# FeaturedA Ed Witten on Symmetry and Emergence

1. Nov 6, 2017

### star apple

I read this interesting passage in Deep Down Things:

"For the case of regular spin, we had to take spin-space seriously because
it was associated with a concrete, measurable, physical quantity—angular
momentum. This was only mildly uncomfortable because, although spinspace
has the somewhat hard-to-stomach property that you have to turn all
the way around twice to get back to your original condition, it’s otherwise
pretty much like regular space. Isospin space, however, is completely abstract;
it bears no relation whatsoever (other than through analogy) to anything
we can grasp with our faculties of perception. How could rotations in
such a space possibly have anything to do with the physical world? And yet
the physical manifestation of the invariance of the strong force with respect
to rotations in this space, the conservation of isospin, is a solidly established
fact in the world of experimental science.
So, what then is isospin-space from a physical point of view? Physicists
usually describe it as an internal symmetry space, but what’s that, really? It’s
your old buddy again, telling you that your car’s carburetion system “works
on a vacuum principle.” How’s that going to help you to understand and fix
the thing? It isn’t.
Regarding the physical interpretation of the notion of isospin space,
again your guess is as good as mine. Perhaps its experimental manifestations
are hinting at some new and deeper truth about the universe that lies just
beyond the current limits of our comprehension. Perhaps not. But one
thing, however, is true: The introduction of the idea of internal symmetry
spaces, of which isospin space was the first example, was an essential step
forward in our understanding of the universe and the nature of the laws that
govern it."

Note The invariance of physical laws with respect to rotations in ordinary space is associated by Noether's theorem with the conservation of angular momentum. The conserved quantity associated with invariance with respect to rotation in the abstract space of isospin is isospin itself. Any connection between the two?

For those so tired of pondering quantum interpretations. It is refreshing to instead ponder on interpretations of gauge symmetry.. lol..

2. Nov 7, 2017

### no-ir

True. We should be more precise: you can make the total action gauge invariant by adding to it a boundary term that precisely cancels the gauge noninvariant contribution of the bulk theory at the boundary. Then your total action is composed of the bulk action, which would be gauge invariant if there was no boundary, and the boundary action, which ensures gauge invariance of the total action (by canceling the gauge noninvariant part of the bulk action on the boundary). The boundary action is thus completely determined by the properties of the bulk lagrangian density under gauge transformations.

Explicitly, if the bulk lagrangian density $\mathcal{L}_{\rm bulk}$ transforms as $\mathcal{L}_{\rm bulk} \rightarrow \mathcal{L}'_{\rm bulk} = \mathcal{L}_{\rm bulk} + \partial_\mu \lambda^\mu$ under gauge transformations, then define the boundary lagrangian density $\mathcal{L}_{\rm boundary} = \partial_\mu l^\mu$ such that it transforms as $\mathcal{L}_{\rm boundary} \rightarrow \mathcal{L}'_{\rm boundary} = \mathcal{L}_{\rm boundary} - \partial_\mu \lambda^\mu = \partial_\mu (l^\mu - \lambda^\mu)$. Now the total lagrangian density $\mathcal{L} = \mathcal{L}_{\rm bulk} + \mathcal{L}_{\rm boundary}$ transforms trivially under gauge transformations $\mathcal{L} \rightarrow \mathcal{L}' = \mathcal{L}$ and so the total action is gauge invariant, and as $\mathcal{L}_{\rm boundary}$ is always a total spacetime derivative it, by Gauss's theorem, really does contribute only on the boundary

Thus we have spontaneously obtained a boundary theory (boundary action) from the non-trivial gauge transformation properties of the, otherwise gauge invariant (if there was no boundary), bulk lagrangian (a nonzero $l^\mu$), when we demanded that the total action be gauge invariant. This would thus be one instance of a bulk-boundary correspondence.

P.S. Of course, in general, if the boundary is not smooth, i.e. if it has corners, we might also consider the "boundary of the (individual pieces of the) boundary", which might further have spontaneous "corner theories" induced by the non-trivial properties of the boundary theory in the presence of corners. Or in the parlance of condensed matter physics, it might have a second-order boundary theory (the "ordinary" boundary theory is called a first-order boundary theory; in general, an $n$-th order boundary theory lives on pieces of the boundary of co-dimension $n$). See e.g. this talk on higher-order topological insulators for a related discussion of higher-order boundary theories in the context of a different example of bulk-boundary correspondence (induced by non-trivial topological invariants of the bulk theory compared to the outside vacuum).

3. Nov 7, 2017

### Demystifier

In this correspondence, the boundary term is uniquely determined by the bulk term, but the bulk term is not uniquely determined by the boundary term. In this sense, the correspondence is not an equivalence (duality). Do you agree?

4. Nov 8, 2017

### no-ir

Yes, I do. In particular, the boundary term is only sensitive to the normal component of the bulk $l$ at the boundary (the scalar $n_\mu l^\mu$, where $n$ is the boundary normal), so adding to the action any bulk term with $n_\mu l^\mu = 0$ at the boundary (e.g. a bulk term with a trivial $l = 0$) does not change the boundary theory, which means that the bulk action is not uniquely determined by the boundary term (bulk theories are "richer"). The inference goes the other way: if you have a known bulk theory you can deduce from it the boundary theory (which might or might not be trivial).

It is also not a duality in the sense that here the bulk and the boundary terms are part of the same action and describe the dynamics of the same field simultaneously. They are not independent ways of looking at this dynamics, but only coupled together describe the full dynamics.

What usually "saves" you in condensed matter physics, such that you can argue that only the boundary term is relevant near the boundary and only the bulk term is relevant in the bulk, is if the bulk theory is gapped (loosely, but incorrectly: "it has mass"), while the boundary theory is gapless (or at least has a smaller gap). Then for energies inside the bulk gap the wavefunctions (or the field, in general) become localized at the boundaries and decay exponentially with distance towards the bulk, as they are in the forbidden energy range for existing inside the bulk. For quick decay (large gap) the dominant part of the action in this energy range is the boundary term as it is independent of the bulk decay rate, while the bulk contribution from these wavefunctions decreases towards zero as the decay becomes quicker. We can thus, to a good approximation, describe the states with energies inside the bulk gap using only the boundary term of the action.

This indeed happens, e.g., in topological insulators, where the bulk is insulating (gapped) and the boundary is conductive (gapless), or in certain quantum wires where the bulk is gapped while the boundary (the two endpoints of the wire) are Majorana zero modes with degenerate energy (the two Majorana zero modes behave as Majorana fermions with respect to themselves, but are non-abelian anyons under mutual exchange, making them useful for quantum computing).

Of course, if the decay towards the bulk is not sufficiently fast, or if opposite boundaries are brought closer together than the characteristic decay length, a pure boundary theory is no longer a good approximation. In the example of a short quantum wire: when the wavefunctions of the two Majorana modes start to significantly overlap in the bulk they hybridize and break their degeneracy, ceasing to behave as non-abelian anyons under mutual exchange.

So in short:
- the bulk term determines the boundary term but not the other way around (bulk theories are "richer"),
- the correspondence is not a duality as both terms are coupled in the same action,
- but under certain conditions (gapped bulk theory, states in the bulk gap) you can still approximate the dynamics by a pure boundary term,
- which is nice, as the boundary theory can be more exciting that the bulk one (e.g. emergent Majoranas and non-abelian anyons).

Last edited: Nov 8, 2017
5. Nov 8, 2017

### Demystifier

I have argued that it is actually so in all bulk/boundary-correspondence theories such as AdS/CFT.
https://arxiv.org/abs/1507.00591

6. Nov 9, 2017

### jakob1111

All this disagreement and confusion about the status of "gauge symmetry" is really puzzling. So many smart people say things that are simply not true, at least not in general. In addition to the guys mentioned above, other prominent example would be Arkani-Hamed, who also likes to stress that gauge symmetries are not physical and merely redundancies, c.f. https://arxiv.org/abs/1612.02797 or Guidice, who in his last paper writes: "Gauge symmetry is the statement that certain degrees of freedom do not exist in the theory. This is why gauge symmetry corresponds only to as a redundancy of the theory description".

Without a careful and precise definition of what they mean by "gauge symmetry" these statements simply do not have any meaning. This is really the main problem that causes all this confusion: people talk about gauge symmetry without defining exactly what they mean by that word.

For some the global group is a subgroup of the local $U(1)$ gauge symmetry. This is possible if you define all transformation of the form $e^{i \alpha_a (x) T_a}$, with arbitrary functions $\alpha_a (x)$ as local gauge transformations. Global symmetry is then a special case where the function $\alpha(x)$ that parametrizes the local transformation happens to be constant. This is a naive definition that is repeated in many textbooks and believed by most students. With this definition, gauge symmetry is, of course, not just a redundancy but physical. It's physical effects are the conservation of electrical charge, the masslessness of the photon, the non-trivial QCD vacuum etc. Therefore, with this naive definition, the statements of Witten and Schwartz quoted above do not make sense. However, it's hard to tell what they really mean. Apparently they do not use this naive definition, but they do not specify any other definition. This is a problem because there is no canonical more precise definition.

As soon as you no longer want to use the naive definition, you run into a big problem: apparently there are as many other definitions as there are authors.
• For example, Urs prefers the notion "gauge symmetry" for the compactly supported symmetries, and "gauge-parameterized gauge symmetry". for all other.
• Other authors, like Strominger, call the "compactly supported symmetries" "trivial gauge symmetries". The group of all gauge transformations modulo the trivial ones is then called "asymptotic gauge group".
• I'm pretty sure that, at least some, of the "Generalized Global Symmetries" by Davide Gaiotto, Anton Kapustin, Nathan Seiberg, Brian Willett are just another incarnation of Strominger's asymptotic symmetries.
• For another even different definition see, e.g. https://arxiv.org/abs/1405.5532, where the local symmetry is defined as a collection of infinitely many global ones. However, the difference between these global gauge transformations and the "real" global ones is that the correct global gauge group is realized linearly, while the others are not and therefore broken. (Gauge bosons are then the Goldstones of this symmetry breaking.)
(I could add lots of other examples to this list).

So to summarize:
1. Talking about the meaning of gauge symmetries makes absolutely no sense unless you specify precisely what you mean.
2. There is a real need for some kind of dictionary that translates between all these different approaches to make the definition of gauge symmetries more precise.

7. Nov 9, 2017

### Urs Schreiber

Exactly.

Actually in the above discussion I did say "gauge symmetry" for "gauge-parameterized gauge symmetry", since that is really what we mean when we say "gauge theory" (as opposed to when we speak more generally about Lagrangian field theories).

But the difference between these definitions, while important for the fine print, is not actually relevant for just seeing that there is a problem at all, that it is in general wrong to say (or even to think) that "gauge symmetry is just a redundancy": Simply consider something like Chern-Simons theory on a closed, hence compact, 3-manifold. Then the condition of "compact support" becomes automatic, and hence then no matter which definition is used, one concludes that there is more than one gauge transformation relating any field configuration and/or state, and hence the space of configurations or states modulo gauge symmetries is a groupoid or stack with non-trivial isotropy, and this is more information than the naive quotient space which reflects the "is just a redundancy" idea.

8. Nov 9, 2017

### Fra

We can see that several approach this from the mathematical theory side, and make excellent contributions here! Regardless of our main areas, I think most of us has experience with both the mathematics, logic or applied mathematics side as well as physics side and some other life sciences, and has observed that the fields sometimes requires different mindsets or approaches. My experience is that alot of mathematicians that work on applied physiscs, do so with a personal motivation slightly different that some physicists. Physicists are admittedely more sloppy and informal, or philosophical so they can focus on what they are building, rather than "respecting" the tools they use. But occasionally physicists happend to actually deform the tools and create new tools, without thinking about it. Some mathematicians feel frustration about these attitudes and feels like they have to take responsibility and make this properly. I just know from from personal relations. You can also feel this yourself, whenever you deep dive into matehematics, and proof thinking where you need to trace it all to axioms vs the sometimes more free philosophical creativity that is required to UNDERSTAND soem things in physics. Or to create for yourself what we called "mental picture".

Anyway, what i wanted to say here, is that as at the core of these discussions are a bunch of the open problems in physics, and such things can not be phrased merely as a axiomatic or mathematical terms. Its not like the question here is like, howto prove a conjecture theory from some axioms. To take the logical perspective i think it more has to do with either extenting the axioms on which theory are built, without adding inconsistencies, butit might well end up so that we need to replace some axioms!

To me the observation is this: Gauge theory and various symmetry princiiples has obviously been extremelt successful, and is at the heart of modernt physics. Why is this? Yet there seems this procedure seems to have hard time to solve some of the current open problems. Why is this?

Can we find a different angle or twist to this successful procedure, that helps us forward? That the question i have in mind when reading this thread.

That said, it is of course important to once things are mature, axiomatise and clean up the theory. I think axiomatising theories often really helps to understand the core of the theory (the axioms), you can then ponder on the one by one though by mapping the axioms to physical postulats like sometimes is done in QM for example. I think Urs insight thread about QFT is awesome work and great contributions on here.

I just feel that it is easy to sterilize discussions by insisting on the axiomatic style approach in the phase where one ponders about possible new schemas or paradigms?

I think if we can have both in parallelll that is the best of both worlds?

/Fredrik

9. Nov 9, 2017

### jakob1111

Fredrik,

reading your comment about different "mindsets" I was immediately reminded of the following quote by Tony Zee:

"Indeed, a Fields Medalist once told me that top mathematicians secretly think like physicists and after they work out the broad outline of a proof they then dress it up with epsilons and deltas. I have no idea if this is true only for one, for many, or for all Fields Medalists. I suspect that it is true for many."

Oftentimes, to make huge steps forward you need to be a bit sloppy. Only if you do incremental research you can do everything rigorous all the time. Nevertheless, before you try a huge leap forward you should have a firm understanding of the current theory.

I think the answer to this question is well known. Gauge symmetries appear because we want to describe particles with spin using fields. Particle transform according to little groups, while fields are representations of the Poincare group. Hence, fields carry too many degrees of freedom. These superfluous degrees of freedom are what we call gauge symmetry. While gauge symmetry certainly can't solve all the open problems, they can indeed solve a lot of them. If you replace the standard model symmetry with a simple group like SO(10), you get almost automatically an explanation for:

• the different strength of the standard model forces
• the tiny masses of the neutrinos
• the baryon asymmetry.
So, the explanatory power of gauge symmetry is still not exhausted. If one day proton decay is observed, lots of problems of the standard model vanish automatically.

However, of course, for other problems you have to look elsewhere.

I'm a sloppy physicist by heart. However, there are certain topics where a bit more rigor would be tremendously helpful. Gauge symmetry is probably the best example. The main problem, as already mentioned above, is that those people who try to work things out more rigorously are often not able to communicate in a way that "normal" - whatever that means - physicists can understand.

So I would like to add that we not only need both worlds, but also translators who are capable of mediating between the worlds.

10. Nov 9, 2017

### Fra

I pretty much agree with what out you said! I just felt i wanted to throw that out.
On this part though, i do not quite find your answer satisfactory. Its not that what you write is wrong, and maybe its because I secretly have something else in mind. What you write here is still living within a context with alot of baggge, alot of which is not conceptually clear to me at least.

/Fredrik

11. Nov 9, 2017

### star apple

Most interesting paragraph in witten paper is the following:

"We can see the relation between gauge symmetry and global symmetry in another way if we imagine whether physics as we know it could one day be derived from something much deeper – maybe unimaginably deeper than we now have. Maybe the spacetime we experience and the particles and ﬁelds in it are all “emergent” from something much deeper."

If gauge symmetry is emergent.. What could be the properties or characteristic of this more fundamental field by extrapolation (do you still call it field?) that create our gauge symmetry? What do Witten and other genius think about this? Since gauge symmetry is connected directly to the wave function.. does it mean the more fundamental nongauge primary field (or whatever) is not based on wave function (or QFT)?

12. Nov 9, 2017

### Fra

Yes this is the key. I can only guess, but the probable idea that fits in string thery is bulk dimensionality is emegent from boundaries. And there new symmetries form. This need to be phrased without starting from 4d continium spacetime baggage.

Ironically if you read my post#5 the two problems are initimatly related :)

The connection is motivated by

Gsuge equivalence ~ observer equivalence

In the laws of physics should be the same to all observers. This is easy to agree with but if you thimk again about the physicsl inferences look like... you may see (or at least i do) that this should be understood as a vision (or equilibrium point) NOT as as logical constraint.

Another way: observer equivalence is not a fundamental constraint in evolving law - it is merely an attractor.

/Fredrik

13. Nov 10, 2017

### star apple

Ah.. ok. i'll read in more details the papers of Urs and Demystifier. Besides boundaries.. no other candidate? how about not related to string theory?

If this is important. How come no other physicists worrying about this. And looking at archives and over the years you seemed to be the only one mentioning it and because you use language that is getting more complex.. I wonder if other physicists here can get a basic of what you were describing so hope you write a paper that gives fundamental and basic introduction to it starting with general relativity, qm and how the observers vary amongst them. Witten should worry about this if it's really important. Or maybe they are using another language, what is the language and jargon they use? I'm asking this because f feel what you were saying is important about the role of observers in GR and QM and how even the observer role in them are not compatible. Thanks.

14. Nov 10, 2017

### Fra

Conceptually this is not dependent on string theory. Its just that just to relate to other ideas to look for common denominators, rather than just find discriminators(which is usually easier but less constructive) i mentioned it. I think many research programs have merits! So why not try to see what we can learn from all of them?

And of course the bulk/boundary ideas, and specifically the holographic principle while in principle again having nothing todo with string theory, has probably is most explicit example in Ads/CFT. So associatiing to strings is natural.

Also interpreting what Witten says, in terms of string also seems natural.

(But myself does not work on string theory, but i still enjoy wittens ponderings of course)
While alot of people have been pondering over the observer and measurement problem over the years, i agree that the specific thinking i have in mind seems to be sparsely represented out there.

I have wondered why as well. One easy answer is course that i am the only one stupid enough to not see its wrong thinking.

Another answer is that i understand the resistance in this directin, because thinking this ways inavoidably LEADS you to the evolving law view. And this
strips us from many of existing tools.
Thats the remote idea of course.

My ambition is to work this out, but due to the fact that this represents non-mainstream ideas there is no context where this really fits. This means partial results would appear completely ad hoc or disconnected to physics. The closest place where the ideas might fit is into AI research, but that is still the wrong place i feelI. It takes too much energy to try to "sell things" before they are done (thats the american way of marketing). I am better of using that energy to make progress, and once its done, there are no selling costs.

So I want to make a nontrivial prediction or postdicition before i will even consider publishing anything. Unfortunately thats close to an unrealistic goal for one man, that also have a regular job. There is one advantage though and that is that the slowly grown crystals are often more perfect than the fast growin ones. I am not in a hurry and the ride is enjoyable meanwhile!

/Fredrik

15. Nov 10, 2017

### star apple

The only nongauge field is the higgs field. Is there a way to create a universe where electromagnetism doesn't come from gauge freedom where phase is the U(1).. or should all strings landscape or even smolin different black hole/universe with different laws of physics always have to reduce to gauge symmetry like U(1) of electromagnetism? What do you think? and Why? Why can't electromagnetism be like the Higgs field that is fundamental and doesn't come from gauge symmetry?

Also for that thing more fundamental or primary than gauge symmetry (which makes this emergy).. does it have to always occur in high energy (small scale)? Because electromagnetism is low energy and so can U(1) itself can derive from more fundamental nongauge low energy stuff or is this not possible because U(1) is always part of the Electroweak SU(2)XU(1) so whatever is more primary (than gauge symmetry) always have to be based on Electroweak and not merely on U(1)?

What is the connection of the incompatibility of different observers in GR and GM to evolving law (stripping us of many of existing tools)? At least Smolin mentions it so at least you have company or it's based on an authority.

16. Nov 11, 2017

### Fra

Fearing the discussing is diverging too much, i will try to keep the follow up short. As speculations arent allowed here.
IMO the physical essence of gauge theory is the concept of "observer equivalence". Ie the law of physics "must"(or must they? see below) be the same to all observers. This constraint as a constructing implies the transformations EXPLAINING the "apparent" disagreements.

In SR and GR, when you apply this to two sub-classes of valid equivalent gedanken observers. However in classical physics the observers is imagined to be able to make gedanken experiments without interacting with the system. The "physics" is contained here in the entire equivalence classes and their internal relations.

QM improves this by describing the "PHYSICS of measurementprocess", not just imaging gedanken experiments, like you can go in classical physics. Also in QM, the gageu equivalences are not as always as CLEARLY interpreted as observer equivalence as they relate to "internal symmetries". But in the below these are unified. There is no principal difference. to understand how spacetime splits off from internal structurs is a different discussion.

However, the measurement process is only PART of the complete what i call inference process.

So howto combined these?

Now, if we try to understand the old contstraint of observer equivalence in terms of inference, what does this mean? That means to say that any observer "must" infer the same laws of physics. IF you think about this, you realize soon that this is not a logical constraint, and its not generally true. It rather corresponds to an kind of equilibrium, steady state or attractor point, where interacting observers are in supporting agreement. The scenario which they do not agree, means that they exert a kind of evolutionary selctive pressure to each other so as to - "revise or die". Ie. evolution. the concept of intertia in spacetime and internal spaces, also gets it unification here. In inference the correspondence of intertia is simply the confidence in the prior, that shows resistance to conflicting new information. In this view, there is now placeholder for timeless law - it is considered "speculative" in the strict inference view.

This is just brief description, as an answer to the question. A longer attemp at explanation would be wrong. Formally all i do here is to hint, and stimulate reflections in the direction. If the above doesnt give you a hint, then cross your fingers that i will be able to work this out an publish something.

/Fredrik

17. Nov 12, 2017

### star apple

I was puzzled by this passage in Witten paper referenced in the first thread myself...

"To put it differently, global symmetry is a property of a system, but gauge symmetry in general
is a property of a description of a system. What we really learn from the centrality of gauge
symmetry in modern physics is that physics is described by subtle laws that are “geometrical.”
This concept is hard to define, but what it means in practice is that the laws of Nature are subtle
in a way that defies efforts to make them explicit without making choices. The difficulty of making
these laws explicit in a natural and non-redundant way is the reason for “gauge symmetry."

To others besides Fra, how do you understand the passage? What did Witten mean the centrality of gauge symmetry in modern physics is that physics is described by subtle laws that are “geometrical.”. He said the concept was hard to define and he only spent 2 sentences for it. At least a paragraph would be more descriptive.. kindly rewords what it means (or the way you understand it). Thanks.

Last edited by a moderator: Nov 12, 2017
18. Nov 15, 2017

### star apple

If no one really understands that passage of Witten either.. here's a simpler question.. what can serve as possible boundary/bulk in reality (in our actual universe).. can the boundary be located inside the planck scale?

19. Nov 16, 2017

### Fra

I assume you mean an explicit example where both the bulk side and boundary side has a standard interpretation without exotic stuff?
I am not aware of any, because no standard things seems to have a natural interpretation as AdS, and this is the only bulk form where i think there is an explicit duality known? Someone correct me if i am wrong.

On one hand the principle is just a mathematical duality, where one version is easier to solve or work with.

But as such a mathematical tool, one need not worry about the physical reality of the dual side, no more than one need to worry about the physical basis of changing dependet varibles. Its just a computational trick, where the boundary version is more strongly coupled and harded to compute things with.

Here is a paper with a very pragmatic name.

"...The AdS/CFT duality originated from string theory, so it had been discussed in
string theory. But the situation is changing in recent years, and AdS/CFT has been
discussed beyond theoretical particle physics. This is because AdS/CFT is be-
coming a powerful tool to analyze the “real-world.” Examples are QCD, nuclear
physics, nonequilibrium physics, and condensed-matter physics..."
-- https://arxiv.org/abs/1409.3575

And one the other hand one cant help but to ponder about if there is any conceptual generalized meaning of the principle. Geometrical interpretations is one thing, cool as it is, beeing the basis for alot, it does not add anything to my intuition, because i do not think of reality in terms of geometry, that maybe einstein did. I seek an an inferential interpretation, as that is the task i see at hand.

IMO, i see the holographic (boundary) side of things as a compressed code, that is the result of trying to encode more information in the same physical memory capacity. Obviously a compressed code is more tricky to work with, having stronger and stranger couplings between parts, than the uncompressed version. So while the bulk version may be easier to work with - it takes up more storage. So there seems to be an interplay between computation complexity and a kind of compression. These two fight each other. This is also intutive for computer users. Sometimes you have to choose between space or speed. And in an inference perspective, both this things are important. There is also lots of research on these things which fringes to computer science, but few approaches make what i think are the right combination of things.

I think we need more cross-sub-discipline thinking to solve this, and some ideas unfortunately get stuck inbetween chairs.

/Fredrik

20. Dec 7, 2017

### star apple

Fra.. when only you described the above.. and because they are not peer reviewed.. naturally serious people would tend to not take serious interest in them. So honestly I didn’t take any serious look at it. But after rereading Lee Smolin Three Roads to Quantum Gravity.. I encountered the concept of Relational Quantum Theory.. and became very interested in all you had to say. At the end of Smolin book was written

· “The present formulation of quantum theory will turn out to be not fundamental
· “The present quantum theory will first give way to relational quantum theory, according to which “the quantum state of a particle, or any subsystem of the universe, is defined, not absolutely, but only in a context created by the presence of the observer”, and there is a “division of the universe into a part containing the observer and a part containing that part of the universe from which the observer can receive information
· Eventually, the new unifying theory of physics “will be reformulated as a theory about the flow of information among events.

Wiki described RQM as “The essential idea behind RQM is that different observers may give different accounts of the same series of events: for example, to one observer at a given point in time, a system may be in a single, "collapsed" eigenstate, while to another observer at the same time, it may appear to be in a superposition of two or more states. Consequently, if quantum mechanics is to be a complete theory, RQM argues that the notion of "state" describes not the observed system itself, but the relationship, or correlation, between the system and its observer(s). The state vector of conventional quantum mechanics becomes a description of the correlation of some degrees of freedom in the observer, with respect to the observed system.”

This makes a lot of sense. About your statement “Another conclusion is that we here have a hiearchy of observers, which corresponds to energy scale. And the symmetries are emergent ONLY when parts interact. The symmetry emerges in the observing systems internal structyre. At least its how i see it.”

Do you have any reference about this? I’d like to establish connections between Rovelli Relational Quantum Mechanics and Witten Symmetry and Emergence.

Lastly. There is something I can’t understand in Smolin book. He said “The final theory will be non-local, or, better extra-local, as space itself will come to be seen only as an appropriate description for certain kinds of universe, in the same way that thermodynamical quantitis such as heat and temperature are meaningful only as averaged descriptions of systems containing many atoms. The idea of ‘states’ will have no place in the final theory, which will be framed around the idea of processes and the information conveyed between modified within them.

I can’t understand the analogy. Does he equal space as like heat? What is he describing.. why would the final theory will be non-local? What is the context.. you know that when there non-local information transfer in SR, there would be frames that would go backward in time.. so how would his model handle this?

21. Dec 9, 2017

### Fra

Hello star apple!

Like i think i said beore the detailed proper explanations on this, are still open questions (to me as well, even thought i have a farily detailed vision to implement this) and due to forum rules i try my best to contribute and participate in some discussions and not merely quoting what others said(=publiched) already, but without crossing the lines.
I think serious people TRY to make their own conclusion based on content. However in the ages of massive information flow, it is merely a survival strategy to filter out information. One efficient way to do that is to reject anything based on its source. I do this too, not because its "ideal" but out of necessity of limiting processing power.
The ramp up to Rovellis reasoning on RQM is excellent, until a certain point, where is strongly disagree with hime. There is a nd old thread.https://www.physicsforums.com/threa...able-in-classical-and-quantum-gravity.220841/

There are alot of other attemps to axiomatize QM that are partially in line with my thinking, but which has problems. Lucien Hardys spirit and some others from cox axioms by ariel caticha are sniffing the right way but looking for generalised inference or probability, but in my view the mistake in hardys axioms is that he is too lighlty in introduction the uncountable numbers and dimenstionality. Ariel does the same. I think there is an alternative way, where you go one step and just talke about complexions.

Let me think if i can add anything more without crossing any lines.
/Fredrik

22. Dec 9, 2017

### Fra

IMO, Smolins writing style is lenghty. In principle he could probably summarise the main points briefly in short paper, but i think smolins writing style is to first start with history to get the reader on the same page, in order to motivate the new ideas. This is motivated because apparently alot of professional scientists does not seem to understand or want to understand why certain things are problematic. But for a reader that are already on the same page, and share the basic descriptions of the problems, smolins books are lenghty.

But i think what he says is that spacetime, is neither fundamental nor a universal background - it is emergent, and so is "state spaces". And at the point where spacetime itself starts to dissolve into something else, then so does "locality" in the traditional sense. I think this is essentially what it means. For this reason extralocal is a better word, to avoid peoeple thining we are violating relativity in its appropriate domain.

IMHO, what likely replaces the locality principle in a theory of inference - when 4D spacetime - as we know it, is undefined, is a principle of locality in an abstraction where an "inference" or computation is only affected by available data", you can even put this so that it becomes self-evident, and plausible as axioms, but the challenege is to connect to known physics.... and to attach the abstractions to physical parameters such as time, mass, energy etc. So there are some gaps to fill in. This locality principle makes locality as referring to spacetime, a special case. But I am not aware of anyone that "cleanly" published anything the way i want it. This way locality is built-in. But its "locality" in a generalized sense.

/Fredrik

23. Dec 9, 2017

### star apple

In Witten Superstrings, spacetime is emergent from the dynamics of the strings even when the background is unknown (or even flat). It is the strings that create spacetime from spin 2 gravitons. Smolin is anti superstrings so I wonder why he would state it. Is it not Loop Quantum Gravity is all about background independence. Here spacetime is not emergent. Is there any further works where Smolin detailed about this emergent spacetime?

Superstrings would make a lot of sense if the strings themselves have hidden access to other dimensions. This is why superstrings is still very attractive.. but if Supersymmetry won't be detected by the LHC even up to 100 TeV. Can Superstings still be true? What you think and others about this. Can Superstrings still work if the Supersymmetry is near the planck scale (I think Urs or Lubos talks about this I forgot where).

Last edited by a moderator: Dec 9, 2017
24. Dec 10, 2017

### Fra

Hmmm...

This kind of "simple" emergence of spacetime geometry, in the perturbative approach from a classical geometry and a given topology is a very weak form of emergence that I dont think is not what Smolin means, and for sure not what i have in mind, without going into details.

Smolin generically talks about emergent statespaces in an evolutionary sense, but this is in his later books, i dont remember how far these ideas was expressed in the early books like three roads.
https://www.amazon.com/Singular-Universe-Reality-Time-Philosophy/dp/1107074061
or
https://www.amazon.com/Time-Reborn-Crisis-Physics-Universe/dp/0544245598
or
http://pirsa.org/08100049/

The connection between "evolution of law", and the emergence of symmetry, and the concept of observer depdenent observer invariance as an hierarchy of observers, is probably not too easy to explain briefly simply because noone to my knowledge does it this way, but you can understand the vision maybe by as a synthesis of the below spirits exemplified by some quotes, like take the good parts of each, try to deform it to make it selfconsistent, dump the rest, and what do you get? ;-)

"However, the rules of classical probability theory can be determined by pure thought alone without any particular appeal to experiment (though, of course, to develop classical probability theory, we do employ some basic intuitions about the nature of the world). Is the sametrue of quantum theory?"
-- Lucien Hardy, https://arxiv.org/pdf/quant-ph/0101012.pdf

"Entropic dynamics, a program that aims at deriving the laws of physics from standard probabilistic and entropic rules for processing information, is developed further."
-- Ariel Caticha, https://arxiv.org/abs/0808.1260

The problematic common denominator of all the various statistical emergence problems is that they fail to give the appropriate observational physical footing to the probability spaces. One part of this is also how lightly the concept of uncountably many alternatives are introduces in the theory, becuase it destroys computability of the inference system. It also seems intuitive that finite physical systems does not encode infinite amounts of information. So why the need for continuum models? That is often easier to work with from the point of view of analytical appraoches, but computers prefer finite sets. And nature might well too, who knows?

" We need determinism only in alimited set of circumstances, which is where an experiment has been repeated many times. In these cases we have learned that it is reliable to predict that when we repeat an experiment in the future, which we have done many times in the past, the probability distribution of future outcomes will be the same as observed in the past. Usually we take this to be explained by the existence of funda mental timeless laws which control all change. But this could be an over-interpretation of the evidence. What we need is only that there be a principle that measurements which repeat processes which have taken place many times in the past yield the same outcomes as were seen in the past."
Lee Smolin, https://arxiv.org/pdf/1205.3707.pdf

To be honest i dont think that Smolin managed to explain this as good as it maybe could. As i see it, you can easily misread this suggestion and find it completely ridiculous, but then think again. The idea is, could the reason for the APPARENT timeless law, that most of use think of as constraints, simply be explained as a principle where nature tends to (in a sense of induction) respond as it always did? Seen the right way, this is a rational action principle in disguise. It also is a kind of solution to the problem of induction, as we know the problem is that the induction can be flat our wrong (ie no black swans). But this might not be how nature works! Its not a matter ot true or false, its a matter of best guess. If you only have seen white swans, betting on another white swan may still be a goot bet. Sometimes the best guess is wrong, and sometimes its exactly this explains certain interactions.

You can apply this reasoing also to "symmetries" if you consider the actual observer symmetries of an observer. If a certain observer has evidence for a certain symmetry, it will itself proabably behave "as if" this was law. But it is not. And sometimes a black swan actaully appears and breaks the illusion. But nature might be a stable illusion, and how else to explain it?

This is a way to also then understand evolution of law.

Then add the ideas of evolving laws of smolin, and you arrive at my position.

/Fredrik

Last edited: Dec 10, 2017
25. Dec 11, 2017

### Fra

It was some time since i read these things, but here is one connection in smolins paper to is getting close to what I am doing.

This connects all this to the inference and computational perspective, and evovling law perspective. If you think about this, you see a way to "attach" a the foundations of a generalized probability theory in physical structures bu identifying the "computing devices" with matter.

/Fredrik