Triangulations study group, Spring 2008

[Fra]

comment on #30

here is the first paragraph of the second article I gave a link to (Planckian...de Sitter Universe)
==quote==
To show that the physical spacetime surrounding us can be derived from some fundamental, quantum-dynamical principle is one of the holy grails of theoretical physics. The fact that this goal has been eluding us for the better part of the last half century could be taken as an indication that we have not as yet gone far enough in postulating new, exotic ingredients and inventing radically new construction principles governing physics at the relevant, ultra-high Planckian energy scale. – In this letter, we add to previous evidence that such a conclusion may be premature.
==endquote==

I am gradually constructing a kind of dictionary: you say BACKGROUND MICROSTRUCTURE and Ambjorn/Loll papers often say fundamental dynamical degrees of freedom of spacetime. In one Utrecht Triangulations paper it began by stating simply that "the goal of nonperturbative quantum gravity is to discover the fundmental dynamical degrees of freedom of spacetime" or words to that effect.

That is how they see their job. And it is not too unlike what you are saying about the quest to determine the "background microstructure" that interests you.

Yes I think (background) microstructure of spacetime as I use the word, is conceptually very close to or the same thing as the fundamental degrees of freedom of spacetime, because both are related to some imagined probability measure defined on the imagined set of distinguishable spacetimes. And if you picture the space of spacetimes as a continuum then of course a high measure density around a particular geometry, means that there are more "microscopic freedom" there (you are likely to "spend more time" there, or "draw more samples" from there, during an imagined "random walk").
However, maybe there are some slight differences in a larger context. But at this stage of the discussion I'd think they are interchangable. I guess a difference is that I consider
the _observable_ degrees of freedom to be relative as well. I'm not sure how the see that.

In what I just quoted they use a different phrase: fundamental quantum dynamical principle. I think the aim remains the same and they just use different words.
==================
In this second paper they present a new piece of evidence that they are on the right track------ They make lots and lots of random universes and then a giant superposition of all these universes, and they discover it is S⁴. Roughly speaking the "wick rotation" of usual de Sitter space. they are often going back and forth between Lorentzian version and Euclidean, substituting imaginary
time for real time and back again.
In doing the Monte Carlo runs, they "wick rotate" in this sense so that complex amplitudes become real probabilities. Only then can they do a random walk, in effect tossing dice or coins to decide which modifications of geometry to do.that part can be a bit confusing. Anyway, according to them, what they got (S⁴ ) is the Euclidean version of the right thing, namely de Sitter space. So it is the right thing, and it is part of the program "To show that the physical spacetime surrounding us can be derived from some fundamental, quantum-dynamical principle."

===================
This then strengthens the argument, which must be familiar to you from the first paper, that it is PREMATURE to resort to exotic and newfangled structures to represent the microscopic degrees of freedom. Like you said earlier, we do not have to resort to "funny wiggling things". Not YET anyway, because a simple nonperturbative path integral appears to be working.

I read this again now, and if I understand you right you are arguing that a possible justification of Loll et all's approach something like "minimum speculation" or "minimum action" and that we should evaluate the options with "low action" first so to speak? And this means that the fewer things we need to change or revise, the less information we need to change, the lower action.

I'm all with you on that principal reasoning, however this reasoning is relative to the current state of accepted information, and the accepted rating system, which may explain our disagreement?

I do not accept the path integral in the sense that it's part of my currently accepted truths. Moreover many of the standard QM axioms simply doesn't make sense IMO, this in particular regards the use of probability theory, and the lack of consistent induction of the probability spaces with measures. I don't find their construction with path integral free of speculation, and from my view it's rate sufficiently speculative to not attract me directly into exactly what they are doing. However, I am still interesting, if those who make the ratings are willing to invest in the evaluations, I am happy to be a curious observer for upcoming papers.

Perhaps one can call this view speculative then ok :) But I see it just the opposite way, because the state of opinion from which that evaluates as speculatie, is speculative itself in the first place - relative to my view.

I see this disagreement as perfectly consistent with my views. There is no reason to expect everyone to agree on every evaluation. As long as I can reach a state of subjective understanding to our disagreement, then I am happy.

( Note that I never claimed anywhere that they are "wrong", because how to we define that measure at this point? and that was also be a style of reasoning too categorical for me.)

Now I am still interested to know if you, regardless of wether you "disagree", understand my point or if you think I am missing soemthing yet, if so I am still very motivated to understand what you mean. Do you consider my line of reasoning, speculative? I mean, not the reasoning about physics, but the reasoning regarding the reasoning?

/Fredrik

 

[Fra]

this is the naive intuition with which I approach equations (1) and (2) on page 4 of the main paper we are looking at (the "Quantum Gravity on Your Desktop" paper)

I want to share my crude intuitive perception of these things because that's really how I think most of the time.
If you have a different way of approaching equations (1) and (2) you could let me know---it might be interesting for me to look at it in a different light.

To answer this more directly. I see equations (1) and (2) as a sort of semiclassical application of feynmanns QM formalism, sort of taken out of context.

My personal analysis of the equations would suggest reanalysing the formalism going back to the questions that were asked by the founders of statistical mechanics and QM. I'd want to ask how the measures, probability and the action connect to physically accessible information. It's my hunch that the concepts of intertia and change/time, that is so central to GR, do have a deep connection to the information view of physics - to which stat mech, and QM are touching.

This is why I have not deep respect for the equations (1) and (2). I think their justification, is also the key to how to interpret them properly. And that seems to be where we stand?

/Fredrik

 

[marcus]

...
Now I am still interested to know if you, regardless of wether you "disagree", understand my point or if you think I am missing soemthing yet, if so I am still very motivated to understand what you mean. Do you consider my line of reasoning, speculative?...

I think we both realize that the benefit of two people presenting their different views is so both can learn and we don't care about agree versus disagree. So you put it in quotes.
No I DON'T completely understand your POV but I understand SOME and I am glad you are patiently explaining it. I think I learn something from this.

Also for me speculative is not a bad word. there are times when only a desperate gamble can succeed. there are times when boldness is worth more than deliberateness.
And there are times when the established methods are the only sensible ones and when speculation is merely naive and foolish. We cannot know in this case. Quantum gravity is so hard a problem that we cannot know the correct path at the beginning. We must have people who are willing to gamble with their professional lives and to try anything.

Your method is to try reasoning about reasoning. And this itself is a daring and unconventional approach! It may lead you to a maze of culdesac where you never reach the point of constructing a model of spacetime to try in the computer! Or with pencil and paper either. But it MAY not. It might work. There is no way to be sure ahead of time what will work.

You asked if I think you are missing anything. Well there is one thing about your comment concerning the EINSTEIN-HILBERT ACTION and equation (1) and (2) that made me think that you might be missing the classic meaning of the action. You know that Planck's h-bar constant is sometimes called the "quantum of action". Action is an old idea that goes back to Lagrange and maybe 18th or 19th century. And Einstein classic 1915 GR theory can be formulated using the E-H action.

So when Ambjorn and Loll show you equations (1,2) with the E-H action what they are doing, at least in part, is saying "Here is how we will slip the Einstein Field Equation into our model, so that it will have the right largescale classical limit!"

They have to do something to tell their theory ahead of time what she must do. So she knows she is to be a gravity theory of spacetime geometry, and not something else. So they give her the antique necklace that her grandmother wore back in the old times, so she knows how to behave.

but you are critical of equations (1,2) and say you mistrust them, they seem arbitrary or unjustified. That is OK and I can understand. But HOW ELSE are they going to put in this essential bit of information? Remember that Tulio Regge in his great paper of 1961 also used the E-H action and found a way of doing General Relativity without any system of coordinates!

the action integral is the antique souvenir that connects the Ambjorn Loll theory to its (honorable, indeed brilliant) ancestors. I find it hard to imagine doing without it. And my hunch is that this makes it very important to understand the technical concept of action.

there is a chapter in Feynman Lectures in Physics about the least action principle.
It could have some deep intuition. Have you seen it?

 

[Fra]

You asked if I think you are missing anything. Well there is one thing about your comment concerning the EINSTEIN-HILBERT ACTION and equation (1) and (2) that made me think that you might be missing the classic meaning of the action. You know that Planck's h-bar constant is sometimes called the "quantum of action". Action is an old idea that goes back to Lagrange and maybe 18th or 19th century. And Einstein classic 1915 GR theory can be formulated using the E-H action.

So when Ambjorn and Loll show you equations (1,2) with the E-H action what they are doing, at least in part, is saying "Here is how we will slip the Einstein Field Equation into our model, so that it will have the right largescale classical limit!"

They have to do something to tell their theory ahead of time what she must do. So she knows she is to be a gravity theory of spacetime geometry, and not something else. So they give her the antique necklace that her grandmother wore back in the old times, so she knows how to behave.

but you are critical of equations (1,2) and say you mistrust them, they seem arbitrary or unjustified. That is OK and I can understand. But HOW ELSE are they going to put in this essential bit of information? Remember that Tulio Regge in his great paper of 1961 also used the E-H action and found a way of doing General Relativity without any system of coordinates!

I think I was unclear in expressing my view on the equations. I didn't actually mean to state that equations (1) and (2) makes no sense "whatsoever", that wouldn't possibly be a sensible statement.

The fact the action and path integrals is very successful in applications significantly improves my confidence in them. I am more talking in terms of degrees of confidence, and in the quest for QG and unified theories, my confidence in these formalisms is not sufficiently high to escape unqestioned, because we are try to extend "proven" ideas into new territories.

A question is, are we confident enough in our current tools, to trust them *blindly* for digging new ground? or do we go one step back to the tools used to make the tools, and find better tools.

What I want to do, is to question them, and doing so I see interesting things, that would not toss away the equations, rather I'd expect them to be generalized (and tweaked), but of course the classical behaviour must be retained. But without an analysis, I can't rate the possible generalizations.

Alot of the old action ideas are IMO formulated first of all relative to a background realism. Even QM has a background realism to it, because there are background microstructures. And with background structure I am not only talking about the spacetime, I am also talking about the probability space themselves (relating to various measurement problems).

With all due reservation for that I'm missing something, I think I failed to communicate my view to you of this in my past posts.

the action integral is the antique souvenir that connects the Ambjorn Loll theory to its (honorable, indeed brilliant) ancestors. I find it hard to imagine doing without it. And my hunch is that this makes it very important to understand the technical concept of action.

there is a chapter in Feynman Lectures in Physics about the least action principle. It could have some deep intuition. Have you seen it?

I don't have his book at home, but I don't know if that contains anything radically different than other standard texts on the variational ideas of analytical mechanics and also applied to geometry.

My personal intuitive idea of the action I guess would be seen in the previous posts, but I guess my starting poitns are too radical relative to yours, that I probably loose you before I got started. Sorry about that. Or I was elaborating too much things at once.

Somehow loosely, the variational idea to minimize action I see related to maximizing the "transition probability". Assuming that the probabilities are sufficiently localized/peaked(a) then with probability sufficiently close to 1, the transformation taking place, will be the one with maximum probability.

So the action is nothing but a rating system. This is entirely clear. But still, the logic around this is not crystal clear and consistent. I'm sure there is a lot I don't get, but on this point I don't think it's just me, I doubt anyone has a full account for this that answers my issues. If so I haven't seen it. The relevant part is the transition probability, and the "action" is IMO a kind of decomposition of the formulate for obtaining a transition probability, and it also oversees the idealization(a).

IMO, this rating system must have a physical justification, it's not just a rating system to human scientists. I try to understand that physics in the formalism. That's why I want to get rid of non-physical embeddings that is common in modelling physics, and of course a result of this is redundancy, or various symmetries. That might better be understood as symmetries of our descriptions rather than physical ones.

The question is what the physical basis is for the "rating system"?

When you think about this, the concepts of entropy and action have a common logic. Moreover they are relative, the trick of unification is to transform the microstructure.

I'm sorry if I can make myself understood. Maybe at a later time i could try to explain this better in a separate thread. Given much more time of work I hope to be able to show explicitly what I mean with transforming the microstructure, and how the rating system itself evolves (adapts ~ learns ~ equilibrates).

If this weid stuff, could evolve and action that comes out as the one reproducing GR, wouldn't that be neat?

/Fredrik

 

[Fra]

Maybe I missed your question...

You know that Planck's h-bar constant is sometimes called the "quantum of action".

If you meant how to get an action quanta from scratch, the idea is that it should follow from the limited information capacity of the observer, and related to the quantization of probability itself. This is because when you remove the non-physical embeddings, what if the result may discrete physical states?

Or rather, as I think of it, the mathematical continuum had no physical correspondence in the first place, it's part of our idealized models. And starting out with a continuum seems strange. It's not the way my mind works, and I don't see why it's the way particles work either.

As to the apparent constancy of this fundamental action remains to be shown, but I see no principal problem why I can't be done, and I've got an idea about how it might work, but this is a vision only. Needless to say, I have proved nada yet. But I have proved for myself, all I need to pursue the ideas further, that the evolutionary strategy of mine, and I think it's also the strategy of nature.

I only mean to point this out, not to explain how I solved it, but to note that I am not ignoring it, or missing it, relating to the past posts.

It may strike some that this sounds mad, as if I am trying to explain everything from nothing, because physics are supposed to come from empirical evidence. But this is more my point than ever. This is what I mean with asking for the physical justification of rating systems. All the imaginary background structures and embeddings takes us farther away from this ideal. What I ma doing is trying to analyze, the physics of science and reasoning, and apply that back to the physical nature.

/Fredrik