Relative information at the foundation of physics by Carlo Rovelli

Dear Carlo Rovelli,

I've long thought about the relationship between subjective information and objective quantities relating to physical systems---the sun's heat, in your example. Your idea, I think, clears up that mystery completely, and it goes to show that there are still simple, but powerful answers out there to be found, of which you've provided one.

I've also been interested in your reconstruction of quantum mechanics for a long time. I've thought about the idea that Bell inequalities/the Kochen-Specker theorem/etc., are ultimately related to the fact that one cannot find a single (ordinary) probability distribution to cover all experimental predictions of QM, especially all correlations between observables---that is, there is no probability distribution such that its marginals reproduce all experimentally obtained probabilities. Unless, of course, you allow the distribution to take on negative values, generalizing to a pseudo-probability; then, you get something like the Wigner function on phase space. I keep thinking that this ought to be related, in some way, to your approach, but so far I haven't thought about it enough. Also perhaps of interest is Kochen's recent reconstruction of quantum mechanics along similar lines.

Anyway, thank you for posting this essay, it was a pleasure to read,

Jochen

Thanks for your insightful essay. I am wondering what the status of single molecule thermodynamics is in your approach, e.g. in the Szilard engine and the derivation of Landauer's principle. Clearly, a single molecule interacts with thermometers and the box walls in a very different way from a gas with a large number of molecules. It has no effect on them except on those rare occasions when it hits them causing a tiny fluctuation. Yet we are still able to use Gibbsian thermodynamics to reason about this system. Do you accept such arguments in your approach and, if not, do you have an alternative derivation of Landauer's principle or an alternative resolution of Maxwell's demon.

I read quickly your article, and it is interesting.

I am thinking that if it is possible to have a bijection between each statistical system and a thermodynamic system (for example the blind child and a thermodynamic process), then it is possible to associate to each statistical system some physical quantity, and it is possible to apply the law of thermodynamic.

So, if there are two boxes, with red balls (hot molecules) and white balls (cold molecules), and a blind child (no physical measure) that make a random choice for each time step, then asymptotically the system is in equilibrium; if we write the second law of thermodynamics (in equilibrium point) for the blind child, then we must write that is impossible the passing of N red balls (for example 20) from a boxe to an other boxes (Clausius say that the entropy fluctutations are impossible).

I can understand the impossibility of the perpetual motion: it is impossible the infinite reproduction of the same sequence of extractions from the two boxes, but I think that the Clausius statement is so weak.

Ciao Carlo,

This is a nice statement of your ideas. Two questions:

1) It seems that on your account systems somehow "know" which degrees of freedom are going to be involved in their interaction. When you write, "If the coupling is such that it depends only on certain macroscopic variables of the gas, then the physical interactions of the gas and this system are objectively well described by thermodynamics", I feel that the coupling of systems somehow precedes its physical description. Who tells us which coupling is correct and which isn't?

2) On Democritus. I leave aside Democritus's argument about infinitely divisible space and no smallest magnitude, which your position obviously contradicts. Not everything in Democritus is the historic source of your account. However there's a contradiction that appears to me subtler than this. Democritus famously claimed that atoms can be any size, even the size of the Universe; they don't have to be small, like in Epicurus. This is good news, because you can favorably compare Democritus's notion of an atom and your notion of a system. Now, Democritus's systems are indivisible - this is absolutely fundamental for an atom. But aren't systems divisible? We routinely speak about subsystems, and this is as fundamental for quantum mechanics (e.g. entanglement) as indivisibility is for Democritus. So the analogy seems to fail on at least one very important point.

Hope to see you around soon.

Amicalement,

Alexei

Carlo, it's good to see you bringing your expertise into the system. I like the idea of using Shannon's relative entropy to resolve the difference between Democritus and Plato/Aristotle.

Since you are interested in ancient philosophy have you heard much about the acataleptic philosophers? There does not seem to be much recorded and interpretations differ.

In the essay I mentioned Carneades and Arcesilaus rather than Pyrrho. What was of interest to me was the debate around whether a skeptic could say anything reliable about their own ideas if they did not consider anything reliable. Hume was more important in my previous essay on causality. At least the ideas are linked.

I think a better modern development might be Bayesian Probability

Carlo,

I found your essay extremely interesting and informative, rich and diverse. I like the closing paragraph, particularly "The world is not just a blind wind of atoms, or generally covariant quantum fields. It is also the infinite game of mirrors reflecting one another formed by the correlations among the structures formed by the elementary objects".

All the best,

Antony

Hi Carlo,

Your essay very worth reading..., I also love your analogy of the box full of balls, characterized by color and charge. Nothing much to criticize but you may wish to ponder the following to which I have not got any satisfactory answer.

1. Since your essay touches on thermodynamics, given the equation

dS = dE/T, if you are given a tiny amount of energy, E and a control knob that can regulate temperature, T, can you cause an astronomical-sized increase in entropy, S by manipulating the temperature, T at the time of energy introduction?

I asked, Anton Biermans, but didn't get a satisfactory answer. I am looking at a cosmological implication.

2. On the discretization of space, which you also touched on... I have asked Edward Fredkin, but I am not fully satisfied with the answer and Stephen Wolfram didn't respond.

It is easy to say planets, air, fish in water, the water itself, atoms, etc, are discrete. Space does the separation for us so that we are able to call them "discrete".

But when the great SEPARATOR itself, space is said to be capable of taking a discrete form, who will do the separation for us? Certainly, the separator cannot separate itself or can it? That is between one discrete representation of space and the adjoining one, what makes us distinguish 1 from 2?

3. Then although you mention the atomism of Democritus, I suggest that you consider monads as well in future. Here is what Leibniz has to say about them, "... something that has no parts can't be extended, can't have a shape, and can't be split up. So monads are the true atoms of Nature--the elements out of which everything is made".

I will be happy to have your expert opinion and criticism of my essay, where I discuss my ideas on how discrete nature of space can be realized.

Regards,

Akinbo

Respectfully Professor Rovelli,

Unique is different once. It cannot be undifferentiatedly fashionable.

Joe

Dear Carlo,

A concept that information is a relative phenomena goes against classical and intuitive view of the world, to the point that even well-meaning grads still try to find a "universal underlying information", were none is present. Not further then one month ago we had such conversation, in two long batches of posts in this very competition at http://www.fqxi.org/community/forum/topic/1597 with Jochen. My use of magic words "Relational Quantum Mechanics" did not trigger at all that "all information is relative", or "there is no underlying universal information/reality", however obvious it may be in my own mind. Yet, in a longish back-and-forward, in a second batch, we came to a little formalism for highlighting the relative nature of information, and, therefore, descriptions. It seemed useful in driving information-relativity point. We even used Schmidt decomposition to provide a bridge between different informational perspectives.

Reading your paper from 1996, which is a 2nd reference in your essay, I like your "... keep in mind that the observer can be a table lamp". I am using in discussions a qubit as an observer, the "smallest" observer in informational sense.

In the 96's paper you had to tame notions of system and system's state, clarify and expose ambiguities. In the essay http://www.fqxi.org/community/forum/topic/1597 we make a guess of what is there in reality, taking cues from seemingly infallible QFTs of Standard Model. Then a notion of system becomes effective, and restricted by initial definitions, removing many common problems (e.g. cannot have priviledged systems, making all same). Then, we ask a question about information flow between interacting and non-interacting systems, which is settled by looking at exepriment, leading to "interaction confinement" concept. Interaction confinement automatically translates into unitary evolution of closed system, and implicitly shows that description and information are relative, using your more exact words. I wonder how we may combine these concepts better to further the common cause for having even smoother description of QM phenomena.

Cheers,

Mikalai.

Carlo,

I find that your statement, "Amon all systems, living systems are those that selection has lead to reproduce continuously their own structure by, in particular, making use of the information they have about the exterior world. This is why we can understand them in terms of finality and intentionality, because they are the ones that have permaned thanks precisely to the finality in their structure. Thus, it is not finality that drives structure, but the other way around, selected structures define finality." is indeed factual.

I have obtained evidence of what you have summarized about selected structures to map gravity with the strong, weak, and electromagnetic forces as one super-deterministc force. I invite you to review my findings and rate my essay when you get the chance:

http://fqxi.org/community/forum/topic/1809

Good luck with your entry of which I have rated highly for its insight.

Regards,

Manuel

Dear Carlo Rovelli,

I was very pleased to read your essay. Indeed, the context of a system has tremendous impact to the system, if we are interested in information, entropy, quantum mechanics, etc. Local depends on global, everything is relative to the context. I like your bold view that the context impacts reversibility even more than the intrinsic properties of the system. I find this natural for small systems, but for large systems is not that obvious, although, as you said, nothing prevents it from being true. As a parenthesis, John Baez just started an interesting series on relative entropy. About the interpretation of quantum mechanics you propose, I like the principle "It is always possible to acquire new information about a system." Each measurement resets the observed system to an eigenstate of the new observable, apparently acquiring new information, and, as you said, part of the old information becomes irrelevant. The system is forever fresh. This reminds me what Moisil said when he asked for a second glass of wine: "every man is entitled to a glass of wine, but after a glass of wine, you are a new man". On the other hand, I would like to make a comment on this, which I consider to be in the spirit of the relativity on the environment you advocate in your essay. The freshness of the system can very well be fueled from the unknown initial conditions of the system combined (and entangled) with the devices with which it previously interacted. If this is the case, the apparent acquiring of new information about the system is in fact acquiring of information about the continuously increasing system obtained by accounting all previous interactions. This becomes somewhat analogous to a classical, mechanical random generator (e.g. a pair of dice), where the freshness of the new randomness occurs by dissipating the previous one in the environment. I am not advocating the view that quantum phenomena can be explained by a classical picture, at least not without allowing the initial conditions to depend on the measurement context.

I think your following remark in the concluding section sheds new light on "it from bit": "The universe is not just simply the position of all its Democritean atoms. It is also the net of information that all systems have about one another."

Best regards,

Cristi Stoica