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

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

Flavio,

Your essay is very thoughtful and well written. But I don't see that you've made determinism at-all plausible, so I don't understand your conclusion that the question of determinism-or-indeterminism is undeterminable.

In my essay I've suggested a third alternative: From the quantum level to the mental, the universe is essentially spontaneous - neither determined nor undetermined/random. As highly organized systems of spontaneity, each of us is self-determined, capable of arbitrarily responding to our surroundings.

Jim

Dear Falvio

This is quite an interesting essay.

I was particularly intrigued by the alternative classical theory possessing some features analogous to quantum theory. The implementation of the ontological indeterminacy aspect is noteworthy.

However as I understand the scheme there seems to be some problematic aspect with the minimal requirements for measurement.

Let's recall that the framework is meant to deal with the in-principle infinite number of digits that determines a real number, (associated with a physical quentity) and pass to a modified scheme in which only a portion of those digits have well defined values.

So let me start with the second requirement :

2 Intersubjectivity: Different agents can access the same measurement outcomes.

This seems to make a lot of sense at first sight however, it must be emphasized that i is only so if it the different agents are truly referring to the SAME quantity. That means among other things the quentity at the same time ( or spactime event). Consider now for instance a particle moving in one dimension. We would like to focus on the value of its velocity ( ina given frame), but of course if we want to assign it, a value we should specify at which time or at what positio . Once those data are specified, it makes all the sense to look at the corresponding value of the velocity... but if time and position are subject to the same indefiniteness as everything else how can we make sure that two agents refer to the same quantity ( i.e. the velocity at time t or at position x).

Related concerns arise when considering the first requirement:

1. Stability: Consecutive measurements of the same quantity leave the already determined digits unchanged.

To start with it seems to me that this can only be sensibly demanded if the quantity in question is one not expected, classically, to depend on time ( i.e. say a quantity which in the normal version would vanishing Poison brackets with the Hamiltonian) , otherwise a change can be expected even in standard situations. So perhaps one should at least place a bound of the time elapsed between consecutive measurements, but how to do so precisely if such precision is discarded ab initio.

Finally, similar concerns apply to the last postulate:

3. Precision improvability: With more accurate measurement apparatuses, more digits become available (with the former two properties)

It seems we might properly talk about improvement of the measurement only as long as it is a measurement of the same quantity at the same time, etc. and as we have seen those notions seem to be made problematic by the basic ideas underlying the proposal.

So perhaps Flavio could clarify these issues for us.

In any event, as I said, the general idea is quite interesting.

I wanted to note that some earlier work reached the same conclusions regarding classical physics being indeterministic and real numbers being non-physical. Also that these things were very likely pointing towards the measurement problem. This was in the context of rejecting points of time, space, and instantaneous magnitudes due to their being non-physical (which, although different, is at least partly related to the infinite precision argument given by Flavio and Nicholas Gisin). This was the first of the papers. Time and classical and quantum mechanics: Indeterminacy vs. discontinuity (2003).聽

I only recently learned聽of Nichola's and Flavio's work, and contacted them a few weeks ago. They were unaware of my work. Although聽we take different approaches, and my writing was terrible, there are enough similarities in the main conclusions that I must admit reading some of the comments here irks a聽little. There was little support for my conclusions at the time! For possible context, see this personal essay

Flavio, if you are not aware of a paper, you obviously can't reference it, but I can't be expected to sit back and say nothing (if a part of me would really prefer to). Although a cough probably wasn't the best choice (particularly now), I also gave you a chance to perhaps say something in connection to acknowledging my work with my "Ahem" comment above.聽

Regardless, yours is a brilliant essay and I hope it does really well.

Best wishes

Peter

Dear Flavio,

What a wonderful essay!聽 It took me on a very insightful journey and I have given it a top vote!聽聽

I enjoyed the historical background, the articulation of the principle of infinite precision, and relating this to ideas on Kolmogorov complexity, information theory and measurement.聽 Your central thesis along with bringing these various topics together was very聽crafted.聽 I very much enjoyed your "surgical" approach to breaking topics and finding their underlying essence.

Good luck for the contest!聽

聽

Cheers,

Del

Thank you for your reply! I think the question of understanding 'what the differences between classical and quantum physics boil down to' is fascinating and is certainly a very important research program, and I have enjoyed your other work on this topic.

I do still have a question though. In order to approach this question, it's important to first resolve the question of what we mean by 'classical physics.' I myself see two ways to answer this:

First, classical physics is what the physicists of the time understood it to be. In that case, the way to understand the difference between classical physics and quantum physics is to study the writings of the classical physicists. Here my understanding is that most classical physicists believed in an ontology which admitted variables that could take any real number value. On its own terms, then, it was deterministic. (Of course, I'm sure that there were some dissenting voices, but I suppose that in this approach to understanding classical physics one should try to identify the 'consensus view' and then run with it).

Second, classical physics is a theory which applies in some specific limit - i.e. the limit of large sizes and low speeds. And it seems that in this limit, classical physics is deterministic, since the problem of infinite precision that you refer to will presumably only appear once one gets down to very small sizes. (At least, this is how I understand what you suggest - please correct me if I'm wrong).

Since you argue that 'classical physics' can be indeterministic, I take it that what you mean by 'classical physics' is neither of those two things. Sp my question is simply - what do you mean when you refer to classical physics? How do you demarcate its domain of applicability?

Dear Falvio,

Your essay was perfect! Not only did you manage to flip current assumptions regarding determinism/indeterminism on their head, you provided grounds on which science in an ultimately non-determined world still makes sense.

Best of luck in the contest!

Rick Searle

Dear Flavio,

In my recently proposed theory, I show that physics is after all deterministic at the Planck scale:

Nature does not play dice at the Planck scale

Hope this alternative view-point interests you.

It is a pleasure to se your essay do so well in the contest, and I wish you every success.

Tejinder

Dear Flavio,

You can certainly write an interesting essay. It will take me quite some time to absorb all the ideas you have covered. I particularly liked: " We can only have the certainty that the future of the battle between determinism and indeterminism is open, too." in your conclusion, as it paves the way for centuries of intellectual sparring.

For my first entry in this competition I have produced a light weight essay that I hope is enjoyable, even though I push the line of indeterminism through free will. I, like Tejinder, think it is the coarse graining of emergence that brings out aspects of indeterminism.

Best wishes

Lockie Cresswell