborated further upon, including in this very post, I agree you aren't doing b), c) and d). The problem is those less familiar with foundations of physics will almost certainly do b), c) and d) - especially if (self proclaimed) experts openly do a) as they in fact regularly do seem to do since foundations started adopting axiomatics starting with von Neumann.And to come back to a point you made earlier:
(a) I don't think so, I know what the terms mean, they're fairly simple
(b) Where am I doing this?
(c) I am explicitly not doing this, as I know the ontological framework axioms and their exact limits, so I know when they don't hold.
(d) This is backwards, some of the theorems show they have fine-tunings, nothing says they are the result of fine-tunings.
I have stated it already in post #64, and moreover argued at length why I believe the definition as given is a mischaracterization i.e. an incorrect operationalization of the concept that ##\psi## is ontological into a technical definition. Even stronger, I believe the strategy for some rigorous definition based on axioms at this stage is itself a misguided quest; we need preliminary mathematical models, not highly rigorous axiomatics.Again where have I done this? I know the ontological framework axioms, so I know where they apply and don't.
Can either of you two state what the ontological framework axioms are in your understanding, considering you have been arguing against it?
Agreed. But I guess my point was that - even in despite proofs, it does not seem to prevent people keep to looking for loopholes, and in this perspective i argue that there is an easier way to argue with yourself against using the type of uncertainty implicitiy in "ignorance" as i defined it above, as universal explanations.Well the ontological models framework show certain such models have pathologies in a rigorous way, one can easily say something is "expected" according to your personal intuition, quite another to actually prove it.
Optimistically, multifractal analysis might already be a sufficient tool, but that is just grasping in the dark.I always thought self-similarity as seen in fractal sets was a way to accommodate Bell's non-local correlations - in an "all structure is emergent structure" approach.
Any two measurements must differ at minimum by some index on an operation (maybe an evolutionary one) that walked them far enough apart to make them stereoscopically observable. Maybe Bell and the rest of the SM (i.e. all conservation laws including super-selection) are just pointing out degrees of similarity in emergent (dissipative) structure.
The problem with fractal sets is that they are not well behaved spaces as manifolds go, to put it mildly.
It's hard to imagine any notion of calculus and algebra on sets that can have have all manner of wild mechanisms of smooth-roughness, continuity (with dis-continuity included) and connections that are truly not-local.
Maybe someday Ai will be able to help with this, discovering brute force what derivative and integral operators do in a big zoo of multi-fractal generated spaces.
Well it eliminates theories that can't work, since many people thought to suggest and build models that align with the theorem, I think it's useful for knowing what's not going on in QM. Since the eliminated models seem to be the most conventional ones and the class eliminated quite broad, I think it's useful, it just shows how weird the explanation will be. Even the fact that it has made anti-realist explanations more plausible is interesting enough on its own.I understand that that is the intention, but it is actually a quite subtle point I am trying to make. I understand that the goal is to make scientific progress, my point is that axiomatics isn't a proper basis for reasoning in (the foundations of) physics: research in foundations needs to lead to experimentally falsifiable statements, not axiomatic theorems. There is simply too much uncertainty regarding the actual range of validity of the known laws of physics, way too much uncertainty in order that one can make definitive axiomatic statements (theorems) without deluding oneself.
Doesn't this just apply to any kind of mathematical research though. I still don't see why something "supporting integration" is epistemological, it depends on how you are viewing it in your theory. You might consider it an underlying state space of ontic states, just that the state space can be integrated over, but it doesn't make it an epistemic object, otherwise the manifold in GR is an epistemic object.The problem with reification of some mathematics as an actual physical concept, especially w.r.t. an overt generalization such as the measurable set - a mathematical construction, which just like ZFC and other standard foundations of mathematics, was purely constructed a posteriori in order to do axiomatics - is that the underlying physical concept originally under research can become divorced from its conceptual properties and so lost during this abstraction process; I am arguing that the ontology vanishes as well leaving one with nothing but epistemology.
The ontological models framework does challenge accepted concepts, because it tells you what won't work. So it eliminates more naive ideas people had. I don't think it is the goal of the framework to provide definitive statements about what is actually going on in QM, just to help eliminate various lines of reasoning.The goal of foundations is to provide exactly such definitive statements...Historically, the goal of foundations of physics has always been to challenge accepted concepts
I genuinely still don't understand what's actually wrong with using axiomatic reasoning to eliminate various mathematical models. I also still don't really understand what is wrong with defining ##\psi##-ontology to be having a state space like ##\Lambda = \mathcal{H} \times \mathcal{A}##, ##\mathcal{H}## being part of the state space seems to be necessary for ##\psi##-ontology as ##\mathcal{H}## is simply the space of all ##\psi##s. Can you explain what ##\psi## being ontic without ##\mathcal{H}## being involved means? I think this would really help me.I have stated it already in post #64, and moreover argued at length why I believe the definition as given is a mischaracterization i.e. an incorrect operationalization of the concept that ##\psi## is ontological into a technical definition. Even stronger, I believe the strategy for some rigorous definition based on axioms at this stage is itself a misguided quest; we need preliminary mathematical models, not highly rigorous axiomatics.
The author convincingly demonstrates that practically everything known about particle physics, including the SM itself, can be derived from first principles by treating the electron as an evolved self-organized open system in the context of dissipative nonlinear systems.
At this stage, not immediately having PDE's or other equations isn't an issue whatsoever: one of the most successful scientific theories ever, evolution through natural selection, was not formulated using any mathematics at all, yet the predictions were very clear once conceptually grasped, but I digress.So, setting the important Bell theorem criticism aside, I can't help but view this paper as furious hand waving followed by an isolated guess. While the ideas seem intriguing (well worth a paper) what is the predictive power of the idea? SOSs need some level of underlying "system" to organize. Without QM what is that system even in principle?
To answer your question: that system is still particles, just not particles resulting from QM but instead from some deeper viewpoint; this is nothing new since viewpoints of particulate matter far precede QM (by millenia).
Actually, section II starts off by considering the evolution into stable existence an electron, i.e. a particle, in the following manner:This isn't an answer IMO, nor does it resemble the state space arguments of section II of the paper in a way that I understand. The argument first postulates a "state space", ##\psi_k##, which is essentially undefined and a transformation, ##F(\psi_k)##, which is assumed to have frequency doubling property which people familiar with SOS likely understand. The author then makes a general argument about the behavior of such systems. All this is fine.
However, clearly one cannot simply utter the word particles and get anywhere. One must also include some form of nonlinear interaction to even have frequency doubling. To extract any information, one must add the existence of electric charge and presumably a whole zoo of other quantum numbers like charm and so on. In the current scheme would these simply be disjoint facts, one parameter per prediction?
A purely qualitative treatment of attractor characterization leading directly to conclusions is standard practice in dynamical systems research and none of the above taken steps seem to be particularly - either mathematically or physically - controversial.
Can't work given certain assumptions, including the full validity of axioms of QM beyond what has been experimentally demonstrated; if QM is shown to be a limiting theory, many utilizations of the theorems to test hypotheses will be rendered invalid.Well it eliminates theories that can't work, since many people thought to suggest and build models that align with the theorem, I think it's useful for knowing what's not going on in QM. Since the eliminated models seem to be the most conventional ones and the class eliminated quite broad, I think it's useful, it just shows how weird the explanation will be. Even the fact that it has made anti-realist explanations more plausible is interesting enough on its own.
If the only relevant property is that 'it supports integration', then you have removed all the physics and are left with just mathematics. 'It supports integration' is equally empty as the statement 'numbers are used in physics'.Doesn't this just apply to any kind of mathematical research though. I still don't see why something "supporting integration" is epistemological, it depends on how you are viewing it in your theory. You might consider it an underlying state space of ontic states, just that the state space can be integrated over, but it doesn't make it an epistemic object, otherwise the manifold in GR is an epistemic object.
It eliminates lines of reasoning yes, it however may introduce lines of reasoning falsely as described above. Every QM foundations paper using or suggesting that no-go theorems can effectively be used as statistical tests to make conclusive statements about different physical hypotheses need to correct for the non-ideal nature of the test, i.e. report the accuracy of this test; this is an empirical matter not a logical or mathematical one.The ontological models framework does challenge accepted concepts, because it tells you what won't work. So it eliminates more naive ideas people had. I don't think it is the goal of the framework to provide definitive statements about what is actually going on in QM, just to help eliminate various lines of reasoning.
I'm not saying ##\mathcal{H}## shouldn't be involved, I am saying in terms of physics it isn't the most important mathematical quantity we should be thinking about.I genuinely still don't understand what's actually wrong with using axiomatic reasoning to eliminate various mathematical models. I also still don't really understand what is wrong with defining ##\psi##-ontology to be having a state space like ##\Lambda = \mathcal{H} \times \mathcal{A}##, ##\mathcal{H}## being part of the state space seems to be necessary for ##\psi##-ontology as ##\mathcal{H}## is simply the space of all ##\psi##s. Can you explain what ##\psi## being ontic without ##\mathcal{H}## being involved means? I think this would really help me.
Yes, there is a blatant use of the theorems as selection criteria for empirical hypotheses, i.e. as a statistical selection tool for novel hypotheses. The use of axiomatics in this manner has no scientific basis and is unheard of in the practice of physics, or worse, known to be an abuse of rationality in empirical matters.I understand if you simply see this sort of axiomatic investigation as not the optimal strategy or unlikely to help with progress. However at times you seem to suggesting their conclusions are also incorrect, or even some of the definitions, this I don't really understand.
The only valid use of such reasoning is selection of hypotheses based on confirming to unquestionable physical laws, such as conservation laws, which have been demonstrated to be empirically valid
Of course, as I have said, the theorems have assumptions, that's a given.Can't work given certain assumptions
That depends on the particular theorem. Bell's theorem for example does not rely on the full validity of QM, similar for many others. This implies to me that you haven't actually looked at the framework and are criticising it from a very abstract position of your own personal philosophy of science and your impression of what it must be.including the full validity of axioms of QM beyond what has been experimentally demonstrated
It's not a proposal that the real space of states only has the property of supporting integration and nothing else. Remember how it is being used here. It is saying "If your model involves a state space that at least supports integration..."If the only relevant property is that 'it supports integration', then you have removed all the physics and are left with just mathematics. 'It supports integration' is equally empty as the statement 'numbers are used in physics'.
I don't understand your use of epistemic I have to say. You seem to use it to mean abstract, but I don't see how a manifold is epistemic. "Stripped of physical content" maybe, but I don't know of any major literature calling this epistemic.it would transform the manifold into exactly an epistemological object
Well then coming back to where this originated, what makes it invalid as a definition of ##\psi##-ontic?I'm not saying ##\mathcal{H}## shouldn't be involved
Not necessarily, there are multiple routes:So, it should be fairly straight forward to reproduce the observed energy levels of a hydrogen atom. Please include hyperfine splitting and the Lamb shift in the analysis. How would such a calculation proceed?
Its more important than you realize as it makes or breaks everything even given the truth of the 5 other assumptions you are referring to. If for example unitarity is not actually 100% true in nature, then many no-go theorems lose their validity.Of course, as I have said, the theorems have assumptions, that's a given.
I have looked at the theorems. I should make clear that I am not judging all no-go theorems equally, I am saying each of them has to be judged on a case by case basis (like in law). Bell's theorem for example would survive, because it doesn't make the same assumptions/'mistakes' some of the other do. I am also saying just because Bell's theorem is valid, it doesn't mean the others will be as well.That depends on the particular theorem. Bell's theorem for example does not rely on the full validity of QM, similar for many others. This implies to me that you haven't actually looked at the framework and are criticising it from a very abstract position of your own personal philosophy of science and your impression of what it must be.
I think you are misunderstanding me, but maybe only slightly. The reason I asked about the properties of the resulting state space is to discover if these properties are necessarily part of all models which are extensions of QM. It seems very clear to me that being integrable isn't the most important property of the state space ##\Lambda##.The fact that you can prove theorems constraining such models shows it isn't as empty as "physics has numbers", to be honest that is just a kneejerk sneer at an entire field.
Yes, definitely. I have seen 'very good' papers across many fields of science, including physics, finance, economics, neuroscience, medicine, psychology and biology with equally bad or worse underlying conceptual reasoning; a mere mention of the limitations of the conclusions due to the assumptions is all a scientist needs to do to cover himself. There is no reason to suspect physicists are better than other scientists in this aspect.Do you think if the framework was as useful as just saying "physics has numbers" that it would be accepted into major journals?
That framework is a class of model, characterizing the properties of many models. The particular theorem(s) in question then in one swoop argue against the entire class.I think you are still treating the ontological models framework as an actual proposal for what nature is like, i.e. objecting to only looking at a state space that involves integration. Rather it is a presentation of general properties common to many models that attempt to move beyond QM and then demonstrating that from those properties alone one gets constraints.
I quote the Oxford Dictionary:I don't understand your use of epistemic I have to say. You seem to use it to mean abstract, but I don't see how a manifold is epistemic. "Stripped of physical content" maybe, but I don't know of any major literature calling this epistemic.
Definition of 'epistemic' in English:
epistemic (adjective): Relating to knowledge or to the degree of its validation.
Origin: 1920s: from Greek epistēmē ‘knowledge’ (see epistemology) + -ic.
Definition of epistemology in English:
epistemology (noun, mass noun):
Philosophy
The theory of knowledge, especially with regard to its methods, validity, and scope, and the distinction between justified belief and opinion.
Origin: Mid 19th century: from Greek epistēmē ‘knowledge’, from epistasthai ‘know, know how to do’.
Not necessarily, there are multiple routes:
How is a differentiable manifold epistemic though?I quote the Oxford Dictionary:
No, partially unknown. It is known that the correct equation:Okay, so what I'm taking from your list of potential approaches is that the answer to my initial question on what the underlying system to which the "method" is applied, is at present completely unknown.
I will let Feynman tell you why having immediately such an unrealistic expectation of a preliminary model such as this one is extremely shortsighted.I chose the example of the hydrogen atom because, at least in the current body of theory, it is a very specific and detailed dynamical system. Apparently, this new approach doesn't work on the hydrogen atom as is. It's going to be a hard sell.
In other words, what you are asking is an important eventual goal post - one of several goal posts - which should be attempted to be reached. Arguing from a QG or QM foundations perspective it is important but definitely not the most important thing for the preliminary model to achieve at this stage.Feynman said:For those people who insist that the only thing that is important is that the theory agrees with experiment, I would like to imagine a discussion between a Mayan astronomer and his student. The Mayans were able to calculate with great precision predictions, for example, for eclipses and for the position of the moon in the sky, the position of Venus, etc. It was all done by arithmetic. They counted a certain number and subtracted some numbers, and so on. There was no discussion of what the moon was. There was no discussion even of the idea that it went around. They just calculated the time when there would be an eclipse, or when the moon would rise at the full, and so on.
Suppose that a young man went to the astronomer and said, ‘I have an idea. Maybe those things are going around, and there are balls of something like rocks out there, and we could calculate how they move in a completely different way from just calculating what time they appear in the sky’. ‘Yes’, says the astronomer, ‘and how accurately can you predict eclipses ?’ He says, ‘I haven’t developed the thing very far yet’. Then says the astronomer, ‘Well, we can calculate eclipses more accurately than you can with your model, so you must not pay any attention to your idea because obviously the mathematical scheme is better’.
There is a very strong tendency, when someone comes up with an idea and says, ‘Let’s suppose that the world is this way’, for people to say to him, ‘What would you get for the answer to such and such a problem ?’ And he says, ‘I haven’t developed it far enough’. And they say, ‘Well, we have already developed it much further, and we can get the answers very accurately’. So it is a problem whether or not to worry about philosophies behind ideas.
In other words, what you are asking is an important eventual goal post - one of several goal posts - which should be attempted to be reached.
Easy: if the manifold doesn't characterize an existing object, but merely characterizes knowledge. There are manifolds in information geometry which can be constructed using the Fisher information metric; these constructions are purely epistemic.How is a differentiable manifold epistemic though?
The research program should be initially limited to 10 years; if no empirical results are reached in 5 years, the budget should be halved. Another 5 years without anything but mathematical discoveries and it should be abandoned.If 50 years of string theory has taught us anything it's something about chicken counting and hatching.
The research program should be initially limited to 10 years; if no empirical results are reached in 5 years, the budget should be halved. Another 5 years without anything but mathematical discoveries and it should be abandoned.
You're more lenient than I am; perhaps 'export to the mathematics department' is the correct euphemism.Well, things don't work that way and I'm kind of glad they don't. The literature is littered with less than successful ideas and programs people push and try to sell.
:)@Auto-Didact , I see your points now and I think we are in agreement. I'm restricted in my ability to reply for the next few days, but I think we're on the same lines just using different terminology. I'll write a longer post when I'm free.
No damage done, to be fair I have probably done some mischaracterization along the way as well.Apologies for getting heated in the previous post, I was mischaracterising you.