Role of in-house concept analysis done by the QG scientists themselves

[marcus]

This is a different topic, not philosophy. In any empirical science, the scientists regularly scrutinize the concepts they are using---keep the definitions definite, the categories categorical, the distinctions sharp.
It is an in-house function they normally do for themselves and do not farm out to professional philosophers.

Science is what scientists do, philosophy is what philosophers do. So it is probably a bad idea to call this regular in-house conceptual analysis "philosophy". It is part of the scientists' own job, not somebody else's. So it is confusing to call it philosophy. I may have inadvertently caused some confusion earlier--sorry about that.

I want to aim a BSM thread at what we see QG scientists doing in this regard.
I'm particularly motivated by a short wide-audience essay by Rovelli from back in 2006 that served as Chapter 1 of a book called "Approaches to Quantum Gravity: Towards a New Understanding of Space, Time, and Matter".

The essay raises basic conceptual issues that are addressed in QG, like what is space? what is time? what is observable, measurable? does spacetime exist? what is geometry? One may imagine that the answers are obvious and in ordinary life perhaps they are, but in a mathematical science one has to be more cautious and rigorous and make sure. So there may be technical distinctions and technical definitions proper to the subject---in-house stuff.

I'll get that Rovelli link. Here it is:
http://arxiv.org/abs/gr-qc/0604045
(see particularly the discussion of the evolution of the concept of time in physics. Section 1.2 starting on page 3)

I should mention that the connection between the conceptual analysis and what one does in QG is immediate and strong. There is a direct connection between the concepts and how different people treat spin-networks and define spinfoams and construct qg dynamics. So there is an active interplay between concept and mathematical modeling, which is part of why the field is currently interesting and active.

 

[friend]

It sounds to me like you're trying to get at the underlying assumptions that QG theorists use to develop their models and how these assumption can be justified. You may be right in that a closer look at these assumptions (or fundamental axioms) may give guidance into how to proceed to better model building.

For example, we may need to take a closer look at the what is meant by spacetime. We all have an intuition of what space and time are because of our experience. But is this translated correctly into our mathematical models of spacetime? And should we consider more carefully whether spacetime is discrete or continuous? For example, it seems like a contradiction to use a model of continuous spacetime to derive discrete lengths, areas, and volumes.

 

[marcus]

Friend, thanks for helping define the topic and get the thread started. I am uncertain about this. I know that there are conceptual problems in the field of QG. It may be the field of theoretical physics which is most rich in conceptual problems. But I am unsure how to organize prioritize and state the issues. How to begin? We could begin anywhere (there seems no obvious correct starting point.) You mentioned the paradoxical idea of discreteness and one could begin there as well as where I suggested: with the idea of time (and spacetime).

 

[marcus]

If we would start where you suggest (with e.g. the idea of "quanta of space") then we could start by reading this from 1010.1939---first column of page 2:

"therefore the transition amplitudes (4) are a general covariant and background independent analog of the Feynman graphs"

You may recall that on page 1, there is a half-page (!) formulation of Lqg as 4. Feynman rules for evaluating quantum geometry transition amplitudes.

A geometric transition is finitized (restricted to a finite number of deg. of freedom) as a bounded 2-complex. The boundary is a network of nodes and links, only the links are labeled. It can consist of two disconnected components: our initial and final geometric information. The 2-complex contained between initial and final then represents (with its unlabeled vertices, edges, faces) ways that initial could evolve to final. Once more from page 2, first column:

"...the transition amplitudes (4), formally obtained by sandwiching the sum over geometries (6) between appropriate boundary states, can be interpreted as terms in a generalized perturbative Feynman expansion for the dynamics of quanta of space (see Section IV-A)..."

This paper does a better job than anything else I know of clarifying what is meant by "quanta of space". The analogies of LQG with both QED and QCD are pointed out. I'll see what more I can come up with.

Anyway to build on your mention of discreteness, in case others might read this thread: I think everyone here realizes that Lqg does not depict space as "made of little grains". Geometric information is quantized the way, in other branches of theory, spin and energy are quantized: in response to measurement. Just as spin was not created in the form of "little bits of spin", so area and volume do not exist as little granules of area and volume. Area and volume are quantized as part of how nature responds to measurement. It is like what Niels Bohr said. "Physics is not about what Nature IS, but rather what we can SAY about Nature." So it is about information---initial and final information about an experiment, transition amplitudes. Or so I think.

 

[marcus]

I also wanted to raise the issue of time and spacetime. It is not clear that spacetime can exist in a quantum theory (any more than can exist the classic trajectory of a particle, with position and momentum unique and well-defined at each step of the way.)

Please comment on the issue of discreteness which Friend raised here, and correct or disagree with my response. We can handle several issues.

As a starting point for discussing time, anyone interested might read section 1.2 of that article i mentioned in the first post. It starts on page 3 and is less than a page long. Easy reading and a good place to start. The physics concept of time has changed over the past 110 years, but not in a completely coherent way. http://arxiv.org/abs/gr-qc/0604045

 

[friend]

Friend, thanks for helping define the topic and get the thread started. I am uncertain about this. I know that there are conceptual problems in the field of QG. It may be the field of theoretical physics which is most rich in conceptual problems. But I am unsure how to organize prioritize and state the issues. How to begin? We could begin anywhere (there seems no obvious correct starting point.) You mentioned the paradoxical idea of discreteness and one could begin there as well as where I suggested: with the idea of time (and spacetime).

Can ANY assumption about "spacetime" be a starting point for deriving the fundamental character of spacetime? That would seems to lead to a circular argument. Or perhaps the starting point is simply a manifold on which a metric is assigned based on dynamical rules. Yes, is there a starting axiom accepted by ALL QG researchers?

 

[friend]

As a starting point for discussing time, anyone interested might read section 1.2 of that article i mentioned in the first post. It starts on page 3 and is less than a page long. Easy reading and a good place to start. The physics concept of time has changed over the past 110 years, but not in a completely coherent way. http://arxiv.org/abs/gr-qc/0604045

The conceptual problem I have with this is that in QM quantized energy, momentum, spin, etc, is derived from differential equations wrt continuous spacetime. Now, if we want to quantize spacetime itself, don't we need other differential equations wrt something other than continuous spacetime? What could that be?

 

[suprised]

The title of this thread... wouldn't it fit better to the Onion?

 

[Kevin_Axion]

The title of this thread... wouldn't it fit better to the Onion?

Clever, it does seem very suitable though, much like the articles that say "Researchers find a way to test String Theory". I must admit though I have done that in the beginnings of my time on this forum.

 

[apeiron]

But I am unsure how to organize prioritize and state the issues. How to begin? We could begin anywhere (there seems no obvious correct starting point.) You mentioned the paradoxical idea of discreteness and one could begin there as well as where I suggested: with the idea of time (and spacetime).

I love your discomfort at having your threads bumped to philosophy, but you really have nothing to fear from real metaphysics.

Anyway, the way fundamental concepts are derived is actually very simple. First we of course generalise. We induce from particular to abstract our way towards universals - concepts that appear universally applicable.

Second - and admittedly less well understood - we dichotomise. In arriving at what is A, we must also simultaneously arrive at what is not-A. So universals (our fundamental concepts) also always come in complementary or asymmetric pairs. If we positively, definitely, feel we have some thing, then the big part of knowing this for sure is that we also know everything that it positively, definitely, is not.

So for example here, you ask where shall we start? Perhaps with discreteness. Yet "paradoxically" we cannot take the discrete as a fundamental universal concept without being equally convinced that its opposite, continuity, is just as true a concept.

Now the standard reaction is reduce - to argue that while both alternatives must exist as crisply defined ideas, only one of them can be a basis of reality. Of course, it makes more sense to see the pairing as the basis of reality. But that is a separate discussion. If you are just talking about the initial step of deciding what are the fundamental concepts of nature, then you will find, throughout the history of philosophy, that logically concepts must always come in complementary pairs - to be well-defined.

There are a host of dichotomies that can be brought to the table. Space and time is one (a sub-type of the more general notion of stasis~flux - that which is located and so unchanged, and that which measures the change and so not located).

If you want to get to the heart of things, the ultimate dichotomy is local~global. At least if you are a holist like me. And all other universals can be mapped onto this most basic distinction.

So with spacetime, for instance, this is really about dimensionality, and so crisply localised degrees of freedom. And a holist takes the view that local degrees of freedom arise as a result of global constraints.

This should be easy to understand. Anything that is not globally being prevented from happening is by definition locally free to happen.

Carry this now across to current physics and you can see that the essential question becomes: there seems no reason why reality could not have an infinity of degrees of freedom, but we live in a universe with just 3 degrees of freedom so far as location goes (and then a global entropic gradient that drives the actual change). What are the constraints that limit the degrees of freedom so severely?

So where to begin? The dichotomy of local~global is arguably the most fundamental complementary pairing when it comes to framing fundamental concepts. So how well does loop thinking, or string thinking, etc., map to a local~global framework?

(I don't want to complicate the discussion too much, but it should be mentioned that there is a second equally fundamental dichotomy of vague~crisp. Local~global describes what is, what exists, the synchronic view. Vague~crisp descrines the diachronic view of how things come into being, how they develop into existence.)

 

[marcus]

The title of this thread... wouldn't it fit better to the Onion?

THAT'S FUNNY!

Kevin, I think you got the idea: I wanted to make it clear that the intended focus is on the conceptual framework developed by the researchers themselves--not by outsiders, be they professional or amateur. It may make the thread unpopular to have that focus, and make the title sound dumb, but that's what I want it to say.

 

[marcus]

...
Anyway, the way fundamental concepts are derived is actually very simple. First we of course generalise. We induce from particular to abstract our way towards universals - concepts that appear universally applicable.

Second - and admittedly less well understood - we dichotomise. In arriving at what is A, we must also simultaneously arrive at what is not-A...

But Apeiron, where do you find that in the work of a working QG physicist? Can you give a citation---an arxiv link? Some paper by Ashtekar Lewandowski Thiemann Rovelli Baez... or one of their grad students? Please give page reference to make it easy to find.

What I want to bring out here is professionally researched ideas and not merely the ideas of professional philosophers of science (that can be discussed in the other thread, in Phil. Fo.)
I just want to be discussed the conceptual thinking of the QG folks themselves.

I'm sure you understand the need for focus. If we don't narrow and spotlight we will never get to what they are saying and the consequences of their ideas.

 

[MTd2]

I suppose that the idea behind LQG it is that space is the picked up choice of a number events out of an infinite number of possible combinations of events.

 

[marcus]

As a starting point for discussing time, anyone interested might read section 1.2 of that article i mentioned in the first post. It starts on page 3 and is less than a page long. Easy reading and a good place to start. The physics concept of time has changed over the past 110 years, but not in a completely coherent way. http://arxiv.org/abs/gr-qc/0604045

The conceptual problem I have with this is that in QM quantized energy, momentum, spin, etc, is derived from differential equations wrt continuous spacetime. Now, if we want to quantize spacetime itself, don't we need other differential equations wrt something other than continuous spacetime? What could that be?

The problem you have with what? I guess "this" refers to section 1.2 of that paper. The section on time.

It describes how the idea of time has changed since around 1900, how it has become, in GR, somewhat nebulous (coordinate time is not observable and the geometry cannot evolve freely with respect to anyone's proper time because that derives from a particular solution.) and then in any quantum version (however "quantized" from something earlier) time is necessarily even more elusive, for reasons given there.

It seems to me that your objection is not targeted at what you quoted since for the point he is making it doesn't matter how the quantum system is arrived at.

=========================

To respond generally. The QG theories I see these days are only indirectly/partially "derived" from classicals. There was a long period when the researchers labored over "quantization" by various means. But by 2007 or 2008 they seem to have cut loose.
The discussion in 1004.1780. 1010.1939, and 1012.4707---in any of those papers as I recall--makes that explicit at the outset. The idea is to get a background independent qft that comes down to the right thing in the appropriate limit and is consistent with past observation. This is hard enough--it has not been done yet. If there were even two such theories it would make sense to argue about which one was the more faithful "quantization". That's a criterion to use if you have plenty of candidates, not to use when you don't fully have even one yet.

I'm arguing back at you, I see. Hope you don't mind a little backtalk.

 

[apeiron]

But Apeiron, where do you find that in the work of a working QG physicist? Can you give a citation---an arxiv link? Some paper by Ashtekar Lewandowski Thiemann Rovelli Baez... or one of their grad students? Please give page reference to make it easy to find.

I am happy to talk about how individual researchers employ various concepts where that is relevant. But my point was that to get anywhere here, it is not enough to go round in circles debating some particular concept. You have to understand the very basis on which our concepts arise.

This is in fact meta-metaphysics. And even though Rovelli wrote a book on Anaximander, Smolin name-checks Peirce, I don't think the QG literature is the place to start when it comes to this issue.

If you just want another fruitless debate about what kind of concepts hold true, rather than stepping back to consider how any concept can ever hold true, then I'll leave you to it...

 

[marcus]

Can ANY assumption about "spacetime" be a starting point for deriving the fundamental character of spacetime? That would seems to lead to a circular argument. Or perhaps the starting point is simply a manifold on which a metric is assigned based on dynamical rules. Yes, is there a starting axiom accepted by ALL QG researchers?

I suppose that the idea behind LQG it is that space is the picked up choice of a number events out of an infinite number of possible combinations of events.

Everybody probably knows what Einstein said about space having no physical existence. "The principle of general covariance deprives space and time of the last shred of objective reality." That is based on the "hole argument". We've been through that before.

You don't have to answer the question "what is space" because it is not a physical thing.

There is geometry. We experience that as a collection of related measurements. Measure the sides of a right triangle. Measure the 3 internal angles. Relate the radius of a ball to the surface area and to the volume. Depending on what relationships you find, you will detect nonzero curvature or else zero curvature. You will be observing geometry.

What we are talking about is not what Nature IS (as Bohr said) but how Nature responds to measurements. In a quantum theory of geometry the relations among measurements are subject to uncertainty.

So to respond to both your posts, Friend and MTd2, i would say that we have to be able to describe geometry (the business of making and relating geometrical measurments) but we do not need a mathematical description of "space".

Several older forms of QG have mathematical representations of "space"---either has manifold or something else. But that is not essential. If you look at a recent qg formulation in 1012.4707 you do not see "space", you see geometric information. (i.e. a spin network) Or you see two sets of geometric information (two spin networks) with a Feynman diagram showing how one can change (transition) into another. There is no space, or spacetime, anywhere in the picture.

 

[marcus]

...
If you just want another fruitless debate about what kind of concepts hold true, rather than stepping back to consider how any concept can ever hold true, then I'll leave you to it...

I do indeed want the kind of discussion I appear to be having with Friend and MTd2. Thanks for leaving me to it.

 

[atyy]

Many QG researchers (I would name Polchinski, Percacci, Reuter, Rivasseau) would agree with the broad classification of approaches in Markopoulou's http://arxiv.org/abs/gr-qc/0703097 and http://arxiv.org/abs/1011.5754 . Markopoulou is careful to say that string is emergent gravity, and background dependent in its initial formulation, leaving open the presumably background independent non-perturbative formulation that dualities between the perturbative theories and gauge/gravity duality seem to point to.

 

[MTd2]

So to respond to both your posts, Friend and MTd2, i would say that we have to be able to describe geometry (the business of making and relating geometrical measurments)

What do you mean by relate geometrical measurements?

 

[marcus]

What do you mean by relate geometrical measurements?

Thanks for asking, we get to take a closer look. I mentioned the relational thing about the sum of the internal angles of a triangle---it might be 180 or it might not. That is what I mean by a relation among some geometry measurements (in this case 3 angle measurements).

Another relational thing you might check, which I think I mentioned, was the relation between the surface area and volume of a round ball.

One thing we haven't talked about is the need for matter. I recall Rovelli saying that in LQG the area operator has to be based on some physical object, like a table top. To give operational meaning to the idea of a surface that you want to observe the area of. Otherwise the surface is simply defined as a set of spinnetwork links (the links which the surface would cut, if we had a real material surface.)

 

[atyy]

A discussion of relational concepts is empty unless the theory contains matter.

 

[MTd2]

Thanks for asking, we get to take a closer look. I mentioned the relational thing about the sum of the internal angles of a triangle---it might be 180 or it might not. That is what I mean by a relation among some geometry measurements (in this case 3 angle measurements).

But area relations, nor volume is everything. What if there are many geometries for just 1 object?

 

[marcus]

A discussion of relational concepts is empty unless the theory contains matter.

Yes Atyy, I alluded to the need for matter in the post right before yours. LQG gradually becomes more complete and part of that is gradually including matter (viz. the paper "Spinfoam Fermions" that appeared just this month.)

To me the relational approach makes sense even with a theory that is still not entirely complete matterwise: that has not dotted all the ayes and crossed all the tees, so to speak Indeed it is the only approach I can think of that makes sense at all! There is no reliable idea of time for physics to depend on, so observations must relate among themselves, to each other.

 

[atyy]

Is there any theory of physics which is not a relational theory?

As far as I can tell, only theories in which the universe is empty are not relational.

Special relativity with matter is relational. It just has more symmetries. Special relativity without matter is unobservable.

 

[marcus]

But area relations, nor volume is everything. What if there are many geometries for just 1 object?

You can answer that as well or better than I! What if there is one object and we change the geometry? What happens?

For example imagine a long round aluminum cylinder being used as a gravitational wave detector. A wave passes through, momentarily changing the geometry. Does not the relation between area and volume, and length, change temporarily?

You could take over part of the job of answering questions in this thread. You have read plenty of QG papers and you watch the current literature. Feel free to jump in when and if you want.

 

[friend]

It seems to me that your objection is not targeted at what you quoted since for the point he is making it doesn't matter how the quantum system is arrived at.

I'm not aware of a quantization procedure that does not depend differentially on a background spacetime. Are we now employing commutation relations on canonical conjugate variables just because we like the algebra, nevermine where it came from?

So to respond to both your posts, Friend and MTd2, i would say that we have to be able to describe geometry (the business of making and relating geometrical measurments) but we do not need a mathematical description of "space".

Several older forms of QG have mathematical representations of "space"---either has manifold or something else. But that is not essential. If you look at a recent qg formulation in 1012.4707 you do not see "space", you see geometric information

How can you have geometry without space? As I understand it, geometry comes from a metric which defines the distance between points in a space/manifold.

A discussion of relational concepts is empty unless the theory contains matter.

Without particles, there's no way to measure the distance between objects or the size or age of the universe. That right there tells us that particles are necessary for a metric. I suspect that the sea of virtual particles is what is creating space and visa versa.

 

[marcus]

How can you have geometry without space? As I understand it, geometry comes from a metric which defines the distance between points in a space/manifold.

Well you can decide you don't like some of the new formulations of geometry without space. I'm not trying to sell you on them. Personally I find them interesting. It is interesting that they work.

Ashtekar GR (1986?) was formulated without a metric. It was clear you can have geometry without a metric, that was already long ago. A "connection" took its place. A parallel transport function.

And then Noncommutative Geometry (NG) came (when? 1990s?). It needs no space manifold, it only has geometry. You have the option to include a manifold, as a special kind of NG. But you don't need it.

You can think of it as just the fashion of the day. At some point (2008? 2009?) Loop QG stopped needing a manifold. It treats geometry but it has no "space" (in the new manifoldless formulations.)

Some people feel threatened/upset by this and they hurry to explain why it cannot possibly work---but plenty of other people who are just as savvy find the idea interesting and think it might work and are trying it. It has to do with comfort level and change.

There is no reason you should take one view or the other. we are not voting or taking sides or keeping score.

One way of having geometry without a metric is to have a network where each node represents a bit of volume and each link between two nodes represents a bit of "contact" area where volumes meet. Given enough of that data you could probably reconstruct an approximate metric. Area+volume data. There are other kinds of data. Some sorts of data are more natural to treat using Feynman-like path integrals. The "path" is the evolving geometry. It is an approach to quantum system, even if it does not use the canonical conjugate pairs and the commutators that you were thinking about.

I'm not aware of a quantization procedure that does not depend differentially on a background spacetime. Are we now employing commutation relations on canonical conjugate variables just because we like the algebra, nevermind where it came from?

A "quantization procedure" is not the only way that one can arrive at a quantum theory.
One does not always have to begin with a classical system and perform some time-honored ritual. One can just use the classicals as heuristics, and try to get insight into other quantum theories, and work by analogy---and then, when you have something, check to see what the classical limit is. Work backwards. Some people are very worried by this, others are not. It may be partly a matter of personal temperament.

Without particles, there's no way to measure the distance between objects or the size or age of the universe. That right there tells us that particles are necessary for a metric. I suspect that the sea of virtual particles is what is creating space and visa versa.

One does not need a metric in order to have a quantum geometry (i.e. a QG). We talked about that before. But I agree that somehow matter has to be in the picture. LQG and the cosmology application LQC use matter, although it tends to be some overly simple kind of matter. That has to be worked on--a richer palette of matter needs to come.

 

[MathematicalPhysicist]

This is a different topic, not philosophy. In any empirical science, the scientists regularly scrutinize the concepts they are using---keep the definitions definite, the categories categorical, the distinctions sharp.
It is an in-house function they normally do for themselves and do not farm out to professional philosophers.

Science is what scientists do, philosophy is what philosophers do. So it is probably a bad idea to call this regular in-house conceptual analysis "philosophy". It is part of the scientists' own job, not somebody else's. So it is confusing to call it philosophy. I may have inadvertently caused some confusion earlier--sorry about that.

I want to aim a BSM thread at what we see QG scientists doing in this regard.
I'm particularly motivated by a short wide-audience essay by Rovelli from back in 2006 that served as Chapter 1 of a book called "Approaches to Quantum Gravity: Towards a New Understanding of Space, Time, and Matter".

The essay raises basic conceptual issues that are addressed in QG, like what is space? what is time? what is observable, measurable? does spacetime exist? what is geometry? One may imagine that the answers are obvious and in ordinary life perhaps they are, but in a mathematical science one has to be more cautious and rigorous and make sure. So there may be technical distinctions and technical definitions proper to the subject---in-house stuff.

I'll get that Rovelli link. Here it is:
http://arxiv.org/abs/gr-qc/0604045
(see particularly the discussion of the evolution of the concept of time in physics. Section 1.2 starting on page 3)

I should mention that the connection between the conceptual analysis and what one does in QG is immediate and strong. There is a direct connection between the concepts and how different people treat spin-networks and define spinfoams and construct qg dynamics. So there is an active interplay between concept and mathematical modeling, which is part of why the field is currently interesting and active.

Well I think we perceive time and space as given apriori.
I mean time perception is given as a consequence of change we experience and our memory is important key in this perception.
Space is just the relative distance between different objects, it's as abstract as any space in maths, but no one stops to enquire what space itself means because it's given to us we born into it.

I heard someone trying to build a theory of physics without the need of time and space, I wouldn't call it physics.

 

[Fra]

I just want to be discussed the conceptual thinking of the QG folks themselves.

Ok, the message is clear, I think this could be interesting. To take one, Rovelli's conceptual views are interesting and regardless of wether we agree with it, analyzing his arguments is instructive indeed.

I'll try to dig out from Rovellis own papers what illustrates the points I tried to make in the thread that got moved.

/Fredrik

 

[sheaf]

Well I think we perceive time and space as given apriori.
I mean time perception is given as a consequence of change we experience and our memory is important key in this perception.
Space is just the relative distance between different objects, it's as abstract as any space in maths, but no one stops to enquire what space itself means because it's given to us we born into it.

I heard someone trying to build a theory of physics without the need of time and space, I wouldn't call it physics.

Is this what Marcus was getting at though ? I interpreted it simply that time and space might not be the most "fundamental" entities, i.e. they could be derived from something more primitive (thinking for example of spin networks and "extracting" area, volume, length measurements from those). I think whatever they come up with has to treat time and space somehow, even if it isn't fundamental.

 

[Fra]

I'll start my attempt at looking into Rovelli's thinking and I hope that I didn't misinterpret Marucs ambition with this thread. If I did let me know and I will drop this.

Since the conceptual things do come with and ORDER as per constructions that IMHO should be respected, I'll start in the right end and make progress in step and hopefully Marucs and everyone would agree or disagree with the characterisation. Maybe we should try to the extent possible to comment on and reflect upon Rovelli's thinking, without adding to much of our own thinking even if it may be hard.

Let's first note how Rovelli defines what he means by QG (this may be relevant as there are some different opinons out there as to what needs to be included in the quest):

"Therefore we expect the classical GR description of spacetime as a pseudo-riemannian space to hold at scales larger than lP, but to break down approaching this scale, where the full structure of quantum spacetime becomes relevant. Quantum gravity is therefore the study of the structure of spacetime at the Planck scale."
-- Rovelli, http://arxiv.org/abs/gr-qc/0604045

As I read this, the question I must pose is: Does "planck scale" refers to the scale of the interactions, or the scale of the observer. I hope we can agree that this makes a difference, right?

I think Rovelli does mean that the interaction scale is Planck scale. The observational scale (ie where the observer it) is still the large scale low energy laboratory frame? Right or wrong?

Interesting things could be said about the other possibility, but do stick to Rovelli's view here it suffices to just flag this point for a different discussion.

Note that, with the observer scale beeing the labframe, I mean that it IMPLIES that the inference of the Planck scale interactions does take place relative to an embedding effective spacetime.

Before going on, does anything disagree with this characterisation of Rovellis view? Or maybe suggest that also the observer scale is Planck scale; should we discuss further?

I think this is a basic point, that will confuse the rest of the discussion unless we're on the same page here. Comments?

/Fredrik

 

[suprised]

Kevin, I think you got the idea: I wanted to make it clear that the intended focus is on the conceptual framework developed by the researchers themselves--not by outsiders, be they professional or amateur. It may make the thread unpopular to have that focus, and make the title sound dumb, but that's what I want it to say.

Lol whoelse could possibly make such an analysis other than insiders? This almost sounds as if laymen could do it...

 

[Fra]

I'm jumping to what friend, Mtd2 and Marucs discussed.

Like how can you have geometry without a manifold? Mathematically I follow Marcus argument: individual manifolds can have the same geometry, or encode the same geoemtric information. This is mathematics.

One can associate one manifold ~ on observer. One can similarly to just make a statement about relations between observers (like what's seemingly Rovelli ambition as defined in his RQM paper), and consider such a thing without observers.

So far clear to me.

But I think there may be a risk at going to fast here and throw the baby out with the bathwater.

Because if we required geometric qualities to be observable, we do need an observer. So it's not trivial if the above makes sense from a physics perspective I think.

For me the question isn't wether we can do away with manifolds in geometric models. We can. Or wether we can do away with observers. We can (at least mathematically). The question is what this is useful for physical understanding?

Contained in the last question I asked about the observer scale vs interaction scale, it's not a far stretch to imagine that the low energy observer A, makes observations and inferences on interacting high energy observers B and B'. In this abstraction it seems to me that Rovelli's view CAN make sense, from the point of view of A. There is no problem with this as long as we keep track of what is beeing doing.

This is also what Smoling means by the "Newtonian scheme" in his evolving law talks. It means that from the perspective of observer A - observing B and B' which are then a small subsystems of A's total control domain, time and space CAN be removed! Just like I think Rovelli suggests.

But picture what happens if A and B switches place. Now what? B is the scientist. A is a cosmological (or LARGE) system relative to B.

Too much mathematical detouring and its' easy to loose track of this. I hope this wasn't detouring from Roveli's ideas.

Smolin's thinking is also interesting: http://pirsa.org/08100049/ (this has been posted many times by Marcus in past threads as well) I do not think this thinking signifies Rovelli, it's rather an interesting constrat to Rovelli. Just beeing aware of the constrasting views I find enlightening, even if one can't take side.

/Fredrik

 

[friend]

Well you can decide you don't like some of the new formulations of geometry without space. I'm not trying to sell you on them. Personally I find them interesting. It is interesting that they work.

Ashtekar GR (1986?) was formulated without a metric. It was clear you can have geometry without a metric, that was already long ago. A "connection" took its place. A parallel transport function.

And then Noncommutative Geometry (NG) came (when? 1990s?). It needs no space manifold, it only has geometry. You have the option to include a manifold, as a special kind of NG. But you don't need it.

You can think of it as just the fashion of the day. At some point (2008? 2009?) Loop QG stopped needing a manifold. It treats geometry but it has no "space" (in the new manifoldless formulations.)

geometry without space... forgive me if that continues to give me trouble. But all the books I've read, or at least remember reading, always have geometry defined on a space. For as soon as you even mention the word volume and area this implies dimensions of length between points.

One way of having geometry without a metric is to have a network where each node represents a bit of volume and each link between two nodes represents a bit of "contact" area where volumes meet. Given enough of that data you could probably reconstruct an approximate metric. Area+volume data. There are other kinds of data. Some sorts of data are more natural to treat using Feynman-like path integrals. The "path" is the evolving geometry. It is an approach to quantum system, even if it does not use the canonical conjugate pairs and the commutators that you were thinking about.

But now we have nodes (let's not call them points) that represent volume, and links between nodes (let's not call them lines) that represent area... that all sounds like a pretty distorted view of "geometry". It sounds like they are trying to define geometry more abstractly just to get around having to start with the metric which they are trying to derive. Maybe you could give me a link to some paper that makes that clear.

A "quantization procedure" is not the only way that one can arrive at a quantum theory. One does not always have to begin with a classical system and perform some time-honored ritual. One can just use the classicals as heuristics, and try to get insight into other quantum theories, and work by analogy---and then, when you have something, check to see what the classical limit is. Work backwards. Some people are very worried by this, others are not. It may be partly a matter of personal temperament.

We don't even know why nature prefers path integrals or commutation rules in regular QM. But now we're free to invent our own quantization rules, and this without experimental evidence. I am highly skeptical.

I remember watching a video on the Perimeter Institute archive in which the instructor wrote a path integral on the board where the D[g] was over the space of geometries. He had to admit that we don't yet know what that means. But at least the path integral has some justification.

My personal opinion is that all we need to do is justify the Hilbert-Einstein action in the path integral in order to get quantum gravity. Is this being seriously looked at in any of the programs you are aware of? What's wrong with doing that? It seems like the most straightforward way to get QG. Thanks.

 

[marcus]

geometry without space... forgive me if that continues to give me trouble. But all the books I've read, or at least remember reading, always have geometry defined on a space. For as soon as you even mention the word volume and area this implies dimensions of length between points.
...

Friend, I appreciate your sticking to a question like this which is central to understanding. I think I have said this before, but haven't emphasized it enough. The sense in which one has geometry without space is in the mathematics. In the theory, there is no mathematical object (no set, no manifold) that stands for space.

Instead, there are, in the theory, mathematical elements and operations that correspond to making measurements.

If you think about it, this is a perfect imitation of real life. There is, in our experience, no physical substance of space. All we do is make measurements, we move around, we experience geometry, we experience angles, distances, volumes. These are inter-related in various ways and the geometry constrains what we do.

But there is nothing called "space" that you can put your finger on.

So it is in real life, in our everyday, and so it is in the Lqg mathematical theory. There are the measurements, the operators, but there is no manifold.
==================

Of course there are a lot of Lie groups in the construction, they are basic tools describing symmetry. We think with Lie groups. And they are manifolds. When I say there is no manifold I mean no manifold representing space or spacetime. Because a theory of geometry does not need one. No mathematical object of any kind, that stands for space, is needed when one describes geometry.

This might be a good time to take a look at these three papers, if you have not done so already.

April 1780: http://arxiv.org/abs/1004.1780
October 1939: http://arxiv.org/abs/1010.1939
December 4707: http://arxiv.org/abs/1012.4707

As you know if you've taken a look, all say the same thing but in different ways---I find it can help me to see something presented several different ways. And sometimes it helps me to see concretely what is giving trouble rather than just thinking about it abstractly with my pre-existing concepts.

 

[marcus]

...But now we have nodes (let's not call them points) that represent volume, and links between nodes (let's not call them lines) that represent area... that all sounds like a pretty distorted view of "geometry". It sounds like they are trying to define geometry more abstractly just to get around having to start with the metric which they are trying to derive. Maybe you could give me a link to some paper that makes that clear.
...

You put your finger on the key thing in this approach---the finite graph.

In a certain sense you could say that what we have instead of "space" is the set of all finite graphs.

A graph represents a kind of truncation of the information we are going to look at and deal with. We declare we are only going to make a finite number of geometrical measurements, at only a finite number of locations, with a limited number of ways information can to get from one to the other.

This is not clear, I realize. In a sense, chosing a graph to work with finitizes the probem of geometry. It restricts the number of degrees of freedom that space is allowed. So it makes it possible to calculate, prepare the geometric experiment so to speak (as one prepares an experiment in other types of of QM).

The graph is also a "cut-off", analogous to cutoffs in power-series calculations. One is truncating on the basis of geometric complexity, rather than energy or scale. But it is still comparable.

One can take limits over all graphs, and sum over all graphs, just as one can take limits and sum using the natural numbers as an index. It is like a power-series in calculus except using graphs instead of n= 1,2,3...

So that's the "trick" which you will have already discovered, if you took a look at those three papers I mentioned:
April 1780
October 1939
December 4707
or some of the other papers that have come out recently working along the same lines.

Instead of "space" being a manifold, and having one Hilbert H of states of all the geometries of that manifold, one has many possible truncations or simplifications represented by graphs gamma Γ. And for each one we have a Hilbert H_Γ of states of geometry of Γ.

You are entirely and cordially welcome to say that you don't LIKE such a picture It is fine to detest it, as far as I can see. But there are signs that it works. The past year or so has seen unexpectedly rapid progress, so it bears watching.

αβγδεζηθικλμνξοπρσςτυφχψωΓΔΘΛΞΠΣΦΨΩ∏∑∫∂√±←↓→↑↔~≈≠≡ ≤≥½∞(⇐⇑⇒⇓⇔∴∃ℝℤℕℂ⋅)

 

[MTd2]

The most fundamental thing is not space but the event. Event is the most basic entity as it is implied, to me, in sec. 1.2, p.5 of gravitation, and it is labeled by coordinates. Don't think in terms of geometry or mathematical space.

The beginning of this section has a very important quote from Einstein:

"Now it came to me: ... the independence of the
gravitational acceleration from the nature of the falling
substance, may be expressed as follows: In a
gravitational field (of small spatial extension) things
behave as they do in a space free of gravitation . ... This
happened in 1908. Why were another seven years required
for the construction of the general theory of relativity?
The main reason lies in the fact that it is not so easy to
free oneself from the idea that coordinates must have an
immediate metrical meaning."

ALBERT EINSTEIN [in Schilpp (1949), pp. 65-67.

A coordinate is just a label, but we must free ourselves from the notion of metric as being geometry. Notice that until Einstein's death, it was predominant the intuitive, and wrong, idea that to a given topology there is only one correspondent equivalence class of metric. This is wrong, specially in 4 dimensions, in which there can be infinitely many. So, things are even more confusing.

So, in our perspective, we have also to stop thinking even about the topology and think that gravity is something about a collection of events, labeled by coordinates, not really geometry. So, we have to go deeper than GR to understand the philosophy behind GR and so to understand LQG.

 

[marcus]

@MTd2, that's a beautiful contribution to this thread. Thanks.

 

[marcus]

I remember watching a video on the Perimeter Institute archive in which the instructor wrote a path integral on the board where the D[g] was over the space of geometries. He had to admit that we don't yet know what that means. But at least the path integral has some justification...

Exactly. D[g] is what all this is about. However do not think of g as standing for a METRIC. A metric is only one possible way to describe a geometry, and after 30-plus years it has not turned out to be such a good way. AFAIK no one succeeded in putting a measure on the space of metrics. But they did put measure (for integration) on the space of geometries---with the geometries described in other ways.

Renate Loll and friends found "random triangulations" a good way to put a measure on the space of geometries. They do the path integral, by a Monte Carlo method. I have a popular article in my signature---the Loll SciAm article. Have you seen it, or read any other CDT stuff?

Everybody wants to do the path integral. So they find various different ways to put a measure (for integration) on the space of all geometries. In the cases I know of, the measure will turn out to live on a subset of all geometries. The hope is that it is somehow representative---this is Loll's tactic. The subset consists of triangulated geometries using essentially identical building blocks (actually two kinds).

If you look at the three LQG papers I offered, you will see yet another way to make D[g], yet another way to define the path integral. You integrate over all geometries (but this time the geometries are limited to those living on a certain graph, which can be as complicated as you want). In a sense it is very much like Loll's CDT method, a representative subset of geometries, a measure on them, an integral using that measure.

Ultimately the LQG path integral method can give a transition amplitude between two spatial geometries---initial and final geometries.

Where classical GR might give a classical trajectory (a spacetime) from the initial to the final, the quantum theory gives a transition amplitude.

The transition amplitude in effect explores a variety of paths or ways of getting from the initial to final configuration. It is based on a version of the GR action called the Holst action.
Classically this would not be distinguishable from the Einstein-Hilbert, same equations come out. No reason to prefer one over the other. But for the LQG path integral approach the Holst form of the action works better.

John Baez TWF #280 has some stuff about the Holst action for GR. Anyone who hasn't already might want to look at it, for breadth, to be familiar with other actions besides Einstein-Hilbert.

Sketchy answer. Best i can do for now.

 

[friend]

So really, if you know, tell me... what is wrong with simply plugging the Hilbert-Einstein action in the path integral to quantize gravity? It seems like the most straightforward way to go. We already know the Euler-Lagrange equation gives Einsteins GR in the classical limit. And what's more natural than to plug and action integral into the path integral? Is this the method that proves non-renormalizable? Thanks.

 

[marcus]

So really, if you know, tell me... what is wrong with simply plugging the Hilbert-Einstein action in the path integral to quantize gravity? It seems like the most straightforward way to go. We already know the Euler-Lagrange equation gives Einsteins GR in the classical limit. And what's more natural than to plug and action integral into the path integral? Is this the method that proves non-renormalizable? Thanks.

I don't know the various things that go wrong, friend. Somebody else will have to answer. My reaction when I read your post was simply "first off, how do you define an integration measure on the space of metrics?"

Everything i was talking about in my last post concerned the difficulty of defining a measure on the space of geometries----which (in the special case where you label each geometry with a metric) comes down to defining a measure on the space of metrics.

I don't offhand see any way to get a finite integral, or even a well-defined measure. Would you call that "non-renormalizable"? or is it something that logically precedes non-renorm'ble and is fundamentally worse than it?

 

[friend]

"first off, how do you define an integration measure on the space of metrics?"... the difficulty of defining a measure on the space of geometries

I remember reading stuff on how the Feynman Path Integral was not well defined; problems arose on defining a measure on the space of paths. I think they were able to get a well defined path integral using the Wiener measure that include the exponential as part of the measure. But then once a complex action was introduced, I'm not sure that did not introduce further complications. So when you start talking about measures on even more complicated spaces as space of metrics, etc. I really have to wonder if that has been well defined.

Also, you were kind enough to link me to some of the introductory papers on some of these research programs. But I seem to be having the same problem you are. I can't wrap my brain around where they come up with there starting points, spin networks, and the like. It all seems quite contrived. I suspect that they are starting off with abstractions from simpler geometric formulations. But I don't know where they come up with these ideas. Is it possible, for example, that spin networks come from the curvature scalar in the Hilbert-Einstein action (curvature=spin, get it?)? I don't know.

 

[atyy]

So really, if you know, tell me... what is wrong with simply plugging the Hilbert-Einstein action in the path integral to quantize gravity? It seems like the most straightforward way to go. We already know the Euler-Lagrange equation gives Einsteins GR in the classical limit. And what's more natural than to plug and action integral into the path integral? Is this the method that proves non-renormalizable? Thanks.

Yes. This method is known not to be perturbatively renormalizable. Even though GR may not be renormalizable, it is a perfectly good effective quantum field theory at low energy.

Asymptotic safety is the search for other fixed points of the renormalization flow that would render pure gravity renormalizable, so that gravity could remain a good quantum field theory to arbitrary high energies, and possibly be a fundamental force. A great resource is http://www.percacci.it/roberto/physics/as/index.html.

Within approaches like string theory, gravity is not fundamental and is seen to be just one aspect of something more fundamental. The major theorem constraining what this more fundamental theory is is the Weinberg-Witten theorem, which says the theory cannot be a 4D Lorentz invariant quantum field theory (though it does not rule out Sakharov's induced gravity approach, for reasons I don't understand). Some examples of this philosophy are http://arxiv.org/abs/1009.5127 , http://arxiv.org/abs/1011.5754.

 

[Fra]

The last posts has focused on the PI over the space of gravitational fields. From a technical perspective this integral seems to be a natural focal point between QM and GR as it seems simple, yet confusing. As everyonye usually points out when talking about this is that the PI is not really something well defined. It's just a symbols that looks like mathematics but which merely rather is a statement of intent. It expresses an IDEA of what logic to apply, but the exact details are missing.

The idea is to use the QM principles for computing an expectations; you simply ADD all possibilities according to their COUNTS, where the ADDITION is made according to quantum logic and superposition principles.

Usually we just use the reciepe and start from classical actions one way or the other and then defined the quantum operators as per som quantisation trick from the classical (q,p). And we plug it in.

After some renormalizations this usually works out.

But I think it's fair to say that this procedure is not well understood even before trying to put in GR. It's gets more ill behaved when putting in GR.

So what's the analysis that Rovellis does of this situation?

As far as I understand him, as which is the impression you easily get also from the paper "unfinished revolution" Martin quote earlier, that Rovelli's thinks that either you accept QM, or you seek to restore realism. We may not agree on that analysis, but nevertheless hence Rovelli has no ambition as I see it to question the QM scheme.

As I see it, his idea is to find in the theory of Gravity, a new set of variables; the RIGHT set of variables, that makes the QM scheme work out (=to be computable and be at least mathematically well defined).

As I see it, that's what this is all about, the NEW variables of GR. If that works, it would indeed be very nice. The question is then also if the same trick works when matter is added.

Correct me if I mischaracterise anything but I think this is also why Marcus spendts quite a lot of great energy into trying to explain geometry without space time etc. It's ultimately about describing "gravity" in NEW variables. And when expressed in these NEW variables, we hope that the Path integral would be easier to define.

/Fredrik

 

[atyy]

I would say ever since Wilson, renormalization is well understood.

 

[Fra]

I would say ever since Wilson, renormalization is well understood.

There are different flavours of understanding IMO. Obviously there is a good deal understanding, but wether it's sufficient for our purposes I'm in great doubt.

Anyway, that's only half the issue. What about quantum logic implicit in the feymann PI prescription. IMO, there is not yet a satisfactory understanding this that makes me happy.

(The ambition of RG, is to adress how "theories" or "force laws" SCALE with observational scale. I don't want to derail anything here but IMO both these things does connect to the quest for the observer dependnet inside views I always bring up when you insist that this can be done by scaling the observer; which is different from scaling the observers microscope. Two different things, becaue the theory still is encoded behind the microscope in the latter scale and doesn't need rescaling. But we shouldn't discuss that here.)

But anway, this is exactly the point of disagreement. IS our understanding of QM enough? our RG theory good enough?

As I read it, Rovelli takes QM formalism without questioning, and thinks the "problem" is that were using the wrong variables as observables. Or would anyone disagree with this simple characterisation of Rovelli's thinking?

Before I started reading Rovelli's book, I thought rovellis attempting something else; by generalizing the spin-networks to general action networks that would apply also to matter, and which could represent the microstructure of the observer. Maybe that's still possible, but my conclusion was thta it was at least not rovellis original idea, just my projection.

/Fredrik

 

[atyy]

I agree with your point about QM (unless one accepts many worlds). I would prefer to reject many worlds (in its original form), and hope that something like quantum darwinism works or if someone can find a way to make QM emergent (Bohmian?). Why do QM and QG both point to nonlocality - coincidence or not?

Also, how does AdS/CFT fit in with this? It is naively a working theory of quantum gravity, maybe not of our universe, but one would imagine that all the issues of QM apply to it.

 

[Fra]

I agree with your point about QM (unless one accepts many worlds). I would prefer to reject many worlds (in its original form), and hope that something like quantum darwinism works or if someone can find a way to make QM emergent (Bohmian?). Why do QM and QG both point to nonlocality - coincidence or not?

Maybe we are in reasonable agreement on this. I don't think it's a coincidence, but the non-locality is only apparent IMO. In fact the nonlocality is the result of sticking to too much realism. If you drop some structural realism and isntead adhere to darwinian style views, a lot of apparent nonlocality goes away.

I feel confidence that at some point a new understanding will come. But I'm not seeking to restore realism like bohmians.

Rovelli's characterization in the paper of unfinished revolution paints a picture that either QM is exactly right or you try o restore realism which I think is a pretty blunt characterization that ignores other more subtle views.

/Fredrik

 

[inflector]

The last posts has focused on the PI over the space of gravitational fields. From a technical perspective this integral seems to be a natural focal point between QM and GR as it seems simple, yet confusing. As everyonye usually points out when talking about this is that the PI is not really something well defined. It's just a symbols that looks like mathematics but which merely rather is a statement of intent. It expresses an IDEA of what logic to apply, but the exact details are missing.

The idea is to use the QM principles for computing an expectations; you simply ADD all possibilities according to their COUNTS, where the ADDITION is made according to quantum logic and superposition principles.

...


But I think it's fair to say that this procedure is not well understood even before trying to put in GR. It's gets more ill behaved when putting in GR.

So what's the analysis that Rovellis does of this situation?

As far as I understand him, as which is the impression you easily get also from the paper "unfinished revolution" Martin quote earlier, that Rovelli's thinks that either you accept QM, or you seek to restore realism.

As I read it, Rovelli takes QM formalism without questioning, and thinks the "problem" is that were using the wrong variables as observables. Or would anyone disagree with this simple characterisation of Rovelli's thinking?

I agree with your point about QM (unless one accepts many worlds). I would prefer to reject many worlds (in its original form), and hope that something like quantum darwinism works or if someone can find a way to make QM emergent (Bohmian?). Why do QM and QG both point to nonlocality - coincidence or not?

Rovelli's characterization in the paper of unfinished revolution paints a picture that either QM is exactly right or you try to restore realism which I think is a pretty blunt characterization that ignores other more subtle views.

(emphasis mine in all above quotes)

Nice topic so far, thanks marcus for keeping the focus tight (and leaving us little room to wander down our respective favorite rabbit holes).

As someone who has been trying to come up to speed on quantum gravity (QG) over the last several years with little prior knowledge, I've noticed the assumption that Fra notes above which seems to me to be quite strongly evident in the entire non-string QG community.

This surprised me at first because one of my first introductions to QG as a problem was reading Smollin's The Trouble with Physics wherein he described two different approaches, the String Theory approach which he characterized as starting with QM, and the LQG approach which Smollin characterized as starting with the principles of GR instead (I can't find the exact words as I'm not home where I have the book but visiting relatives for the holidays). To me, GR has two core principles, background independence and continuous geometry. I believe that what Smollin meant by the idea that LQG starts with the principles of GR is really a statement about the first core idea, background independence and decidedly not about continuity.

Rovelli agrees with this perspective. Note Rovelli's comments from the bottom of page 2 in Unfinished Revolution, the introduction to his book on QG that marcus pointed us to above, http://arxiv.org/abs/gr-qc/0604045:

Roughly speaking, we learn from GR that spacetime is a dynamical field and we learn from QM that all dynamical field are quantized. A quantum field has a granular structure, and a probabilistic dynamics, that allows quantum superposition of different states. Therefore at small scales we might expect a “quantum spacetime” formed by “quanta of space” evolving probabilistically, and allowing “quantum superposition of spaces”. The problem of quantum gravity is to give a precise mathematical and physical meaning to this vague notion of “quantum spacetime”.

(emphasis mine)

So it is pretty clear that Rovelli assumes that this idea is a given and indisputable as he defines quantum gravity as the search for the solution to the formulation of "quantum spacetime."

In all this, it seems to me that little attention, by comparison, is being paid to the idea of taking both key insights of GR as fundamental, i.e. both background independence and continuity. The Bohmian-approach that Fra alludes to as typified by Benjamin Koch in Quantizing Geometry or Geometrizing the Quantum?: http://arxiv.org/abs/1004.2879, for example, is this third approach and one that does not take QM as fundamental. From Koch:

Given the problems in applying the laws of quantum mechanics to the geometry of space-time we want to ask the following question: “Could it be that (classical) geometry is more fundamental than the rules of quantization?”

Now, if one is going to take the position that LQG starts with GR's principles, then it seems to me that this is missing the second important aspect of GR, namely the idea of continuous geometry. Is geometry continuous? GR says it is. So Koch's Bohmian approach seems the one that takes GR seriously and looks at the idea that QM is emergent whereas LQG assumes that QM takes precedence and the observed continuity of GR is emergent. Therefore Smollin's characterization of the dichotomy between the LQG approach and the String Theory approach to quantum gravity is incomplete and misleading.

 

[atyy]

@inflector: Not sure about Smolin, but Rovelli says it's quantum field theory versus general relativity - not quantum mechanics versus relativity. (I don't agree much with Rovelli's philosophy, but would this make more sense to you as the conceptual background to Rovellian LQG?)