Is the GLO definition of emergence a good one? (Girelli Livine Oriti)

[marcus]

This is how GLO define emergence on page 18 of their March 2009 paper:

http://arxiv.org/abs/0903.3475

Let us first of all clarify what we mean by emergence. We call “emergent” some degrees of freedom which are only defined in a given regime, and there in terms of more fundamental degrees of freedom. For example, emergent degrees of freedom can be perturbations around some given vacuum state, like in our GFT results, or collective degrees of freedom. In general, the classical theories for these emergent degrees of freedom only give effective theories upon quantization, in other words their quantum counterpart would be meaningful only in a limited regime. A complete quantization procedure can therefore take place only on the fundamental degrees of freedom. A symmetry is called “emergent” if it applies to emergent degrees of freedom only and thus is valid only in the same limited regime in which they can be consistently defined. In general, the emergent symmetry is not related to nor part of the symmetries of the fundamental system. Moreover, if the emergent symmetry is not already among the fundamental symmetries, then it is never exact but it is realized only approximately in the effective theory.

To illustrate what they are saying, we could look at the idea of pressure. The pressure of the gas inside a box. Say there are 1000* helium atoms in the box and the classical system is described by 6000 degees of freedom, for each atom we have 3 position and 3 momentum.

The pressure would be "emergent" in the sense described here. It would only be meaningful in a limited regime---not too cold, not too dense, etc. If you quantized the pressure and got a quantum theory of the pressure it would not be meaningful except in a very limited way. And the pressure could, in principle, be expressed IN TERMS OF the more basic 6000 degrees of freedom

*here 1000 stands for some much larger number

I think the pressure is an example of what GLO refer to as "collective degrees of freedom".

 

[atyy]

Well, that's pretty much what I mean when I use the word "emergent". I believe Jacobson and Verlinde too intended the GLO meaning in their papers. In the GLO sense, AS is the approach in which gravity is clearly not emergent. "First, the gravitational field itself is taken seriously as the prime carrier of the relevant classical and quantum degrees of freedom. http://relativity.livingreviews.org/Articles/lrr-2006-5/ "

Smolin acknowledges this usage, but also suggests a different one in his latest paper. I think CDT folks used to use the word in the Smolin sense, at least while it was looking like AS. But now that CDT is looking more like Horava, I guess they are using it in the GLO sense.

 

[Fra]

We call “emergent” some degrees of freedom which are only defined in a given regime, and there in terms of more fundamental degrees of freedom.

I would like to know if with "more fundamental" they actually mean

a) "more fundamental than the emergent degrees" - in which case I think it's good, or if they mean that

b) there has to exist a set of absolutely fully fundamental degrees of freedom, from which the emergence is defined from more of these (ie. "more" as in larger numbers!)- that would not be something I think is viable.

I also think "given regime" can be interpreted in at least a couple of ways. I do not think that any universal "set of regimes" can be observer independent, therefor there may still be IMO a distinction here between something one might call deterministic emergence or just undecidable emergence that is only emergent by evolution. The deterministic description of regimes are replaced by uncertain, but still guiding expectations.

Maybe effective theories is all there is, and all we can do is try to understand how effective theories relate as a function of the corresponding relations between the observers encoding them?

But I think the statistics example of pressure is good, but since the atom in turn, might be emergent from even more fundamental degrees of freedom, all we have are hiearchies of degrees of freedom. And each observer can only see a "window" here, surrounded by an effective horizon which limits information resolution.

To me an important difference is if you see the emergent as happening on an absolute complexity scale, or if you see it all as windows along an hierarchy scale whose absolute existence infact does not matter.

But for effective purposes one can also say that each observer has their own "absolute scale" but which is of course subjective.

Objectivity is also then only effective as negotiated democrazy. Disagreeing parties interact until some level of objective consensus emerges that's defined as "absolute" only for the local interaction group.

/Fredrik

 

[Fra]

statistical selforganisation vs evolution

In this context I see two distinctions that I think is partly like the external vs internal view of the same phenomena.

Consider so called statistical self-organisation where a large number of degrees of freedom code states that can be considered to emergy a statistically preferred microstate, and where the equilibirum state has a certain symmetry that perturbed state does not. This is one view of things, that is valid in the external view, which is complex enough to distinguish the system with a large resolution, and just not the expected self-organisation as an internal self-equilibration (closed system).

The other view, is of an inside observer that is doing a random walk and have to respond to unpredictable feedback from the environment during this walk, the random walker can not predict his own future. So the "emergent" inside-view is really just like an evolution, where the focus is not on deductions of future states, but only the responses to actual feedback.

I think both views are partially valid, but we need both the inside and the effective-outside view to make sense to the overall picture.

I think the effective nature of the external picture is exactly what smolin means when he says that timeless nature of law is only "effective" when we study small quasi-isolated subsystems. It breaks down if we consider cosmological models. I think it's philosophically and conceptually wrong to think of stats of the universe, in the same statistical way we think of states of the atom.

I think the message here applies also to "emergence". The external view corresponds IMO to "deterministic emergence" and the inside view corresponds to "evolution".

The interesting question is I think wether trying to see the "inside picture" makes it easier to understand the particular symmetries we have also in particle physics? Because, after all, the elementary particles are themselves inside observers. This is I think the relevance to this objection also in particle physics, not ONLY cosmology. There is a connection here since the inside view of an elementary particle would be to him, what "cosmology" is to humans?

/Fredrik

 

[oldman]

...I think the pressure is an example of what GLO refer to as "collective degrees of freedom".

I like very much your giving pressure as an example of what is meant by an emergent force (or is it a degree of freedom?) The concept of pressure as a resultant force simplifies the description of a impossibly complex situation, never to be understood by impractical n-body calculations of involving six classical degrees of freedom per particle.

Examples are of the essence when defining a muddy but useful word like emergence.
But GLO use concepts that are themselves ill-defined in physics, like "regime" and "degrees of freedom (emergent or fundamental, perturbations or collective)" without giving specific examples.

I much prefer the discussion given by Smolin in his The Trouble With Physics (p.132 Penguin edition), where the example of phonons in solids is used. But one gets the gist of what GLO are sensibly trying to say.

Having defined "emergence", what about some other useful but muddy concepts that give some people trouble (I'm an example), with the help of specific familiar examples? Such as "effective theory", "entropic force" (pressure again?) and "holographic principle". They crop up quite often in this forum.

 

[Finbar]

Well, that's pretty much what I mean when I use the word "emergent". I believe Jacobson and Verlinde too intended the GLO meaning in their papers. In the GLO sense, AS is the approach in which gravity is clearly not emergent. "First, the gravitational field itself is taken seriously as the prime carrier of the relevant classical and quantum degrees of freedom. http://relativity.livingreviews.org/Articles/lrr-2006-5/ "

Smolin acknowledges this usage, but also suggests a different one in his latest paper. I think CDT folks used to use the word in the Smolin sense, at least while it was looking like AS. But now that CDT is looking more like Horava, I guess they are using it in the GLO sense.

Well so far the evidence for AS has mostly come from the functional RG approach which is very closely related to effective field theory. So I wouldn't rule out a connection to emergent gravity ideas. Maybe the UV fixed point will disappear with some truncation of the effective action indicating that the metric is not the correct degree of freedom to use on a fundamental level.

How does Smolin's sense of emergent differ?

 

[atyy]

How does Smolin's sense of emergent differ?

I don't know, but he says it's different. It's in the discussion of http://arxiv.org/abs/1001.3668. Yes, agreed that the current evidence of a fixed point is not rigorous in studies of AS, and may actually be due to from something else, as CDT folks are beginning to suspect. Mainly just using AS, if it exists, as the definition of non-emergent.

 

[Finbar]

I don't know, but he says it's different. It's in the discussion of http://arxiv.org/abs/1001.3668. Yes, agreed that the current evidence of a fixed point is not rigorous in studies of AS, and may actually be due to from something else, as CDT folks are beginning to suspect. Mainly just using AS, if it exists, as the definition of non-emergent.

Hmm, still I wouldn't be so sure as to say that ideas of AS and emergence as exclusive. AS, as supposed to asymptotic freedom, implies that there is some fundamental interactions which occur at the UV fixed point. Whatever this interacting theory is it will surely not look like general relativity and these interacting degrees of freedom will not be gravitons. Gravity is almost the reverse of say QCD where physics is perturbative in the UV(i.e. it can be understood in terms of quarks and gluons) and non-perturbabative in the IR(where quarks and gluons are no longer degrees of freedom).

 

[atyy]

Hmm, still I wouldn't be so sure as to say that ideas of AS and emergence as exclusive. AS, as supposed to asymptotic freedom, implies that there is some fundamental interactions which occur at the UV fixed point. Whatever this interacting theory is it will surely not look like general relativity and these interacting degrees of freedom will not be gravitons. Gravity is almost the reverse of say QCD where physics is perturbative in the UV(i.e. it can be understood in terms of quarks and gluons) and non-perturbabative in the IR(where quarks and gluons are no longer degrees of freedom).

Yes, the Einstein-Hilbert action is "emergent" in some sense even if AS exists, since AS works with the most general generally covariant action. However, the fundamental degrees of freedom are the same in the sense that it is still a generally covariant action in the metric field (and actually, those terms should be there anyway since the equivalence principle and "no prior geometry" that underlie general relativity cannot exclude them).

I guess roughly speaking I would say the question is: is the "renormalization group" is a "group" or a "semi-group"?

 

[Finbar]

Yes, the Einstein-Hilbert action is "emergent" in some sense even if AS exists, since AS works with the most general generally covariant action. However, the fundamental degrees of freedom are the same in the sense that it is still a generally covariant action in the metric field (and actually, those terms should be there anyway since the equivalence principle and "no prior geometry" that underlie general relativity cannot exclude them).

I guess roughly speaking I would say the question is: is the "renormalization group" is a "group" or a "semi-group"?

http://arxiv.org/abs/0811.3888

"The most important motivation, at least from a conceptual point of view, is probably the following. In our approach the primary definition of the quantum field theory is in terms of an EAA-trajectory with a UV fixed point. Its endpoint is the ordinary effective action Γk=0, so we can easily compute all Green’s functions. However, what we have no easy access to is the microscopic (or “classical”) system whose standard quantization gives rise to this particular effective action."

So you see its not clear what the microscopic degrees of freedom are that are being quantized such that we get generally covariant effective action.