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

Dear Falvio

This is quite an interesting essay.

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

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

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

So let me start with the second requirement :

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

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

Related concerns arise when considering the first requirement:

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

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

Finally, similar concerns apply to the last postulate:

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

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

So perhaps Flavio could clarify these issues for us.

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

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

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

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

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

Best wishes

Peter

Dear Flavio,

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

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

Good luck for the contest!聽

聽

Cheers,

Del

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

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

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

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

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

Dear Falvio,

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

Best of luck in the contest!

Rick Searle

Dear Flavio,

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

Nature does not play dice at the Planck scale

Hope this alternative view-point interests you.

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

Tejinder

Dear Flavio,

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

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

Best wishes

Lockie Cresswell

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