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

Dear Flavio and Shawn,

I'm questioning the accepted definitions of information; and I'm wondering if you have ever questioned the logic of these definitions. I would think that it is abundantly clear that the accepted definitions of information are completely illogical:

"Information entropy" is not "information" in the same sense that "car speed" is not a "car".

"Shannon information" is about the probability or surprisal value of information: it is not the actual information.

Symbolic representations of information are not information: they are symbols.

Is it any wonder that people are confused about what information is, when the above illogical definitions of information are guaranteed to muddy the waters for everybody? The problem is that the label "information" is illogical: other words need to be found to describe these categories of information. Physics needs clear and logical concepts, or it will continue to confuse itself about the issue of information.

Dear Lorraine,

Don't get too upset... you're part of the majority.

- Shawn

Dear Flavio and Shawn,

As I am trying to explain, the issue is NOT me or "the majority". I doubt "the majority" is even slightly interested in this issue. But I have been interested in this issue, ever since I studied Information Science at university.

The issue is that, in both physics and computing, "information" is not a clear, unambiguous or logical concept. And one cannot solve this problem by imposing a mathematical concept or mathematical definition onto the issue. The mathematical concept/ definition does NOT solve the "information" problem.

Dear Lorraine,

I give you an A for tenacity. :)

- Shawn

So Shawn,

I would say that information is a general term, where all information is representable as category names and associated numbers, or representable as category names and associated TRUE/ FALSE values. "Shannon information" is just one such category of information. "Shannon information" does not define what information is.

Information is information because it always exists in context/ relationship to other categories of information. If it has no context, it is not information.

And symbols only represent information from the point of view of those who know what the symbols are meant to represent.

- Lorraine :-)

I enjoyed your arguments that classical mechanics was sometimes views as indeterministic. I think that is correct, and determinism is not really the big difference between classical and quantum mechanics.

A couple of very minor nits: "its nineteenth decimal digit is a 4."

I think you meant the 19th decimal digit after the decimal point. I would say the 20th decimal digit is 4, because the 1st decimal digit is 3.

"a theory id said to be causal" -- You mean "is".

Hello Dr Del Santo,

I liked a lot your essay, one of my favorites. You describe so well this uncertainty compared with our classical physics to predict thus future.

I wish you all the best in this Contest.

Regards

Dear Flavio, Very interesting and groundbreaking essay, well informed by history, philosophy, physics, and mathematics (in the Newtonian tradition criticized here for other reasons!). It seems to me that we are only at the beginning of dealing with the drawbacks of the use of the real numbers in physics, and similar idealizations which have led to the conclusion that determinism itself is an idealization, even or especially in classical physics (which is what I take to be the main message of this essay). My own hunch is that intuitionistic and constructive mathematics may provide a way out, although, as Hilbert feared, this means we are driven out of Cantor's Paradise and we have to start all over again. In view of the tremendous success of even classical physics (think of putting men on the moon) this might be too much to ask, so there should be some result to the effect that physics based on the real numbers gives valid results with high probability (from the point of view of the new physics based on finite approximations), or so. Alternatively, think of results (due to Gödel and others) that theorems of classical mathematics are valid even intuitionistically if they are replaced by versions that are classically equivalent but intuitionistically different (typically by adding a double negation). In this spirit, results of classical physics based on the real numbers should be replaced by results that are empirically equivalent but logically different in your system, and provable in that system.

Best wishes, Klaas

I really enjoyed this essay. The insight into the importance of infinite precision to classical physics is a really valuable one and I'm very interested in your work on an indeterministic formulation of classical physics.

I did have some questions about the overall motivation for this work. As I understand it, your argument is that real numbers cannot be physically meaningful because they contain an infinite amount of information. This is supposed to be a problem because it would violate the Bekinstein bound; but the Bekinstein bound comes from GR and/or quantum physics, so is there any reason to think it should hold in classical physics?

Alternatively, it supposed to be a problem because 'physical systems have finite size' and this implies a limit on density of information - but do physical systems have finite size in classical physics? Perhaps there is a coherent interpretation of classical physics where the world is constituted of pointlike particles?

These questions are linked to a larger questions about what an 'interpretation' of classical physics is supposed to do. When we try to `interpret' quantum mechanics, I take it that we are making hypotheses about what the actual reality underlying quantum mechanics might be like. But we don't need to do this in the case of classical mechanics, since the reality underlying classical mechanics is understood to be quantum mechanics. So when we ask whether classical mechanics is deterministic, we're not asking about whether reality is deterministic, rather I guess we're asking whether the view that classical physics is deterministic was a coherent one - but in that case it seems unfair to make an argument based on facts that are not inherent in classical physics? Does it make sense to try to 'interpret' classical physics from the point of view of a modern physicist?

Dear Flavio,

Re "Information is a well defined mathematical concept (defined by Shannon and others) and I used it in that sense in my essay", Author Flavio Del Santo replied on Mar. 11, 2020 @ 20:58 GMT:

Despite its usefulness in physics' mathematical calculations, I would think that "Shannon information" does not get to the essence of what information is. Because "Shannon information" is about the probability or surprisal value of information: it is not the actual information.

So, I would think that information is a general term, where all actual information is representable as category names and associated numbers, or representable as category names and associated TRUE/ FALSE values. "Shannon information" is just one such category and quantity of actual information.

And, I would think that information is information because it always exists in context/ relationship to other categories of information. One can only build information out of existing information, and "Shannon information" is built out of existing information.

I know that there are plenty of people that, like you, seem to consider that "Shannon information" IS information. But I would like to know how physics and philosophy justifies this redefinition of the meaning of the word information, this takeover of the meaning of the word information, by "Shannon information".

Dear Flavio,

I have come up with my own little collapse model, which came to me when pondering collapse within the context of your essay. I think the pictures speak for themselves:

https://vixra.org/abs/2003.0385

Does this remind you of anything in quantum physics? I'm asking as a novice.

- Shawn

Dear Dr. Flavio Del Santo,

I really enjoyed reading your essay. Your wonderful words in the beginning .....................One specific story that seems to have crystallized among practitioners is that classical physics (i.e., Newton's mechanics and Maxwell's electrodynamics) would allow, in principle, to predict everything with certainty. The standard story continues by telling that the foundations of such theory are perfectly well understood and free of any interpretational issues. In particular, it is widely accepted that classical physics categorically entails a deterministic worldview.

Indeed, due to the tremendous predictive success of Newtonian physics (in particular in celestial mechanics), it became customary to conceive an in principle limitless predictability of the physical phenomena that would faithfully reflect the fact that our Universe is governed by determinism. .................

I want to say few words about "Dynamic Universe Model". It is a singularity free N-Body problem solution uses NEWTONIAN PHYSICS and IS free of any interpretational issues,and it got very good predictive success IN YOUR WORDS...

For further details have a look at my essay please.

"A properly deciding, Computing and Predicting new theory's Philosophy"

Best Regards

=snp.gupta

Dear Flavio,

Thanks for a thought-provoking and well-written essay. We need to question conventional "truths" once in a while, such that classical physics is self-evidently deterministic. However, I think you play down the difference between classical and quantum physics too much when it comes to determinism.

It is true that we can evolve ensembles R in phase space to E(R) according to the classical equations of motion, but we do not have to. The naked classical equations happily eat single points P and spit out evolved points E(P) in a completely deterministic manner. E(R) equals the union of the evolution E(P) of all the points P that define R.

In contrast, we must evolve ensembles R to E(R) in quantum physics because the quantum of action defines a minimum ensemble area, as you discuss in relation to Fig. 2. It is not possible in quantum mechanics to "decompose" the evolution of R to the union of the evolution of all points P in R. Interference prevents such point-wise, deterministic evolution.

Another way to put is to say that if R = R1 U R2, then E(R) = E(R1) U E(R2) in classical physics, but not necessarily in quantum physics.

I guess my point is that while it is true that both classical and quantum physics allow an indeterministic interpretation, only classical physics allows a deterministic one. (I am aware that Bohmians and MWIers would not agree.)

I have rated the Essay not so well, because I strongly disagree, that Science as presented in the Essay is inherently undecidable. The model of reality called "classical science" is deterministic within the model. If it would be indeterministic, then e.g. the Navier-Stokes equations would have such property. But latter is not discovered yet. The quantum science consists of two fundamental notions: observer and nature, and how they co-relate. Yes, the indeterminism comes into reality through freewill of observer, but the nature itself -which is subject of Physics- is perfectly deterministic even while talking about Quantum Physics.