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RECENT POSTS IN THIS TOPIC

**Peter Lynds**: *on* 5/20/20 at 0:58am UTC, wrote Hi Flavio, Regarding my earlier message, I'll try a different tack. In...

**Flavio Del Santo**: *on* 5/18/20 at 11:52am UTC, wrote Dear Lachlan, thanks for your feedbac and glad that you find my conclusive...

**Flavio Del Santo**: *on* 5/18/20 at 11:49am UTC, wrote Dear Tejinder, thanks for pointing it out. In fact, I had already read...

**Flavio Del Santo**: *on* 5/18/20 at 11:46am UTC, wrote Dear Rick, thanks very very much for your kind appreciation. I am glad...

**Flavio Del Santo**: *on* 5/18/20 at 11:44am UTC, wrote Thank you, Del, for your very kind words! Glad that you found my essay...

**Flavio Del Santo**: *on* 5/18/20 at 11:41am UTC, wrote Dear Prof. Sudarsky, thank you for your feedback and your very interesting...

**Lachlan Cresswell**: *on* 5/18/20 at 3:02am UTC, wrote Dear Flavio, You can certainly write an interesting essay. It will take me...

**Tejinder Singh**: *on* 5/17/20 at 18:33pm UTC, wrote Dear Flavio, In my recently proposed theory, I show that physics is after...

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RECENT FORUM POSTS

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Philosopher Jenann Ismael invokes the thermodynamic arrow of time to explain how human intelligence emerged through culture.

Grounded physicists are exploring the use of online and virtual-reality conferencing, and AI-controlled experiments, to maintain social distancing. Post-pandemic, these positive innovations could make science more accessible and environmentally-friendly.

Untangling how the human perception of cause-and-effect might arise from quantum physics, may help us understand the limits and the potential of AI.

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FQXi FORUM

October 29, 2020

CATEGORY:
Undecidability, Uncomputability, and Unpredictability Essay Contest (2019-2020)
[back]

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

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

A tradition handed down among physicists maintains that classical physics is a perfectly deterministic theory capable of predicting the future with absolute certainty, independently of any interpretations. It also tells that it was quantum mechanics that introduced fundamental indeterminacy into physics. We show that there exist alternative stories to be told in which classical mechanics, too, can be interpreted as a fundamentally indeterministic theory. On the one hand, this leaves room for the many possibilities of an open future, yet, on the other, it brings into classical physics some of the conceptual issues typical of quantum mechanics, such as the measurement problem. We discuss here some of the issues of an alternative, indeterministic classical physics and their relation to the theory of information and the notion of causality.

Flavio Del Santo is a PhD student in theoretical physics at the University of Vienna and the Institute of Quantum Optics and Quantum Indormation Vienna. His main research interests comprize foundations of quantum mechanics, and history and philosophy of science.

Dear Flavio del Santo,

very nice essay. I will add a link on my website. I like the suggestion of view from pointlike classical orthodox to quantum and atlernative classics. This perfect to show the flaws in Gravity (GRT) as well as in Quantum Theory and how they merge.

Thanks a lot for the essay!

Manfred U.E. Pohl

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very nice essay. I will add a link on my website. I like the suggestion of view from pointlike classical orthodox to quantum and atlernative classics. This perfect to show the flaws in Gravity (GRT) as well as in Quantum Theory and how they merge.

Thanks a lot for the essay!

Manfred U.E. Pohl

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Dear Manfred (if I may),

thank you for your kindness. I think indeed that investigating more the foundations of classical physics, which is regarded as a paradigm of perfect explanation, could teach us a lot about GR and QM as well.

All good wishes,

Flavio

thank you for your kindness. I think indeed that investigating more the foundations of classical physics, which is regarded as a paradigm of perfect explanation, could teach us a lot about GR and QM as well.

All good wishes,

Flavio

Dear Flavio,

during the contest, i advanced a lot in trying to explain the meaning of pi=1. It ist like a meditation between two competitors.. the small child and the old theoretical physicist. Hard stuff to explain that all our pocet calculaters ar "fake news".

As my native language is german it is hard for me to explain in english.

I tried here to explain the final theory of everything in quantum-biology (finalazing the ideas of A Turing)

For some people of course this is "shocking". : https://www.youtube.com/watch?v=EIBjt_5TU0U

(Language should be understood also by "non-scientist")

All good wishes.

Manfred

post approved

during the contest, i advanced a lot in trying to explain the meaning of pi=1. It ist like a meditation between two competitors.. the small child and the old theoretical physicist. Hard stuff to explain that all our pocet calculaters ar "fake news".

As my native language is german it is hard for me to explain in english.

I tried here to explain the final theory of everything in quantum-biology (finalazing the ideas of A Turing)

For some people of course this is "shocking". : https://www.youtube.com/watch?v=EIBjt_5TU0U

(Language should be understood also by "non-scientist")

All good wishes.

Manfred

post approved

"... the information I (in number of bits) contained in a system circumscribed by a sphere of radius R is smaller than the mass-energy enclosed in the same sphere ..."

Is the Bekenstein bound based upon a concept of black holes compatible with string theory with the infinite nature hypothesis but incompatible with the finite nature hypothesis?

Bekenstein bound, Wikipedia

In 2006, Seiberg gave a review of "the case for the idea that space and time will end up being emergent concepts; i.e. they will not be present in the fundamental formulation of the theory and will appear as approximate semiclassical notions in the macroscopic world. This point of view is widely held in the string community ..."

"Emergent Spacetime" by Nathan Seiberg, arXiv, 2006

Near the Planck scale, do the concepts of spacetime, energy, and quantum information fail? After quantum averaging, are Einstein's field equations 100% correct? I have suggested 3 modifications to Einstein's field equations, i.e., Koide cutoff, Lestone cutoff, and dark-matter-compensation-constant = (3.9±.5) * 10^–5 . I say that Milgrom is the Kepler of contemporary cosmology. I conjecture that the Gravity Probe B science team erroneously assumed that the 4 ultra-precise gyroscopes had a problem — instead the gyroscopes worked correctly and actually demonstrated what I call the Fernández-Rañada-Milgrom effect — have you looked into this?

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Is the Bekenstein bound based upon a concept of black holes compatible with string theory with the infinite nature hypothesis but incompatible with the finite nature hypothesis?

Bekenstein bound, Wikipedia

In 2006, Seiberg gave a review of "the case for the idea that space and time will end up being emergent concepts; i.e. they will not be present in the fundamental formulation of the theory and will appear as approximate semiclassical notions in the macroscopic world. This point of view is widely held in the string community ..."

"Emergent Spacetime" by Nathan Seiberg, arXiv, 2006

Near the Planck scale, do the concepts of spacetime, energy, and quantum information fail? After quantum averaging, are Einstein's field equations 100% correct? I have suggested 3 modifications to Einstein's field equations, i.e., Koide cutoff, Lestone cutoff, and dark-matter-compensation-constant = (3.9±.5) * 10^–5 . I say that Milgrom is the Kepler of contemporary cosmology. I conjecture that the Gravity Probe B science team erroneously assumed that the 4 ultra-precise gyroscopes had a problem — instead the gyroscopes worked correctly and actually demonstrated what I call the Fernández-Rañada-Milgrom effect — have you looked into this?

report post as inappropriate

Dear Flavio,

Interesting essay!

I dare say that I believe that what you call information is actually data (which are comprised of signs and symbols). This is because information emerges from data. Without distinct data, there is no average information per datum(e.g. log(1) = 0). Can you please explain your understanding of information in a sentence or two, on how it differs from my understanding.

- Shawn

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Interesting essay!

I dare say that I believe that what you call information is actually data (which are comprised of signs and symbols). This is because information emerges from data. Without distinct data, there is no average information per datum(e.g. log(1) = 0). Can you please explain your understanding of information in a sentence or two, on how it differs from my understanding.

- Shawn

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Dear Shawn,

thanks for your comment, which I find interesting. I am not familiar with the distinction you make between data and information. Do you have a reference where I can look this up? Information is a well defined mathematical concept (defined by Shannon and others) and I used it in that sense in my essay. Intutively, in a physical sense à la Landauer, it can be related to the amount of distinct states of a system. However, this is somehow independent of the specific physical means of encoding. I would call data a specific way of encoding information.

All the best,

Flavio

thanks for your comment, which I find interesting. I am not familiar with the distinction you make between data and information. Do you have a reference where I can look this up? Information is a well defined mathematical concept (defined by Shannon and others) and I used it in that sense in my essay. Intutively, in a physical sense à la Landauer, it can be related to the amount of distinct states of a system. However, this is somehow independent of the specific physical means of encoding. I would call data a specific way of encoding information.

All the best,

Flavio

Dear Flavio,

Thanks for reading my message with an open mind. I'm going to target my reply at those readers who don't yet know what we're talking about:

Information, in base-2 for mental simplicity's sake, is the average number of bits required to N states (e.g. log(N)/log(2)).

Information's a property of the data as a whole, not the actual data themselves; information's metadata.

Like, if you have 10 integers, and they're all set to the value of, say, 4, then the average information per datum is log(1)/log(2) = 0. The data are real, and the information is ephemeral.

Does that make any sense?

- Shawn

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Thanks for reading my message with an open mind. I'm going to target my reply at those readers who don't yet know what we're talking about:

Information, in base-2 for mental simplicity's sake, is the average number of bits required to N states (e.g. log(N)/log(2)).

Information's a property of the data as a whole, not the actual data themselves; information's metadata.

Like, if you have 10 integers, and they're all set to the value of, say, 4, then the average information per datum is log(1)/log(2) = 0. The data are real, and the information is ephemeral.

Does that make any sense?

- Shawn

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P.S. Sorry for the error in my earlier reply. It should read:

Information, in base-2 for mental simplicity's sake, is the average number of bits required*to encode* N states (e.g. log(N)/log(2)).

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Information, in base-2 for mental simplicity's sake, is the average number of bits required

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Dear Flavio,

you've presented an eminently readable and well-reasoned overview of the notion that classical physics can be interpreted in an indeterministic way. I think the point of view you suggest is a very intriguing one---with the 'orthodox' interpretation of classical mechanics being akin to a hidden variable interpretation, with real numbers obviously forever beyond experimental...

view entire post

you've presented an eminently readable and well-reasoned overview of the notion that classical physics can be interpreted in an indeterministic way. I think the point of view you suggest is a very intriguing one---with the 'orthodox' interpretation of classical mechanics being akin to a hidden variable interpretation, with real numbers obviously forever beyond experimental...

view entire post

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Sorry, it appears the link to the presentation I alluded to didn't make it into the post... See here: https://www.academia.edu/37587972/Epistemic_Horizons_and_Rec

onstructions_of_Quantum_Mechanics

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onstructions_of_Quantum_Mechanics

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Dear Jochen,

thanks so much for your extremely kind comments and the interesting remarks.

Let me address your valuable questions. You are somewhat right that Bekenstein bound brings along a huge amount of theoretical background from quantum thereory and gravity. I cite this just to prove that there exist formal arguments in support of what I want to tell, but, in fact, my ideas are more fundamental and try to be free of that theoretical baggage. My main argument is not as formal, but perhaps can be conceived as an operational approach that takes as a primitive the Landauer's principle.

As for saving the finite information by appealing to "computable analysis" only instead of removing realm nummbers, I don't see any arguments against this at the moment. It looks to me as an alternative approach. However, I should think more about its consequences determinism in that case. I discuss some other alternatives in my paper with Gisin (https://arxiv.org/pdf/1909.03697.pdf).

Indeed, you hit the nail on the head on your comment on intersubjectivity, if you are thinking of some supposed constant of nature. With my intersubjective requirement of measure I mainly had in mind two agents measuring the very same object in different moments. We have received several comments on what is the status of constants of physics (say the charge of electron) in the FIQ-based model of physics. While this is still object of our research, my current understanding is that -assuming that the Universe has been expanding from a very localized region- the peculiarity of constants of nature is that they have been determined with very high precision in the first instants of the Universe. So, even if they are now in space-like separated regions when the get measured, very many of their digits are already stable.

All the best!

Flavio

thanks so much for your extremely kind comments and the interesting remarks.

Let me address your valuable questions. You are somewhat right that Bekenstein bound brings along a huge amount of theoretical background from quantum thereory and gravity. I cite this just to prove that there exist formal arguments in support of what I want to tell, but, in fact, my ideas are more fundamental and try to be free of that theoretical baggage. My main argument is not as formal, but perhaps can be conceived as an operational approach that takes as a primitive the Landauer's principle.

As for saving the finite information by appealing to "computable analysis" only instead of removing realm nummbers, I don't see any arguments against this at the moment. It looks to me as an alternative approach. However, I should think more about its consequences determinism in that case. I discuss some other alternatives in my paper with Gisin (https://arxiv.org/pdf/1909.03697.pdf).

Indeed, you hit the nail on the head on your comment on intersubjectivity, if you are thinking of some supposed constant of nature. With my intersubjective requirement of measure I mainly had in mind two agents measuring the very same object in different moments. We have received several comments on what is the status of constants of physics (say the charge of electron) in the FIQ-based model of physics. While this is still object of our research, my current understanding is that -assuming that the Universe has been expanding from a very localized region- the peculiarity of constants of nature is that they have been determined with very high precision in the first instants of the Universe. So, even if they are now in space-like separated regions when the get measured, very many of their digits are already stable.

All the best!

Flavio

Dear Flavio:

Thank you for a fresh interpretation of our deterministic problems.

During reading your essay I had the following thoughts:

I agree with your quotes of Rovelli and Born.

Also, Landauers principle“Information is physical”, is leading to the conclusion that information needs space. Space is restricted to the emergent phenomenon “reality”, and there...

view entire post

Thank you for a fresh interpretation of our deterministic problems.

During reading your essay I had the following thoughts:

I agree with your quotes of Rovelli and Born.

Also, Landauers principle“Information is physical”, is leading to the conclusion that information needs space. Space is restricted to the emergent phenomenon “reality”, and there...

view entire post

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Flavio,

the answer to determinism/indeterminism is straight forward: the 'determinism' of classical physics is just the catastrophic result of the transposition of KOWLEDGE into the Humean domain of historicity, that is, the psychologisation of physics. Real progress in the natural sciences is halted by empiricism!

Heinz

post approved

the answer to determinism/indeterminism is straight forward: the 'determinism' of classical physics is just the catastrophic result of the transposition of KOWLEDGE into the Humean domain of historicity, that is, the psychologisation of physics. Real progress in the natural sciences is halted by empiricism!

Heinz

post approved

Dear Flavio,

Are you saying that chaos is random, or only pseudorandom? I cannot tell.

- Shawn

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Are you saying that chaos is random, or only pseudorandom? I cannot tell.

- Shawn

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Dear Shawn,

the whole point of my view is that there is ALWAYS an element of genuine randomness. If you accept my alternative interpretation, even the lenght of a metal rod would not be fully determined.

Cheers,

Flavio

the whole point of my view is that there is ALWAYS an element of genuine randomness. If you accept my alternative interpretation, even the lenght of a metal rod would not be fully determined.

Cheers,

Flavio

Dear Flavio,

OK, sounds good. Thanks for your reply, and patience.

Can you explain in a word or two where the classical randomness comes from? Chaos?

- Shawn

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OK, sounds good. Thanks for your reply, and patience.

Can you explain in a word or two where the classical randomness comes from? Chaos?

- Shawn

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Dear Flavio,

Thank you for your comment on randomness.

It reminds me of the Microsoft browser lottery, where one was presented five browser options, in some random order. Instead of using the pseudorandom number generator built into the browser, like Microsoft did, it could have relied on human randomness (e.g. based on the system time mod 120 at time of browser lottery initialization).

https://motls.blogspot.com/2010/02/microsoft

-browser-lottery-do-js-random.html

"A period for the 5! = 120 permutations might be produced from the integer system time [added: in microseconds] mod 120."

- Shawn

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Thank you for your comment on randomness.

It reminds me of the Microsoft browser lottery, where one was presented five browser options, in some random order. Instead of using the pseudorandom number generator built into the browser, like Microsoft did, it could have relied on human randomness (e.g. based on the system time mod 120 at time of browser lottery initialization).

https://motls.blogspot.com/2010/02/microsoft

-browser-lottery-do-js-random.html

"A period for the 5! = 120 permutations might be produced from the integer system time [added: in microseconds] mod 120."

- Shawn

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Flavio I enjoyed your essay. In my essay “Clarification of Physics —“ I introduced a new definition of information and relate it to intelligence, mathematics and the creation of the physical world. I think you will find it interesting. Also I would appreciate your comments on my essay. John D. Crowell

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Brilliant! Extremely simple and demolishing a very common (sloppy) way of thinking.

Carlo Rovelli

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Carlo Rovelli

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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:

Your “information” actually represents information*about* information; it is higher-level information. Higher-level because logical steps have to be taken to derive your so-called “information”, as well as mathematical calculations. Your “information” cannot be a foundational basis of anything.

The actual foundational information in the world seems to be fully categorised: categories like mass, charge and velocity, which exist in fixed relationships with other such categories. Your/ Shannon “information” is a derived category of information, with associated numbers (that can seemingly only be derived by entities that have a capacity to perform logical steps as well as do mathematical calculations).

Mass is a category of information; velocity is a category of information; but you and Shannon and Shawn and others are in effect saying that information is a category of information. See the problem? The problem is the inappropriate labelling of a CATEGORY of information with the label “information”.

post approved

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:

Your “information” actually represents information

The actual foundational information in the world seems to be fully categorised: categories like mass, charge and velocity, which exist in fixed relationships with other such categories. Your/ Shannon “information” is a derived category of information, with associated numbers (that can seemingly only be derived by entities that have a capacity to perform logical steps as well as do mathematical calculations).

Mass is a category of information; velocity is a category of information; but you and Shannon and Shawn and others are in effect saying that information is a category of information. See the problem? The problem is the inappropriate labelling of a CATEGORY of information with the label “information”.

post approved

P.S. So what I'm trying to say is that there are many existing and potential categories [1] of information in the world. Shannon "information" is seemingly one of these categories of information . But Shannon "information" shouldn't be called "information" because it is only one of many existing and potential categories of information.

Lorraine

1. Not Platonic categories, but categories that exist from certain points of view, where categories are built out of logical analysis and/or mathematical relationships involving other such categories. E.g. mass and velocity are categories.

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Lorraine

1. Not Platonic categories, but categories that exist from certain points of view, where categories are built out of logical analysis and/or mathematical relationships involving other such categories. E.g. mass and velocity are categories.

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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.

post approved

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

post approved

Dear Flavio,

Now do you see? When I said that the essay was interesting, I wasn't kidding around! :D

- Shawn

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Now do you see? When I said that the essay was interesting, I wasn't kidding around! :D

- Shawn

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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...

view entire post

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...

view entire post

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Dear Harrison,

thanks so much for your kind comments. I could not agree more with your sentence: "Determinism is not empirically necessary, and indeterminism is a far more reasonable, and objective, explanation of time asymmetry and causality."

I will study more in detail your DCM, and comment in your page, if I can.

Best wishes,

Flavio

thanks so much for your kind comments. I could not agree more with your sentence: "Determinism is not empirically necessary, and indeterminism is a far more reasonable, and objective, explanation of time asymmetry and causality."

I will study more in detail your DCM, and comment in your page, if I can.

Best wishes,

Flavio

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.

post approved

“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.

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Dear Lorraine,

It's a physics essay. We are talking about information theory, not the lay, dictionary definition of information.

Basically, I say data, metadata. You say information, 'metainformation'. Where do data fit into your model? Or are data and information the same thing?

- Shawn

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It's a physics essay. We are talking about information theory, not the lay, dictionary definition of information.

Basically, I say data, metadata. You say information, 'metainformation'. Where do data fit into your model? Or are data and information the same thing?

- Shawn

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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?

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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?

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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.

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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.

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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".

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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".

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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

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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

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Yes of course, you are welcome also , I loved your essay, it is one of my favorites.

best regards

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best regards

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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

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Best wishes, Klaas

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Dear Klaas,

thanks, I really appreciate your kind comments. I totally agree that we are just now scratching the surface of problems that have been either not recognized, or deliberately ignored, putting them under the carpet for ages. I think that we will soon reach a critical mass, though, of people that recognize this issues in a non trivial way. I believe we should rediscover the eneasyness of some eminent scholars of the past, as I try to do in my essay by pointing out some historical arguments. Fore instance, only today I found a very interesting document; Thomas Kuhn interviewed a student of Boltzmann, who reported: " there was in Boltzmann’s ideas some anticipation of quantum theory [...]. He had from the beginning the idea that the space of phases must be fundamentally quantized".

Moreover, you are completely right that we should seek new mathematical ways to model our physics. And constructive mathematics, perhaps intuitivism, seems most promising.

All the best,

Flavio

thanks, I really appreciate your kind comments. I totally agree that we are just now scratching the surface of problems that have been either not recognized, or deliberately ignored, putting them under the carpet for ages. I think that we will soon reach a critical mass, though, of people that recognize this issues in a non trivial way. I believe we should rediscover the eneasyness of some eminent scholars of the past, as I try to do in my essay by pointing out some historical arguments. Fore instance, only today I found a very interesting document; Thomas Kuhn interviewed a student of Boltzmann, who reported: " there was in Boltzmann’s ideas some anticipation of quantum theory [...]. He had from the beginning the idea that the space of phases must be fundamentally quantized".

Moreover, you are completely right that we should seek new mathematical ways to model our physics. And constructive mathematics, perhaps intuitivism, seems most promising.

All the best,

Flavio

"constructive mathematics, perhaps intuitivism, seems most promising."

Perhaps you meant intuitionism?

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Perhaps you meant intuitionism?

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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.

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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.

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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?

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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?

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Hi Emily, thank you for your appreciation and your comments.

The Bekenstein bound, indeed, brings along a huge amount of theoretical background from GR. I always mention this just to prove that there exist formal arguments in support of what I want to tell, but, my (and Gisin's) ideas are more intuitive and fundamental. My main argument is not as formal, but perhaps can be conceived as an operational approach that takes as a primitive the Landauer's principle.

You ask: "Does it make sense to try to 'interpret' classical physics from the point of view of a modern physicist?" I think this is a fair criticism. My original motivation, was that of a quantum physicist. Indeed, my whole research program is devoted to the understanding of what the differences between classical and quantum physics boil down to. Read any textbook maual, encyclopedia entry, or review article on QM and you will see that they introduce the first conceptual difference of quantum mechanics was to introduce indeterminism (and it is historically is quite true that the physicist at that time focused a great deal on this). So, showing that good old, familiar, harmless classical physics could perhaps be seen already as deterministc let us rethink the scope of the conceptual gap between classical and quantum physics. Moreover, as gisin points out in his motivations (https://arxiv.org/abs/1803.06824) classical physics is seen as the paradigm of the perfect scientific explanation, the one to which all theories should strive for. Our contribution, I believe, scales down thongs a litte.

The Bekenstein bound, indeed, brings along a huge amount of theoretical background from GR. I always mention this just to prove that there exist formal arguments in support of what I want to tell, but, my (and Gisin's) ideas are more intuitive and fundamental. My main argument is not as formal, but perhaps can be conceived as an operational approach that takes as a primitive the Landauer's principle.

You ask: "Does it make sense to try to 'interpret' classical physics from the point of view of a modern physicist?" I think this is a fair criticism. My original motivation, was that of a quantum physicist. Indeed, my whole research program is devoted to the understanding of what the differences between classical and quantum physics boil down to. Read any textbook maual, encyclopedia entry, or review article on QM and you will see that they introduce the first conceptual difference of quantum mechanics was to introduce indeterminism (and it is historically is quite true that the physicist at that time focused a great deal on this). So, showing that good old, familiar, harmless classical physics could perhaps be seen already as deterministc let us rethink the scope of the conceptual gap between classical and quantum physics. Moreover, as gisin points out in his motivations (https://arxiv.org/abs/1803.06824) classical physics is seen as the paradigm of the perfect scientific explanation, the one to which all theories should strive for. Our contribution, I believe, scales down thongs a litte.

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?

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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?

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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”.

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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”.

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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

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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

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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

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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

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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.)

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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

In contrast, we

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.)

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Per,

I agree that quantum physics and classical one are not quite the same. But not necessarily for the resons you explained. You clearly expounded a text-book (or "orthodox" as it were) interepretation of these two theories.

There is, indeed, a kind of indeterminism that the violation of Bell's inequalities entails, which cannot be retrieved in classical physics. However, notice that appealing to the uncertainty principle is not enough, because this means that you believe unconditionally that QM is a complete theory. You might not like Bohm's hidden variable model (I am also not a great fan for the same reasons Eintein was not) but it does convincingly demonstrates that the uncertainty principle could be merely epistemic and not fundametal, if QM is completed with hidden variables. In this sense, Classical and quantum physics can be both INTERPRETED in aither deterministic and indeterministic fashions.

I agree that quantum physics and classical one are not quite the same. But not necessarily for the resons you explained. You clearly expounded a text-book (or "orthodox" as it were) interepretation of these two theories.

There is, indeed, a kind of indeterminism that the violation of Bell's inequalities entails, which cannot be retrieved in classical physics. However, notice that appealing to the uncertainty principle is not enough, because this means that you believe unconditionally that QM is a complete theory. You might not like Bohm's hidden variable model (I am also not a great fan for the same reasons Eintein was not) but it does convincingly demonstrates that the uncertainty principle could be merely epistemic and not fundametal, if QM is completed with hidden variables. In this sense, Classical and quantum physics can be both INTERPRETED in aither deterministic and indeterministic fashions.

Dear Flavio,

I wanted to compare the mathematical structure of classical and quantum evolution equations, to see what kind of interpretations they allow. That is, I wanted to "ground" the discussion in the formalism.

From that perspective, my last paragraph was ill-chosen and obscure. I agree with what you write in response.

I think we need to highlight**interference** as a distinguishing feature of quantum evolution equations, in addition to the uncertainty principle and the quantum of action. Interference is the reason why we cannot "decompose" the evolution of an ensemble in phase space in quantum mechanics to the evolution of its subsets, or to the deterministic evolution of its points. And that's the reason, as I see it, why quantum mechancis cannot be interpreted deterministically - in a certain sense.

Trying to be more precise what I mean by this, I'm talking about the standard postulates of quantum mechanics (thus excluding the additional stuff in Bohmian mechanics), and the evolution of observables, or points in phase space. (In contrast, the determinism in MWI resides in the wave function, that is, in the deterministic evolution of points in Hilbert space.)

The standard example is, of course, the double-slit experiment. You cannot "decompose" the evolution of the setup to the alternatives R1 and R2 where the particle goes through the left and right slit, respectively. Then you lose the interference pattern, which exludes som final particle destinations that are allowed in the "decomposed" evolution.

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I wanted to compare the mathematical structure of classical and quantum evolution equations, to see what kind of interpretations they allow. That is, I wanted to "ground" the discussion in the formalism.

From that perspective, my last paragraph was ill-chosen and obscure. I agree with what you write in response.

I think we need to highlight

Trying to be more precise what I mean by this, I'm talking about the standard postulates of quantum mechanics (thus excluding the additional stuff in Bohmian mechanics), and the evolution of observables, or points in phase space. (In contrast, the determinism in MWI resides in the wave function, that is, in the deterministic evolution of points in Hilbert space.)

The standard example is, of course, the double-slit experiment. You cannot "decompose" the evolution of the setup to the alternatives R1 and R2 where the particle goes through the left and right slit, respectively. Then you lose the interference pattern, which exludes som final particle destinations that are allowed in the "decomposed" evolution.

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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.

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Dear Flavio,

great essay with many good arguments, i like it. As i just wrote on Klaas Landsman's page, 1-randomness isn't that shocking since it must also obey some logical rules. True enough, since if we presuppose some generic randomness at the level of QM, this randomness nonetheless has to obey the statistics of QM.

If you like, check out my own essay. I would be happy if you would leave a comment there.

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great essay with many good arguments, i like it. As i just wrote on Klaas Landsman's page, 1-randomness isn't that shocking since it must also obey some logical rules. True enough, since if we presuppose some generic randomness at the level of QM, this randomness nonetheless has to obey the statistics of QM.

If you like, check out my own essay. I would be happy if you would leave a comment there.

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Dear Flavio,

You conclude the essay with the phrase:

*"We can only have the certainty that the future of the battle between determinism and indeterminism is open, too."*

But do we need a “battle” of determinism and indeterminism? ... I believe that the dialectic of “coincidence of opposites” and the most extreme ontology overcome the need for this epistemological “battle”. It is time to complete the Big Ontological Revolution in the philosophical basis of Science, begun by Planck and Einstein. And the first step is the rejection of the unclear and unclear concept of “classic”, which introduced maximum uncertainty primarily in the understanding of “space / absolute space”.

“We repeat: worldunderstanding is spaceunderstanding.” (Pavel Florensky).

The first most important problem for fundamental science is the problem of the ontological basification of mathematics, which means knowledge in general. Do not be afraid of dialectics and understand the dialectics of Nature, whose language is mathematics. To understand is to “grasp the structure” (G. Gutner “Ontology of mathematical discourse”). "Grasp" primordial generating structure.

With kind regards, Vladimir

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You conclude the essay with the phrase:

But do we need a “battle” of determinism and indeterminism? ... I believe that the dialectic of “coincidence of opposites” and the most extreme ontology overcome the need for this epistemological “battle”. It is time to complete the Big Ontological Revolution in the philosophical basis of Science, begun by Planck and Einstein. And the first step is the rejection of the unclear and unclear concept of “classic”, which introduced maximum uncertainty primarily in the understanding of “space / absolute space”.

“We repeat: worldunderstanding is spaceunderstanding.” (Pavel Florensky).

The first most important problem for fundamental science is the problem of the ontological basification of mathematics, which means knowledge in general. Do not be afraid of dialectics and understand the dialectics of Nature, whose language is mathematics. To understand is to “grasp the structure” (G. Gutner “Ontology of mathematical discourse”). "Grasp" primordial generating structure.

With kind regards, Vladimir

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Hi Flavio,

I like your essay a lot -- well argued and well written! Very nice food for thought!

Perhaps two remarks / questions:

1. I suppose that your main hypothesis is quite independent of the specific construction of FIQs? Probability theory would probably give you many alternative ways to implement finite information quantities, without spoiling your conceptual conclusions?

2. Your remarks at the end of Section IV are somewhat disjoint from the rest. Isn't this all about the interpretation of conditional probability, P(A|B), as what you can *learn* about A given what you know about B, not as causal influence? I didn't really get the point of this part.

Otherwise I enjoyed reading it a lot!

Best,

Markus

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I like your essay a lot -- well argued and well written! Very nice food for thought!

Perhaps two remarks / questions:

1. I suppose that your main hypothesis is quite independent of the specific construction of FIQs? Probability theory would probably give you many alternative ways to implement finite information quantities, without spoiling your conceptual conclusions?

2. Your remarks at the end of Section IV are somewhat disjoint from the rest. Isn't this all about the interpretation of conditional probability, P(A|B), as what you can *learn* about A given what you know about B, not as causal influence? I didn't really get the point of this part.

Otherwise I enjoyed reading it a lot!

Best,

Markus

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Dear Markus,

thanks so much for your kind apprecition and comments, which I will try to address.

1. I fully agree -if I understand correctly what you meant- that the model of FIQs we construct is just one possibility. In fact, there could be many more approaches to formalize the concept of finite information quantities. In particular, the attribution of a propensity to each digit could perhaps be replaced by some different mathematical modeling. One concrete way is the one that Gisin is currently pursuing (partly together with me) of considering intutitionistic mathematics. How exactly "probability theory would probably give [me] many alternative ways to implement finite information quantities" is not clear to me. I would be glad to discuss this, should you have any thoughts on this.

2. Admittedly, the last paragraphs of my Section IV are not spell out in as much detail as I would have liked. The aim there was to briefly comment, mostly as a matter of completeness, on the logical relation between determinism and causality. Following the philosophical tradition of probabilistic causality, which I extensively quote, in fact, there seem to be consensus that while determinism implies causality, the opposite does not hold. I have myself stated this in an older paper. Hoowever, I recently found out (thanks to D'ariano's pupil Marco Erba) that in the paper I cite they disprove this belief. This gave me a lot to think, and I am now quite convinced that neither determinism implies causality nor causality implies determinism, but for a reason more elementary than the ones the authors of that work claim. Unfortunately, I have perhaps been not clear enough in explaining this in my essay. But I am working on making my thoughts on the subject matter more clear.

All the best!

Flavio

thanks so much for your kind apprecition and comments, which I will try to address.

1. I fully agree -if I understand correctly what you meant- that the model of FIQs we construct is just one possibility. In fact, there could be many more approaches to formalize the concept of finite information quantities. In particular, the attribution of a propensity to each digit could perhaps be replaced by some different mathematical modeling. One concrete way is the one that Gisin is currently pursuing (partly together with me) of considering intutitionistic mathematics. How exactly "probability theory would probably give [me] many alternative ways to implement finite information quantities" is not clear to me. I would be glad to discuss this, should you have any thoughts on this.

2. Admittedly, the last paragraphs of my Section IV are not spell out in as much detail as I would have liked. The aim there was to briefly comment, mostly as a matter of completeness, on the logical relation between determinism and causality. Following the philosophical tradition of probabilistic causality, which I extensively quote, in fact, there seem to be consensus that while determinism implies causality, the opposite does not hold. I have myself stated this in an older paper. Hoowever, I recently found out (thanks to D'ariano's pupil Marco Erba) that in the paper I cite they disprove this belief. This gave me a lot to think, and I am now quite convinced that neither determinism implies causality nor causality implies determinism, but for a reason more elementary than the ones the authors of that work claim. Unfortunately, I have perhaps been not clear enough in explaining this in my essay. But I am working on making my thoughts on the subject matter more clear.

All the best!

Flavio

Flavio,

Good essay. Well written & pertinent. I certainly agree the option that nature is causal without being entirely deterministic.

A couple of questions;

How do you see the question of "exchange of momentum", and so OAM 'vector addition', as a key measurement criteria?

And, can you provide me a link or link to a paper regarding the finding I recall from the Vienna web site a few years ago that "*after interaction there is no memory of previous polarisation."* I assume that hasn't changed?

I agree that digging down to the deepest foundations is required, and indeed present some interesting results from dong so in my own essay.

Well done,

Peter

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Good essay. Well written & pertinent. I certainly agree the option that nature is causal without being entirely deterministic.

A couple of questions;

How do you see the question of "exchange of momentum", and so OAM 'vector addition', as a key measurement criteria?

And, can you provide me a link or link to a paper regarding the finding I recall from the Vienna web site a few years ago that "

I agree that digging down to the deepest foundations is required, and indeed present some interesting results from dong so in my own essay.

Well done,

Peter

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Dear Flavio Del Santo,

Isn't a child, an effect resulting from more than just a single cause, father and mother? In other words, weren't reductionist monotheism and the following to it physics naive when they believed in just one cause and in particular in initial conditions?I got the impression, your conclusion confirms Karl Popper. You and me seem to entirely agree with him.

However I slightly disagree when you wrote:"Again, determinism assumes that given an initial state of the universe and universal laws everything causally follows. But this is misleading because there is only one specific initial state and, without alternatives, causation seems avoid concept. On the contrary, indeterminism introduced ...". Creationists need an initial condition. Are there any consequences?

Alan Kadin might be wrong. Nonetheless, if he is correct, this will have serious consequences.

Regards,

Eckard Blumschein

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Isn't a child, an effect resulting from more than just a single cause, father and mother? In other words, weren't reductionist monotheism and the following to it physics naive when they believed in just one cause and in particular in initial conditions?I got the impression, your conclusion confirms Karl Popper. You and me seem to entirely agree with him.

However I slightly disagree when you wrote:"Again, determinism assumes that given an initial state of the universe and universal laws everything causally follows. But this is misleading because there is only one specific initial state and, without alternatives, causation seems avoid concept. On the contrary, indeterminism introduced ...". Creationists need an initial condition. Are there any consequences?

Alan Kadin might be wrong. Nonetheless, if he is correct, this will have serious consequences.

Regards,

Eckard Blumschein

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Dear Flavio,

I thought your essay was very good, and enjoyed reading it. When tackling questions like these, it's good to remove any myths and false ideas at the outset.

I think with classical physics, what many thought would turn out to be fully deterministic was not just the known laws, but also future physics with the undiscovered laws. They were probably wrong, but that's why Laplace said "...an intelligence which could comprehend all the forces by which nature is animated...".

There's also the risk, though it doesn't invalidate your points, of looking back at classical physics with the hindsight of quantum theory, and finding things (particularly at a small scale) that didn't add up as a result. So at times you may be updating classical physics to align it with more recent discoveries. But some excellent points, and in distinguishing between the different approaches that still exist to some extent within our present ideas, you clarify physics generally. To me, the issues about determinism also raise questions about block time, and the tension between that and the open future of QM.

What you say about chaos theory is very relevant - incidentally, some recent work, referred to in my essay, shows that some chaotic paths (of the three-body problem modelled with black holes) cannot be traced in principle, due to the limitation of the Planck length.

You gave my earlier essay on 'what is fundamental' a high rating, and we had a good exchange. At the time I could only hint at my interpretation for QM, but since then it has been completed, this time it's outlined in my essay. It's a new approach, and a documentary has been made partly on it, with a conversation about the interpretation with Rovelli. It adds, or attempts to add, a further layer of explanation underneath RQM. As I see you work in quantum optics, you might find it of interest.

With best wishes,

Jonathan

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I thought your essay was very good, and enjoyed reading it. When tackling questions like these, it's good to remove any myths and false ideas at the outset.

I think with classical physics, what many thought would turn out to be fully deterministic was not just the known laws, but also future physics with the undiscovered laws. They were probably wrong, but that's why Laplace said "...an intelligence which could comprehend all the forces by which nature is animated...".

There's also the risk, though it doesn't invalidate your points, of looking back at classical physics with the hindsight of quantum theory, and finding things (particularly at a small scale) that didn't add up as a result. So at times you may be updating classical physics to align it with more recent discoveries. But some excellent points, and in distinguishing between the different approaches that still exist to some extent within our present ideas, you clarify physics generally. To me, the issues about determinism also raise questions about block time, and the tension between that and the open future of QM.

What you say about chaos theory is very relevant - incidentally, some recent work, referred to in my essay, shows that some chaotic paths (of the three-body problem modelled with black holes) cannot be traced in principle, due to the limitation of the Planck length.

You gave my earlier essay on 'what is fundamental' a high rating, and we had a good exchange. At the time I could only hint at my interpretation for QM, but since then it has been completed, this time it's outlined in my essay. It's a new approach, and a documentary has been made partly on it, with a conversation about the interpretation with Rovelli. It adds, or attempts to add, a further layer of explanation underneath RQM. As I see you work in quantum optics, you might find it of interest.

With best wishes,

Jonathan

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Dear Jonathan,

thank you for your comments and inputs.

I will have a look at the filmed conversation you had with Carlo and at your paper soon. Will come back to you if I have something sensible to say.

If fact, my research and main interest is not at all quantum optics, but foundations of quantum physics.

All good wishes,

Flavio

thank you for your comments and inputs.

I will have a look at the filmed conversation you had with Carlo and at your paper soon. Will come back to you if I have something sensible to say.

If fact, my research and main interest is not at all quantum optics, but foundations of quantum physics.

All good wishes,

Flavio

Thanks Flavio,

and great to hear that your main interest is quantum foundations. I don't know if you'll like my interpretation, but I hope so, I do think your work is among the best I've seen on this site.

About the conversation below, yes, there's someone going through the new essays and marking them down - several have had only one rating, of 1/10. The problem with that is, others tend not to read it if they see a rating of 1, so it stays like that. Mine was given that soon after being posted, I don't know if they even read it. Ah well... J

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and great to hear that your main interest is quantum foundations. I don't know if you'll like my interpretation, but I hope so, I do think your work is among the best I've seen on this site.

About the conversation below, yes, there's someone going through the new essays and marking them down - several have had only one rating, of 1/10. The problem with that is, others tend not to read it if they see a rating of 1, so it stays like that. Mine was given that soon after being posted, I don't know if they even read it. Ah well... J

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Dear Flavio,

I don't know if you've read my essay yet, but when you do, I'd appreciate it if you'd rate it - just for relevant/interesting, you don't have to agree with it, though I'd very much like to hear any comments. It has only had one rating so far, and people aren't reading it as a result, even though Carlo found what's in it interesting.

Thanks a lot, best regards,

Jonathan

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I don't know if you've read my essay yet, but when you do, I'd appreciate it if you'd rate it - just for relevant/interesting, you don't have to agree with it, though I'd very much like to hear any comments. It has only had one rating so far, and people aren't reading it as a result, even though Carlo found what's in it interesting.

Thanks a lot, best regards,

Jonathan

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Hello, I have put this post because I find this totally odd , you don t merit this kind of comportment, so I wrote this on the blogs

Hi FQXi, it is totally not neutral the comportment of one or TWO members inside the community, because Del Santo was First with 13 or 14 votes with 8,4 and now with one or 2 votes he is at 7,9 , What is this stoty, of memebers prefer the bad compettion instead to be neutral and rational so we understand why this planet does not turn logically, this kind of comportment shows that this memeber is not a real universal generalist, I don t understand how it is possible inside a Community of conscious and intelliegnt persons, it is a shame because the member has probably put a 0 , see in your algorythms this member because he does not merit to be in your team,simply lets name a cat a cat,Friendly

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Hi FQXi, it is totally not neutral the comportment of one or TWO members inside the community, because Del Santo was First with 13 or 14 votes with 8,4 and now with one or 2 votes he is at 7,9 , What is this stoty, of memebers prefer the bad compettion instead to be neutral and rational so we understand why this planet does not turn logically, this kind of comportment shows that this memeber is not a real universal generalist, I don t understand how it is possible inside a Community of conscious and intelliegnt persons, it is a shame because the member has probably put a 0 , see in your algorythms this member because he does not merit to be in your team,simply lets name a cat a cat,Friendly

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Dear Dufourny, I truly appreciate you stepping up for me here. Some time ago when I was first in the partial rating Dmitri Martila wrote me a comment stating that he rated my essay "not so well" and gave me a 1 (the minimum you can give!). The other day, without even leaving a comment, one person gave me 1 again. No much to say, it's just unfortunate to see people feeling this initiative as such a competition that makes them act dihonestly and irrational.

It would be much better if the votes were not visible during the rating period, because they only introduce a strong bias on the judgement.

Thank you again for the support!

Flavio

It would be much better if the votes were not visible during the rating period, because they only introduce a strong bias on the judgement.

Thank you again for the support!

Flavio

You are welcome, these comportments irritate me a lot and I don t know why FQXi accept this, they could maybe sort the fake searchers, You merit to have very good votes simply and it is a game but we must be just and neutral.

I have put this too on blogs

Frankly let s consider the human conportements and the Vanity because it is totally sad. These comportments prove that the person having made this is nor a generalist nor a universalis, maybe just a simple intelliegnt for some details prefering the competion and strategies without really understanding the real meaning of the theory of Game. For me this comportment does not merit to be a member inside the FQXi Community and maybe you could change the algorythms to have a pure tyransparence , like that we can see who are the real universalists, just, logic , neutral and the others forgetting the basis. Even If I had a problem with a searcher, never I d make this, I d be neutral and just. We know why this planet is in this state, just due to these comportments at big scale for decisions. Can we accept this , is it democratic, no I don t Think, these persons decrease the velocity of evolution and they just satisfy their Vanity.

My best regards, and I repeat your essay is one of the best and it is sad to see the comportments against your essay, they don t merit to be members of FQXi simply, take care

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I have put this too on blogs

Frankly let s consider the human conportements and the Vanity because it is totally sad. These comportments prove that the person having made this is nor a generalist nor a universalis, maybe just a simple intelliegnt for some details prefering the competion and strategies without really understanding the real meaning of the theory of Game. For me this comportment does not merit to be a member inside the FQXi Community and maybe you could change the algorythms to have a pure tyransparence , like that we can see who are the real universalists, just, logic , neutral and the others forgetting the basis. Even If I had a problem with a searcher, never I d make this, I d be neutral and just. We know why this planet is in this state, just due to these comportments at big scale for decisions. Can we accept this , is it democratic, no I don t Think, these persons decrease the velocity of evolution and they just satisfy their Vanity.

My best regards, and I repeat your essay is one of the best and it is sad to see the comportments against your essay, they don t merit to be members of FQXi simply, take care

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Flavio,

This was an excellent read. Very clear, which I value highly. Thank you for the work put into this.

Could I ask what your stance is on the many-worlds interpretaion is, if you take one? I saw your footnote about it, but as you know, it ended there.

Thank you,

Ernesto

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This was an excellent read. Very clear, which I value highly. Thank you for the work put into this.

Could I ask what your stance is on the many-worlds interpretaion is, if you take one? I saw your footnote about it, but as you know, it ended there.

Thank you,

Ernesto

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Dear Ernesto,

thank you so much for your kind words.

Frankly, I don't like the many-world interpretation very much. Firstly, as Carlo Rovelli always puts it, there is a cost for every interpretation that you have to be ready to pay. Many worlds has an enourmous ontological cost, for it requires to assume this irrisonable moltiplication of worlds, universe, or whatever. Secondly, interpretations not only provide a consistent backstory to a theory, but are also supposed to solve some conceptual issues. In particular the interpretaion of QM should address the nptorious measurement problem. The many-world interpretation claims to provide a nice (deterministic) solution, but this is clearly not true. Indeed, whiile it "solves" the problem of which outcome occurs and has even some arguments on how probabilities emerge from determinism (so, it somehow recovers the Born rule), it does not tell when the branching occurs.Why the universe splits when you go in the lab and activate a photodetector, but not in most ofother interactions?

I hope this addressed your question. All of this, however, is not really pertinet to my essay.

Thank you again and all the best,

Flavio

thank you so much for your kind words.

Frankly, I don't like the many-world interpretation very much. Firstly, as Carlo Rovelli always puts it, there is a cost for every interpretation that you have to be ready to pay. Many worlds has an enourmous ontological cost, for it requires to assume this irrisonable moltiplication of worlds, universe, or whatever. Secondly, interpretations not only provide a consistent backstory to a theory, but are also supposed to solve some conceptual issues. In particular the interpretaion of QM should address the nptorious measurement problem. The many-world interpretation claims to provide a nice (deterministic) solution, but this is clearly not true. Indeed, whiile it "solves" the problem of which outcome occurs and has even some arguments on how probabilities emerge from determinism (so, it somehow recovers the Born rule), it does not tell when the branching occurs.Why the universe splits when you go in the lab and activate a photodetector, but not in most ofother interactions?

I hope this addressed your question. All of this, however, is not really pertinet to my essay.

Thank you again and all the best,

Flavio

Flavio,

Yes, it was a tangential question, but I appreciate you taking the time to answer. I like your point of view.

Best,

Ernesto

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Yes, it was a tangential question, but I appreciate you taking the time to answer. I like your point of view.

Best,

Ernesto

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Dear Flavio,

I enjoyed reading your essay! It's well written, well documented, and interesting, giving a fresh perspective on classical mechanics. And I loved the way you concluded, with the epistemic modesty coming from the acknowledgment that both classical and quantum mechanics can be interpreted both deterministically and indeterministically, without the experiment being able to tell them appart.

You wrote:*leave the dynamical equations of Newtonian mechanics unchanged*

Considering that you reject the*ontological principle of infinite precision*, what do you think happens with the dynamical equations of Newtonian mechanics? Should them also be replaced with some computable dynamical equations?

Your essay raises many interesting questions. Some of them are of course related to my own interest. One is the following. Do you think that in classical mechanics indeterminism enters at various times, as part of the dynamics, or only in the initial conditions? This interests me personally because of the way I see quantum mechanics, but I decided to take this part of discussion in private, since I think your FQXi page should stay about your essay.

Thanks for the great reading, and I wish you success in this contest!

Cheers,

Cristi

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I enjoyed reading your essay! It's well written, well documented, and interesting, giving a fresh perspective on classical mechanics. And I loved the way you concluded, with the epistemic modesty coming from the acknowledgment that both classical and quantum mechanics can be interpreted both deterministically and indeterministically, without the experiment being able to tell them appart.

You wrote:

Considering that you reject the

Your essay raises many interesting questions. Some of them are of course related to my own interest. One is the following. Do you think that in classical mechanics indeterminism enters at various times, as part of the dynamics, or only in the initial conditions? This interests me personally because of the way I see quantum mechanics, but I decided to take this part of discussion in private, since I think your FQXi page should stay about your essay.

Thanks for the great reading, and I wish you success in this contest!

Cheers,

Cristi

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Dear Cristi,

thank you very much for appreciating my work! Indeed, my main motivation is to show that what is considered one of the greatest novelties of quantum mechanics, indeterminism, is not necessarily inherent in that theory. I don't claim, of course, that there are not fundamental differences between classical and quantum theory, but one can surely be more thoughtful and symmetrize...

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thank you very much for appreciating my work! Indeed, my main motivation is to show that what is considered one of the greatest novelties of quantum mechanics, indeterminism, is not necessarily inherent in that theory. I don't claim, of course, that there are not fundamental differences between classical and quantum theory, but one can surely be more thoughtful and symmetrize...

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Dear Flavio

I think that, in one way or another, we (physicists) have been aware that the way we are mathematically representing our physical experience has not been the most suitable. For instance, (1) measurements always have an associated uncertainty that arises from the limited resolution of the instruments. (2) It is assumed that the measurement process does not affect the system under study. (3) Physical objects are extended objects. All of this is ignored in the mathematical representation of classical physics. The novelty that I see in your essay is that by a deep and well documented analysis you are showing a way to relax this problem. You are setting an equilibrium between experience and mathematical representation. Your essay and the work behind have the potential for a breakthrough in physics. In my view, it is also a knock down to modern mathematics which, as Scott Guttery argues (another participant), has been completely disconnected from experience, and it is better for us to invent our own mathematics.

My essay discusses how physics has given too much importance to mathematical representation and measurements on top of our physical understanding, perhaps you will find it interesting.

By the way, just as feedback, to my knowledge the photoelectric effect was discovered in 1887 by Heinrich Hertz, you say that in 1895 no quantum effect was discovered. Congratulations for your great essay, I am sure it will make to the finals.

Best Regards

Israel

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I think that, in one way or another, we (physicists) have been aware that the way we are mathematically representing our physical experience has not been the most suitable. For instance, (1) measurements always have an associated uncertainty that arises from the limited resolution of the instruments. (2) It is assumed that the measurement process does not affect the system under study. (3) Physical objects are extended objects. All of this is ignored in the mathematical representation of classical physics. The novelty that I see in your essay is that by a deep and well documented analysis you are showing a way to relax this problem. You are setting an equilibrium between experience and mathematical representation. Your essay and the work behind have the potential for a breakthrough in physics. In my view, it is also a knock down to modern mathematics which, as Scott Guttery argues (another participant), has been completely disconnected from experience, and it is better for us to invent our own mathematics.

My essay discusses how physics has given too much importance to mathematical representation and measurements on top of our physical understanding, perhaps you will find it interesting.

By the way, just as feedback, to my knowledge the photoelectric effect was discovered in 1887 by Heinrich Hertz, you say that in 1895 no quantum effect was discovered. Congratulations for your great essay, I am sure it will make to the finals.

Best Regards

Israel

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Dear Israel,

I am flattered by your compliments on the potential you see in my modest work. I am glad that you find it interesting. I will look at your essay as well and comment if I have something to say about it.

Best regards,

Flavio

I am flattered by your compliments on the potential you see in my modest work. I am glad that you find it interesting. I will look at your essay as well and comment if I have something to say about it.

Best regards,

Flavio

Dear Dr Flavio Del Santo

Thank you for presenting a wonderful essay... Your words ..... classical physics (i.e., Newton’s mechanics and Maxwell’s electrodynamics) would allow, in principle, to predict everything with certainty.....are very much true in case of Dynamic Universe Model. Many of its predictions came true.

Let me hope you will have time visiting my essay to have a CRITICAL examination of my essay... "A properly deciding, Computing and Predicting new theory’s Philosophy".....

Best Regards

=snp

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Thank you for presenting a wonderful essay... Your words ..... classical physics (i.e., Newton’s mechanics and Maxwell’s electrodynamics) would allow, in principle, to predict everything with certainty.....are very much true in case of Dynamic Universe Model. Many of its predictions came true.

Let me hope you will have time visiting my essay to have a CRITICAL examination of my essay... "A properly deciding, Computing and Predicting new theory’s Philosophy".....

Best Regards

=snp

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Dear Flavio

I came here to comment by seeing the popularity of your essay and by reading the abstract I understood your view point at least (I guess). Then, going through the successive posts I encountered your comment: ``the whole point of my view is that there is ALWAYS an element of genuine randomness. If you accept my alternative interpretation, even the length of a metal rod...

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I came here to comment by seeing the popularity of your essay and by reading the abstract I understood your view point at least (I guess). Then, going through the successive posts I encountered your comment: ``the whole point of my view is that there is ALWAYS an element of genuine randomness. If you accept my alternative interpretation, even the length of a metal rod...

view entire post

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Dear Flavio,

Your ideas are brilliant and the essay itself is extremely well prepared. You touch the deep problems related to real numbers, no infinities in the Universe, nondeterminism, unpredictability and arguments are impeccable. Then the only question which remains is how come all this is like it is which is the domain of mystical Theory of Everything. Arguments like yours and other led me to conclusion that such theory has to be grounded in uncomputability. But how? I sketched the out-of-the-mainstream ideas in my essay.

Best regards,

Irek

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Your ideas are brilliant and the essay itself is extremely well prepared. You touch the deep problems related to real numbers, no infinities in the Universe, nondeterminism, unpredictability and arguments are impeccable. Then the only question which remains is how come all this is like it is which is the domain of mystical Theory of Everything. Arguments like yours and other led me to conclusion that such theory has to be grounded in uncomputability. But how? I sketched the out-of-the-mainstream ideas in my essay.

Best regards,

Irek

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Dear Flavio,

I found your paper persuasive and powerful. The only content issue I think of is that a few comments about how your ideas relate to the popular block universe concept would have been nice. I am myself very solidly in the now-is-real column, but I also deeply respect both Einstein's concerns on frame foliation reconciliation, and quantum arguments such as Wheeler-Feynman...

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I found your paper persuasive and powerful. The only content issue I think of is that a few comments about how your ideas relate to the popular block universe concept would have been nice. I am myself very solidly in the now-is-real column, but I also deeply respect both Einstein's concerns on frame foliation reconciliation, and quantum arguments such as Wheeler-Feynman...

view entire post

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Dear Terry,

thank you very much for your feedback!

Indeed, you correctly point out a difficulty of our approach, which is a tension between the time that really passes due to the dertermination of new physical quantities and the relativistic time, which is just another component of the space-time manifold (which indeed is defined in terms of homeomorphisms with the Euclidean space R^n). We are working on this and have already discussed possible solutions.

However, I am not sure whether I agree with what you then say about the continous limits:

"These limits often occurs at scales far smaller than our unaided senses can perceive. If physics did not work this way, the calculus never would have worked well enough for modeling this universe to have been worth the trouble."

In fact, quantum mechanics occurs at scales far smaller than our unaided senses can perceive and yet there the we found the first impossibility of thinking in terms of continuity. So I would say that it is the other way around: our human-scale made us think that everything is smooth and continous, but when you observe from much closer you are forced to introduce quantizations.

Thank you once more and all the best,

Flavio

thank you very much for your feedback!

Indeed, you correctly point out a difficulty of our approach, which is a tension between the time that really passes due to the dertermination of new physical quantities and the relativistic time, which is just another component of the space-time manifold (which indeed is defined in terms of homeomorphisms with the Euclidean space R^n). We are working on this and have already discussed possible solutions.

However, I am not sure whether I agree with what you then say about the continous limits:

"These limits often occurs at scales far smaller than our unaided senses can perceive. If physics did not work this way, the calculus never would have worked well enough for modeling this universe to have been worth the trouble."

In fact, quantum mechanics occurs at scales far smaller than our unaided senses can perceive and yet there the we found the first impossibility of thinking in terms of continuity. So I would say that it is the other way around: our human-scale made us think that everything is smooth and continous, but when you observe from much closer you are forced to introduce quantizations.

Thank you once more and all the best,

Flavio

Flavio, thanks! I must have worded that badly: I was trying to say *exactly* what you just said: It's just the huge number of atoms in human-scale objects that fools us into believing in "continuity" that is actually quantized.

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Dear Flavio,

As an engineer we are taught early on that all the problems that we are going to solve are idealization also all of the laws of physics classical or otherwise are idealization of the problems being solved, theoretical or applied. So I don't know in that sense what is the real discovery. Moreover, the problem with the standard QM interpretation(the minimum) in terms of predictibility is fundamentally vastly different in quality and quantity, so I don't see how you casting doubt on the uncertainity in classical helps in QM.

My solution has been to try to deal with the problem with the only and final way to solve all these problems, that is to find the correct ontology which leads to to a fairly simple system that can be comprehended easily.

It is also very baffling for me when all the respectable physicists (not talking about amateur philosopher) here in this contest go on about Turing and Godel yet we have been doing physics in the past 400 years with regular math with fairly good success. So it should have been obvious that it is only about a correction to the model and deducing some ontology, that is all and not go on a wild goose chase.

Sorry for being direct, I don't mean to be unfriendly, just my opinion. Thanks

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As an engineer we are taught early on that all the problems that we are going to solve are idealization also all of the laws of physics classical or otherwise are idealization of the problems being solved, theoretical or applied. So I don't know in that sense what is the real discovery. Moreover, the problem with the standard QM interpretation(the minimum) in terms of predictibility is fundamentally vastly different in quality and quantity, so I don't see how you casting doubt on the uncertainity in classical helps in QM.

My solution has been to try to deal with the problem with the only and final way to solve all these problems, that is to find the correct ontology which leads to to a fairly simple system that can be comprehended easily.

It is also very baffling for me when all the respectable physicists (not talking about amateur philosopher) here in this contest go on about Turing and Godel yet we have been doing physics in the past 400 years with regular math with fairly good success. So it should have been obvious that it is only about a correction to the model and deducing some ontology, that is all and not go on a wild goose chase.

Sorry for being direct, I don't mean to be unfriendly, just my opinion. Thanks

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I should just mention that I don't mean that my system is correct as is, but I think it is highly suggestive of the correct physics since it closely follows present understanding and the general set up of today's physics, yet more fundamental.

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Dear Adel Sadeq, there is a deep conceptual difference between the way engeneers and (even experimental scientists) are trained and the foundations we groumd our scientific theories upon. You are referring to the unavoidable finiteness of the error bars in actual measurements. Clearly this is not the same as having fundamental limits of determuninacy, as I discuss in my essay.

Dear Flavio,

Thank you for the reply. The problem of fundamental limits of determinacy is very hard to be determined experimentally whether classical or QM as discussed in the link below by you colleague in the math department Dr. A. Neumaier. Moreover, I agree with his interpretation as a basis, which my theory sort of confirms it because the probability density is shown to be just the density of energy and momentum very much like in QFT. Also EPR is trivial in my idea since the system is inherently a nonlocal theory. Thanks again.

https://www.physicsforums.com/threads/the-thermal-inte

rpretation-of-quantum-physics.967116/

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Thank you for the reply. The problem of fundamental limits of determinacy is very hard to be determined experimentally whether classical or QM as discussed in the link below by you colleague in the math department Dr. A. Neumaier. Moreover, I agree with his interpretation as a basis, which my theory sort of confirms it because the probability density is shown to be just the density of energy and momentum very much like in QFT. Also EPR is trivial in my idea since the system is inherently a nonlocal theory. Thanks again.

https://www.physicsforums.com/threads/the-thermal-inte

rpretation-of-quantum-physics.967116/

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Dear Flavio Del Santo,

Your essay seems to be exactly what the framers of this topic were looking to generate. My essay went in a totally different direction. Your writing style made this dense topic relatable. I was just going to glance at the essay, but ending up reading it in one sitting. Excellent work.

A topic for a future essay could be a clearer link between quantum mechanics and measurable classical mechanics. Your phase space diagram showed a strong similarity between the two. This relationship gave me an idea about how the square well problem, which famously has opposite result for classical and quantum could be shown to be similar if measurement was accounted for in the set-up.

There is also the issue of larger scale events like sound waves, which contain information, but seem independent of the atomic scale.

Sincerely,

Jeff Schmitz

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Your essay seems to be exactly what the framers of this topic were looking to generate. My essay went in a totally different direction. Your writing style made this dense topic relatable. I was just going to glance at the essay, but ending up reading it in one sitting. Excellent work.

A topic for a future essay could be a clearer link between quantum mechanics and measurable classical mechanics. Your phase space diagram showed a strong similarity between the two. This relationship gave me an idea about how the square well problem, which famously has opposite result for classical and quantum could be shown to be similar if measurement was accounted for in the set-up.

There is also the issue of larger scale events like sound waves, which contain information, but seem independent of the atomic scale.

Sincerely,

Jeff Schmitz

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Dear Flavio,

This is really an impressive and excellent essay. I enjoyed it very much.

I have not much to comment but to ask some questions with regards to where your essay could lead:

- There is an interesting trend in mathematics (I find it interesting at least) which attempts to extend concepts of standard mathematics to fuzzy sets. This is sometimes called fuzzification. I am wondering whether your essay could not be a starting point for a fuzzification of classical mechanics. Note that fuzzification has also the advantage of using fuzzy logic which has a working procedure to determine entailments and the like (this could be relevant to your notion of cause and effect).

- Your last optimistic quote and paragraph on the openness of the future does remind me of the interpretation of probability by Carl Friedrich von Weizsacker. As far as I understand his view, probability can only be about the future because the future is "open" to re-use your wordings. Are you aware of his work on the matter (like his temporal logic) and, if so, do you have particular thoughts about it?

While your essay mostly focuses on indeterminacy, the essay I have submitted focuses on undecidability and asks a similar question in substance "As physics and science ever been decidable?". If you are interested you can read it there https://fqxi.org/community/forum/topic/3477 .

Best of luck for the contest.

Fabien

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This is really an impressive and excellent essay. I enjoyed it very much.

I have not much to comment but to ask some questions with regards to where your essay could lead:

- There is an interesting trend in mathematics (I find it interesting at least) which attempts to extend concepts of standard mathematics to fuzzy sets. This is sometimes called fuzzification. I am wondering whether your essay could not be a starting point for a fuzzification of classical mechanics. Note that fuzzification has also the advantage of using fuzzy logic which has a working procedure to determine entailments and the like (this could be relevant to your notion of cause and effect).

- Your last optimistic quote and paragraph on the openness of the future does remind me of the interpretation of probability by Carl Friedrich von Weizsacker. As far as I understand his view, probability can only be about the future because the future is "open" to re-use your wordings. Are you aware of his work on the matter (like his temporal logic) and, if so, do you have particular thoughts about it?

While your essay mostly focuses on indeterminacy, the essay I have submitted focuses on undecidability and asks a similar question in substance "As physics and science ever been decidable?". If you are interested you can read it there https://fqxi.org/community/forum/topic/3477 .

Best of luck for the contest.

Fabien

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Dear Fabien,

thank you for wrtiting and to kindly appreciate my work.

Indeed, what you say about the "fuzzification" program is very pertinent and similar to the aims expressed in my essay. Gisin with other collaborators and me is considering different (constructive) mathematical structures to capture this feature of fuzziness.

I was not aware of von Weizsacker's work that you mention. I will surely have a look at it, as I will do with your essay as soon as time allows.

Thanks once more and all the best,

Flavio

thank you for wrtiting and to kindly appreciate my work.

Indeed, what you say about the "fuzzification" program is very pertinent and similar to the aims expressed in my essay. Gisin with other collaborators and me is considering different (constructive) mathematical structures to capture this feature of fuzziness.

I was not aware of von Weizsacker's work that you mention. I will surely have a look at it, as I will do with your essay as soon as time allows.

Thanks once more and all the best,

Flavio

Flavio,

Your essay seems to put the foundation's question, the 3 Uns, in a more reasonable light that helps to reset the anthropocentric tilt toward objectivity regarding outcomes in physics -- classical and quantum. Furthermore your concepts are quite accessible. Your use of figure 3, for example, I feel introduces the graphic realism in the classical world that is missing, perhaps also in the realm of subatomic particles as well. A probability factor is always relevant in engineering projects. Hope you have time to give mine a look: https://fqxi.org/community/forum/topic/3396.

Great job. My rating is your 22nd. Having that many protects you against the 1s given by some with no comments.

Jim Hoover

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Your essay seems to put the foundation's question, the 3 Uns, in a more reasonable light that helps to reset the anthropocentric tilt toward objectivity regarding outcomes in physics -- classical and quantum. Furthermore your concepts are quite accessible. Your use of figure 3, for example, I feel introduces the graphic realism in the classical world that is missing, perhaps also in the realm of subatomic particles as well. A probability factor is always relevant in engineering projects. Hope you have time to give mine a look: https://fqxi.org/community/forum/topic/3396.

Great job. My rating is your 22nd. Having that many protects you against the 1s given by some with no comments.

Jim Hoover

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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...

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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...

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post approved

Your essay was interesting. However, it raises at least one major question that I don't think was sufficiently addressed.

For example, in figure 3, why could the (indeterministic) graph on the right not be considered to be deterministic? It appears that it is interpreted to be indeterministic simply because events*could have* gone in a different direction.

Let me state this in...

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For example, in figure 3, why could the (indeterministic) graph on the right not be considered to be deterministic? It appears that it is interpreted to be indeterministic simply because events

Let me state this in...

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post approved

Dear Jason W Steinmetz, it seems that your criticisms are based on misconceptions. You write: "A popular interpretation of unpredictability is that the initial conditions cannot be known with sufficient enough precision to construct accurate predictions. I find this interpretation to be, at the very least, weak". I disagree that this is populuar, for that matters, but most importantly that this is weak. It is a totally legit way of thinking of plausible indeterministic theories. The other main one being, what would perhaps make you happier, a fundamentally stochastic dynamics. Please have a look at my paper where we discuss these distinctions https://arxiv.org/abs/1909.03697 (section "FORMS OF INDETERMINISM IN CLASSICAL AND QUANTUM PHYSICS"). The argument is NOT merely epistemic, for the initial conditions are in my model supposed to be indeterminate (as opposed to anckown, as an experimentalist would claim).

Determinism is absolute, making it just a little bit fuzzy makes it untanable. Think of any chaotic system and you will see this. Moreover, we have Bell's inequalities: If there is less than one bit of randomness in the universe, we can create unbounded one (again see my paper below).

Best regards,

Flavio Del Santo

Determinism is absolute, making it just a little bit fuzzy makes it untanable. Think of any chaotic system and you will see this. Moreover, we have Bell's inequalities: If there is less than one bit of randomness in the universe, we can create unbounded one (again see my paper below).

Best regards,

Flavio Del Santo

You are absolutely correct that my "criticisms are based on misconceptions."

You wrote an interesting and well-reasoned essay based on the (legitimate) premise that the existence of what cannot be determined amounts to a refutation of determinism. Subsequently, since some things are indeterminate then these things cannot be predicted, which is technically correct. I simply made the case that this does not refute determinism unless, as you postulated, these things are*inherently indeterminate* and thus *determined by "nothing"*.

It certainly appears that the concepts of*what is* (ontology) and *what can be known* (epistemology) are inextricably linked and their exact fundamental difference ineluctably *fuzzy*.

I wish you well in the contest.

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You wrote an interesting and well-reasoned essay based on the (legitimate) premise that the existence of what cannot be determined amounts to a refutation of determinism. Subsequently, since some things are indeterminate then these things cannot be predicted, which is technically correct. I simply made the case that this does not refute determinism unless, as you postulated, these things are

It certainly appears that the concepts of

I wish you well in the contest.

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Hi Flavio,

Thanks for the really well written essay. The principle of infinite precision is super useful in highlight the tension, either ontologically or epistemically, of formal axiomatic systems and physics. I'd never read Max Born's essay that you quote on page 2, but its an excellent reference!

I completely sympathise with your idea of finite information quantities are loved the reference to Gisin's recent work. As you mentioned, Landauer has written extensively on this---I lent heavily on Landauer's perspectives in my essay.

You wrote that

``In this view, the orthodox interpretation of classical physics can be regarded as a deterministic completion of an indeterministic model, in terms of hidden variables''.

The finite information quantities seem to suggest that indeterministic models are fundamental. For example, a lot of powerful claims can be made from statistical physics or thermodynamics. Would these kinds of ideas occupy a more fundamental, rather than derivative role, in a theory of finite information quantities?

Again, thanks for the great essay! It was a pleasure to read!

Cheers,

Michael

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Thanks for the really well written essay. The principle of infinite precision is super useful in highlight the tension, either ontologically or epistemically, of formal axiomatic systems and physics. I'd never read Max Born's essay that you quote on page 2, but its an excellent reference!

I completely sympathise with your idea of finite information quantities are loved the reference to Gisin's recent work. As you mentioned, Landauer has written extensively on this---I lent heavily on Landauer's perspectives in my essay.

You wrote that

``In this view, the orthodox interpretation of classical physics can be regarded as a deterministic completion of an indeterministic model, in terms of hidden variables''.

The finite information quantities seem to suggest that indeterministic models are fundamental. For example, a lot of powerful claims can be made from statistical physics or thermodynamics. Would these kinds of ideas occupy a more fundamental, rather than derivative role, in a theory of finite information quantities?

Again, thanks for the great essay! It was a pleasure to read!

Cheers,

Michael

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Dear Michael,

Thanks for your kind feedback. Indeed, I think our essays have a great deal in common, although your is more concerned with limits of computation. (I am about to comment more precisely on the dedicated page of your essay).

As for your question, indeed, statistical (indeterministic) laws would be just a reflection of an indeterministic microscopic behaviour. So it would surely attribute a more fundamental value to this. Moreover, this would even out the tension between microscopic determinism and statistical irreversibility. Gisin and I have gone through this problem in our paper (https://arxiv.org/abs/1909.03697), where we stated: "In the perspective of the alternative indeterministic interpretation (based on FIQs), instead, the deterministic law of the ideal gas, ruling the behavior at

the macroscopic level, emerges as a novel and not reducible Notice that the historical debate on the apparent incompatibility between Poincar´e’s recurrence theorem and Boltzmann’s kinetic theory of gases does not arise in the framework of FIQs."

Thank you once more and all the best,

Flavio

Thanks for your kind feedback. Indeed, I think our essays have a great deal in common, although your is more concerned with limits of computation. (I am about to comment more precisely on the dedicated page of your essay).

As for your question, indeed, statistical (indeterministic) laws would be just a reflection of an indeterministic microscopic behaviour. So it would surely attribute a more fundamental value to this. Moreover, this would even out the tension between microscopic determinism and statistical irreversibility. Gisin and I have gone through this problem in our paper (https://arxiv.org/abs/1909.03697), where we stated: "In the perspective of the alternative indeterministic interpretation (based on FIQs), instead, the deterministic law of the ideal gas, ruling the behavior at

the macroscopic level, emerges as a novel and not reducible Notice that the historical debate on the apparent incompatibility between Poincar´e’s recurrence theorem and Boltzmann’s kinetic theory of gases does not arise in the framework of FIQs."

Thank you once more and all the best,

Flavio

Dear Flavio,

The refusal of actual infinities goes back to Aristotle, and those who followed always thought of measurement in terms of rational numbers with finite representations. And as the inverse square laws were established, classical determinism came to be understood in the same way, with laws restricted to quadratic equations, or conic sections, with rational solutions.

When Poincare went beyond that to transversals, and the symbolic sequences that constrain them, he was exploring a new physics of chaotic dynamics, beyond what was possible for Laplace and classical rationalism. Those *infinite sequences give you the Kolmogarov-Sinai entropy, as a measure of entropy production, and thereby unpredictability. The axioms for probability of both Kolmogarov and Karl Popper both assume infinite sequence representations.

Of course there is also the classical rationalism of games of chance, working from finite binomial distributions, but there measurement with complete precision becomes possible, and Maxwell's Demon is very much in business. If you insist on viewing reality as a computer it becomes hackable.

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The refusal of actual infinities goes back to Aristotle, and those who followed always thought of measurement in terms of rational numbers with finite representations. And as the inverse square laws were established, classical determinism came to be understood in the same way, with laws restricted to quadratic equations, or conic sections, with rational solutions.

When Poincare went beyond that to transversals, and the symbolic sequences that constrain them, he was exploring a new physics of chaotic dynamics, beyond what was possible for Laplace and classical rationalism. Those *infinite sequences give you the Kolmogarov-Sinai entropy, as a measure of entropy production, and thereby unpredictability. The axioms for probability of both Kolmogarov and Karl Popper both assume infinite sequence representations.

Of course there is also the classical rationalism of games of chance, working from finite binomial distributions, but there measurement with complete precision becomes possible, and Maxwell's Demon is very much in business. If you insist on viewing reality as a computer it becomes hackable.

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Dear Flavio,

Your essay gave me an idea. If you have time, I wish to know what you think.

Indeterminism leads to irreversibility, which leads to entropy. A true reversible system would require infinite information density. Because we have the arrow of time that is entropy, we cannot be in a deterministic University, since a net increase in entropy requires irreversibility. It does not matter if this is a quantum or classical system.

Thank you,

Jeff Schmitz

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Your essay gave me an idea. If you have time, I wish to know what you think.

Indeterminism leads to irreversibility, which leads to entropy. A true reversible system would require infinite information density. Because we have the arrow of time that is entropy, we cannot be in a deterministic University, since a net increase in entropy requires irreversibility. It does not matter if this is a quantum or classical system.

Thank you,

Jeff Schmitz

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Dear Flavio,

Thank you for your very interesting essay. Your angle of attack is quite original, and I completely agree with your argument that indeterminism is a matter of interpretation, and can both be chosen for quantum or classical theory. Indeed Laplace’s demon is often considered as being exorcised by quantum theory, but its existence is already facing difficulties by the only fact...

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Thank you for your very interesting essay. Your angle of attack is quite original, and I completely agree with your argument that indeterminism is a matter of interpretation, and can both be chosen for quantum or classical theory. Indeed Laplace’s demon is often considered as being exorcised by quantum theory, but its existence is already facing difficulties by the only fact...

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Dear Hippolyte,

thank you for your kind words; I am glad that you found some of my ideas interesting.

I am especially thankful for the references you pointed out to me. In fact, I was aware neither of Breuer’s theorem nor of Zwick's paper, nut they look of the utmost interest to me. I will surely scrutinise their ideas. On spot, from what you wrote me, I am not sure if the classical measurement problem stem from the same motivations as mine -I never considere the self reference problem which seems central to the argument of Zwick- but surely it's nice to see that others had similar ides from different paths.

I will gladly read your essay and comment on its dedicated page soon.

All the best,

Flavio

thank you for your kind words; I am glad that you found some of my ideas interesting.

I am especially thankful for the references you pointed out to me. In fact, I was aware neither of Breuer’s theorem nor of Zwick's paper, nut they look of the utmost interest to me. I will surely scrutinise their ideas. On spot, from what you wrote me, I am not sure if the classical measurement problem stem from the same motivations as mine -I never considere the self reference problem which seems central to the argument of Zwick- but surely it's nice to see that others had similar ides from different paths.

I will gladly read your essay and comment on its dedicated page soon.

All the best,

Flavio

Dear Flavio,

what an interesting topic. I was happy to see, you have a contribution in the contest. The problem of the origin of randomness, which is not merely epistemic is a big puzzle to me. The investigation of indeterministic classical physics is interesting in order to see, where the structural/conceptual differences are between classical and quantum physics. And to recognize that it...

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what an interesting topic. I was happy to see, you have a contribution in the contest. The problem of the origin of randomness, which is not merely epistemic is a big puzzle to me. The investigation of indeterministic classical physics is interesting in order to see, where the structural/conceptual differences are between classical and quantum physics. And to recognize that it...

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Hi Flavio,

I take it this excellent essay more or less summarizes your development of Gisin’s application of constructive maths to classical mechanics? I’d be interested to know how you might see Brouwer’s intuitionistic philosophy in relation to this mathematically indeterminate approach.

As I understand it, his intuitionism was derived from Kantian intuition (anschauung, intuitus) as intuiting/apprehending/perceiving the forms of sensibility, space, and time given in empirical (phenomenal) experience. From that perspective we intuit/perceive phenomenal patterns in our empirical experience of the world (thus information is physical!), and the constructive mathematics is based on that empirically intuited pattern perception. The formal, intersubjective communication of these empirical patterns (or information) is effected in that constructive mathematics, for which classical mechanics thus becomes necessarily indeterminate, at least from this intuitionist (also phenomenological) perspective.

What is objectively real in this sense are the phenomenal patterns themselves (or real patterns cf. Dennett) as given in empirical/phenomenal experience, rather than say, the Laplace demon’s idealized external world of point particles with infinitely precise, initial physical conditions. Does this mean intuitionism, in your view, must reject the notion of a classical world defined as ‘objective external reality’ in favour of the actual empirical experience of such a merely potential reality? Or can potentia remain an idealized unobservable continuum from which our discrete actualitas emerges?

Best regards,

Malcolm Riddoch

Je suit, nous sommes Wigner!

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I take it this excellent essay more or less summarizes your development of Gisin’s application of constructive maths to classical mechanics? I’d be interested to know how you might see Brouwer’s intuitionistic philosophy in relation to this mathematically indeterminate approach.

As I understand it, his intuitionism was derived from Kantian intuition (anschauung, intuitus) as intuiting/apprehending/perceiving the forms of sensibility, space, and time given in empirical (phenomenal) experience. From that perspective we intuit/perceive phenomenal patterns in our empirical experience of the world (thus information is physical!), and the constructive mathematics is based on that empirically intuited pattern perception. The formal, intersubjective communication of these empirical patterns (or information) is effected in that constructive mathematics, for which classical mechanics thus becomes necessarily indeterminate, at least from this intuitionist (also phenomenological) perspective.

What is objectively real in this sense are the phenomenal patterns themselves (or real patterns cf. Dennett) as given in empirical/phenomenal experience, rather than say, the Laplace demon’s idealized external world of point particles with infinitely precise, initial physical conditions. Does this mean intuitionism, in your view, must reject the notion of a classical world defined as ‘objective external reality’ in favour of the actual empirical experience of such a merely potential reality? Or can potentia remain an idealized unobservable continuum from which our discrete actualitas emerges?

Best regards,

Malcolm Riddoch

Je suit, nous sommes Wigner!

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" Or can potentia remain an idealized unobservable continuum from which our discrete actualitas emerges?"

Or put another way ... can the unobservable potentiality of quantum states best be described by the continuum of real numbers whereas our discrete actuality is a constructive/intuitionistic concern?

And what implications might this real vs natural number distinction have for the 'from potential to actual' measurement problem?

m

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Or put another way ... can the unobservable potentiality of quantum states best be described by the continuum of real numbers whereas our discrete actuality is a constructive/intuitionistic concern?

And what implications might this real vs natural number distinction have for the 'from potential to actual' measurement problem?

m

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Dear Flavio,

Congratulations on the well-organized essay on the new notation of the randomness. As you visited my essay, I really enjoyed learning this. In the past essay contest, I wrote the essay on information to be finally published in the book. On this essay, the FIQ is not discussed. However, one-bit is not enough to well defined. Therefore, we seem to need more than two bits on the well-defined FIQ.

Also, from your perspective, how do you understand the integrated information theory (IIT)? Since mathematical formulation of IIT, the conditional probability related to the certain randomness is implicitly assumed. What do you think?

Best wishes,

Yutaka

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Congratulations on the well-organized essay on the new notation of the randomness. As you visited my essay, I really enjoyed learning this. In the past essay contest, I wrote the essay on information to be finally published in the book. On this essay, the FIQ is not discussed. However, one-bit is not enough to well defined. Therefore, we seem to need more than two bits on the well-defined FIQ.

Also, from your perspective, how do you understand the integrated information theory (IIT)? Since mathematical formulation of IIT, the conditional probability related to the certain randomness is implicitly assumed. What do you think?

Best wishes,

Yutaka

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Flavio - Thanks. A coherent, well-written essay bringing a key, and incorrect, premise of classical physics to light. Your discussion and critique of the principle of infinite precision is impressive and should, if widely read, put the notion of classical determinism to bed permanently.

Where I was disappointed however, was in the very limited perspective your essay gives to the much broader epistemological issues of incompleteness and undecideability. These issues also point to invalid premises in our conceptual views and understanding of the world. I've taken a stab at these broader issues and would be very grateful if you gave my essay a look.

Sincerely - George Gantz: The Door That Has No Key. https://fqxi.org/community/forum/topic/3494

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Where I was disappointed however, was in the very limited perspective your essay gives to the much broader epistemological issues of incompleteness and undecideability. These issues also point to invalid premises in our conceptual views and understanding of the world. I've taken a stab at these broader issues and would be very grateful if you gave my essay a look.

Sincerely - George Gantz: The Door That Has No Key. https://fqxi.org/community/forum/topic/3494

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Dear George, thank you for your feedback and your constructive criticisms. Indeed I believe that undecideability and perhaps (but I am not really sure) even incompleteness play a central role in the foundations of science. My work and my priorities, hence the focus of my essay, are however on determinism and predictability at the moment. But I will be glad to read what you have to say about it.

All the best,

Flavio

All the best,

Flavio

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...

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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...

view entire post

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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....

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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....

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Dear John,

thanks so much for your kind feedback. You already know how highly I think of your essay as well.

As for your questions comments: "(i) it's hard to imagine a way to experimentally distinguish between determinism and indeterminism". Indeed, there are sound arguments whuich say that it's not only hard, but impossible (see references [41-42] in my essay).

As for the different interpretations of quantum mechanics, a central feature is trying to interpret the measurement problem. If classical physics is regarded as indeterministic, like in my model, there is also a classical measurement problem to be explained. We have discussion in more detail this issue in my paper with Nicolas Gisin on this topic. However, to my knowledge no systematic discussion on different interpretations of classical physics has been attempted.

Thank you again and all the best,

Flavio

p.s. thanks for the reference!

thanks so much for your kind feedback. You already know how highly I think of your essay as well.

As for your questions comments: "(i) it's hard to imagine a way to experimentally distinguish between determinism and indeterminism". Indeed, there are sound arguments whuich say that it's not only hard, but impossible (see references [41-42] in my essay).

As for the different interpretations of quantum mechanics, a central feature is trying to interpret the measurement problem. If classical physics is regarded as indeterministic, like in my model, there is also a classical measurement problem to be explained. We have discussion in more detail this issue in my paper with Nicolas Gisin on this topic. However, to my knowledge no systematic discussion on different interpretations of classical physics has been attempted.

Thank you again and all the best,

Flavio

p.s. thanks for the reference!

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...

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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...

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Dear John S,

thank you for your appreciative feedback and your interesting comments. I reply point-by-point:

1) I am not sure if I understand your comment fully. However, there are two main arguments expressed in my essay, independent but related: (i) information-theoretic arguments (Landauer's principle, Bekenstein bound, etc.) point at the fact that the information content encoded...

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thank you for your appreciative feedback and your interesting comments. I reply point-by-point:

1) I am not sure if I understand your comment fully. However, there are two main arguments expressed in my essay, independent but related: (i) information-theoretic arguments (Landauer's principle, Bekenstein bound, etc.) point at the fact that the information content encoded...

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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

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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

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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.

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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...

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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...

view entire post

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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.

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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.

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Dear Ian,

thanks so much for reading my essay and your kind words!

I have read Bohm's book some years ago, and I found it really insightful (although I must admit I don't remember the arguments about waves. I will look it up).

I look forward to receiving more from you concerning the relation between infinite precision and calcolus, a topic which I have myself though about for awhile.

I am not sure I understood your comment on FIQ, what do you mean when you say that. like real nombers, they are based on "the idea that numbers are ultimately outgrowth of the notion of counting"?

Thanks again and very much looking forward to discuss this more.

All the best,

Flavio

thanks so much for reading my essay and your kind words!

I have read Bohm's book some years ago, and I found it really insightful (although I must admit I don't remember the arguments about waves. I will look it up).

I look forward to receiving more from you concerning the relation between infinite precision and calcolus, a topic which I have myself though about for awhile.

I am not sure I understood your comment on FIQ, what do you mean when you say that. like real nombers, they are based on "the idea that numbers are ultimately outgrowth of the notion of counting"?

Thanks again and very much looking forward to discuss this more.

All the best,

Flavio

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...

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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...

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Flavio,

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

Jim Hoover.

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

Jim Hoover.

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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

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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

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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

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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

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Dear Dean,

thanks so much for your feedback and the interesting comments.

Indeed, what you point out, that my proposal of "indeterministic classical mechanics amounts to something like an ontological/physical interpretation of chaos" is a way of regarding this matter.

As for your second question, this is a natural assumption. We don't assume a discrete space(-time). But we just try to remove the infinities (and the infinitesimals) from the physical domain by positing that a finite region of space can only contain a finete amount of information. Landauer's principle and Beckenstein bound back up this idea.

Thanks again and all the best,

Flavio

thanks so much for your feedback and the interesting comments.

Indeed, what you point out, that my proposal of "indeterministic classical mechanics amounts to something like an ontological/physical interpretation of chaos" is a way of regarding this matter.

As for your second question, this is a natural assumption. We don't assume a discrete space(-time). But we just try to remove the infinities (and the infinitesimals) from the physical domain by positing that a finite region of space can only contain a finete amount of information. Landauer's principle and Beckenstein bound back up this idea.

Thanks again and all the best,

Flavio

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

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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

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Dear Jim,

thank you for your comment. I made determinism less plausible than before, but clearly its tenability stands as usual. For more insightful discussion of why the question of determinism vs indeterminism is undecidable on an empirical basis have a look at, for example, Suppes' "The Transcendental Character of Determinism" (referenced at the end of my essay).

Best wishes,

Flavio

thank you for your comment. I made determinism less plausible than before, but clearly its tenability stands as usual. For more insightful discussion of why the question of determinism vs indeterminism is undecidable on an empirical basis have a look at, for example, Suppes' "The Transcendental Character of Determinism" (referenced at the end of my essay).

Best wishes,

Flavio

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 ...

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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 ...

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Dear Prof. Sudarsky,

thank you for your feedback and your very interesting comments on the minimal requirements for a (empirically adequate) measurement process.

Let me instead start my reply in inverse order with respect to your question:

1. Stabilty. Your concerns are torally right, and I should have been more precise. What I had here in mind is an axiom similar to that of quantum mechanics. Namely, the state of a system remains unchanged when it is not measured, modulo a unitary evolution. I was here assuming the trivial evolution and focusing only on the chenges of the states due to measurements.

3. Precision improvability. Here it does not need to be at the same time. I am again thinking of repeated measurements on the same system. If even time is smeared and not sharply defined, there is an operational procedure that we call measurements that returns a certain number of digits. If one improves the precision of the measurement (dividing into ten a ruler, for instance) we should be able to find a new digits. However, all the previous determined digits are required to remain stable.

1. Intersubjectivity. I think what you say about this is a good point. Indeed, admittedly time remains the most difficult issue of our FIQs framework. At least, if one wants to determine a quantiti which does not depend on time (a natural constant of physics, for example) this must apply. Then, to compare two dynamical quantities at the same instant, is indeed not fully spelled our in our model.

I inted to wrote ore about general processes of measurement in non-deterministic theories. I will treasure your latter criticism to clarify this matters.

Thank you again and best wishes,

Flavio

thank you for your feedback and your very interesting comments on the minimal requirements for a (empirically adequate) measurement process.

Let me instead start my reply in inverse order with respect to your question:

1. Stabilty. Your concerns are torally right, and I should have been more precise. What I had here in mind is an axiom similar to that of quantum mechanics. Namely, the state of a system remains unchanged when it is not measured, modulo a unitary evolution. I was here assuming the trivial evolution and focusing only on the chenges of the states due to measurements.

3. Precision improvability. Here it does not need to be at the same time. I am again thinking of repeated measurements on the same system. If even time is smeared and not sharply defined, there is an operational procedure that we call measurements that returns a certain number of digits. If one improves the precision of the measurement (dividing into ten a ruler, for instance) we should be able to find a new digits. However, all the previous determined digits are required to remain stable.

1. Intersubjectivity. I think what you say about this is a good point. Indeed, admittedly time remains the most difficult issue of our FIQs framework. At least, if one wants to determine a quantiti which does not depend on time (a natural constant of physics, for example) this must apply. Then, to compare two dynamical quantities at the same instant, is indeed not fully spelled our in our model.

I inted to wrote ore about general processes of measurement in non-deterministic theories. I will treasure your latter criticism to clarify this matters.

Thank you again and best wishes,

Flavio

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).

I only recently learned of Nichola's and Flavio's work, and contacted them a few weeks ago. They were unaware of my work. Although 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 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.

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

Best wishes

Peter

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I only recently learned of Nichola's and Flavio's work, and contacted them a few weeks ago. They were unaware of my work. Although 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 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.

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

Best wishes

Peter

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Dear Flavio,

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

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. Your central thesis along with bringing these various topics together was very crafted. I very much enjoyed your "surgical" approach to breaking topics and finding their underlying essence.

Good luck for the contest!

Cheers,

Del

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

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. Your central thesis along with bringing these various topics together was very crafted. I very much enjoyed your "surgical" approach to breaking topics and finding their underlying essence.

Good luck for the contest!

Cheers,

Del

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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

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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

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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

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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

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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

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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:

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

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Hi Flavio,

Regarding my earlier message, I'll try a different tack. In your essay you write:

"As we will show in the next section, one can indeed envision an alternative classical physics that maintains the same general laws (equations of motion) of the standard formalism, but dismisses the physical relevance of real numbers, thereby assigning a fundamental indeterminacy to the values of physical quantities, as wished by Born. In fact, “as soon as one realizes that the mathematical real numbers are not really real, i.e. have no physical significance, then one concludes that classical physics is not deterministic.” [13].

In relation to the above anyway, can you explain whether or not you think there is anything different between our two works? Also, and although they're in a somewhat different context, do you or not think my work is closely related to the idea of infinite precision? Finally, had you known about my paper, do you think that you and Nicolas Gisin would have referenced it?

I'm sorry to push Flavio, but considering a few things, I don't think I have much choice.

Once again, I wish your essay and your work all the very best.

Peter

post approved

Regarding my earlier message, I'll try a different tack. In your essay you write:

"As we will show in the next section, one can indeed envision an alternative classical physics that maintains the same general laws (equations of motion) of the standard formalism, but dismisses the physical relevance of real numbers, thereby assigning a fundamental indeterminacy to the values of physical quantities, as wished by Born. In fact, “as soon as one realizes that the mathematical real numbers are not really real, i.e. have no physical significance, then one concludes that classical physics is not deterministic.” [13].

In relation to the above anyway, can you explain whether or not you think there is anything different between our two works? Also, and although they're in a somewhat different context, do you or not think my work is closely related to the idea of infinite precision? Finally, had you known about my paper, do you think that you and Nicolas Gisin would have referenced it?

I'm sorry to push Flavio, but considering a few things, I don't think I have much choice.

Once again, I wish your essay and your work all the very best.

Peter

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