Smolins 3 roads: new logic

Fra

I finally started to read Smolin's Three roads to Quantum Gravity and only read the first two chapters so far. It doesn't contain any math, but it does seem to present a particular choice of reasoning on howto make progress on the matter, which I think is interesting in it's own because it may be a valuable guide in the world of theories and on a very early stage in the reasoning, it may hint us about flaws in reasoning.

I am not sure if anyone else is interested in such things but I will give it a try. My aim is to see if the logic of reasoning used in science can have any constructive outcomes.

In chapter 2 Smolin argues that that classical logic, that there is an objectivity to the notion of true and false, is not well designed for the task of quantum gravity. One of the reasons is that due to limited information of each observer (no observer can hold compelte information about everything in the universe at once), and prescription to establish truth or false, would be observer-dependent.

I agree with that.

But then Smolin seems to argue that a measure ofthe rationality of actions/decisions can be construced without the use of an "superobserver" knowing everything at all times. He says it's enough to assume that the observers are honest, and argues that in that way, two observers facing "the same information" will always make the same decision.

This makes me suspect, and I am curious to se how he builds onto this later in his reasoning. The problems I see is the feedback, that also "logic of reasoning" of a particular observer is evolved in the observer history. So it could still be that different observers facing the same information, responds differently, becase the very notion of "logic of reasoning" is different.

This is what I see as the basis for backgroudn independence at a fundamental level. There seems to be a feedback and self-reference between the way information is processed, and the evolution of the logic of information processing.

The reason I find common language analysis of very simple things interesting is that, I think differences in reasoning does have implications when you choose the mathematical formalism later. And at the later stages there is such much details and baggage that it's hard to analyse. Defects in the line of reasoning will propagage throughout the entire constructions.

Comments are appreciated.

/Fredrik

Fra

Perhaps Smoling will argue later in the book but, he mentions something that the topos theory formalism is a formalism that naturally resolved the issue of the new logic.

Set aside the abstract definition of topos theory as a mathematical subject, is anyone aware of the logic that Smolin implies exists - that topos theory formalism, somehow would naturally emerge as the natural solution to the problem of replacing classical logic in the context of modelling reality?

Is there some paper where this reasoning is lined out explicitly in some way? And how is this exploited to constrain the approach? ie what are the constraints of the topos formalism when applied to strategies?

/Fredirk

Fra

As many times before Baez appears to have made some nice summaries!

If found this page
http://math.ucr.edu/home/baez/topos_physics/

which contains the following papers

(1) A Topos Foundation for Theories of Physics: I. Formal Languages for Physics
-- http://arxiv.org/abs/quant-ph/0703060

(2) A Topos Foundation for Theories of Physics: II. Daseinisation and the Liberation of Quantum Theory
-- http://arxiv.org/abs/quant-ph/0703062

(3) A Topos Foundation for Theories of Physics: III. The Representation of Physical Quantities With Arrows
-- http://arxiv.org/abs/quant-ph/0703064

(4) A Topos Foundation for Theories of Physics: IV. Categories of Systems
-- http://arxiv.org/abs/quant-ph/0703066

Judging from the titltes, theis sounds interesting enough that I have to put Smolins book aside and at minimum skim these papers.

/Fredrik

Fra

This is somewhat interesting! just skimming the first paper... to mention one thing a new formalism where "the law of excluded middle need not hold" is intuitively plausible to me. It is in line with my thinking that there is always an uncertainty in the microstructure itself. Because the microstructure (beeing the discrete basis for the analogy of the continuum probability space) is in my thinking itself a sort of state in a series of inductions.

I'll keep reading later when I ahve more time

/Fredrik

Careful

I don't get that : if one observer would have limited information, he or she could say ''I don't know'' :-) BTW, the rest you say is true in classical GR too and classical logic works impeccably there.


There must be plenty of dishonest people out there :-) Could you tell me what physical operator measures the honesty/dishonesty of a person? What you say is not even true in standard QM where there is no reason why a person facing the state |cat dead > + |cat alive > decides to see a dead cat :-)

You might want to ask yourself what such philosophy implies in the context of Ockham's razor...

Fra

Yes, but one problem with that thinking is that then we don't know anything. "I don't know" is not a very constructive action. If we don't know, as is always almsot the case, we gamble. I think one can argue that, to not gamble (to not bet), is not free of risk either. It is also a choice of action.

So those players who consistently refuse to take any risks whatsoever, are IMO doomed!

Maybe I made a different interpretation that you on this :) One does of course not "choose" the see a dead cat of course. The choice is to ask the question: is the cat dead or not. To fire the question may be a risk. The consideration is that perhaps may ask another question instead!

The answer is part of the unpredictable feedback, it's part of the game. Then the next choice is, once you for example found out that the cat is dead - what do you do about it? What do you learn from this new valuable data? :) How do you choose respond to a given answer? What response pattern is of highest utility to You? Of course, we don't know that either :) So we gamble again, the action rules are also evolving... and one would imagine that bad actions are not preseved since they self-desctruct.

/Fredrik

Fra

Smolins argumentation is not crystal clear to me, and it is still in the early chapters... but I got the feeling that what he means is something like that any two observers will respond to the information that the cat is dead in the same way. That there is somehow a objectively logical action, that is the rational response to this input if the observer is beeing "honest" about what he sees.

But in that case, I disagree with that. Which was my point. But OTOH I am not totally sure that is really what Smolin means. It's early in the book, and it's difficult to express things uniquely.

My view is that the observers actions isn't always "rational", because it's difficult to define the measure of rationality. Instead I see it a way where progress is close to unavoidable. The actions that survive are those which are self-preseving, which means that they have to be in some kind of harmony with their neighbours. (Here I'm thinking of abstract physical systems interacting, not humans).

And perhaps an analysis of this logic, will reveal interesting things. I would expect the rational view to emerge in equilibrium - defined at some level of the actions, where local agreement on rationality exists.

Edit: So perhaps the most "stable abstraction" here is the emergent rationality. But the rationality is never certain. Specifying the action is analogous the the physical action, it determines the response pattern of the system. But if there is no such level at which there is a truly fundamental, universal action... then perhaps this is the wrong way of asking the questions? Maybe the actions themselves are always in motion too? What kind of formalisms does that lead to?

/Fredirk

Careful

Funny, I was just giving you a simple example. In reality, a scientist would find out a few "simple" principles, compute trough a particular setup and calucate the probability of some particular answer getting out. Now, scientific discours consists of using well tested principles or at least those which confirm a lot of data with an incredible accuracy (and yes we do assume that measurement apparati do not lie :-) ) or at least deeper new axioms which lead to the former. Despite of lots of debate and intensive work ''I don't know'' is a phrase which sometimes expresses a deep knowledge and humility about the adequacy of such process.

I was merely saying that even if two different observers have the same information they can still draw different conclusions and since indeed, he does not choose to see the cat dead, it is difficult to understand how he could call the other person dishonest.

Fra

Yes and I think is the interesting part. Implicitly I guess you here assume that this probability, is used as a basis for making decisions? or?

What is the utility of computing a probability?

Then, one asks, how do we know wether the probabilitiy is correct? One way of imagining is to repeat the situation an inifite times and get statistics. But that isn't realistic. For particle experiments it is, but hardly for cosmological scale things. Yet, there seems to be an utility to compute the probability?

So if we can't verify in advance if our computer probabitliy is correct, then is there another way to verify it? could there somehow be a more or less unique law of inducing an "expected probability" based on current information? Then the correctness would be a matter of correct induction. So one can imagine that the correctly expected proability, is in violation with what the future shows. How is such a situation handles constructively from the point of view of a theory builder? And how does the computational scheme for these probabilities revise, in the event that the future data is in disagreement with the original guess?

If you think this is silly questions, then note the context in which I ask this. I am trying to understand the meaning and utility of physical law, and what the physical basis for that is. There is a strong case of self-reference here which is what makes this complex. But given this problematic situation, what is the best way forward?

/Fredrik

Careful

Euh, such questions are all well answered within statistics, it is called hypothesis testing and it is used in economics every day to determine parameters of probability distributions.

Ok, so we agree that for particle physics this makes sense. Right, for cosmology you use a reasoning called extrapolation. That is: we know that the dynamics on the large scale should be an effective theory obtained by a renormalization procedure applied to the well tested microscopic theory. There is of course always the issue of the state of the universe (or initial data if you like classical theories), but that is a problem for ANY cosmological theory. Therefore, we should only be concerned about the dynamics and extrapolation severly limits the acceptable number of approaches. Now, even within this class, you have a selection procedure called ockham's razor which states that the fewer assumptions a theory requires, the more constraints your theory imposes on the physical universe, the easier the explanation of some phenomena occurs, ... the better is your theory. Of course these criteria are not satisfied uniformly for most proposals, and that is where the disagreement begins. But a theory which does not explain the (why of the) matter sector, has no classical limit, a prospect towards some unique microscopic dynamics ... is not even wrong.

A good way forward must for sure keep contact with well known and accepted physics and at the same time may scatter may upheld beliefs. People did not accept Einstein in the first place because he came up with the equivalence and covariance principle, but because the first thing he did was to show that the Newtonian limit of GR existed and to show that his theory made new predictions. The latter principles only became important later on although for him, they were the guidelines to this kind of physics. So, I do believe in theories of principle, but you have to choose them wisely and make contact as quickly as possible with the well known laws (even if such reasoning makes plausible extra assumptions).

Therefore, starting by throwing away the queen of science - that is logic - does not appear very fruitful to me.

Fra

Careful, I appreciate your comments. To make sure I understand you right and what the focus is here.

Are you effetively questioning Smolins initial note that a prescription to establish truth or false, would be observer-dependent?

I am not throwing away logic in favour of madness or chaos, I am just suggesting that if we are to see it from a realistic view, the procedure, say the logical line of reasoning, that deduces the value true or false, are IMO is a physical process, and whatever is evaluating this truthness can't be anything but a part of the universe subject to the same issues as everything. To ignore an apparent issue, is not logical to me either.

I rather think that taking a too idealistic view of this, may inhibit a more fundamental awareness.

Just for the perspective what is your personal take one these things?

/Fredrik

Careful

I do not know that this sentence - which is very vague and rich in grotesque words - has as originator Smolin. In this thread, Careful is talking to Fra and if Fra has no ideas himself and is merely interested in who is presumably saying what, then he or she should go in political and social sciences and as such is located in the wrong forum. What I do believe is that in science, you have to make the assumption that many circumstances in which measurements are about to take place are more or less identical and should therefore lead to a huge majority of consistent answers unless you have some very strong theoretical arguments and model to show otherwise or unless experiment forces you to consider that something else is going on (as was the case for the double slit experiment in quantum mechanics). If this were not possible, then science would degenerate into some postmodernistic blah blah. Now, the very concept of observation has always been delicate, since our theories are at the same time describing our observations while the observer itself should also satisfy the same theory: you cannot question that simple premise since other observers in the universe should make more or less the same theory and those will describe your physical movements. Now, the way you can decide about the best theory is by looking at phenomena which excludes both of them, using the same measurement apparati - there is no room for subjective interpretation here since experience shows that almost everyone agrees upon these facts. Therefore the physical laws should be constructed as such. Assuming that the very physical laws would leave the possibility for perception to differ in different universes effectively adds an infinity of degrees of freedom to your theory and is therefore an ideal victim for Ockham's razor.

It is not because something bewilders you, that you have to take an easy way out and go on the metaphysical tour. Note that this has nothing to do with my comment about the braids in another thread; these comments stand even in the case of MWI like interpretations.

jal

Hi Fra … Careful!
May I join the discussion? I might add a different prospective?
I would agree!
Let’s not bring the cat into the discussion. Is it possible to determine if the “laws” that are observed at the macro/classical level are the same at the sub atomic level.
Uncertainty would then be base on the “laws of nature”.

In a few words …. Is this what we observe?

Classically, or at the macro level, two objects can be only be placed beside each other. Two objects cannot occupy the same location/position at the same time. Continuity.
At the molecular level, two molecules/objects cannot be placed beside each other. Crystal structures of atoms.
At the atomic level, two atoms/objects cannot be placed beside each other. Nucleon structures. Quarks structures are confined.

Now … into the unknown … (for me)

At the quark level, do we have any evidence that there is a “minimum length”. Do we have a cause for confinement? Do the quarks behave classically? Can they be placed beside each other? Can they occupy the same position/location at the same time?
Can a quark occupy two locations/positions at the same time?
=========

Careful

Are you joking? :-) If you are truly interested in questions about the scientific method, you will find two excellent columns over here http://motls.blogspot.com/

jal

Stop pushing ... I'm gone!

Fra

Careful, thanks for the contribution but I choose not to comment further because I can't relate to your comments in the intended context. My feeling though is that you either are making fun of the discussion or aren't appreciating the questions or maybe it's because of my poor way of posing them or not I don't know. Either way it's not interesting to I'll drop that.


Hello Jal, I have no idea what the cat had to do with this in the first place.

I don't understand the follow-up reflection, but what I have in mind suggest that the "laws" themselves aren't the same but they are related in feedback between dynamics of the microstate and the microstructure itself. And this feedback might be able to formulate as and induction principle that may also be subject to change, but less so. But this is immature conceptual ideas only. I am working on finding the formalisms for this, but it's not yet mature and definitely not anyting standard so it's not something that's appropriate to discuss here. (But for sure, my starting points are not continous structures, I start with notions of distinguishability in the context of an observer - which impliticlty replaces the probability space with a discrete microstructure. The continuum approximation is recovered as the information capacity -> infinity. Actions are treated combinatorically, but the difference is that the action is part of the mictrostructure. So the action/logic is evolving along with the microstructure.) My starting point is that of reasoning, and my fundamental idea is that there is a strong connection between reasoning and the laws of physics themselves.

The seleciton of formalism that realises the idea is the motivation for the thread. In particular I was looking into some thinking of Smolin.

I'll try to read up on those papers later and keep reading Smolin.

/Fredrik

Coin

I read Three Roads recently and is a bit of an odd book. It is a lot like Penrose's Road to Reality in that it has a lot of little divergences where Smolin takes up a speculative idea and takes it in some direction for a few pages-- but then moves onto something else without actually arriving anywhere, and does not take the idea up again. Although these divergences are a lot of the time more interesting than the text's main thrusts, it makes it kind of difficult to discern exactly what it is the author thinks. The whole "everything is relative" theme is kind of like that, but:

So, as I understood what he was saying in Three Roads, Smolin's general argument seemed to be something slightly different-- not that our reasoning "can" be constructed this way, but that it must be constructed this way. I.E., we have no choice, because of the logical difficulties of discussing relative theories like QM in an absolute way, and because of the impossibility of performing any experiment from the "superobserver" position. Smolin seemed to be of the opinion that whether or not we want to find a way of discussing physical theory in a purely relative fashion, we have to find some way to do so or we will never get any sensible results out of cosmology. I don't think he really comes to a conclusion in this book about what that way is.

Anyway to me the important application of this idea in Three Roads actually wasn't the topos bit near the beginning but actually later on, when Smolin gets into an extended exploration of various things related to the holographic principle. In this part of the book Smolin seems to be providing a solution to the "how do we do this?" question: If you have two observers in a relational theory, you cannot objectively or meaningfully define the state of either observer-- but you can rigorously define and reason about the boundary between those observers. Smolin talks about defining sort of "surface areas" (? so to speak...) between regions in space, and goes on quite a bit about the idea that the information flowing across this boundary actually fully specifies what is happening on either side (though his main focus in doing so is on black holes and the Bekenstein bound). The overall argument, then, seemed to be that since the state of individual observers is not real or at least fuzzily defined, we should just ignore the observers and concentrate on the boundary as the "real" thing for purposes of constructing our theories.

To me this approach of using the holographic principle as the solution is actually somewhat familiar, since it is analogous I think to the reasoning in gauge theory-- local states are arbitrary and inaccessible, therefore we ignore the local states and treat our mechanism for translating between local states as the fundamental object. Right?

What is confusing to me about this bit-- as with much of Three Roads-- is that I have trouble connecting Smolin's apparent conclusion here with what Smolin himself did afterward, forcing me to question to what degree the conclusions are particularly useful (considering even the author did not in the long run really find a use for them). Smolin presents a compelling argument in Three Roads for the importance of the holographic principle-- and if one looks at Smolin's papers from the 2000-2001 period (when I assume he would have been writing Three Roads) one finds a LOT of holographic related work!-- but to my knowledge he did not significantly work with the holographic principle afterward. In fact the only really recent work in my (limited!) understanding of QG research to seriously apply holographic reasoning of the kind Smolin seems to be arguing for is occurring in the String camp (I am specifically here thinking of the ongoing work on AdS/CFT).

Of course, Marcus tends to argue that Smolin is not really relevant to LQG today as regards cosmology (and recently seems to have expressed that Smolin may be in his recent work wandering away from LQG altogether), and I believe he has said a few times that Ashtekar's camp in particular are the people to look at if you want to know what's happening with LQG as applied to cosmology. The topos/holographic arguments in Three Roads, it seems to me, were quite specifically about cosmology (since it is only on the cosmological scale that we really lose the ability to select a preferred "superobserver"), so it is unsurprising that if Smolin lost interest in cosmology he'd not be following up on his cosmological ideas. So perhaps this would be a good point to pick Marcus's memory banks on-- has the holographic principle turned out to be a useful tool for modern loop quantum cosmology for those who are working in the field today? What about, for that matter, topos?