# Rovelli's QG: background measures ?

• Fra
In summary, Rovelli's book discusses how he thinks about probability and information, and how these concepts are related. He seems to think that there are no absolute probabilities, only relative probabilities. He also believes that there is no absolute information, only relational information. He asks if the measure m(s) is really a measure of s, or if there is a hidden background information in the measure itself. He suggests that we may need to create a new measure to solve this problem.
Fra
Rovelli's QG: "background measures"?

In https://www.physicsforums.com/showthread.php?t=209161 I wrote that I started to read Rovelli's Quantum Gravity book, and my focus is more on his conceptual foundations. I'm curious to hear reflections on this. But since the topic is huge I think it's good to pose narrow questions.

Here is a basic and premature(maybe I get the answer myself in the latter part of his book) one.

It seems (my impression of barely starting to read his book) Rovelli, rather than thinking of absolute probabilities, thinks in terms of relative probabilities (ie. transition probabilities) $$P(s|s')$$ or transition amplitudes $$W(s|s')$$, where s and s' are two - to the observer - distinguishable states.

So far there is not much to object against that, on the contrary does that make perfect sense if you adhere to the idea there are no certain absolute probabilities, only conditional ones. Moreover this touches the information concept suggesting that there is not absolute information, only relational. Any claimed absolute probability is necessarily containing a background preference in an abstract sense.

So far this makes perfect sense to me and is right in line with background independent thinking.

But question is, wether the state s' really contains all information? or wether there is a hidden background information contained in the measure $$P(|)$$ itself?! Because the mesure P obviously contains information itself right?

The question is if it makes sense to consider an objective measure, and only allow the states to evolve? or does the measure itself also evolve?

If not, one would expect a good objective motivation for the definition of this measure. And my issues is that I have a hard time to see how that could be constructed. My personal view of background independence suggest that we should not just focus on "spacetime", I think we should think in terms of any measure.

Isn't any sort of nondynamical background measure unsatisfactory?

I can't help thinking that the core of the point is how we define measures, subjectively and objectively.

Wouldn't one expect that a background independent QM, would suggest a non-linear feedback that evolves the measures and measure spaces themselves, just like the dynamics on spacetime according to general relativity implies a evolution OF spacetime?

I'm mixing my thinking here with my attempt to analyse Rovelli's ideas.

It might be that all answers are contained in his chapter om QM, which I haven't read yet, but I thought I'd pop this question to see what others think.

/Fredrik

Fra said:
or wether there is a hidden background information contained in the measure $$P(|)$$ itself?! Because the mesure P obviously contains information itself right?

What I meant to say is that, don't we for consistency expect also a measure of the measure so to speak?

If the measure itself isn't measureable, then what's up with that?

/Fredrik

I suspect I didn't make myself clear as usual. I'll add this.

If we informally consider a notion such as m(s) as a measure of s.

Now if one might argue that this measure is in fact relative, and subjective. It seems to suggest that the measure m itself is relative.

One possible solution to this, is to "make up" a parametrisation of this family of measures so as to take the form m'(s|x) where one could say that m() ~ m'(|x), and where m' is now a fixed non-relative measure, and the set of x is not just seen as as indexing of the set of possible original measures m?

The ambigous part here is the choice of m', isn't it?

The question is if this is good enough, or just pushing the same objection "farther away"?

What prevents this scheme from diverging into a neverneding measure of measure of measure of measure... ?

Shouldn't the same objection be applicable to the relativity of m'?

The basic "premature" question was, wether Rovelli provides a solution to this objection, or if the objection isn't raised?

/Fredrik

Fra said:
Isn't any sort of nondynamical background measure unsatisfactory?

Another clarification of my reflection is that any "indexing" of the unknown, does contain a hidden implicit "structure", and this in IMO qualifies as information (although how to measure can and should be discussed).

So a background measure, is conceptually equivalent to a background "space" (indexing) loosely speaking. But wether it's the ordinary "3Dspace", or a space of spaces, doesn't seem to change the principal point to me. It's all information and structure.

I know the main point of LQG is that they are background independent. But I wonder if it really is background independent in the general sense I think of, or background independent relating specifically to the spacetime metric.

Perhaps it would be interesting to hear both with advocates and non-advocates say about this.

To me background in the infromation view could be anything, background microstructures such as strings in strange spaces, or background spaces of geometries - which induces a sampling density in any continuous space of geometries.

Even something as assuming a form of an action is in my eyes a "background", in the "space of actions".

In the language of informmation, and information processing. Where we expect information and knowledge to emerge by learning, and interaction, shouldn't the rules of reasoning themselves fit in the same description, if we consider that the rules of reasoning in a non-human context to simply be the "rules of evolution"?

/Fredrik

Rovelli's relational QM

I tried to skim parts of chapter 5 on QM last night and I definitely like his relational view.

The only thing, from skimming chapter 5 only, I got a subtle feeling that he doesn't pay sufficient attenation to the concept of store&hold information.

He notes that if an observer interacts enough with a system, this observer can "learn enough" about the system to predict it's probability distribution and it's evolution. In that sense in 5.6.3 he says that the obsever "has information" about the system. Then he notes that this information need not be stored, but then he notes that it's existence is necessary for beeing able to "potentiall store it".

I think this should be a key point, and perhaps he will come back to this in the later chapter nad interpret this in terms of spin-networks.

If he is going to take the information capacity constraints, relating to the _constraints_ of possible storage, seriously, I really like his reasoning so far. _Maybe_ this information capacity issues will relate to the point I tried to make in this thread, I am not sure yet. I think I need to read more on to his spin network formalism to tell. The conection would then be that the issues of information capacity in the observer that worries me, is "hidden" in the choice of background measure. But this may be a premature concern of mine. Considering the pre-conception of the spinnetwork it seems unlikely that he would do something like that.

What confused me in the beginning of the book is that he says that he is not trying to solve foundational QM issues, and not trying to unify all interactions. That may be true in this book, but if the continuation of his reasoning is what I hope it will be, it seems to have potential, if you with he spinnetworks make a more abstract interpretation and not necessarily constrain it to spacetime only?

I'll keep on reading. So far it's still interesting!

/Fredrik

I noticed there is an old and huge thread started by Marcus on Rovelli's relational quantum elephants.

Everybody sees the same elephant (says Carlo Rovelli)
https://www.physicsforums.com/showthread.php?t=117286

I thought it might be illustrative to reflect my last post to that.

The first paragraph, in the first post in that thread, Marcus quotes Rovelli:

It is clear that everybody sees the same elephant. More precisely: everybody hears everybody else stating that they see the same elephant he sees. This, after all, is the best definition of objectivity.

I love this statement, and it makes perfect sense, except for one little detail that relates to the information capacity constraint:

Pick somebody. One can now imagine that this somebody "hears everybody say they are in agreement with some somebody". The only issue is that, somebody may not have the capacity to actually hear _everybody_. That kind of seems unreasonable. This is why I think that, while I am 100% in agreement that this is the "best" measure of objectivity we can think of, the relational capacity constraint of any given observer, does bound the level of "universality" of this objectivity. (Fuzzy I know, but hopefully the message goes through)

To imagine that everybody hears _everybody_ "in principle" isn't good enough I think, or at least it is disturbing.

With this reservation, I really like Rovelli's thinking so far.

Comments? What I HOPE to find later in the book, is that Rovelli will deal with this. Then it would be very interesting indeed.

/Fredrik

Another, equivalent reflection, could be that "everybody" is relative as well.

Clearly everybody, as per a particular observer, means everybody that this observer can _relate to_.

Given a second observer, the collection of "everbody", may not be the same.

By construction an observer can't relate to anything that is so to speak out of "relatability".

/Fredrik

## What is Rovelli's QG theory?

Rovelli's QG theory, also known as loop quantum gravity, is a theoretical framework that attempts to reconcile general relativity and quantum mechanics by describing space-time as a network of interconnected loops. It proposes that space-time is quantized and made up of discrete units, rather than being continuous.

## What is a background measure in Rovelli's QG?

In Rovelli's QG theory, a background measure is a mathematical tool used to quantize space-time. It is a way of assigning a discrete volume to each point in space-time, which is necessary in order to make calculations in the theory. The background measure is an essential part of the theory, as it allows for the quantization of space-time.

## Why is the concept of background measures important in Rovelli's QG theory?

The concept of background measures is important in Rovelli's QG theory because it helps to reconcile the principles of general relativity and quantum mechanics. By quantizing space-time, the theory is able to address the limitations of both theories and provide a more complete understanding of the universe.

## How is the background measure calculated in Rovelli's QG theory?

The background measure is calculated using a mathematical formula that takes into account the properties of space-time, such as curvature and topology. This calculation is complex and relies on advanced mathematical tools, such as differential geometry and functional analysis.

## What are the implications of Rovelli's QG theory for our understanding of the universe?

Rovelli's QG theory has significant implications for our understanding of the universe, as it suggests that space-time is not continuous but rather made up of discrete units. This challenges our traditional understanding of space and time and could potentially lead to a deeper understanding of the fundamental laws of the universe. It also has implications for the study of black holes and the origins of the universe.

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