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

We call it data, and data about the data is called metadata.

- Shawn

Dear Flavio,

Thank you for a well-written and highly accessible essay. I particularly appreciate your historical perspective on classical indeterminism.

I totally agree with your distinction between empirical observations, which only address finite-resolution states, and the "orthodox" interpretation, which assumes that variables (e.g. coordinates of position and momentum) are infinitely precise. As I emphasize in my essay, PIP describes a conceptual model and interpretation of physical reality, based on assumptions that cannot be empirically verified.

You note that the orthodox interpretation of classical mechanics is causal and deterministic. Causality implies that cause precedes effect in time, i.e. time asymmetry. Time asymmetry, along with determinism, is typically (I suspect necessarily) attributed to an initial low-entropy low-probability state. The origin of an exceptional low-probability initial state, one that has deterministically led to the current universe including this essay and response, is problematic. In addition, a deterministic model cannot formulate a definition of entropy as a fundamental property of state. This makes the asymmetrical increase in entropy a property of perception, rather than an objective property of nature. A much simpler and objective explanation for time asymmetry is irreducible indeterminism, as you propose. Determinism is not empirically necessary, and indeterminism is a far more reasonable, and objective, explanation of time asymmetry and causality.

Your alternative conceptual model, FIQ-based Interpretation, is very similar to my alternative conceptual model, DCM. Both replace infinite precision variables with finite precision variables. In DCM, I relate finite precision to a new physical property of state, ambient temperature. Ambient temperature is based on the recognition that absolute zero does not exist and no system is perfectly isolated from its ambient surroundings. The universe's background microwave radiation permeates all of space and it defines a positive ambient temperature for the universe as a whole.

The DCM defines irreducible objective randomness by the partition function of statistical mechanics, evaluated at the ambient temperature (see end-note 7 in my essay, and "reinventing time" reference). It is immediately evident that that the PIP and the orthodox interpretation represent a special case, in which the ambient temperature is assumed equal to absolute zero. Absolute zero, however, is an unattainable idealization and does not exist in physical reality.

You conclude that no experiment will ultimately discriminate between determinism and indeterminism. While I agree that there will always be some wiggle room for anyone who wants to maintain determinism, the cost is abandoning objective time asymmetry and causality or asserting that the universe's evolution is nothing but the playing out of fate for an exceptionally crafted, and unexplained, universe.

Harrison

Shawn,

As a former long-time computer analyst and programmer, I can tell you that "data" and "metadata" are pretty well meaningless labels. You, being a software developer, would understand this. "Data" and "metadata" don't get to the essence of what information is.

"Shannon information" is a category with associated numbers that does not define information, and does not get to the essence of what information is because there are plenty of other existing and possible somewhat similar categories and associated numbers.

It is not necessary to define information; but it IS necessary to say that information is a thing that can only be represented with categories and numbers, where categories are understood to have an internal relationship structure.

Dear Lorraine,

The entropy is the average information per datum. It's perfectly well-defined. If the datum's states are all equiprobable, then the entropy simplifies down to log(num states)/log(2) = num bits.

- Shawn

Dear Lorraine,

As a software developer, one of my first GitHub repositories calculates the entropy of a string. Multiple languages are included, such as C++, and JSP.

sjhalayka/entropy-calculation

- Shawn

Flavio and Shawn,

"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.

It is important to refrain from muddying the waters when it comes to the subject of information: words which mean one thing should not be redefined to mean another thing.

Dear Shawn,

I'm questioning definitions of information; I'm not questioning your knowledge of these definitions. I have (accidentally) replied below.

Lorraine

Flavio and Shawn,

I'm questioning accepted definitions of information; and I'm questioning your logical abilities.

If you do physics or anything else, you need logic. This is the logic of it:

"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 information when both of you blindly and unthinkingly accept illogical definitions of information that muddy the waters for everybody?

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