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Trick or Truth: The Mysterious Connection Between Physics and Mathematics
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How Should Humanity Steer the Future?
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It From Bit or Bit From It
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Which of Our Basic Physical Assumptions Are Wrong?
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Is Reality Digital or Analog?
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RECENT POSTS IN THIS TOPIC

Tim Palmer: on 2/23/20 at 8:29am UTC, wrote Please take a look at the referenced paper by Simant Dube. He finds...

Lawrence Crowell: on 2/22/20 at 22:06pm UTC, wrote I finally got to reading your paper. I have been working to get a piece of...

Yehonatan Knoll: on 2/20/20 at 17:41pm UTC, wrote Tim, What Bell had in mind (and explicitly expressed so in many...

Tim Palmer: on 2/18/20 at 8:04am UTC, wrote My view (which I tried to express in the essay) is that such undecidability...

Jack James: on 2/18/20 at 1:27am UTC, wrote Thanks Tim, I am very glad you are thinking (with the great tools of...

Tim Palmer: on 2/17/20 at 12:49pm UTC, wrote Yes I do think that relativistic space-time will be found to be emergent...

Jack James: on 2/17/20 at 10:34am UTC, wrote Dear Tim, Great essay, congrats. Wish I had a background in physics to...

Jonathan Dickau: on 2/14/20 at 15:52pm UTC, wrote That was a satisfying answer Tim... This speaks to the question of what...


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FQXi FORUM
February 27, 2020

CATEGORY: Undecidability, Uncomputability, and Unpredictability Essay Contest (2019-2020) [back]
TOPIC: Undecidability, Fractal Geometry and the Unity of Physics by Tim Palmer [refresh]
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Author Tim Palmer wrote on Jan. 25, 2020 @ 17:48 GMT
Essay Abstract

An uncomputable class of geometric model is described and used as part of a possible framework for drawing together the three great but largely disparate theories of 20th Century physics: general relativity, quantum theory and chaos theory. This class of model derives from the fractal invariant sets of certain nonlinear deterministic dynamical systems. It is shown why such subsets of state-space can be considered formally uncomputable, in the same sense that the Halting Problem is undecidable. In this framework, undecidability is only manifest in propositions about the physical consistency of putative hypothetical states. By contrast, physical processes occurring in space-time continue to be represented computably. This dichotomy provides a non-conspiratorial approach to the violation of Statistical Independence in the Bell Theorem, thereby pointing to a possible causal deterministic description of quantum physics.

Author Bio

Tim Palmer is a Royal Society (350th Anniversary) Research Professor in the Physics Department at the University of Oxford. Tim's PhD (under Dennis Sciama) provided the first quasi-local expression for gravitational energy-momentum in general relativity. Through most of his research career, Tim worked on the chaotic dynamics of the climate system and pioneered the development of ensemble methods for weather and climate prediction, for which he won the Institute of Physics's Dirac Gold Medal. However, Tim has retained an interest in foundations of physics and published a number of papers on non-computability in quantum physics (the first in 1995).

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David Brown wrote on Jan. 26, 2020 @ 01:54 GMT
From page 6, "In a local deterministic theory, each pair of entangled particles is described by a supplementary variable λ, often referred to as a hidden variable ... " — is this meant to be the definition of a "local deterministic theory" or is it a statement about the conventional wisdom of physicists concerning a "local deterministic theory"? Is it possible that time, space, energy, quantum...

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Author Tim Palmer replied on Jan. 27, 2020 @ 19:25 GMT
You can take it as a statement about conventional wisdom, allowing me to relate my uncomputable model to more conventional computable models.

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Dizhechko Boris Semyonovich wrote on Jan. 27, 2020 @ 16:55 GMT
Dear Tim Palmer, Your essay is the most verbose and most abstract of those that I have seen here. Fractals, attractor, Cantor set, p-adic numbers are very cool. To say a lot and to show your awareness of everything is a feature of scientific luminaries. I cannot compete with you with my neo-Cartesian generalization of modern physics, which is based on the identity of Descartes' space and matter and which claims that space moves because it is matter. Only in my essay I briefly show that the principle of uncertainty takes the opposite meaning, i.e. becomes the principle of definiteness of points of space, which is matter; further I show the relationship of the probability density of states with the Lorentz factor; I further explain the formula mass-energy of equivalence by the fact that for each corpuscle there is a flow of forces equal to the product of the Planck constant and the speed of light - ch (Casimir force); further I propose the definition of mass as a stream of centrifugal acceleration through a closed surface of a corpuscle, etc.

         I invite you to discuss my essay, in which I show the successes of the new Cartesian generalization of modern physics, based on the identity of space and matter of Descartes: “The transformation of uncertainty into certainty. The relationship of the Lorentz factor with the probability density of states. And more from a new Cartesian generalization of modern physics. by Dizhechko Boris Semyonovich. "

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Author Tim Palmer replied on Jan. 27, 2020 @ 19:26 GMT
Thank you. I look forward to reading your essay.

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Jochen Szangolies wrote on Jan. 28, 2020 @ 07:37 GMT
Dear Tim,

congratulations on an eminently readable and engaging essay on a difficult topic! I will need some time to fully digest your arguments, but I wanted to leave a few preliminary comments---also because our two approaches have some overlap, in particular as regards undecidability and Bell/EPR.

I'll state my biases upfront: I'm skeptical of any sort of 'completion' of quantum...

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Author Tim Palmer replied on Jan. 28, 2020 @ 08:03 GMT
Thanks indeed for these very kind remarks.

A few comments. I do not really view my approach as a completion of quantum mechanics in the sense of providing extra structure to be added to the quantum theoretic formalism. As mentioned in the Appendix to the essay, the closed Hilbert Space of quantum mechanics only arises in the singular limit where my finite fractal parameter p is set equal to infinity, and this is an unphysical limit! Hence, rather than complete quantum mechanics, my own view is that, guided by quantum theory, we have to go back to basics taking ideas based around non-computability and fractal geometry seriously!

You are right to be sceptical of superdeterminism. However, the reasons to be sceptical - e.g. that it would imply statistically inequivalent sub-ensembles of particle pairs in a Bell experiment, simply do not apply to this model. Instead, I focus on a violation of Statistical Independence which only has implications when considering hypothetical counterfactual measurements in a Bell experiment. This interpretation of the violation of SI only makes sense in the type of non-computable model proposed.

In fact this same point will also lead to a negation of the Pusey Barrett Rudolph theorem, through a violation of Preparation Independence. However, once again such a violation only occurs when considering counterfactual alternative preparations.

The bottom line here (something I focus on in the essay) is that we have to think very carefully about what we mean by things like free choice and causality in these quantum no-go theorems: counterfactual-based and space-time based definitions (c.f Newton clapping his hands in the quad) are inequivalent in the type of non-computable model I am proposing here.

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Joe A Nahhas replied on Jan. 29, 2020 @ 00:39 GMT
I can produce general relativity experimental numbers and special relativity experimental numbers 5000 times using any of 5000 physical sciences laws and using any level mathematics including 5th grade arithmetic and I can produce entire Einstein's relativity theory from Newton's equation contrary to what main stream scientists claim and I can produce it 5000 times as visual effects between (27.321 days, 365.256 days) motion (PHD dissertation subject 1990 University of Michigan Nuclear engineering department) I introduced "Hacking Physical Reality" and ended "Nobel Physics" decades ago. I know I sound unbelievable but it is a fact and is a well established fact.

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Jochen Szangolies replied on Jan. 29, 2020 @ 16:57 GMT
I've been thinking about differences and similarities between our respective models. I focus on a function which assigns values for all measurements and all states of a certain system, and show that there must be measurements such that this function is undefined---which yields the backdrop for Bell inequality violations. This also needs a restriction on admissible counterfactuals---otherwise, the...

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Joe A Nahhas wrote on Jan. 29, 2020 @ 00:23 GMT
Physical reality can be hacked. First method of hacking physical reality is visual hacking. Visual hacking of physical reality is a display of physical objects motion in real time and physical objects motion has nowhere to hide caught naked for the first time since the beginning of time on display and in real time.

1 – Visual Hacking of Earth’s motion or a display of Earth’s motion in real time = 27.321 days cycle wrongly assigned to the Moon.

2 – Hacking the Sun’s motion or a display of the Sun’s motion in real time = 365.256 days cycle wrongly assigned to Earth.

3 – Physical sciences 5000 laws of physics, astronomy, physical chemistry, physical biology, physical engineering and technology in its entirety is based on light sources as a measuring tool and as used it only measures physics lab physical motion or Earth’s motion in 27.321 days.

4 – The (27.321 days, 365.256 days) Time cycles distance equivalence cycles = (R meters, C meters); R = Earth’s theoretical radius = 6371000 meters and C = 299792458 meter claimed as light speed/second

4 – The Space – Time errors = NASA’s space data sheets

5 – The Inverse Space – Time errors = CERN’s atomic/nuclear data

Meaning: Physical Sciences 5000 physics laws can be produced as (27.321days, 365.256 days, 6371000 meters, 299792458 meters) space –time errors is the subject of this contest of Extermination of Modern and Nobel Prize winners physics and physicists from 1610 Copernicus to 2020 Nobel winners using any level mathematics including 5th grade arithmetic and starting with Physics Most Erroneous Equation E = MC2. Are you ready to hack and strip the incontestable truth of physical reality?

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Jonathan J. Dickau wrote on Jan. 30, 2020 @ 19:33 GMT
I very much like this idea Tim...

But I will have to re-read your paper a few times to fully grasp the depth of your reasoning. It seems reminiscent of some of the wild-sounding ideas about Cantorian space from Mohammed El Naschie when he was editing 'Chaos, Solitons, & Fractals' but with a different flavor. I think maybe your ideas have a more solid basis, but with El Naschie it is hard to tell - because so many of his references are self-citations from earlier work, hidden behind a pay wall.

I also talk about fractals in my essay, but the context is rather different. For what it is worth; I like the work of Nottale on Scale Relativity, and I admire the breadth of its explanatory power as a model, though I don't think he got every detail right. When sent a copy by the publisher of his book for review; I enthusiastically recommended its publication. And it inspired my departed colleague Ray Munroe, who I think used it in an FQXi essay.

More later,

Jonathan

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Author Tim Palmer replied on Jan. 31, 2020 @ 07:49 GMT
I think the mathematics in my talk is pretty solid. As to the physics, well at the end of the day it will come down to experiment. I expect the crucial experiment to test invariant set theory will lie in the field of table-top experiments which probe the accuracy of quantum theory in domains where the self gravitation of a quantum system is not negligible. For example, based on the idea that gravity represents a clustering of states on the invariant set, the theory predicts that gravity is inherently decoherent and cannot itself encode entanglement.

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Jonathan J. Dickau replied on Jan. 31, 2020 @ 15:30 GMT
I like that answer Tim...

There was recently published a paper describing an experiment that claimed to disprove objective reality, using a system with 6 entangled qubits. I think this is wrong. There are too many co-linear points, and the entire apparatus is co-planar. There are also 6 points instead of the 7 required by projective geometry. An experiment designed to correct these flaws could also search for the effects you describe. A ball of osmium placed at one end of the bench could be used to detect gravity-induced decoherence, and so on.

In other words; I think it could be done.

All the Best,

Jonathan

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Jonathan J. Dickau replied on Jan. 31, 2020 @ 15:41 GMT
For what it's worth...

I had some interaction with Phil Pearle, when he was first developing statevector reduction theory, which later blossomed into CSL. I have followed that evolution somewhat. But I recall a recent paper by Ivan Agullo that also talked about gravity-induced decoherence and broken EM symmetry, which I will try to find.

I'd love to discuss this further. I will try to read your paper again first.

Best,

Jonathan

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Robert H McEachern wrote on Feb. 1, 2020 @ 20:53 GMT
Tim,

On page 6 of your essay, you state that "The principal obstacle in drawing together chaos and quantum theory is therefore not the linearity of the Schrodinger equation, but the Bell Theorem."

You appear to be unaware of the fact that Bell's theorem only applies to entangled, perfectly identical particles, like identical twins. There is no evidence that such idealized particles actually exist in the real world. Consequently, it is easy to demonstrate that entangled, non-identical, "fraternal twin" particles, will reproduce the observed "Bell correlations", with supposedly impossible-to-obtain detection efficiencies, and without any need for hidden variables, non-locality or any other non-classical explanation. This has a direct bearing on your issue of "drawing together chaos and quantum theory", since the underlying cause for the "quantum" behaviors, turns out to be, one single-bit-of-information removed from chaos (unrepeatable behavior).

Rob McEachern

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Lorraine Ford wrote on Feb. 5, 2020 @ 12:27 GMT
Tim Palmer,

You recently co-wrote an arxiv paper titled Rethinking Superdeterminism together with physicist Sabine Hossenfelder [1].

I happen to think it is rather strange for an internationally renowned meteorologist to think that the climate and everything else is superdetermined anyway. Here is an exchange I had today with your co-author Sabine Hossenfelder about whether the fires and the destruction in Australia are/were superdetermined [2]:

Lorraine Ford 1:31 AM, February 05, 2020

Re "your paper with Dr. H[ossenfelder]" (on superdeterminism): I hope Dr. H[ossenfelder] and Dr. P[almer] are enjoying the smell of burnt koala flesh and fur wafting over from Australia. It was all superdetermined, according to them.

Sabine Hossenfelder 2:34 AM, February 05, 2020

Lorraine, You think you are witty. You are wrong.

Lorraine Ford 3:16 AM, February 05, 2020

Sabine, I DON'T think I'm witty. I'm Australian, living with smoke-hazy skies, the horror of a billion animal deaths, let alone the people who have died, and more than 10 million acres of land burnt. You are saying that this was all superdetermined.

Sabine Hossenfelder 4:12 AM, February 05, 2020

Lorraine, Correct. If you have a point to make, then make it and stop wasting our time.

1. https://arxiv.org/abs/1912.06462v2

2. http://backreaction.blogspot.com/2020/02/guest-post-undecida
bility.html

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Author Tim Palmer replied on Feb. 5, 2020 @ 13:28 GMT
Lorraine

Perhaps the most important thing to say in relation to my essay is that there is a difference between "superdeterminism" and "determinism". The former questions whether it is the case that, in a hidden variable model of the Bell experiment, the distribution of hidden variables are independent of the measurement settings. Without bizarre conspiracies, such distributions certainly...

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Lorraine Ford replied on Feb. 6, 2020 @ 00:43 GMT
Tim Palmer,

Thanks for your detailed reply. I think I WAS a little confused about the difference between determinism and superdeterminism: thanks for explaining. However, you are still in effect saying that every single koala death by fire was pre-determined.

I will put the determinism issue another way, in terms of the problem of decidability: how we make decisions, and how we...

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Author Tim Palmer replied on Feb. 6, 2020 @ 07:44 GMT
We are going a bit off topic here. However, as I discuss in my essay, one can view free will as an absence of constraints that would otherwise prevent one from doing what one wants to do, a definition that is compatible with determinism. From this one could form a theory of how we make decisions based on maximising some objective function which somehow encodes our desires. This does allow one to learn from previous bad decisions, since such previous experiences would provide us with data that a certain type of decision, if repeated, would lead to a reduction, not an increase, in that objective function.

However, we are veering into an area that has exercised philosophers for thousands of years and I suggest this is not the right place to discuss such matters. Of course, I respect your alternative point of view - there are many eminent philosophers and scientists who would agree with you.

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Domenico Oricchio wrote on Feb. 5, 2020 @ 17:46 GMT
I have a problem with the idea that the chaos is incompatible with relativistic invariance; I cant’t give an example now, but a differential equation that is relativistic invariant and chaotic could be possible: I am thinking that in the solution set of the Einstein Field Equation there could be a solution that covers the space with a non-integer dimension, thus obtaining chaos for the metric tensors dynamics. I think that, for example, the Black Hole merger has an attractor (fixed point or almost limit cycle).

An Einstein field equation with weak field is a linearizable theory, so that there is an approximation nearly linear.

I don’t understand: is a quantum non-locality the effect of the quantum field theory? The gauge boson interact between parts of the system, that transmit quantum information. So that to say that a system must satisfy bell's theorem is not equivalent to say: must a gauge boson exist?

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Author Tim Palmer replied on Feb. 6, 2020 @ 07:51 GMT
Actually what I say is that chaos is only superficially incompatible with relativistic invariance. The key is to "geometrise" chaos and that can be done by considering the invariant sets of chaos. I then try to show that these invariant sets may in turn help make chaos compatible with quantum theory.

My own view is that the resolution of the Bell Theorem is not through quantum field theory, since that is an extension of quantum theory. Rather my belief is that there is a deeper deterministic formalism based on non-computable fractal invariant sets which has quantum theory as a singular limit.

I am currently working on an extension of these invariant set ideas to incorporate the formalism of relativistic quantum field theory.

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Domenico Oricchio replied on Feb. 6, 2020 @ 14:43 GMT
Your essay is interesting.

Reading it made me think.

For example if there was a chaotic state in general relativity, then is it possible that Hausdorff's measure of particle trajectory an relativistic invariant? If it were not so, then there would be an observer for whom the relativist trajectory is non-fractal, but this seems unlikely to me (it's like a change of topology, to change from a chaotic trajectory to a non-chaotic trajectory).

Also for the Bell theorem (or the Einstein-Podolsky-Rosen paradox), it is possible to study the Feynmann diagram for the cross section in the scattering of two polarized Dirac particles (I read today the results in Greiner book) and to obtain the probability of the final state (with elicities). If there are interaction, so gauge bosons, then there is not an instantaneous effects; the collapse of Alice state communicate the state to Bob using the gauge bosons interaction, with the light speed.

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Author Tim Palmer wrote on Feb. 6, 2020 @ 07:42 GMT
We are going a bit off topic here. However, as I discuss in my essay, one can view free will as an absence of constraints that would otherwise prevent one from doing what one wants to do, a definition that is compatible with determinism. From this one could form a theory of how we make decisions based on maximising some objective function which somehow encodes our desires. This does allow one to...

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Colin Walker wrote on Feb. 6, 2020 @ 23:20 GMT
Hi Tim,

It is quite a revolutionary program you have embarked on, overthrowing the infinitesimal and subverting the continuum. Your standard of rationality includes its mathematical definition: that any rational quantity can be expressed as a ratio of whole numbers. The conviction that the infinite and the infinitesimal have no place in physics goes well with the idea that appropriate...

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Author Tim Palmer wrote on Feb. 7, 2020 @ 08:15 GMT
Thanks Colin.

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Jonathan J. Dickau wrote on Feb. 13, 2020 @ 22:18 GMT
Hello again Tim,

After reading Lawrence Crowell's paper; I have a greater appreciation for your work, and even moreso that you are able to write so lucidly about it for lay audiences. I am impressed. I will have more questions now, after all that fuel for thought.

Would the correctness of your theory imply that the fabric of spacetime is fractal? This is a feature of several quantum gravity theories, in terms of the microstructure. Does that project onto the large scale structure of the cosmos in your view? Would it surprise you if I said it appears some of your starting assumptions would follow naturally, if my own theory pans out?

Tip of the old iceberg for you.

More later,

Jonathan

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Author Tim Palmer replied on Feb. 14, 2020 @ 07:32 GMT
Thanks for these kind comments Jonathan.

You ask a good question. However, to be honest, I am not 100% sure at present what my model implies about the structure of space-time, so I prefer to be agnostic about this for now. However, I am working on a generalisation of my model so that the properties of momentum/position commutators are (like spin commutators) describable by number theory. This will allow me to start reformulating relativistic quantum field theory in a more deterministic framework, and from there answers to your questions should emerge. However, I want to do this slowly and carefully, and not jump to conclusions that may at first sight seem reasonable, but will ultimately turn out to be wrong.

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Jonathan J. Dickau replied on Feb. 14, 2020 @ 15:52 GMT
That was a satisfying answer Tim...

This speaks to the question of what sort of evidence of your theory would we see in the cosmos that might provide verification or refutation for its veracity. I asked a similar question of Gerard 't Hooft at one point and his answer was similar - that it was too early to tell what the cosmic evidence would be.

The following year at FFP11; he elaborated in his talk about the desirability of and difficulties with obtaining Lorentz invariance in a CA based QG theory, but still no hard predictions about what we would observe (in black hole emissions perhaps) that would distinguish it from the standard.

I've seen or heard several predictions from Loop Quantum Gravity folks about possible signature detections - such as Lorentz invariance violations, comb filtered emissions from black holes, and so on. But I see that each time such a prediction is made, folks will jump on it as excluding a theory if the exact signature predicted is not found. And String Theory folks seemingly refrain from making any hard predictions at all.

All the Best,

Jonathan

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Jack James wrote on Feb. 17, 2020 @ 10:34 GMT
Dear Tim,

Great essay, congrats. Wish I had a background in physics to completely understand. Please indulge me if you have time.

1) Are you essentially suggesting that mathematical incomputability/undecidability exists as space-time, emergent from quantum non-linearity (as that is what the wave function seems to suggest, which may in effect be the cause of macroscopic gravity?

2) If something (anything that exists as part of detectable science) is incomplete as a matter of ontology (incomplete in the Godel sense) how could that ontology possibly verify determinism or superdeterminism?

Best,

Jack

(Essay: Misalignment Problem - You may enjoy the amalgamated sleuths section)

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Author Tim Palmer replied on Feb. 17, 2020 @ 12:49 GMT
Yes I do think that relativistic space-time will be found to be emergent from this fractal state-space geometry. However, making this a precise notion, and not just an aspiration, is something that I am currently thinking hard about!

I'm not sure I fully understand your second question. However, it triggers in my mind an important question: are there experimentally testable consequences of determinism? Again, this is something my collaborator Sabine Hossenfelder and I are currently thinking about.

So, in short, I can't answer either question, but they both touch on important issues!

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Jack James replied on Feb. 18, 2020 @ 01:27 GMT
Thanks Tim,

I am very glad you are thinking (with the great tools of physics) about the same questions I am.

Re Q2 I think you have grasped my question in your statement "are there experimentally testable consequences of determinism?" Because if Godel's incompleteness manifests physically (space-time & mass) then you could never test determinism because the physical system would have unknowable states that cannot be determined by the system itself. So you couldn't have a determinable system, could you?

Best,

Jack

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Author Tim Palmer replied on Feb. 18, 2020 @ 08:04 GMT
My view (which I tried to express in the essay) is that such undecidability only manifests itself in questions about the structure of state space, not in questions about the structure of, or processes in, space-time. Hence I do think there are experimentally testable consequences of determinism.

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Yehonatan Knoll wrote on Feb. 20, 2020 @ 17:41 GMT
Tim,

What Bell had in mind (and explicitly expressed so in many interviews) is that, if particles are little machines, then his inequality must be respected. Now, as with any statement regarding the physical world, it tacitly assumes also `common sense'. One can bend this vague notion to an arbitrary extent, but there is a more direct attack on Bell's theorem, which has been staring us in the face for over a century: Particles (and chaotic systems and humans) are not machines! (no new-age stuff)

You are invited to read my essay which is further relevant to your main area of expertise - predicting the behavior of chaotic systems. Ensemble average over initial conditions is probably not the right way to do so.

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Lawrence B. Crowell wrote on Feb. 22, 2020 @ 22:06 GMT
I finally got to reading your paper. I have been working to get a piece of instrumentation developed meant to go to another planet. In reading this I think what you say is maybe not that different from what I develop.

Your paper drives home the point on using the Blum, Shub, and Smale (BSS) concept of computability. This is an odd concept for it involves complete computation of the reals...

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Author Tim Palmer wrote on Feb. 23, 2020 @ 08:29 GMT
Please take a look at the referenced paper by Simant Dube. He finds essentially the same computability result as Blum et al, studying the fractal attractors of iterated function systems.

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