Indeterminism, causality and information: Has physics ever been deterministic? by Flavio Del Santo

Dear Flavio,

It appears that the following differences in ideas on determinism and on information may require clarification.

1. Principle of infinite precision: Ontological - there exists an actual value of every physical quantity, with its infinite determined digits (in any arbitrary numerical base)... It is only when its formalism is complemented with this principle that classical physics becomes deterministic.

An argument may be constructed against infinite precision describable as sequence of infinite digits. Value of pi in, say, binary digits does have infinite expansion, but it is just a point on a real line. And in the units of pi, its value is just 1. So, a system may have a state that corresponds to pi, infinite digits are not needed to construct infinite precision. What can be said instead is that not all points on real line may be traversed by the state of a physical system. Irrationality of numbers is relative to unit of measures as all datum. Also, one has to give a mechanism by which indeterminism can be realized in physical systems. Both the points are dealt with in my essay (Mother of all existence).

2. Though following Rovelli, you have discussed quantization of space, yet a distinction is warranted. Usually, we do not interpret classical dynamical expressions as quantized, it does not necessarily mean that one cannot think of deterministic quantized changes in observable spaces. This statement has nothing to do with quantum physics of superposition and entanglement -- quantization can exist in classical domain too, e.g., at Planck's scale as you refer. Since we do not have quantization limited precise measuring instruments the possibility of quantized determinism does exist -- this is only for arguments sake. Then all measures get translated into integers, which will avoid the requirement of infinite precision. It is like spring loaded switch, which can be either on or off only by classical function, or checker board like time and space. The determinism must be killed with some other arguments. Therefore, the statement, "This clearly shows that the principle of infinite precision is a necessary condition for determinism", does not hold. The classical quantization seems to directly oppose the statement, "as soon as one realizes that the mathematical real numbers are not really real, i.e. they have no physical significance, then one concludes that classical physics is not deterministic."

3. You state -- This view goes under the name of Landauer's principle, in short, "information is physical". In Ref. [13], Gisin gave sound arguments to support the claim that "a finite volume of space cannot contain more than a finite amount of information".

Landauer's principle refers to how all information are represented by states of matter, referring to what they mean or express. But in Gisin's view information is reduced to quantity of information in bits, losing the reference to the meaning. This is an example of why we have not been able to construct mechanism of processing of semantics of information as brain does. Moreover, physicists' interpretation of information content of a system being its own state description causes so many issues with the reality of information. If it was to be so, then no matter what information processing results from interaction, an information can never be anything but the description of physical state. This is how physicists have artificially created a barrier between this interpretation of information and what a physical device like brain does in dealing with the semantics of information. Instead, the reality of information relates to what an observable state of a system causally correlates with, as dealt with in my essay. A single elemental state of a system may represent the information of very high level structured and abstract semantics if processing is organized in modular hierarchy as is also evident from neuronal processing in the brain. It is bizarre that physicists are blinded to this apparent reality.

It is because of Gisin's like interpretation that requires information to have certain amount of physical space. Moreover, such interpretation also runs in opposition to the fact that even in artificially designed devices, information is assigned to and coded by the states of registers (systems), not to and by the registers themselves. Physicists and computer scientists have hijacked the term information to mean amount of information measurable in bits leaving the most apparent phenomena of all to us humans, semantic processing in the brain unresolved.

Rajiv

Wonderful essay, Flavio! Probably the best I've read so far, in fact (and I've read a lot...). Well written, full of lovely ideas about determinism and indeterminism in physics, and a clever take on the central question of the essay contest.

I still wonder whether classical physics "is" deterministic, a la the views expressed by Boltzmann and Exner you quoted at the beginning of your essay. But I guess this is a non-question, since physics isn't classical anyway. And even if it were classical, (i) it's hard to imagine a way to experimentally distinguish between determinism and indeterminism, and (ii) whether such a description is useful in a world where measurements provide only finite information is another question all together. You seem to take the view that this indeterminate view is more useful, which I agree with.

Your essay also makes me wonder about the possible different interpretations of classical mechanics. I see you've already thought about this a bit (e.g. you mention in section 3C a classical analogue to objective collapse models, and you mention in footnote 8 a possible analogue to the Everettian interpretation). Has someone written about this? If not, we should write an article about it! There are already many different mathematical formulations of classical mechanics (e.g. the amusing Koopman-von Neumann formulation, involving a Hilbert space and operators); perhaps the issue of the different interpretations has been overlooked.

Some miscellaneous comments/questions:

In a classical world, what prevents knowing an arbitrarily large number of digits of some observable? If I take more and more time and measure more and more carefully, can't I measure more and more accurately, in principle?

Stability property of measurement: I understand what you're getting at, but can't consecutive measurements have slightly different values? I guess it depends on what you mean by a digit being "determined". Determined in the sense of being reliably to known to be some value? As you know, there is uncertainty in later digits of some measurements (and less trivial measurements may have more than one uncertain digit, in practice).

Also, how does this uncertainty affect ideas about the arrow of time? Stochastic theories are not time reversible, in a certain technical sense.

John

P.S. A book that was recommended to me a few months ago may be up your alley: "Reductionism, Emergence and Levels of Reality" by Chibbaro et al.

Dear Flavio

Thanks for your wonderful essay that deals quite beautifully with several delicious subtleties!

I do have a few questions/comments. (Perhaps if I were less busy, I would find answers by studying your references, but, sadly, that will not be possible for me any time soon.)

1) (Perhaps important) You have, I believe, misidentified "real numbers" as the culprit in your "principle of infinite precision." I take "infinite precision" to refer to the precision of the limit of a hypothetical infinite string of ever-more precise measurements. If your spacetime is modeled by any topological space that is dense, you will have the potential for an "infinite precision" problem. It springs from spacetime being dense, rather than from it being continuous. This means that as far as the principle of infinite precision is concerned, rational numbers have the same potential as real numbers. For example, you can build your "Figure 1" argument equally well on a small piece of the rational number line.

Perhaps it's important to add that it is clear that none of the above impacts your nicely constructed, alternative model of classical mechanics. So perhaps it's of no real consequence.

2) (Probably quite minor) Near the top of page 5 you say (statement 1) "Note again that without REAL NUMBERS, one cannot any longer uphold determinism." Even if we change that to (statement 1a) "... without INFINITE PRECISION, one cannot...." it appears to be incorrect, and it is certainly not justified (or even broached) by anything you say earlier in the essay. Everything earlier was more along the lines of the inverse (statement 2) ".....WITH real numbers one cannot avoid determinism." And in addition, statement 2 is also all you need or use for everything later in the essay. So statement 1 appears to be just an odd extraneous claim that appears to be of no importance for your essay. Or am I missing something?

3) (I seem to be lost, here.) You cite Landauer's Principle but, I guess I'm confused. I see nothing there to justify singling out information from any other real world concept that can also be treated mathematically. To be sure, one can make a case against Platonic Ideals "existing" in any meaningful way, but is the statement "information is physical" in some way independent of the more pedestrian idea that "all circles, all parallel lines, .... all geometry is physical" or "all counting is physical" or, etc...??? It seems almost capricious to single out information. OK. What am I missing?

John S

Dear flavio. Wow.one of the best essays I've read and rated this season. I particularly like your expose on the measurement problem.i too was also particurlary interested in our human nature and limits that lead to the 3uns here https://fqxi.org/community/forum/topic/3525.please take your time to review. all the Best in the contest.

Intuitionism (not intuitivism) refers to a so called Urintuition, to the counting. Real numbers are uncountable even in the sense of they cannot be arranged one to one along the natural numbers. In principle, already the old Greeks were aware of this calamity. Accordingly, Brouwer's constructivism was merely a bit more complicated but not superior. I suggest calculating as if because I don't expect any practical progress from putting mathematics on new basics. Of course, abandoning idolization of Cantor's alephs in excess of aleph one might be overdue.

Well, in contrast to the mentally tangible dot, Euclid's point is an ideal fiction.

The original meaning of being infinite is likewise quite different from Leibniz's mathematical infinity.Nonetheless calculate as if.

I indirectly asked for imaginable consequences in science.Given you are right or wrong. Does it matter?

Eckard Blumschein

Hi Flavio...

Thanks for providing a broader conceptual framework in witch to structure the classical Indeterminate/Determinate discussion, and for "relaxing" prior constraints on reductionism that seemingly denied initial state condition analysis.

In that a digital processor's capacity to "determine" is a measure of its intelligence, info processing specific language is highly applicable to the discussion, and analysis of an initial state condition, in terms of a geometry framework that facilitates spatial minimum/indivisible unit (QI) addressing for mapping emergence of an intelligent network... i.e. network root architecture... suggest Causality is deterministic, but not a random process... i.e. it must be resolved.

REF: Cause Energy Pulsed Emergence as Space-Time Energy http://www.uqsmatrixmechanix.com/UQSMarcelMLTD.jpg

REF: Unified Quantization of a Sphere (UQS) http://www.uqsmatrixmechanix.com/UQSOSE.jpg

REF: UQS Directionally Unbiased Point Source QE Emission www.uqsmatrixmechanix.com/UQST-TVNH.php

If, as per Stephen Wolfram REF:

"Finally we may have a path to the fundamental theory of physics and its beautiful" https://writings.stephenwolfram.com/2020/04/finally-we-may-have-a-path-to-the-fundamental-theory-of-physics-and-its-beautiful,

one can conceptualize discrete 3D Space, and spatially defined Energy quanta, then in a manner analogous to the evolving logic functionality of conventional digital processors, Causality, utilizing a fundamental info process, that on each Q-tick pulse, apparently harmoniously resolves emission and field wide distribution of minimum/indivisible spatially defined Energy quanta (QE), which facilitates an intelligence that emerges as a consequence of logic derived from sequential resolve of QE distribution within the minimum/indivisible address (QI) mapped spatial network, would likely develop logic circuits to monitor what occurs locally... i.e. Space-Time Energy events within the perception range of the monitoring entity.

Given a concise differentiation between PHYSICAL and META-PHYSICAL... i.e. PHYSICAL as occupying Space and META-PHYSICAL as Spaceless.. if the monitoring PHYSICAL logic circuit... e.g. humankind... can not perceive the Space-Time PHYSICAL scale at which system intelligence resolves distribution of QE/QI for the entire field, on each Q-Tick, this does not verify that Causality is indeterminate, nor does it imply that Causal META-PHYSICAL processes do not exist, but if the monitoring entity's "self-awareness", as distinct from "system-awareness", is of the opinion that the system is indeterminate... i.e. not intelligent... that entity can not conceptualize utilization of system intelligence, by PHYSICAL and/or META-PHYSICAL means.

In an environment in which an inability to process decisions is constraining functionality of one's Reality, if one can conceptualize an emerging intelligent network, the possibility of accessing that intelligence becomes a passion... i.e. resurgence of Laplace Demon???

REF: - Topic: "Modeling Universal Intelligence" by Sue Lingo

Thanks Flavio, for your thought provoking essay, and I am looking forward to your thoughtful comments on my essay.

Sue Lingo

UQS Author/Logician

www.uqsmatrixmechanix.com

Ahem

Hi Flavio,

Fantastic essay! I see this builds on your work with Gisin. It is interesting to note that many years ago I made similar arguments about precision in classical physics. In fact, in Bohm's book on Quantum Theory (before he set about devising Bohmian mechanics), he makes a related argument regarding waves. There's an interesting relationship here to locality in that one can argue that some classically imprecise quantities stem from the non-locality of certain concepts, e.g. even in classical physics a wave is a non-local concept.

At any rate, I think the faith in infinite precision in classical physics has its origin in the development of calculus. I'll e-mail you a few links about this, but the basic idea is that one develops a certain faith in precision if one accepts the physical truth of infinitesimals. This is actually even a debate in mathematics itself as it led Abraham Robinson to develop non-standard analysis in the 1960s.

I am still a little fuzzy on the concept of an FIQ. I mean, while it clearly functions differently in your theory than a real number, it appears to still be based on the same basis as real numbers, i.e. the idea that numbers are ultimately an outgrowth of the notion of counting. Bertrand Russell discusses this in his book on the philosophy of mathematics.

Anyway, this is good stuff and we'll have to chat about it further at some point.

Dear Del Santo:

It is a pleasure reading your essay. It is very well presented. Worthy of receiving high grades.

Fundamentally, we are in agreement. Nature does not work out of two orthogonal worlds of Classical Mechanics and Quantum Mechanics. Nature is working out of one single undivided space using one set of rules, however complex they may be.

However, as an experimentalist, I find that indeterminism in our universe emerges without the need of sophisticated math or philosophical deliberations.

Please, make time to read my essay and grade it.

"Complete Information Retrieval: A Fundamental Challenge"

https://fqxi.org/community/forum/topic/3565

The universe is fundamentally stochastic because the observable radiations and particles are emergent oscillations/vibrations of the universal cosmic space, which is, at the same time, full of random "background" fluctuations. These fluctuations, however weak they may be, nonetheless are perturbing any and all other interactions going on in the universe. Since, human initiated measurements are also interactions between our chosen interactants in our apparatus, stochastical changes will be inevitable in every measurements, classical or quantum.

I am an experimentalist. Our measurements will always be imprecise. That we had been, we now are, and we will always be, information limited, emerges naturally when we enumerate the basic steps in any measurement:

(i) Data are some physical transformation taking place inside the apparatus.

(ii) The physical transformation in a detectable material always require some energy exchange between the interactants, the "unknown" and the "known", where the "known" is the reference interactant.

(iii) The energy exchange must be guided by some force of interaction operating between the chosen interactants.

(iv) Since we have started with an unknown universe, from the standpoint of building physics theories, the "known" entities are known only partially, never completely. This also creates information bottleneck for the "unknown" entity. Note that in spite of innumerable experiments, we still do not know what electrons and photons really are.

(v) All forces of interactions are distance dependent. Hence, the interactants must be placed within the range of each other's mutual influence (force-field). Force-field creates the necessary physical "entanglement" between interacting entities for the energy transfer to proceed. In other words, interactants must be "locally or regional" within their physical sphere of influence. They must be "entangled" by a perceptible physical force. Our equations are built on such hard causality.

(vi) The final data in all instruments suffer from the lack of 100% fidelity. This is another permanent problem of imprecision. We can keep on reducing the error margin as our technology enhances; but we do not know how to completely eliminate this error.

Many of my earlier papers have also articulated this position. They can be downloaded from:

http://www.natureoflight.org/CP/

You can also download the paper: "Next Frontier in Physics--Space as a Complex Tension Field"; Journal of Modern Physics, 2012, 3, 1357-1368,

http://dx.doi.org/10.4236/jmp.2012.310173

Sincerely,

Chandra.

Prof. Chandasekhar Roychoudhuri

Flavio,

Hope you have time to check mine out before the deadline: https://fqxi.org/community/forum/topic/3396

Jim Hoover.

Dear Dr. Flavio Del Santo,

As a layperson (I am a lowly undergrad and majoring in CS), I found your work to be simultaneously profound and accessible!

Prior to reading your work, I presumed determinism was built into the foundations of classical physics, and it was a joy to discover otherwise.I kept a copy your essay on my computer for repeated reading and future references ( some of the formalism eluded me).

Indeed, showing how determinism contradicts physicality provided me with a lot of food for thought ( determinism implies infinite information content, which violates the physical nature of information was a very interesting thing for me to know)

I dare to say the common view of classical physics as inherently deterministic is usually told and taught to everyone ( I was never told otherwise until now) is because:

a) Many find determinism to be powerful;knowing a sufficiently advanced intellect can predict with absolute certainty gives us hope that human civilization may become that intellect, so this tacit assumption is mistaken to be a part of the orthodox position.

b) Mathematics is deterministic in most cases ( we can prove with certitude certain statements from a set of axioms; thought Godel's Theorem gets in the way of perfect determinism, some statements cannot be proven) and we like physics to confirm as closely possible to mathematics ( something my and my co-author's essay (link: https://fqxi.org/community/forum/topic/3563) addresses).

Kind Regards,

Raiyan Reza

Dear Flavio,

Perhaps we are just talking past each other, but I must ask you to reread your Principle of Infinite Precision and ask yourself why you include the important qualifier THROUGH MEASUREMENTS. Then think about generating an uncomputable Real as follows:

1. Write down the first million digits of the square root of 2.

2. Bring a radioactive atom into the room

3. Continue writing down digits of the square root of 2 until the atom decays as you write the Nth digit

4. Then change and start writing down digits of pi, starting with the Nth digit of pi

From an information point of view this an uncomputable Real

From a measurement point of view it is completely equal to (utterly indistinguishable from) the square root of 2.

Now perhaps if you review my comments, my insufficient clarity will nevertheless become intelligible.

Thank you

John

Dear Flavio,

Very nice.

It sounds almost like you want to say that an indeterministic classical mechanics amounts to something like an ontological/physical interpretation of chaos. While usually the sensitivity to initial conditions is just a result of our ignorance of the initial state so that our models diverge from physical reality (which is itself deterministic), here you are saying such a state cannot even exist (since real numbers are not physically meaningful, and yet seem to be demanded by determinism). Would this be one way of interpreting the basic idea in this paper?

Secondly. Does your position depend on a discrete view of space (i.e. to rule out the infinite capacity)? What if space is dense so that it can contain infinite information? I don't see how the spatial limitation of Gisin's follows from Landauer's Principle - it itself should follow whatever the best physics says about spacetime, not the other way around.

This is just a nitpicking point - I thought it was a great paper.

Best

Dean