Is Smolin's Approach to Quantum Gravity Logic Revolutionary?

[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