Is Entropic Gravity the Future of Physics?

[MTd2]

Marcus, Erik indeed thinks gravity does not exist. Check this radio interview out:

http://www.thetakeaway.org/2010/jul/14/argument-against-gravity/

The way I think out of this is imagining a nonquantized space time where it has a texture of rubber, where it bends according to entropy, not matter. And this rubber, by itself, is made of nothing, so it is like a space time without any self interaction. It is a perfect void.

 

[my_wan]

Marcus, Erik indeed thinks gravity does not exist. Check this radio interview out:

http://www.thetakeaway.org/2010/jul/14/argument-against-gravity/

The way I think out of this is imagining a nonquantized space time where it has a texture of rubber, where it bends according to entropy, not matter. And this rubber, by itself, is made of nothing, so it is like a space time without any self interaction. It is a perfect void.

Gravity does not "exist" is a major distortion of what Verlinde actually said. It was the interviewer who kept representing it that way without correction, whereas Verlinde was merely attempting to convey that gravity wasn't a fundamental force, i.e., it was derivable.

 

[my_wan]

This question of the existential nature of gravity has taken several forms. Started out with Newton, in which it was an existential force. The Einstein represented it as a force free geometry, which could be described as non-existent wrt force. What Verlinde is actually claiming as non-existent is gravity as a 'fundamental' property. It's on par with claiming temperature is non-existent on the grounds it's derivable from mechanics, but spacetime doesn't specify a consistent mechanics to embed the thermodynamics.

Non-existence has taken on different meanings in different context. It's basically semantics.

 

[MTd2]

Yes, right, that's what we understand from his paper. But there is more to that when he says there is no gravity. For example, suppose we have an action for gravity and try to quantize that. But whatever method we have or theory, quantizing gravity does not make sense because there is no microstates for pure gravity, but just microstates for fields on space time. So, there is no graviton (consequently no string theory), no loop, no spin foam that leads to gravity.

 

[Fra]

quantizing gravity does not make sense because there is no microstates for pure gravity

This phrase makes good sense to me - there is no such thing as "pure gravity" in a measurement theory, since all measurements requires a non-trivial complexity with observers.


/Fredrik

 

[marcus]

So, there is no graviton (consequently no string theory), no loop, no spin foam that leads to gravity.

Good! You have effectively made a prediction. It might be stated as: nobody (say in the next 3 years) will come up with a version of LQG (including spin foam models) with the right largescale limit.

I think your position predicts this because, according to your view, that cannot happen. It would be a version of LQG that leads to gravity---leads to the right classical behavior, which is presumably GR or something very close to it. According to you, that line of development must inevitably slow down and come to a halt.

We can see who is right, over the course of some arbitrary timeframe like 3 years (or less if you prefer). I have different views and expectations from yours. I see indications that people are rapidly nearing the point of demonstrating the correct limit behavior. This keeps being verified in more special cases. I could be wrong of course, but my impression is that the positive results are coming more and more frequently. It is a time of rapid progress in the program, not a time of "slowing to a halt".

Certainly matter must be included in the dynamics. This is in progress. So far rudimentary matter can already be included in the kinematics, and also is already included dynamically in LQC models. But I don't know of it being included in the dynamics of the full LQG theory however. Maybe someone can tell us what the situation is in that regard.

Your argument "no graviton therefore no string theory" makes a certain amount of sense. But it does not carry over to LQG.

The graviton is not natural to LQG, one has to work hard to artificially constrain the states to be flat and only then, after a struggle, one gets something that looks like a graviton propagator. LQG is not about a fundamental force, it is a quantum theory of the disturbances of geometry. The characteristic observables are of geometric measurements like area and volume.

It is very natural that the micro DoF that determine area and volume expectations should have entropy and temperature. This is just the picture that Verlinde was talking about when he referred to the heat bath and the entropic force along a polymer chain. Micro DoF able to assemble themselves in various configurations. Spin network dynamics, and at large scale, spin network thermodynamics. Verlinde just didn't happen to mention that possible realization of his idea.

The notion that "no graviton" implies no LQG seems like an odd conclusion.

 

[MTd2]

Hmm. If LQG is not about gravity, what is the "G" doing there? '

 

[marcus]

Like the old saying goes, "gravity=geometry". LQG is obviously about gravity, because it is about geometry (which GR teaches us is the correct way to look at gravity).
QG has come to have the double meaning of quantum geometry/gravity.
You know all this, no need to say it really. No need to kid around either: that's what the G in LQG stands for and you know it.

Personally I don't think flat space exists (it is only more or less well-approximated by dynamic curved geometries) and I don't think any mathematical theory deserves to be called QG unless there is some mathematical entity in the formalism which represents the geometry of the universe.

Or at least the underlying degrees of freedom from which the geometry of the universe emerges.

So field theories, like conventional QFT, which are based on classical flat geometry, cannot be right. I assume that the quantum field theory of all matter fields will eventually be carried over and defined on a quantumdynamic geometry.

Various ways have been proposed to do this. What comes to mind are proposals which involve labeling the nodes and links of spinnetworks with extra matter field labels.

 

[MTd2]

] (which GR teaches us is the correct way to look at gravity).

Almost the correct way because there is no gravity as a fundamental force. There is no gravitational field. Gravity does not have a Lagrangian nor Hamiltonian just like there isn`t any of these for a continuous flux of 1 atom of the oxygen inside H2O.

The nature of things are too different to name the entropic attraction as gravity when you are looking at very tiny levels. It is better then to call LQG as Loop Quantum Geometry, no gravity. It is like call an isolated atom of hydrogen inside H2O as water.

 

[marcus]

... It is better then to call LQG as Loop Quantum Geometry,..

Indeed I often do think of LQG in exactly that way. And for me, that has always meant the same as Loop Quantum Gravity because, as members of the community often point out, gravity IS geometry.

Gen Rel teaches us that the gravitational field is not a field of force or a field of "gravitons". The gravitational field is simply, and nothing else but, the geometry.

Typically (according to vintage 1915 Gen Rel) the geometry is described by an equivalence class of metrics. The essential web of geometric relationships among events that remains after one throws away every specific spacetime manifold and all systems of coordinates.
This is what Gen Rel has been trying to tell us for almost 100 years. Gravity is a responsive geometry on top of which other fields are to be defined. Except in an approximate sense it should not be treated as a force operating in flat geometry (à la "gravitons" of string.)

 

[atyy]

Almost the correct way because there is no gravity as a fundamental force. There is no gravitational field. Gravity does not have a Lagrangian nor Hamiltonian just like there isn`t any of these for a continuous flux of 1 atom of the oxygen inside H2O.

The nature of things are too different to name the entropic attraction as gravity when you are looking at very tiny levels. It is better then to call LQG as Loop Quantum Geometry, no gravity. It is like call an isolated atom of hydrogen inside H2O as water.

In Verlinde's view, gravity=geometry. Hence if gravity is not fundamental, neither is geometry. Both gravity and geometry are emergent.

http://arxiv.org/abs/1001.0785 "Of course, Einstein's geometric description of gravity is beautiful, and in a certain way compelling. Geometry appeals to the visual part of our minds, and is amazingly powerful in summarizing many aspects of a physical problem. Presumably this explains why we, as a community, have been so reluctant to give up the geometric formulation of gravity as being fundamental. But it is inevitable we do so. If gravity is emergent, so is space time geometry. Einstein tied these two concepts together, and both have to be given up if we want to understand one or the other at a more fundamental level."

 

[MTd2]

Well, if that`s the case, we need some kind of spin foam formulation. Spin foams do not have a geometric description of gravity.

 

[marcus]

Well, if that`s the case, we need some kind of spin foam formulation. Spin foams do not have a geometric description of gravity.

I think I understand, and I agree.

Maybe there is a semantic confusion surrounding what Atyy says. The LQG focus is on finding the microscopic DoF from which conventional geometry emerges.

Conventional "diffy manifold" geometry is, indeed considered NOT fundamental.
One looks for something deeper from which the traditional manifold geometry emerges.
And therefore also must gravity emerge.

Spin networks are not conventional geometry (they are combinatorial objects).
Spin foams are not conventional geometry (they are the diagrams describing evolution of spin networks)

OK! So I see what you are saying!

Atyy puts forward the view that neither conventional manifold geometry nor the "force" picture of gravity is fundamental. One response is to say well therefore what we need is LQG with networks and foams, because those things emerge from the combinatorial objects (with which we can moreover do computations.)

 

[MTd2]

Marcus, I have a little dirty homework for you. Tell me the list of finite list of finite subgroups of SU(2). Next, think of surfing and foams.

 

[marcus]

Marcus, I have a little dirty homework for you. Tell me the list of finite list of finite subgroups of SU(2). Next, think of surfing and foams.

The irreducible representations correspond to half-integers...but finite subgroups is something different.
I can't tell you the classification. I would have to walk onto campus tomorrow and look it up at the math library.
I think the classification of the finite subgroups of SU(2) may be available in this book by a former teacher of mine.
Joseph A. Wolf, Spaces of Constant Curvature (1967 McGraw-Hill).

You are younger than I am. Please tell me your idea and don't make me work for it. Probably Heaven will reward you. And in any case I would not succeed in guessing your idea even if I did go look up the SU(2) subgroups.

===================
Wait! I used google and found something more recent about the finite subgroups of SU(2). Maybe everybody knew this except me. It was over my head. Too technical. But seemed quite interesting. The paper is by Wulf Rossman.
http://arxiv.org/pdf/math/0307121

It refers to a discovery by John McKay and also to some followup work by Bertram Kostant (who was at that Banff Lisi workshop)
Here is from the introduction:

"In 1980 McKay announced his astounding discovery that the finite subgroups of
SU(2) are in natural 1-1 correspondence with the extended Coxeter-Dynkin graphs
of type ADE in the following way..."
====================

I have to pass on your homework. But please tell me what you have in mind.

 

[MTd2]

http://www.pnas.org/content/81/16/5275.full.pdf

One of them is E8. This looks like the one with the highest entropy out of all finite subgroups, due its more homogenous distribuition (basically a superposition of 2 600 cell polytope). So, we could we expect that one likely spins to organize around some kind of E8 quantum ressonant state, somewhat similar to phonoms. Make the system colder and colder and we would get E8 broken, because other levels of ressonance would dominate, like the particles of the SM. Well, this is how I think we could get particles from a spin foam...

 

[Fra]

Well, if that`s the case, we need some kind of spin foam formulation. Spin foams do not have a geometric description of gravity.

Or some information theoretic style formulation; which after all, is the natural home of entropic type inferences? But this direction of the quest essentlally conincides with a better understnding of the foundations of QM.

As far as LQG goes, what I seek is a first principle motivation for the spin networks, that does not use backward-arguments from reforulated GR. With some imagination that might be possible, if you instead consider "action networks" that live in more abstract state spaces, but each time I've tried to read up details on that at least from rovelli it's clear to me that is *not* how He sees it.

/Fredrik

 

[my_wan]

Yes, right, that's what we understand from his paper. But there is more to that when he says there is no gravity. For example, suppose we have an action for gravity and try to quantize that. But whatever method we have or theory, quantizing gravity does not make sense because there is no microstates for pure gravity, but just microstates for fields on space time. So, there is no graviton (consequently no string theory), no loop, no spin foam that leads to gravity.

Funny thing is that Verlinde stated in that paper that it was consistent with string theory, as far as he knew. Makes you wonder what entropy is without microstates to...

 

[atyy]

Funny thing is that Verlinde stated in that paper that it was consistent with string theory, as far as he knew. Makes you wonder what entropy is without microstates to...

The graviton is not fundamental in string theory.

 

[MTd2]

Actually, gravity is the first consistency check for string theory (besides having no ghosts):

http://www.superstringtheory.com/basics/basic5a.html

 

[rod_worth]

Here's my two-cents worth of emotional analogy: String Theory is the modern equivalent of epicycles; modify it until it works.

 

[humanino]

CDT---an Entropic Theory of Quantum Gravity
J. Ambjorn, A. Goerlich, J.Jurkiewicz, R. Loll
(Submitted on 15 Jul 2010)

In these lectures we describe how a theory of quantum gravity may be constructed in terms of a lattice formulation based on so-called causal dynamical triangulations (CDT). We discuss how the continuum limit can be obtained and how to define and measure diffeomorphism-invariant correlators. In four dimensions, which has our main interest, the lattice theory has an infrared limit which can be identified with de Sitter spacetime. We explain why this infrared property of the quantum spacetime is nontrivial and due to "entropic" effects encoded in the nonperturbative path integral measure. This makes the appearance of the de Sitter universe an example of true emergence of classicality from microscopic quantum laws. We also discuss nontrivial aspects of the UV behaviour, and show how to investigate quantum fluctuations around the emergent background geometry. Finally, we consider the connection to the asymptotic safety scenario, and derive from it a new, conjectured scaling relation in CDT quantum gravity.

 

[Haelfix]

That abstract and paper is a good example of advertisement in theoretical physics. Its basically the standard CDT story to the T (albeit written well, its one of the better review papers for CDT on the market).

The authors pay lipservice to just about every other approach in the field, and only write 2 handwavey sentences about Verlinde's ideas (which admittedly is the very definition of handwaving in theoretical physics).

Its designed as a 'cite me' paper, most likely to raise some needed funding for better computers or somesuch.

 

[Orbb]

A brief comment about the direct quantization of gravity: I think it does make sense to quantize gravity even perturbatively as long as you restrict yourself to a limited energy regime. It works perfectly fine for computing quantum corrections to classical gravity as an effective field theory. Jacobson was pointing out that quantizing gravity makes no sense in the thermodynamic picture, but I think he has refrained from this statement. It is similar to condensed matter systems: Phonons are quantized sound waves. They are collective excitations and an emergent phenomenon. Still, they exhibit quantum properties. Compare this also to Fermi theory: it doesn't use the 'fundamental' degrees of freedom and is nonrenormalizable, but still it's convenient for some calculations.

(Of course, there are other questions that cannot be answered in such an effective treatment and that need to be adressed in a nonperturbative quantum theory of the underlying degrees of freedom)

 

[qsa]

http://arxiv.org/PS_cache/arxiv/pdf/1003/1003.2312v3.pdf

Statistical Origin of Gravity

Rabin Banerjee, Bibhas Ranjan Majhi†
S. N. Bose National Centre for Basic Sciences,
JD Block, Sector III, Salt Lake, Kolkata-700098, India

Abstract

Starting from the definition of entropy used in statistical mechanics we show that it is
proportional to the gravity action. For a stationary black hole this entropy is expressed as S = E/2T , where T is the Hawking temperature and E is shown to be the Komar energy. This relation is also compatible with the generalised Smarr formula for mass.

 

[marcus]

http://arxiv.org/PS_cache/arxiv/pdf/1003/1003.2312v3.pdf

Statistical Origin of Gravity

Rabin Banerjee, Bibhas Ranjan Majhi†
S. N. Bose National Centre for Basic Sciences,
JD Block, Sector III, Salt Lake, Kolkata-700098, India

Abstract

Starting from the definition of entropy used in statistical mechanics we show that it is
proportional to the gravity action. For a stationary black hole this entropy is expressed as S = E/2T , where T is the Hawking temperature and E is shown to be the Komar energy. This relation is also compatible with the generalised Smarr formula for mass.

For more information about the Banerjee Majhi paper see http://arxiv.org/abs/1003.2312
The abstract page indicates that it will be published in Physical Revlew D.
Even though it first appeared as recently as March 2010, the paper already has 17 cites.

Here is a brief quote from the introduction, just to serve as a sample:

"There are numerous evidences [1, 2, 3] which show that gravity and thermodynamics are closely connected to each other. Recently, there has been a growing consensus [4, 5, 6] that gravity need not be interpreted as a fundamental force, rather it is an emergent phenomenon just like thermodynamics and hydrodynamics.

The fundamental role of gravity is replaced by thermodynamical interpretations leading to similar or equivalent results. Nevertheless, understanding the entropic or thermodynamic origin of gravity is far from complete..."

I see that MTd2 spotted the Banerjee Majhi paper when it came out and added it to our bibliography of non-string QG links.
https://www.physicsforums.com/showthread.php?p=2619817#post2619817
The abstract is in post #1124 around page 71 of the biblio thread. I am glad that one of us saw it and included the link!

 

[catilina]

If gravity depends on entropy, and entropy depends on temperature, gravity would depend on temperature, isn't it?

http://www.enginsci.cn/ch/reader/create_pdf.aspx?file_no=20091215001&flag=1&journal_id=chinaes

 

[Fra]

Recently, there has been a growing consensus [4, 5, 6] that gravity need not be interpreted as a fundamental force, rather it is an emergent phenomenon just like thermodynamics and hydrodynamics.

I just want to note that a perfectly plausible possible future for the entropic business is also in connection to Smolin/Ungers idea of evolving law in general - ie. not JUST for gravity. Rather all laws as emergent.

This idea Unger basis on analogy with evolution of social laws are IMHO a much deeper vision thatn "just" the statistical emergence (from fundamental degrees of freedom) it ALSO contains the concept of negotiation and evolution of the fundamental degrees.

understanding the entropic or thermodynamic origin of gravity is far from complete..."

I think that what the future understanding of this, has to be MORE than just the simpler form of statistical emergence based on a timeless state space.

I'm personally convinced that this idea, in combination with evolution of statespaces is viable for the future.

In this view I think essentally all forces as of entropic, and that even strong weak and EM are branches of the same process. But I think to see that, we need to look beyond statistical emergence in the sense of simple entropic flows in fixed state space, I think one needs to ackwowledge that entropy and state spaces are observer dependent and that there exists no objective measures of these things. Fundamental degrees of freedom needs to also be subject to distinguishability and observability criteria, in an intrinsic measurement theory.

In ST - I think a possible hope exists if strings, including their background are replaced by an evolving picture. But there seems to lack such ideas so far. As I see it, the string, or a system of strings is to be seen as "the observer" interaction with other strings.

In LQG - I would like to see a more inference abstraction of their spin network, that does not harcode any dimenstionality, and that picutre generically interaction networks without prior reference to notions such as geometry or manidolfs or anything like that. As I see it, the spin networks or spin foams or a system theorof could represent the observers state, and this system itneracting with other spin networks...

It doesn't seem impossible either that there is a possible convergence there in the remote future. Even if all roads lead to Rome there should be better starting points that any of those as it's clear that the original founding principels of ST and LQG seem to me to be unsatisfactory.

/Fredrik

 

[oldman]

...(I, Fra) am a advocate of a view that includes kind of "entropic forces" (as another expression of rational action which is the idea that the action of any systems basically follows "random" motion in a evolving state space) ... /Fredrik

Pardon me for butting in on such an interesting thread, populated by folk who have views much more informed than mine, but your mention of "an evolving state space" is new to me. Is a 'state space' not a cousin to Hilbert space and to the old classical phase space?

If so, such spaces seem always to be taken as a fixed backdrop against which the system being considered evolves as the point? vector? that represents the system wanders about ergodically.

But it seems to me that there are situations where the abstract space itself (or at least the rather arbitrarily drawn subdivisions in it, or boxes (as Penrose calls them) which delineate macroscopically distinguishable systems) also evolves. I tried to ask a question about this in a recent thread in the Cosmology forum (Do changes of spacetime geometry affect entropy?), but perhaps that was the wrong place to ask it. Maybe you can enlighten me, here or there, Fredrik.

 

[Fra]

Pardon me for butting in on such an interesting thread, populated by folk who have views much more informed than mine

Then I should also pardon myself. There are a lot of knowledable people here but as I see it they each represent their own perspective. These are also open question so I would assume that as long as the discussion remains intellecutally sound, the more "butting in" the better discussion.

Is a 'state space' not a cousin to Hilbert space and to the old classical phase space?

If so, such spaces seem always to be taken as a fixed backdrop against which the system being considered evolves as the point? vector? that represents the system wanders about ergodically.

Yes, that's right. This is the *standard scheme*, and the historical ones of how physics has been abstracted.

But this standard scheme (which Smolin labeled the "Newtonian scheme" in his some of his recorded perimeter-talke on evolution of law; not to be mistaken with Newtons mechanics) is the picture that is challanged by for example the smolin/Unger reasoning. It is also a picture that I personally challange.

This standard picture, of timeless laws, initial conditions and timeless state spaces, is a form in which all known physics can be cast in. Classical mechanics, stat mech, qm, gr etc.

But it seems to me that there are situations where the abstract space itself (or at least the rather arbitrarily drawn subdivisions in it, or boxes (as Penrose calls them) which delineate macroscopically distinguishable systems) also evolves.

I don't know what example you have in mind but I agree with your general statement.

I tried to ask a question about this in a recent thread in the Cosmology forum (Do changes of spacetime geometry affect entropy?), but perhaps that was the wrong place to ask it. Maybe you can enlighten me, here or there, Fredrik.

I'll look at that thread later and see what the context is and if I can relate to it.

There are several arguments and ways to see why the notion of timeless law and timeless fixed state spaces are inadequate to describe certain situations and that they are even to a certain extent "unscientific" I won't repeat all arguments here but Smolin and Unger has presented some of them, they come from biology, social theory, cellular automata and other things.

One problem with the "entropic methods" in the context of the standard scheme, is the choice of the "right" entropy measure, or the right microstructure. Because the predictions or inferences made from this, depends on this CHOICE. If you don't take this seriously, the entropic reasoning still becomes "ad hoc". This problem is something that becomes very different if you instead acknowledge that there is no such universal measure, no intial value problem - instead the problem becomes how, and why, this evolution works and to explain the emergence of the de facto effective objective structure that we are familiary with from our human classical perspecitve.

/Fredrik

 

[friend]

...,instead the problem becomes how, and why, this evolution works and to explain the emergence of the de facto effective objective structure that we are familiary with from our human classical perspecitve.

/Fredrik

I'm wondering if the idea of "evolving laws" can be described alternatively as changes in symmetry as the universe expands. It might be that there are different symmetries at work in an early, tightly curved universe that break down into more recognizable symmetries as the universe becomes more flat. This would require symmetry breaking, right? This would require a change in the physical laws, right?

 

[humanino]

That abstract and paper is a good example of advertisement in theoretical physics. Its basically the standard CDT story to the T (albeit written well, its one of the better review papers for CDT on the market).

The authors pay lipservice to just about every other approach in the field, and only write 2 handwavey sentences about Verlinde's ideas (which admittedly is the very definition of handwaving in theoretical physics).

Its designed as a 'cite me' paper, most likely to raise some needed funding for better computers or somesuch.

I agree with your comments. I think it was worth (for people at my level) both pointing to the paper, as well as making your comments. I am glad you provided the comments, as I would not have considered myself qualified to formulate them.

 

[apeiron]

I'm wondering if the idea of "evolving laws" can be described alternatively as changes in symmetry as the universe expands. It might be that there are different symmetries at work in an early, tightly curved universe that break down into more recognizable symmetries as the universe becomes more flat. This would require symmetry breaking, right? This would require a change in the physical laws, right?

Isn't this standard thinking? That cooling results in a series of phase transitions that causes symmetries to crystalise out.

But rather than tightly curved, which implies closed globally hyperspheric curvature, I would associate the early hot state with local open hyperbolic curvature. A spacetime roil which is not flat but going off in many directions. A fat spacetime, so to speak. Room for multiple symmetries to be expressed still (in fleeting manner). But with cooling, the correlation length shortens. Fluctuations in "other" directions die away quickly. There is a phase transition so that generally spacetime is thin and flat (a crystalline structure) and trapped pockets of gauge symmetry (trapped quasi-particles).

So early on, all symmetries can be globally expressed. Hot spacetime is a mess of them. There can be fluctuations in any particular symmetry over all available scales - a critical state.

Then later, with cooling and thinning, the higher symmetries are globally suppressed. They can only exist as trapped hot pockets. The laws of physics would evolve with each change of state. Though really you still want a single description of the whole process.

 

[Fra]

I'm wondering if the idea of "evolving laws" can be described alternatively as changes in symmetry as the universe expands. It might be that there are different symmetries at work in an early, tightly curved universe that break down into more recognizable symmetries as the universe becomes more flat. This would require symmetry breaking, right? This would require a change in the physical laws, right?

The notion of Symmetry is indeed closely related to the notion of physical law. However IMO, the questioning of a deeper understandin of physical law, also then implies the quest for a deeper understanding of symmetry.

The common way of thinking, to picture - in a given fixed state space - a perfect symmetry in the sense that the laws of physics are invariant with respect to that, and that this symmetry is broken down in phase transitions as the energy scale changes, to produce a set of smaller symmetries, is still tied to the "old scheme" that I think is inadequate.

Just to explain how I see it: If we like to instead use the symmetry language, evolving law, means evolving symmetries, and the radical view I advocate and which I beleivce is in line with Ungers vision is not just a simple "breaking of a perfect symmetry". The reason is that the notion of symmetry is a bit complex too, becuase if you require that "knowing the symmetries" means having information about something, one must ask how the process looks like whereby this symmetry is a result of an inference. This thing is typically ignored in the standard scheme, if one tries to explain broken symmetries from a perfect fixed master symmetry.

To establish a symmetry, ie. to establish that some action is invariant with respect to certain transformations or complexions, one first need to establish the distinguishability of these complexions. And this is actuqally qa bit paradoxal, because if you have a strict invariance, then how is it possible to make an inference about this invariance? Something with the inference is wrong here. The conclusion seems to be that symmetries by nature are always unstable and evolving, and that a symmetry needs to be challanged in order to make sense.

To take an example, consider a blind man tell you that "I am indifferent to wether your clothes are red or blue". At first that may seem sensible, but the problem is that how can a blind man, in the first place, acquire the NOTION of COLOURS? This is not consistent.

It would be different is this guy had a history, where he used to see, and thus has a prior notion of something, that he by now have concluded is redundant (a symmetry).

Edit: instead the proper behaviour would isntead be that a blind man IS invariant with respect to your colours, BUT he would never launch such a statement! Rather if you mention the word red or blue, he just would understand you.

(Of course I'm simplifying here, but I think the point is illustrated; that the notion of INFERRING an INVARIANC is subtle)

This analysis of how an observer inferes, and relates to a symmetry, really connects the set of possible symmetries to the microstructure and makeup of the observer itself. Ie. symmetries are necessarily also observer dependent, in the sense that I think we should only talk about _inferrable_ symmetries.

In the standard framework, we talk about symmetries as existing in mathematical worlds, that are not subject to scientific inference process. To me this is a serious flaw.

I agree that evolving law, can similary be phrased in terms of evolving symmetries. But just like entropy observer dependent, so are laws and so are symmetries. And I mean observer dependent in a more general sense that JUST energy scale dependent. Energy scale does set constraints or limits, of the complexity of law - this is why inferrable laws are destined to unification (all beeing one indisitinguishable interaction) as the energy scale increases (which from the inside view means the opposite! the compleixty of inside observers goes to zero - this is why encoding complex diverse law just isn't possible from an information theoretic inference persepctive)

/Fredrik

 

[John86]

A new Mathematical framework (less rigid) is than needed, maybe something transcending nowadays mathematics ?..