Is Smolin's Approach to Quantum Gravity Logic Revolutionary?

[Fra]

Thanks Coin for your expansions!

In my initial skimming of Doering and Isham's first paper it was the exclusion of "law of the excluded middle" that attraced my attention. To me this has a an intuitive meaning, and the connection I see is to violation of unitarity. And to try to treat this at the deepest level of abstraction, rather than technical level is the right way to go IMO. Still I'm not a mathematician, so I have limited interest in mathematical reasonings which has to me, no utility.

A quickly identifiable issue with QM is exactly the definition of the logical operators. What exactly does (A and B) and (A or B) mean in the general case? In particular what does x and p mean. The obvious problem is that x and p are not cleanly in the same set (probability space). They are however related. I think somewhere in this reasoning, the superposition principle can be understood by different definition of logical operations.

I also see a close connection of "the logic of reasoning" and the physical action principles. I think the action forms, are somehow the physical basis, or at least analogous to the logic of reasoning. So I see the logic of reasoning as evolving long with whatever well call "states". Your comments on the connection between truth object and the observer is interesting! I will keep this in mind the next round I read the same paper and see if it helps me get it.

Now, wether topos logic is the right thing for this I don't know. But it spawned my curiousity, and Isham's paper poses many good questions that motivates the development of the topos thinking.

When I finished Smolin's book i will try to read up on this again.

/Fredrik

 

[Fra]

another reflection

It strikes me that there are similar structures of many formalisms...

For example standard logic one has "hard implications" such as A => B.
Or deterministic time evolution such as A(0) => A(t).

(Wether A are classical variables or quantum states makes no principal difference here. There is still a layer of deterministic logic.)

It seems the degree of truth in B depends on the confidence not only in the premise A, but also in the implication itself. Here the implications serves the purposes of logic of reasoning.

A implies B, as per some particular choice of reasoning. And in my thinking, the choice of reasoning is not obvious, and it is itself subject to change. Therefore uncertainties, applies not only to premises and conclusions under the flow of certain logic of reasoning, it also in my view apply to the logic of reasoning itself.

To understand this reflection, is similar to understand the "logic" behind how (A or (not A)) isn't necessarily true. It's a simplification. I would argue that this sort of softer logic, is more intuitive and realistic than the idealistic logic.

> They think, for example, that quantum physics needs to be described using the complex
> numbers, but maybe at some point they'll have to revise that. So what they do is decide
> that whatever rules they pick, they will demand those rules have some specific Topos
> which they spring from.

Hmm.. all the various papers I have ever read on trying to "explain QM superposition" under various names, quantum logic, consistency of amplitudes etc... all one way or the other sneak in the complex choice as and implicit assumption.

In what I envision, the dynamics of logic, should be able to explain from more first principles why the logic of superposition appears in nature. If I am about to guess about the topos talk I still don't quite graps, I would suspect from your expansion that what is challange here is to explain how different topos spontaneously evolve into each othe - ie. the "choice of topos"? must be a physical process.

Here I also associate to Smolins generic reflections of what the nature of physical law is, and what selects it. This is to me a special case of what is the nature/physical basis of reasoning (logic).

I am about to start section III of smolins book, so I want to finish it before I distract myself too much in reading up on topos. It seems to be embedded in a lot of context, that I also need to read up on. My first impression are purely ituitive, based on what I "hope it its", if it is what I am looking for.

This is interesting stuff.

/Fredrik

 

[Phrak]

It's fairly obvious whether or not this soft logic applies to reality. The answer is yes and no.

 

[Fra]

I read Smolins argumentation in favour of the weak holographic principle last night and I agree with what Coin mentioned in post #17 that so far this was the better part of the book.

The abstraction of observer and screen, and how the size of the screen can grow and shrink are pretty much a setting in which I feel good. There may be a need to dicsuss details and versions of the principle, but it's something that in my opinion provides part of a good starting point.

The complication is of course that the "screen" itself is also dynamical. It is at least the conclusion I've made from thining in terms of a microstructure. I picture the observer itself to be represented by a microstructure and I was trying to find the decomposition of internal degrees of freedom and the interfacing degrees of freedom. The latter would correspond the the screen. But as far as I can see there is internal equilibration processes that is transforming the surface and internal degrees of freedom. And my conceptual view of that is that it is like tradeoffs between distinguishable statements and confidence thereof. And in a given environment the observer will find that there is an preferred balance. So the observer can conceptually shrink his screen to gain more confidence in what he can distinguish. Or can can transform the confidence into a larger screen. But I figure this internal equilibrations are part of the time evolution.

I think this is a good focus, but there still seems to be quite some headache here due to the strong self reference. I didn't see so far that smolin offered any solution to this. Unless it's in the even later chapters.

I expect to see gravity emerge when one starts to consider the dynamics of the screen sizes. And Smoling refers to Ted JAcobsson who derived GR from the holographic principle and second law. That sounds like something to check.

I am particulary interested to see what entropy they use. My own thinking of this suggest that shannon entropy isn'y the right one because it's not usually relationally constructed.

Does anyone know which the key paper is? Strangely in the text he mentions Ted Jacobsson's famous paper but gives no reference. And googling he has a lot of papers.

/Fredrik

 

[Fra]

A good quotes from the holography chapter.

"space is nothing but a way of talking about all the different channels of communication that allow information to pass from observer to observer. And geometry, as measured in terms of area and volume, is nothing but a measure of the capacity of the these screens to transmit information"

I would like to extend this to not only refer to ordinary "space". Also other things, other interactions of the standard model that is usually considered to be taking place IN spacetime, must also fit into this framework if it is to be satisfactory.

This suggests to me at least, that one fundamental rethinking of all this, would for a second forget about the notions space and time, and instead start to consider information: what to we seem to know, and how do we rate our confidence? Then as information is rational structured and processed, one would expect that structures would inevitable be emergent and perhaps here we can identify the familiar notions of dimensions, space and time, and hopefully all the known interaction phenomenology.

I associate here logic of reasoning with a particular observer, his strategy of taking actions. And in the information view suggested in this chapter there seems to be a connection with analysing *logic of reasoning in context* and analysing the laws of nature. Since like Smoling argues in this chapter at fundamental level, our world could be nothing but a game of a network of relative information processing. This is an idea I support 100% :)

/Fredrik

 

[friend]

This suggests to me at least, that one fundamental rethinking of all this, would for a second forget about the notions space and time, and instead start to consider information: what to we seem to know, and how do we rate our confidence? Then as information is rational structured and processed, one would expect that structures would inevitable be emergent and perhaps here we can identify the familiar notions of dimensions, space and time, and hopefully all the known interaction phenomenology.

I don't think you're going to get any answers about QM by considering "information". For information is calculated on the basis of probabilities. So you would be starting with probabilities in the first place in order to explain QM. All you could possibly come up with is just a reformulation of QM and not an explanation for it.

 

[mhill]

The answer would be 'degrees of truth' in the sense of fuzzy logic (?)

a known experiment is this let us suppose i am in the middle of a door connecting the Kitchen and the bedroom, you could not say 'I am in the Kitchen' or 'I am in the bedroom' but there is an 80 % of probability of being in the Kitchen and 20 % of being in the bedroom .. this logic is not new and has been invented.

 

[Fra]

I don't think you're going to get any answers about QM by considering "information". For information is calculated on the basis of probabilities. So you would be starting with probabilities in the first place in order to explain QM. All you could possibly come up with is just a reformulation of QM and not an explanation for it.

Starting with the axioms of probability theory is not my intention. I agree that would lead nowhere. What I envision is a formalism where probability spaces are emergent.

Normally information measures, and entropy measures usually boil down to probability theory or various microstructures, which can be seen as a discrete version of the probability space. But if you try to acknowledge the strong self-reference, there will be an uncertainty in the probability spaces themselves. So there is no solid background probability space to rely on.

I think we need a generalised measure of information. Shannon entropy is not satisfactory since it's a measure that is relating to a given microstructure. But when the microstructure itself is changing, I think what we need is a kind of coupled formalism where also the measure of information changes. My view of "probability" is the subjective bayesian sense. The probability represents my best guess, and the logic that forms this guess, based on the retained past is also subject to change. So I see it as a hierarchy of reflections defined by a sort of induction. But the looping are bounded by the complexity.

Anyway, these are my personal ideas, still in progress, but the point is that I am definitely not starting with a universal measure. The measures themselves are evolving in my view. It's totally relational and relies on no background, no probability spaces, or spaces of spaces.

Only the notion of distinguishability is what I start with. And also the notion of information capacity.

This thread isn't supposed about talking about my personal ideas in detail though. I am reflecting over what the common professionals do and comment on them from my point of view.

So I agree on your comment but I have in mind also a clarification of what information means. I do not refer to information in shannon way. It's not a relational form of information and thus inadequate IMHO. That said I am still looking for a better solution.

/Fredrik

 

[Fra]

Ok, well shannon does relate to the implicit microstructure (or probabiility space with a equiprobability hypothesis), but the point is that this again contains information! And this is not accounted for in shannon thinking. IMO all information relates to something, and in a chain of constructs the information is conditional on all the relating steps.

To ignore the prior information, is to assume infinite confidence in the prior, and this to me is to consider an infinite information pool that provides the "massive" reference. This is unphysical IMO. This is what I meant in post 28, on Thomas comment. But perhaps I fail to explain it properly. But that's not too surprising since this is currently abstract and not yet formalised ideas.

/Fredirk

 

[Fra]

The answer would be 'degrees of truth' in the sense of fuzzy logic (?)

a known experiment is this let us suppose i am in the middle of a door connecting the Kitchen and the bedroom, you could not say 'I am in the Kitchen' or 'I am in the bedroom' but there is an 80 % of probability of being in the Kitchen and 20 % of being in the bedroom .. this logic is not new and has been invented.

One issues I have with this thinking is that, suddently we inflate a boolean state (in/out) to a continuum probability [0,1]? How much information is represented in a boolean state as compared to a continuum between 0 and 1?

I agree to the basic idea, but if we look at the capacity constraint, something is missing in that logic.

/Fredrik

 

[LukeD]

"Fuzzy logic" is not the only model of intuitionist logic. There are many. The one that I remember Smolin advocating in his book is one in which you essentially do not know whether a statement is true or false (or either of them at all) until get get more information, so just knowing that the statement is true doesn't mean that it's false because it could be neither true nor false.

One thing that make Topos theory really interesting (I haven't studied it yet, but I have some book on Category theory and I intend to eventually get to Topos theory) is that the logic of a topos can be very different from classical logic. For instance, many of them are intuitionist logics. Some of them are even stranger though. Duel (in a sense) to the intuitionist logics are paraconsistent logics, which also arise from topoi. In a paraconsistent logic, a statement can be both true and false simultaneously. In classical logic, if this happens, then every statement in your theory is trivially true (from the principle of explosion), but with paraconsistent logic, your theory is not necessarily trivial.

 

[Coin]

Duel (in a sense) to the intuitionist logics are paraconsistent logics, which also arise from topoi. In a paraconsistent logic, a statement can be both true and false simultaneously. In classical logic, if this happens, then every statement in your theory is trivially true (from the principle of explosion), but with paraconsistent logic, your theory is not necessarily trivial.

Luke, that is VERY interesting! I was familiar with paraconsistent logics but I did not know this bit about paraconsistent and intuitionist logics being effectively dual. Is there somewhere you know of that expands on or provides a proof of this?

(I notice now that there is a brief treatment of the subject on wikipedia, I was just curious if there was a source you had in mind.)

 

[Fra]

Nice to hear more reflections and expansions on all angles of this!

The one that I remember Smolin advocating in his book is one in which you essentially do not know whether a statement is true or false (or either of them at all) until get get more information, so just knowing that the statement is true doesn't mean that it's false because it could be neither true nor false.

The way I conceptually and intuitively see this is that.

We can have a question that seems to have a set of possible answers.

But one may also also wether the question itself is right, how confident are we in the question? Somehow that possible answers are usually relational to the question.

That's a conceptual thing to digest. What is the meaning of that?

How can a question be wrong? And where do questions come from? :)

As I see it, if you see logic as interactions, the answer to a question often leads to new questions. And in an evolutionary perspective, there is clearly an utility in asking questions! And as we know, asking the right questions is sometimes a matter of "economy". So, at least there seems to be a natural meaning to degrees of relevance of questions.

Maybe the extreme interpretation of a wrong question, is one who is simply of minimum utility.

There seems to be a clear connection here between "logic of reasoning" and evolutionary reasoning, and in that context there may be a meaningful way to rate questions.

This is indeed borderline to philosophy, but I find that such an analysis is unavoidable if you are seeking for fundamental understanding. And it seems the foundations of philsophy, logic and physics meet. Now is that to be dismissed as a conicidence or is it a sign?

/Fredrik

 

[LukeD]

Luke, that is VERY interesting! I was familiar with paraconsistent logics but I did not know this bit about paraconsistent and intuitionist logics being effectively dual. Is there somewhere you know of that expands on or provides a proof of this?

(I notice now that there is a brief treatment of the subject on wikipedia, I was just curious if there was a source you had in mind.)

Huh, turns out that the article that I read is the one linked at the bottom of the Wikipedia article.

----

Like I said, I don't know much about Topos theory.

The article that I read was just an overview of some of the uses and motivations for paraconsistent logics.

It said that paraconsistent logics are duel in a sense to intuitionist logics (in fact, if one takes the duel of the standard intuitionist logic, one gets a specific type of paraconsistent logic, though I forgot the name of it). However, while it would be nice for the categorical duel of a topos corresponding to a intuitionist logic to be a topos corresponding to a paraconsistent logic, I don't know if this is what was meant (is the duel of a topos another topos? I don't know)

What the article I read said is that you can create intuitionist logics by building your topos out of open sets, and if you instead build a topos out of closed sets, you get a paraconsistent logic.

Edit: There is also a book titled Inconsistent Mathematics which can be found on Amazon that develops and applies paraconsistent logics.

 

[Fra]

I've finished the main chapters now, I have the epilogue left.

It was an inspiring and easy read, but I do not feel that I have acquired any substantially new ideas from the book. Many key questions are touched and reflected over, as is seems with the purpose of explaining and inspiring. OTOH, if that is the main purpose of the book, omitting too much details is probably wise, because it sure leaves a good amount of space for the readers own imagination.

The main inspiration from the book is to compare my own thinking in terms of the holographic principle, becaues that seems to have a natural place. I have identified the "screen", the only problem I see is that there is ongoing transformations that mixes up screen degrees of freedom with internal degrees of freedom. I need to figure out what a detailed definition of the holographic principle would be. At equilibrium, this will be stable so I can easily imagine that near equilibrium (whatever that will mean exactly) there will be a form of the principle that is easy to define. But during fast changing of the screen, the whole principle seems hard to define in the sense that the timescale for establishing the relation with reasonable confidence will be longer than the screen itself is reasoably stable.

/Fredrik

 

[Coin]

In my initial skimming of Doering and Isham's first paper it was the exclusion of "law of the excluded middle" that attraced my attention. To me this has a an intuitive meaning, and the connection I see is to violation of unitarity.

Hm, this is an interesting idea. How do you mean, though?

And wouldn't violation of unitarity be a bad thing?

> They think, for example, that quantum physics needs to be described using the complex
> numbers, but maybe at some point they'll have to revise that. So what they do is decide
> that whatever rules they pick, they will demand those rules have some specific Topos
> which they spring from.

Hmm.. all the various papers I have ever read on trying to "explain QM superposition" under various names, quantum logic, consistency of amplitudes etc... all one way or the other sneak in the complex choice as and implicit assumption.

Well... that was maybe not a good example, it was just off the top of my head. An example they use a few times in the Topos papers is that maybe they want to affix certain propositions with a time index, to express the idea that there may be certain propositions which are true at time X but not at time Y. So the question they bring up is, how should the time parameter be indexed? Are time "indices" a continuum of reals, are they discrete, are they some crazy thing that only comes up when you get heavy into consistent histories? Here they legitimately don't know ahead of time what to use, and they probably would like to be able to just formulate their theory and then afterward worry about how they index time. They seem to be claiming that they can do that by just twiddling with the specification of their topos so that the type of the time parameter is whatever they like, and they can then derive the theory anew from there.

Also something I don't think I made clear about why the truth objects are so interesting to me is it gives them a way to define logics in which the "values" of some statement is something other than true or false. By which I mean not just, "neither true nor false", but it appears you outright can give the "values" any type you like-- you can specify a heyting algebra that the "truth" values live in, and that heyting algebra can take whatever potential values you like. For example skimming their second paper, where they try to define quantum theory using topos, one finds that on page 27 they define their truth object in that case as just:

<br /> \begin{eqnarray}<br /> \ps\TO^{\ket\psi}_V&amp;:=&amp;\{\hat\alpha\in \G_V\mid<br /> {\rm Prob}(\hat\alpha;|\psi\rangle)=1\}<br /> <br /> &amp;=&amp;&amp;=&amp;\{\hat\alpha\in \G_V\mid<br /> \langle\psi|\hat\alpha|\psi\rangle=1\}<br /> \end{eqnarray}<br />

Even without fully understanding their notation, and even given I kinda garbled the Tex there, that's pretty evocative! You can see the notation for a bra-ket "expectation value" for the observable/proposition â just slapped right in there. The quantum notion of "truth" seems to be directly representable and embeddable within their formalism just as easily as "true or false" is.

 

[Fra]

So about the main topic, "new logic". After reading the whole book it is not clear to me what Smolin thinks in detail.

But IMO the new logic I want should somehow bring the logic of reasoning to the inside. Ie. it makes little sense to make use of external logic, to reasoning about inside information. I think that the reasoning itself must be defined in terms of inside logic. This should imply that the logic itself is also incomplete.

Ie. we do not only reason based on incomplete information (which is commonly used phrase), we are doing incomplete reasoning, based in incomplete information. And the reasoning itself is subject to development. So the logic of reasoning itself, must find a generalized "background independent" forumlation. Somehow it's part of the problem that this formulation itself is bound to be incomplete too! But the rescue here, could be to focus on the evolution, rather than conclusions! This means that the formulation itself is evolving as per again inductively evolving "logic". This expresses to me the deepest intent to find a description of fundamental physics in terms of evolutionary thinking.

So the focus isn't on making immortal conclusions, the focus is, at each stag to make progress. And progression, well that's what time is isn't it? That's also a possible identification of time in this mes - time is a measure of "progression". But not a progression relative to a fixed background, rather it's a strange relative progression.

This is my clear lead, and smolin's book give me no reason to change it, it seems to be somewhat in line with his thinking as well, but still it is not clear exactly what the best formalisation of this is.

/Fredrik

 

[Fra]

This is going to be fuzzy...

I'm not sure if I should expand onthis... the respons involves some of my personal thinking, but here is some reflections. I try my best to keep it at a reasonable level of reasoning in despite the lack of rigour. This thread is about the search for possible new logic formalism relating to fundamental physics after all.

Hm, this is an interesting idea. How do you mean, though?
And wouldn't violation of unitarity be a bad thing?

Good or not, that's a matter of debate of course. For sure things are far easier in a sense in unitary models. But IMO it's not bad as long as there is a good reason for it. Also my main argument is the lack of confidence in the conclusion that we have unitarity in the first place. The main reason what presents unitary models, is the limiting info capacity.

With unitarity here I really mean conservation of probability, which is of course trivially true in probability theory, it's one of the "axioms". But as I see it, in physics we're not concerned with arbitrary axiom systems, we're trying to understand the world we live in, constrained by our own limits.

So to avoid misunderstandings here I prefer to use the word microstructure. Which to me is
pretty much analogous to a probabiltiy space, but it's discrete (but the continuum is recovered as the limiting case of where the numbre if distinguishable microstates -> infinity.

The problem is more how to see how microstructures(probability spaces) (discrete or continuous versions) emerge. And in that context, the microstructures themselves are uncertain, and they contain information. What this means is that the axioms or probability are not innocent or void of information. The contain information. I am suggesting to find formalism where these choices are explicitly accounted for and brought into the dynamics.

In this thinking, conservation of probability can be understood as an expectation. But this expectations has limited confidence. Ie. we are not certain about the conservation, but it's our a priori best guess. This also means that if we leap in the assocations here, I imagine to assign an "entropy" (but not the shannon style one!) and an energy/mass to the probability space itself.

Perfect certain convservation would then correspond to an infinitely massive probability space.

If this is unrealistic - like I think, then unitarity is similarly an expectation at best, not
a known fact. Therefore I see no good reason to hardcode conservation laws in the formalism. Unitarity will emerge when evidence is in favour of it, and it will be violated when our expectations are not met.

In a sense one can also assign information to the reasoning itself. I think of the reasoning
to be encoded in the substructures of the microstructure. This is also how there is a limit
to the inside reasoning.

So uncertainty in the very reasoning itself, implies that there is no such thing as a completely confident deduction. Therefore, it's possible to sum all the apparent possibilities, and still find that there appears a previously not distinguishable possibility. But also that previously distiniguishable possibilities loose their distinction and become indistinguishable.

As I see it, the _degree of deviation from "unitarity"_ is a measure of the lack of confidence in the microstructure itself. If all "confidence" (associate energy/mass) in the microstructure is lost, then the mictrostructure becomes indistinguishable and dissapears, sometimes in favour of other structures. I sometimes tend to think of different microstructures as communicating buckets, which almost conserve information capacity. I think this will later be the key to explain emergence of superposition. I have a fairly clear idea on this but haven't found the right calculations yet.

So simplified \sum_i p(i) \rightarrow 1 as the confidence in the microstructure becomes infinite, but this can not happen to a finite observer. Due to uncertainty the sum can be lower as well as larger than 1 IMO. Moreover I suspect all constructible measures (constructible by the observer - not by means of external logic) will be similary uncertain, bounded by the observers total information capacity. The reason how this is possible is because I see the summation is a physical process. It happens by the observers progression in time, and the "summation" involves the observers retention, and internal encoding of past events. But due to the limited encoding power, choices of what to keep, and howto encode the data needs to be made. On this level I picture the physical action to be encoded. And this action evolves.

When I can provide a more rigorous reasoning then of course, I would almost have the answer. And I don't. That's my defense for this fuzzy talk.

Edit: I'm not quite happy with this explanation. Maybe I should try to formulate a better response. Need to get to be.d

/Fredrik

 

[Fra]

An example they use a few times in the Topos papers is that maybe they want to affix certain propositions with a time index, to express the idea that there may be certain propositions which are true at time X but not at time Y. So the question they bring up is, how should the time parameter be indexed? Are time "indices" a continuum of reals, are they discrete, are they some crazy thing that only comes up when you get heavy into consistent histories? Here they legitimately don't know ahead of time what to use, and they probably would like to be able to just formulate their theory and then afterward worry about how they index time. They seem to be claiming that they can do that by just twiddling with the specification of their topos so that the type of the time parameter is whatever they like, and they can then derive the theory anew from there.

I don't understand exactly what it means but that sounds interesting to me!

Perhaps I need to look this up more. Do you recall where you might have seen this example of time indexation?

From my viewpoint I don't see how it would be possible to define, even from the point of view of a given observer, a global time index. This is because the references are I think not in general evolving deterministically.

First regarding continuous or discrete time, as I see it that is almost to ask wether we can distinguish changes continously or discretly. But this is of course observer relative, which to me means that one observer may see a discrete jump, and another observer may see a continuous transition (or a jump composed of so many steps that it's "effectively" continous). This is why I want to keep the reasoning inside the observer. Otherwise it seems you, by choosing logic of reasoning at will, in principle could come to any conclusion you want.

I think of time as expectations of changes. Therefore the future is not unique. However in some cases the expectations may be so peaked that there is effectively a unique future. One can picture time as a indexation of the possible path's of expected changes. But as there is progression (we evolve into the future), we generally received new information, which in general deforms our expectations, which then may revise the previous expectaions
on the time index.

I am not sure if that can have any connection to the topos definition you refer to? If so, to me the interesting key part, is the logic by the topos definitions are deformed on the fly to rectify the choice of "time index". If they have some ideas on that it sounds very interesting.

Since I consider time to be a mesaure of progress, the time between two states is related to the expected transition probability that there is a transition between these states. And due to the updates view of "probability" relating to possible new logic, these transition probabilities are highly relative and dynamical.

Coin, if you have any refefences to their reflections upon the time index problem it would be very interesting to see if I can make some connections!

As a note: In Smolins epilogue he presents some personal expectations on the future, and one of them is again connecting to topos.

"The present day formulation of quantum theory will turn out to be not fundamental. The present quantum theory will first give way to a relational quantum theory of the kind I discussed in chapter 3, which will be formulated in the language of topos theory. But after a while this will be reformulated as a theory about the flow of information among events."
-- Epilogue of "Three roads to quantum gravity", Smolin,

This expectations could well overlap with mine, except of course I don't know _exactly_ what the topos formulation is. But that QM is not fundamental appear close to obvious to me.

/Fredrik

 

[_Mayday_]

I have completed Smolin's "The problem with Physics" and would probably call myself a layman in this field. Would this be OK for me? I found the book I read to be quite straight forward after reading the odd chapter a few times.

 

[Fra]

I have completed Smolin's "The problem with Physics" and would probably call myself a layman in this field. Would this be OK for me? I found the book I read to be quite straight forward after reading the odd chapter a few times.

I haven't read any of Smolin's other books so I can't compare, but three roads is very easy reading, and written as to focus on conveying conceptual issues, and provide some insight into the problem of quantum gravity and what some of the current main views.

When I got it I must admit I did execpt a higher technical level and was dissapointed at first - the book IMO contains very little explicit solutions. It contains mainly elaboration of ideas and conceptual frameworks in a way so that outsiders should understand it. But of course some of the problems on the table are conceptual, so it's still fairly appropriate.

So I think you would have no problem to read this book. But don't expect too much. See it as a source of inspiration, it's how I view the book. It also contains some personal adventures of Smolin, like driving people to the airport and so on.

/Fredrik

 

[Fra]

And Smoling refers to Ted JAcobsson who derived GR from the holographic principle and second law. That sounds like something to check.

I am particulary interested to see what entropy they use. My own thinking of this suggest that shannon entropy isn'y the right one because it's not usually relationally constructed.

Does anyone know which the key paper is? Strangely in the text he mentions Ted Jacobsson's famous paper but gives no reference. And googling he has a lot of papers.

My problem was that Jacobson spells with one s.

I found it, the paper is

"Thermodynamics of Spacetime: The Einstein Equation of State", Ted Jacobson
-- http://arxiv.org/abs/gr-qc/9504004v2

/Fredrik

 

[Coin]

I don't understand exactly what it means but that sounds interesting to me!

Perhaps I need to look this up more. Do you recall where you might have seen this example of time indexation?

From my viewpoint I don't see how it would be possible to define, even from the point of view of a given observer, a global time index. This is because the references are I think not in general evolving deterministically.

Well, they discuss this general problem of "how to index" on page 5 of the first paper. Their stated general problem with this approach here is that it rules out or makes difficult theories in which the spacetime manifold is not smooth:

Why are physical quantities assumed to be real-valued?... If conceded, this claim means that the assumption that physical quantities are real-valued is problematic in a theory in which space, or space-time, is not modeled by a smooth manifold. Admittedly, if the theory employs a background space, or space-time—and if this background is a manifold—then the use of real-valued physical quantities is justified in so far as their value-space can be related to this background... however, caution is needed with this argument since the background structure may arise only in some ‘sector’ of the theory; or it may exist only in some limiting, or approximate, sense.

On the next page they have a confusing digression on the subject of giving unusual types to probabilities.

They cover the notion of "time dependence" for the first time on page 14-15 of the first paper. They then go into it in more detail on page 28 of the second paper, section 4.2.5. I honestly do not understand how they deal with the problem you observe, that there is in reality no "global time" and therefore the global time index they seem to be nonchalantly defining is difficult to interpret. I think the answer is hinted at in the second paper's 4.2.5, where they define a set of truth objects (which interpret the truth or falsehood of propositions, based on some state |psi> internal to the truth object), indexed by "t" and mention that "the states |psi>_t satisfy the time-dependent Schroedinger equation."

In other words, I guess it appears those parts of their paper which are making use of these "time-dependent" truth values are actually representing nonrelativistic quantum theory, where the time-dependent Schroedinger equation can be used and we simply assume a global time parameter. One would hope they somewhere have, or eventually intend to, move beyond this to define a version of their theory with a more flexible notion of time... I unfortunately do not understand what they are doing well enough to say whether they are actually close to doing this.

 

[Fra]

I started to skim this first paper again. As compared to many other "ideas" or approaches to QG this at least seems to be deeper than most in that it seriously questions many fundamental questions.

Like, why are probabilities required to line in the real interval [0,1] and why physical quantities are assumed to be real values? This are a very good questions that I also consider primary that are elsewhere rarely asked. But the real questioning here is what the meaning of probability and physical value is, in a realistic scenario that does not make use of ridicilous infinite measurement trials or imaginary ensembles. What is the physical realistic basis for the continuum?

But the choice of abstraction is still not clear to me. Probably because I have zero background on topos. But the fact that in despite of this, it is attractive may be a reason to look deeper.

I associate their notion of "a certain formal language attached to the system" to my thinking of a choice of "logic of reasoning" which I further associate to lie behind the construction of the physical actions and interactive properties. And each observer, may indeed have different encoded "logic of reasonings", which is a result of their evolution. And there is in my thinking a feedback between information processing as per the given logic of reasoning, and the development of hte logic of reasoning itself. This is not too unlike the coupling in GR between "dynamics relative spacetime" and the "dynamics of spacetime" so to speak. There is a self reference here that I see traced down to the logic of reasoning itself, which includes mathematics, continuum issues and all other stuff they raise - the logic of reasoning could be thought of as the "dynamical background" from which we reason about things, but just like the geometry of spacetime is deformed by changes in matter and energy distritbution in it, our logic of reasoning are bound to deform in respons to changes in information.

This is shows my more radical view of "background independence" as has been discussed in some other threads. To me, the metric in a manifold is nothing but a special case of a deeper concept of background independence. MAYBE topos logic is the way, or maybe not. Now at least I have given attention to this field, and for sure I'll try to read up more on it and try to see if this is the answer to my questions.

Anyway I still do not quite what exactly they mean with system. Are they talking about an observer, as a system? or are they talking in some omnipotent way of the system of all observers?

If they associate the system to an observer, it is more interesting to me. Then the next question is how their logic can be applied to suggest how this "logic of choice" is changing, presumably as the result of the observer interacting with it's environment.

Exactly the choice of reasoning, as in the form of ideas or mathematical formalisms, is the striking baggage that you see in most papers. Last night I read some of Ted Jacobson's reflections on the nature of black hole entropy. He argued that the entropy should not be thought of as counting internal states, it should rather be thought of as counting states of the horizon. It was interesting but still my impression is that the whole discussion would benefit from a true fundamental revision of the logic of reasoning used in the physical theories. Clearly different choices of reasoning, will come to different conclusiosn from the same starting point. So I don't see how we can avoid questioning the origin and physical basis of logic!

/Fredrik

 

[Fra]

Mmm... given that I definitely lack a solid perspective in the general formalism they use, I'm getting a feeling that maybe they aren't quite doing what I hoped.

The seem to have a strong perspective on the formal language itself, such as "set of all strings" etc, relative to us human scientists - my focus is on the utility of it. They seem to argue that

"constructing a theory of physics is equivalent to finding a representation in a topos of a certain formal language that is attached to the system"

But, whatever representations or symbols we use, how does the formal language develop? And do they treat the logic of this development? If not, I am not sure what they are getting at? Whatever "abstractions" they use, progress must come from the _development_ of the same, right?

The associations I made above, and "want to make" are more induced from my own thinking rather than a first principle understanding of _their thinking_. I have the habit of often reading too much out of things.

But I guess the first papers just talk about the "background" which explains my lack of satisfcation, but I wonder if there is a more pedagogic paper that explains in a brief way the utility and application of their formal ideas, to provide the motivation you need to look at details?

Maybe if someone else on here knows more of the topos stuff, that could briefly argue what the core of their suggested strategy is? (ie. beyond a "reformulation" from one thing to another)

/Fredrik

 

[Fra]

But, whatever representations or symbols we use, how does the formal language develop? And do they treat the logic of this development? If not, I am not sure what they are getting at? Whatever "abstractions" they use, progress must come from the _development_ of the same, right?

Of course, in line with previous reflections, my expectation would be that the "development" of the abstractions are more or less related to the emergence of time (relational time), rather than referring to a global index.

But the limited reading so far, doesn't reveal anything like this. And this is an important point IMHO. I would need at least a fuzzy hint of treatise of this, to motivate myself.

/Fredrik