Logic of E-H action, ricci scalar, cosmological constant?

[Fra]

Seeing that some of our ideas converge, I would like you to explain this point better.

I'm not sure this helps, I think not but try to give the simplest possible hint, I've used this example.

Consider the multinomial distribution, where you store data of events, but having one bucket for each distinguishable event and then you have a certain number of balls to drop in each bucket. The a simple illustraion is to have the history define a relative frequency, and have this provide the basis for expectations on the future.

$$P = \left\{M! \frac{ \prod_{i=1..k} \rho_{i}^{(M\rho_{i})} }{ \prod_{i=1..k} (M\rho_{i})! } \right\} e^{-M{S_{KL}}}$$

The M is the total number of balls, k is the number of distinguishable events.

P is like the induced "relative probability" for observing a future distribution/microstate. And the interesting part is that the exponential contains M, the total numbers of samples (as a kind of inertia) and the information divergence. If M -> infinity, then any non-zero information divergence would yield zero probability. This corresponds to infinite stability in the case of large number of dregrees of freedom. There is automatic averging out high information divergences, so convergence is guaranteed by construction, so there is never need for any RE-normalisations.

Note that $$M\rho_{i}$$ are integers, so $$\rho_{i}$$ doesn't in general fill the continuum [0,1], which means P is bounded from below, and this bound is related to M-number characterizing the observer. One can also associate - ln(P/Pmax) with a kind of higher order entropy or action (which then implies a maximum excepected entropy/action bound)

But I am still working on implementing this idea, and combined this with emergent dimensionality as in spontaneous decomposition of the microstructure into several ones having particular relations. This would for example by the case for q and p, and I expect thus the superposition to be related to the inertia of each information structre and also the limited information capacity. But I am still thinking of this. In this case time evolution will also be more interesting.

This means that in this view, each observer has it's own expected arrow of time, and the relation with the different arrows of time can only be compared by interactions.

The set of microstates corresponds to the hilbert vector, and the set of microstructurs correspond to the hilbert space, but the microstructures are in constant evolution. So not only is the microstructure observer dependent, it's also time-dependent and evolving in each view. And it's the tension of disagreement in this picture that I imagine generates the known physical interactions.

The problem is that since I am still working on this, at this point I can not present a full blown theory, for you to test. What I can do is try to convince you about he plausability in my personal reasoning and unavoidable gets fuzzy. I think it makes sense to a certain point only, and the rest has to be "my personal problem" for now.

/Fredrik

 

[MTd2]

What is the meaning of that $$S_{KL}$$?

 

[Fra]

It's a discrete version of the the Kullback-Leibler divergence
http://en.wikipedia.org/wiki/Kullback-Leibler_divergence

$$S_{KL} = - \sum_{i=1..k} \rho_{i} ln(\rho_{i,prior}/\rho_i)$$

It's a measure of deviation between two distributions, a kind of "relative entropy" is another way of thinking of it.

But it migt be mistake of me to even try to make a simple example. I am working on putting all down in a paper, and explain not only the reasoning but also the construction of the formalism from the beginning but it's in progress and I have plenty of problems yet so solve myself. I sure doesn't have all answers.

/Fredrik

 

[MTd2]

Does the number of states i changes with time?

 

[Fra]

> Does the number of states i changes with time? '

First note that in the simple abstraction above there is no time defined yet.

But if you mean if k changes with "time" the answer is yes.

Pretty much everything can change with time, M as well.

/Fredrik

 

[MTd2]

If the number of k varies, it means that some states are not measured at a given time, because otherwise you will have illdefined amplitudes. It means that the communication channel is almost saturated, like I said before.

 

[Fra]

Yes I think there are strong analogies even to continuum models, no doubt.

To me, k represents the distinguishable "area" of the communication channel. M limits of the history of the communication that can be retained. Obviously M >= k, because non-occupided channel states collapse and become indistiniguishable, and thus decrease k. So like you mentioend before, the observer does get "saturated", and what then happens is that either the observer grows larger M, or information must be released. I am pondering the exact rules for this and there are here remote similarities to possible black hole radiation, which is a sort of "relative random radiation", so that it contains NO distinguishable information from the point of view of the observer himself, but it may well contain information relative to a second observer. A massive observer can thus generate "more random" radiation, than a light one can. The concept of "no information" is thus also relative.

Thus one silly predictions based on the intuitive analogy here is this would predidct that a small black hole would radiate "less random" than a large one, if you are to rate the "degree of randomness".

So the question of randomness is in the eye of the beholder, what observer is complex enough to decode it?

/Fredrik

 

[MTd2]

Thus one silly predictions based on the intuitive analogy here is this would predidct that a small black hole would radiate "less random" than a large one, if you are to rate the "degree of randomness". /Fredrik

Hmm, that's right.

The scattering amplitude and for any particle decresases in near the horizon, so the particles just become free near the black hole. Since the fermions with same quantum number don't repeal each other anymoe, the entropy is maximized and can't increase anymore, everything tends to a bose-eisntein condesate. So, that's why black holes are cold. That looks like Wilzec proposal for an anology between GR and condensed matter.

If S,M are small, that is, near the vicinity of the usual particles we know, the scattering amplitude is big becasuse ( exp(-MS)->1), so, they scatter like in QFT as usual. So, small particles are not quite black holes, unless they are very massive. Interesting.

 

[MTd2]

I need a way to consider the particles that are measured, but the interaction do not occur for lack of "information" space. So, there must be a way to convert real particles into phantom particles. I guess, more degrees of freedom here. Perhaps using quaternions, maybe...

 

[Fra]

I am currently trying to read up on others thinking, I've ordered wilczek's and also some other string-bash classics I never gotten around to read before.

Another interesting phenomenon that happens during the small M, that is different from the continuum thinking is that in the P = w*exp(-MS), w -> 1 as M is large. But when M is small it's no longer close to unity. This can be interpreted so that as the evidence counts is small, there is simply no way to achieve certaity. This is also a key in my picture of emergent structure and dimension. ANY structure is formulated in such terms, and when the sample count (or information capacity) drops, complex structures spontaneously destabilise. This is why it takes certain masses to support certain complexity. And I think in this dynamics a gravitational attraction might emerge (I can't show this now, but I hope to in the future; so far it's intuitive properties of the presumed formalism) in the sense of self-inforced complexity. Structures self-stabilize by try to attrach other mass, which means increasing it's information about degrees of freedom in the environment, so as to eventually grow it's M. This is I think remotely connected to Ariels Catichas ideas to derive GR from a fundamental ME principle, although completely different. Ariel works with classical and continuum models, but I share some of what I perceive to be his basic vision of a connection between the logic of reasoning and the laws of nature - gravity included.

/Fredrik

 

[MTd2]

Last night, before sleeping, I had a vision:

Near the saturated bound, the particles tend to live largely undetected, so it's like they are almost ghost particles, in the sense that they almost never show up, almost never measured.

Today, I thought of something:

Conversely, in theories like QCD, you have the overcounting of states because of the gauge freedom, so you must get rid of the ghost states. But, in your equations, that means M->INF, whereas S keeps finite, but big relatively big. Then, the holographic bound is saturated by these states, and the ghosts happens because they are really something that exists, but are expelled from the physical world (that is, they don't interect with the physical world), because there is no place for the dead under the sun.

So, basicaly, if a black hole means a cold place in the lattice, these ghosts have negative temperatures. Usually, people would say that these are a negative energy, but your equation re interprets ghosts as an overflow of information. Perhaps, you can see them as holes in a semiconductor.

 

[MTd2]

Better:

The QCD particles are fluctuations, as it is any other particle in the lattice, but instead, they appear as a single entity, just like in a semicoductor one hole is a particle, with one state, but formed with a multitude of the abscence of electrons.

So, a quark is confined because it have to present itself as a component of a defect in field of the lattice, simply because it IS THE component of a defect, the source of a defect, in the field of the lattice.

 

[Fra]

We are perhaps using different abstractions as source of inspiration, so until more progress is made it's difficult to compare the ideas exactly :) I faintly see some of your associations but don't understand your guiding principle.

When I work out my visions, I should get predictions for emergent structures - ordered by complexity("mass") - and these structures (I avoid calling them familiar names at this point, like particles or fields) interact with each other in a way that is implicit in the the way they emerge.

Now if I am on the right track, I should find that the emergent structures and interaction properties matches the known physical laws and particles. If this is not so, I am probably way off track. But I am optimistic. Nothing so far in principle, except the complexity of the task itself, has discouraged me.

/Fredrik

 

[MTd2]

don't understand your guiding principle

It changes with time, right now, it is roughly this:

1. There is an upper bound to the amount of information that can be measured in a volume, because any volume is a channel of information.

2. What is not measured is virtual (e.g. particle).
2.1 You get more virtual particles when the channel is more saturated.

3. The degree of virtuality associated to a channel gives you potential energy.

4. Geometry is such that it tries to maximize the saturation of a channel.

5. Wave functions just exist in the virtual regime.
5.1 Wave functions follows geometry but doesn't interact with geometry.
5.1.1 The space, in which the wave function propagates, has the same geometry of space time, that is, it is a kind of wick rotation of any parametrization given to the 4-minkowski manifold
5.1.2 If that results in multiple kinds of 4-euclidean manifolds, take the average.

6. The wave function manifold must be such that is some kind of lattice.
6.1 There must be an analogy with condensed matter.
6.2 Gauge groups are "molecular bands and orbits" in the lattice.

7. Information is causal and lorentz invariant.

 

[MTd2]

Fra,

I just found this: http://en.wikipedia.org/wiki/Quantum_group

Is that helpful to you?

 

[atyy]

I think this is available free, but I'm not sure.

Gravity: the inside story
T. Padmanabhan
http://www.springer.com/physics/journal/10714
http://www.springerlink.com/content/l403540q87606463/

 

[Fra]

MTd2, thanks for hinting your guiding principles, although I may not understand your logic completely. But it looks somewhat different from mine.

You talk about the 4-manifold - does this mean that you somehow take a 4-manifold as a unquestioned starting point? If so, what is the status of the "information of this manifold"?

atyy, thanks for those links, I'll read them and see what it is. I'm waiting for some books I ordered and until them I've got some slots to read papers.

/Fredrik

 

[MTd2]

what is the status of the "information of this manifold"?

What do you mean by status here?

 

[Fra]

What do you mean by status here?

I mean at what level in the theory is this defined? Is it a background entity assumed to make sense, or is it something emergent as per a described process?

I mean, when we start by "consider a 4D manifold". Is that a fundamental starting point, or can you reduce to introduction of this manifold to something more fundamental?

Edit: Ie. is it the notion of 4D-manifold part of your basic premises for reasoning? Or is the 4D-manifold a result of an interaction or evolution of an observer, that is defined without a manifold?

/Fredrik

 

[Fra]

http://www.springer.com/physics/journal/10714

On first skim those essays seem very well written! I have to print them all and read them carefully.
Thanks again for the link! :)

It seems to be the top 5 of

Gravity Foundation Essay Awards 2008!
1. Gravity: the inside story - T. Padmanabhan
2. Noncommutative gravity, a ‘no strings attached’ quantum-classical duality, and the cosmological constant puzzle - T. P. Singh
3. On the physical interpretation of asymptotically flat gravitational fields - Carlos Kozameh, Ezra T. Newman, Gilberto Silva-Ortigoza
4. Quantum field theory in curved spacetime, the operator product expansion, and dark energy - Stefan Hollands, Robert M. Wald
5. The delocalized effective degrees of freedom of a black hole at low frequencies - Barak Kol

/Fredrik

 

[MTd2]

Or is the 4D-manifold a result of an interaction or evolution of an observer, that is defined without a manifold?

The observer is just a classical concept, so I did not include it in the list... But the 4D should be a kind of minimized action.

Did you notice the similarity between your solution for the probability as a vector in a quantum group space?

 

[MTd2]

Another reason to use the 4-Manifold, besides that we probalby live in one, it is that it probably encodes certain kind of beautiful structures, typicaly found in theories that requires a lot of dimensions, like string theory. One example it is that the classification of many smooth 4-d manifolds requires the use of lattice presentation of the E(8).

Also, note that a string structure is used in 4 dimensions to classify. It is differentiable, but there is no diffeormorphism between structures in with the same topology. In fact, the number of diffeomorphic structures for a given topology can be densly infinite. Its name is Casson Handle.

 

[Fra]

Did you notice the similarity between your solution for the probability as a vector in a quantum group space?

Yes there are direct apparent similarities and indeed my intended simple expression evolves, there will appear what one might see as non-commutative microstructures. But I have never been attracted to mathematics itself, this is why I argue the other way and map out the math.

As for the non-commutative microstructures that will emerge, in the construction I have in mind there is a reason for why the don't commute, and it's that they are both constrained by a common complexity bound. There will be equilibrium between the microstructures which is a solution to a sort of optimation problem. So perhaps it's similar to what you think after all. But again like the random walk / diffusion analogy, I think the route to optimum is more like a random walk. The actual "optimation process" is part of the physics in my thinking.

It seems you think of the observer as classical. It's not quite how I see it. To me the observer is the implicit reference. With observer I don't mean an observer inthe classical sense of "a classical measurement device". An observer can well be uncertain realtive to a second observer.

Anyway, I think there is ALOT of interesting things about this that I hope we will all find out in the future.

/Fredrik

 

[MTd2]

Tell me more about the implicit reference.

 

[Fra]

I am going for a trip the next few days so I won't be much online, but to respond shortly of what I mean.

I have given some thought of all these things in the past, the problem of decomposing the observer and the observed, and it sure is true that in standard QM the measurement device (the observer) is a classical system. This is not good enough for serveral reasons.

Nevertheless my opinon is that the problem is not that we have an observer, because there always is one. The problem is howto define the observer. And the solution I envision to this, is that the observer is continiously evolving. The problem of defining the observer, is thus resulting in an evolution.

So with the implicit reference, I mean that any information is relational, and whenever I make a statement, there is always an imlpicit reference to which that statement relates, and this defines an observer.

It's a bit like Zurek's sentiment that "What the observer knows is inseparable from what the observer is".

This means that in my representation, an observer is technically a system of related microstructures, and this system is the observer. So the information is the identifier of the observer. And information is evolving, and identification of observers are a result of spontaneous structure stable formations which are relations to it's environment.

I am still working on this of course, but it at least responds to your question. I am certainly not ignoring this problem, I take it seriously.

/Fredrik

 

[Fra]

It's a bit like Zurek's sentiment that "What the observer knows is inseparable from what the observer is".

This means that in my representation, an observer is technically a system of related microstructures, and this system is the observer. So the information is the identifier of the observer. And information is evolving, and identification of observers are a result of spontaneous structure stable formations which are relations to it's environment.

An implication of this, is that there is not much sense in the notion that "two different observers has the same information" if we by this also also means that the information has the same confidence levels etc. Because if two observers really have the same information, then the two observers conincide.

The distinction between observers, is measured by their disagreement, which in turn is measured by their interaction. And with observer, I also include any subsystems of the universe. And my idea is to extract from the process of disagreeing (a process of communicating opinions) the structure of interacations.

So my picture is that the laws of physics and the physical interactions, are the laws of information processing and communication. And to incorporate the "observer" in these "interactions" is to include the information processors or transcievers in the communication.

This is to me a generalisation of Einsteins Gravity, in that spacetime itself "responds" to the the dynamics in spacetime. IE. the observers "respond" to the communication that is relative to them. The result are evolving observers. And the observer-observer interactions, analysed starting from the simlpest possible observers and scaling up the complexity, should chart out the structure of all interactions. Classifications will emerge here.

/Fredrik

 

[Fra]

This is to me a generalisation of Einsteins Gravity, in that spacetime itself "responds" to the the dynamics in spacetime. IE. the observers "respond" to the communication that is relative to them. The result are evolving observers.

This also shows the problem. Given the original association the geometry of spactime responds to what's going on relative to it, the missing step was still, exactly how does this relation look like. Einsteins equation is a solution to this in GR.

In this case, the question is, exactly HOW does the interaction "the observer" participates in provides a selection for it's evolution. This is the problem I am trying to solve in my way. At first there is the simple idea of random walking towards some optimum, as per some ME principle, but the interesting part is that the space the walk takes place in is also dynamical, and the optimum is moving. So there is no global optimum, just some strange kind of relational optimum. This is a bit unpredictable and I don't know for sure what will come out of this, but I've already convinced myself that a local speed limit in line with lorentz stuff will be emergent, but this is deformed as everything evolves. I also think a universal attraction of structures will emerge, and I think this can explain gravity. And the supposed "explanation of this attraction" lies in the connection that causes an evolution in the observer, given interactions it participates in.

That is a lineout. But the details are in progress of course. Unfortunately I have not found that awfully many existing papers that is doing just this, although many approaches share elements of tihs.

/Fredrik