Intrinsic geometry vs intrinsic information

[Fra]

I think I raised this before but I am curious to hear the reflections from all of you about one simple thing. The context of my question is the quest for a deeper theory of QG, along the lines of an intrinisic measurement theory, but the principal question can be easily phrased in terms of classical geometry.

As we know, long before Riemann, curvatures was formulated in terms of, an imagined external embedding space. But Riemann seeked an "instrinsic formulation" with "intrinsic curvature measures" of differential geometry that was not referencing to these external objects.

He sort of succeeded, but of course Riemann was not going an instrinsic measurement theory, his constructs were fully of mathematical realist types.

One thing has bothered me since way back, and I get even more bothered by the fact that a lot of people seem to not see this as a big issue.

If we now consider _information_ about geometry, we know from Riemann that an inside observer can _in principle_ infer the geometry by making "measurements" with sticks and rods, or light rays or something similar. So far so good. But this totally ingores the quantity of information required to define say a local chart, not to mention an atlas.

In particular if one imagines an inside observer, like an ant crawling on the surface - how this this ant (which must be infinitely small, in order to not violate the manifold iabstraction)

1) construct sticks and rods
2) store map information

It seems clear to me, that we currently do not yet have an instrinsic theory of information. It seems already from this general starting point, that the complexity of the _visible_ manifold must somehow be bounded by the complexity of the inside observer - right?

Somehow, this is also partly the essence of an ultimate implementation of a holographic principle and bound?

Does this have any implications on what it means to "quantize gravity" or wether we can make sense of something like a "hilbert space" for the gravitational field? Because the hilbert space itself would be constrained by our "ant" analogy, or?

I don't exepect any full solutions but I'm curious how you people "consider" this type of question? do you dismiss it as philosophical things of no relation to physics? or do you think it is trying to tell us something?

/Fredrik

 

[tom.stoer]

I am not sure if I really get your point: do you say that it is impossible to store information regarding a manifold within that manifold (in the same way as it is impossible to draw a one-to-one picture of the whole universe inside the universe as it must contain itself)?

Maybe you are right, but this could simply be irrelevant as physics does not require that the information regarding a manifold is stored somewhere. It is enough that this manifold exists.

(I think your argument applies to all mathematical structures)

 

[Fra]

I am not sure if I really get your point: do you say that it is impossible to store information regarding a manifold within that manifold (in the same way as it is impossible to draw a one-to-one picture of the whole universe inside the universe as it must contain itself)?

Something like that yes.

Maybe you are right, but this could simply be irrelevant as physics does not require that the information regarding a manifold is stored somewhere. It is enough that this manifold exists.

(I think your argument applies to all mathematical structures)

At a certain level, I agree with you, but at another level I don't. I guess this is what I wanted to know - I think your answered my question about how you view this, and I think your view is different than mine. And I think your view is also more common than mine.

To say that inference and representation of something doesn't matter as long as it just exists, doesn't IMHO quite resonate welll with the deeper request for the intrinisic measurement theory I seek. So I guess you say that we do not need an instrinic measurement theory? If so, I agree with your conclusion.

This relates to the question of what exactly does quantizaion mean? As I see it, in the deepest sense it's the ambition to construction a measurement theory and do away with the realist theories. But to do this seriously, the measurement requires a context providing not only sticks and clocks but also complexity to store&hold information in a code.

/Fredrik

 

[czes]

Something like that yes.
This relates to the question of what exactly does quantizaion mean? As I see it, in the deepest sense it's the ambition to construction a measurement theory and do away with the realist theories. But to do this seriously, the measurement requires a context providing not only sticks and clocks but also complexity to store&hold information in a code.

/Fredrik

For me it is also a problem. In old Copenhagen interpretation the point particle appears in any point of the space with a probability= a squared wave function. The quantum information disapeears and appears with a probability.
Due the Quantum Decoherence approach we know the quantum superposition doesn't vanish but leaks into the environment. Therefore the particle is non-local and the quantum information is conserved. It suggests something like infinite many hidden variables of Bohm-de Broglie or many worlds of Everett.

I think we have to use the knowledge about the non-locality of the particle which is obvious now. If the particle is non-local we have the information about the particle everywhere with a certain probability.

I would like to defend it is a non-local information about the Compton wave length of the particle. We can't observe an information alone , therefore we observe the interference of the many information of the Compton wave from different particles and it shows us the Vacuum with its virtual particles-antiparticles as the tension caused by relation (product) between quantum information.

May be it is crazy because such a topology seems to be to simple and naive. Just non-local quantum information - nothing more. It doesn't need space and time on the fundamental level. (Wheeler-de Witt equation)

 

[Fra]

Czes, I don't understand what you said in the response.

But it sounds like you are seeking for hidden variable things and restoring realism?

I think you have a point the the decoherence view, only works given the context of the environment. Which means the information of the envire environment is under consideration.

That is a problem, and my objection is also why I think that most decoherence approaches are not solving the problem.

One must be able to see the difference in decoherence of an atom system in a monitored environment (which is fine for practilca purposes) which is an extrinsic view where the action of the context is ignored, and the intrinsic view where the external context doesn't exist and where the action can not by any reasonable measure be ignored, but an action nevertheless has to take place.

/Fredrik

 

[czes]

Endophysics literally means “physics from within”. It is the study of how observations are affected and limited by the observer being within the universe. This is in contrast with the common exophysics assumption of a system observed from “outside”. The term endophysics has been coined by David Finkelstein in a letter to the founder of the field, Otto E Roessler.

Exophysics is the basis of the standard Copenhagen interpretation of Quantum Mechanics. In endophysics, on the other hand, observers and systems are all part of a greater whole.

One essential difference between exophysics and endophysics lies in the meaning of information acquisition and storage. In exophysics, whenever something is measured in a system, the information is registered in some form of memory carried by the observer. The nature of the memory is rarely, if ever, discussed in exophysics, whereas it becomes crucial in endophysics to explain in what sense endophysic observers „record” measurements.

Another consequence arises when we explain how the classical world that we see on macroscopical scale could arise from a purely quantum theory (the problem of emergence).
http://arxiv.org/abs/quant-ph/0401006v1

In quantum mechanics, I think, the crucial role plays the non-locality. It is even more important than non-reality which is also a fact. The non-locality of the information creates a background for the energetic information like photon and all electromagnetic interactions.
Gravity is not an electromagnetic interaction it is a space curvature and we use metric tensors in General Relativity and it works good. The problem is what is the space background.
I propose it is just the information background. "At the beginning was the information" - many physicists wrote the papers with this title.
Information is a thing helps us to distinguish the things.

We recognise the information in relation to an another information. If an electron is not defined it is everywhere. When it is joint to more information (absorbs more than emits) it oscillate faster and its velocity increases and its uncertainty decreases.

One may replace an information by an energy but it isn't the case. Energy is a relation between the information. Information is something more fundamental than energy.
John von Neumann said - information is not a matter nor an energy. It is an information.

 

[Fra]

Czes, yes endo vs exo terminolgoy seems to be synonmous to what I used as intrinisic vs extrinsic.

Not to nitpick but I'm not sure why I find your respons cryptical, I noticed your entire first paragraph is taken exactly from a wiki entry. I think my posts are probably unstructured at times too but maybe the flow got more confusing for me when quotes and your own phrasings are mixed in the posts without marking.

Thanks for the link to that paper, I'll skim it to see if I find it interesting!

So as for the basic question of the thread, it seems your opinon is that this is an important and relevant question!

As for the non-locality I am not sure how you suggest your view. I know some people discuss the choice or realism vs locality in entanglement, but as I see it there is no non-locality, since there is no non-local influence. That one observer might suddent learn that two remote events are related is not a non-local interaction a I see it.

The natural form of locality I think we can keep is that "local information influences the local action", entangelment does not violate this IMO. That local information influences information about remote actions is different to me. Sine location relates to the observers knowledge, expected non-local actions would be a contradiction since it's like to say that we expect something that is unexpected. I think what we have is a natural "ordering" or infromation, from certain to unkonwn, this ordering is how I envision spacetime and distance is built up.

Like Ariel Caticha put it : things far from each other in space are not lacking causal contact because they are far apart, it's rather the fact that they are in fact lacking correlation that produces the emergent space structure of distance. So one might say that space is the effect, not the cause of locality.

Thanks for your comments.

/Fredrik

 

[czes]

Hi Fredrik
I think, we have both the same question.
The non-locality is an experimentally confirmed fact. I like Zeilinger's articles:
http://www.quantum.at/zeilinger/
I have read all of them. Zeilinger is a coauthor of the GHZ effect;
http://en.wikipedia.org/wiki/Greenberger–Horne–Zeilinger_state

The quantum entanglement is an effect derived from non-locality. I thnk it has something to do with a gravitational field.

Haish, Puthof proposed the Zero Point Energy due to quantum fluctuations of the Vacuum. We measure speed of light in the vacuum. Therefore the vacuum is a medium for light. Nobody shows other possibility. The particle oscillate because it absorbs and emits this oscillations (information). The quantum information is conserved.
http://ldolphin.org/zpe.html
http://www.calphysics.org/

Recent observations shows that every real particle is surrounded by its virtual particles-antiparticles (I forgot a link).

All of them are mainstream now.
Therefore many articles - time, space, gravity are emergent phenomenons.

 

[Fra]

Thanks for the links, I know of Zeilinger but I've certainly not read all his papers. From what I recall he didn't hold any magic keys for me, but I will look it up again, thanks.

The non-locality is an experimentally confirmed fact.

I don't know what you refer here to but I suspect you are inferring non-local interactions from non-local correlations, which is an invalid inference. But yes in a statistical model, unexpected events are not banned - they are possible and expected to a certain extent, but they are not dominating.

Maybe it's also a matter of what exacly we mean by "locality". For me the fundamental form of locality is more something like that the expected local action depends only the only the local information. That is somehow a constructive principle, from which spacetime locality is emergent as a result.

So as I see it, "locality" can be formulated indepedent of space. Space is rather the emergent structure, following from interactions between system implementing the generalise locality principle.

Still I can stretch myself to agree that indications of non-local interactions exist, but as these indications accumulate the space itself would deform to respect locality. I think of non-local correlations as noise around equilibrium or transient, or off-equilibrium during an equiblirium shift.

So it souds like maybe we partly agree. But I do not quite appreciate "conservation of information" as fundamental, I see it as on part with the generalised locality, in that it's expected. Meaning, information is not actually necessarily conserved, but all subsystems interaction, act as if it would - this explains what it is conserved at equiblirum

The explanation for these assumptions of traits of the actions, local, information preserving etc I think of as the only constructive ones, in the sense that they are again the "expected" rules since it's hard to imagine that constructivity and persistence of nature would be wtithout them.

It's at this level I start with my "postulates". But I consider them truly minimal, and somewhat innocent. Not near as complex as say postulating continum strings or other higher constructs.

/Fredrik

 

[Fra]

My point was, thta this generalised form of locality, has never as far as I know been shown to be in conflict with any entanglement experiments. On the contrary.

/Fredrik

 

[czes]

There are two ideas how to understand the non-locality:
1. Copenhagen school - the point particle is found in any point of the space with a probability due to its squared wave function (Max Born).
2. Decoherence approach - the particle is in all points of the space with a probability of the interaction with another particle due to a product of their wave functions.
Roger Penrose has its own interpretation here:
http://en.wikipedia.org/wiki/Penrose_interpretation

All above ideas are in agreement with Bell's theory that locality doesn't exist.
The recent experiments with lasers shows that this non-locality is deeper than it was considered in Copenhagen. Therefore Copenhagen interpretation isn't accepted as it was 30 years earlier.

I like Cramer's Transactional Interpretation because it shows the non-local interactions between the particles and it may create something like a gravitational field made of information. Our space-time is an information background like in a computer. It doesn't need space nor time. All points of our space are appointed by a product of the information (non-local wave functions) - therefore this holographic effect.

 

[Fra]

I see more than those two ways to see that.

Bell's theorem and the experimentlly verified inequalities rules out local realism - not locality per see. At least thta's my opinon.

Penrose quest for a gravitationally induced objective collapse is very realist minded in comparasion to my view. But even given the disagreement, I share his view that there is a connection. But I see the connection the other way. Subjective collapses gives the impression of gravity (among other things! in fact I think it gives the impression of all forces, not only graivity - this is the key difference between what I think and penrose idea). Penrose do it the other way, and work from gravity only.

Unless you stick to realism, which it seems to you do? I think one should distinguish between

- local events having beeing instantaneously indepedenet of remote events
- local information beeing instantaneously independent of remote information

The distinction is clear that information about remote events may exists/beeing encoded locally. To compare locally store information and remotely stored, an interaction mus take place, and this takes time.

Furher one needs to define what "remote" refers to, prior to existing of space? IMO, the seed to these measures are information meausres that induces a "distance measures" simply in the sense of "the amount of information, as per some measures" that separates two information states.

Ultimately the measure of 1m, chould be understood as the _AMOUNT_ of information required to distinguish two systems. To say that two systems are 1m apart, is equivalent in this view to constrain the different in AMOUNT of information where they differ. But ths is not new either, it's the basic ideas of information geometry.

In this latter view, it's clear to me that I see no reason to abandon this general locality. Note that no experiment has shown non-locality in the sense of instantaneous information transfer. Correlation of local and remote information is something different. it's not hte same thing. /Fredrik

 

[czes]

I see more than those two ways to see that.

Bell's theorem and the experimentlly verified inequalities rules out local realism - not locality per see. At least thta's my opinon.

Unless you stick to realism, which it seems to you do? I think one should distinguish between

- local events having beeing instantaneously indepedenet of remote events
- local information beeing instantaneously independent of remote information

The distinction is clear that information about remote events may exists/beeing encoded locally. To compare locally store information and remotely stored, an interaction mus take place, and this takes time.

Furher one needs to define what "remote" refers to, prior to existing of space? IMO, the seed to these measures are information meausres that induces a "distance measures" simply in the sense of "the amount of information, as per some measures" that separates two information states.

Ultimately the measure of 1m, chould be understood as the _AMOUNT_ of information required to distinguish two systems. To say that two systems are 1m apart, is equivalent in this view to constrain the different in AMOUNT of information where they differ. But ths is not new either, it's the basic ideas of information geometry.

In this latter view, it's clear to me that I see no reason to abandon this general locality. Note that no experiment has shown non-locality in the sense of instantaneous information transfer. Correlation of local and remote information is something different. it's not hte same thing.
/Fredrik

You are right. Therefore quantum computers are possible though very difficult to keep them working. At may 2009 they reported the 7 bit quantum computer worked 0,1 s which was a very long time.

I wrote a trivial equation:
Tp / T(x) * Tp / T(y) = -a Fg / Fe
where Tp is Planck's time, T(x), T(y) are Compton wave length/speed of light, a=alfa (fine structure const.), Fg=gravitational interaction, Fe=EM interaction.
It is just a transformation of the basic equation.
I was intrigued that it shows that for each quantum oscillation of the particle there is a Planck's time dilation and Planck's length contraction. It shows that gravity is just a space curvature in information background.
Therefore as you wrote above the distance of 1m is just a constant amount of the quantum information between the objects with a distance of 1m.
These information are more compact in a stronger gravitational field or in a relativistic motion but the speed of light measured by a local rule is always constant.

The Compton wave length is very important here. It is a quantum information about a particle. Such an information has to be local and I assume it is distributed with a probability inversely proportional to the squared distance from a source of the oscillation.
The Compton wave length h/mc is seen also in Klein-Gordon and Dirac equations. In Schroedinger equation it is a little bit obscured.

If we can see an interference of the photons we can see also the interference of electrons, neutrons. Zeilinger group shows an experiment with fullerens containing 600 hydrogen masses. May be the microbs may interfere in some circumstances.

It is not easy to observe the interference because it is obscured by the quantum decoherence from the particles of the environment. Therfore the quantum computers are isolated in the magnetic traps and use special frequencies.

The quantum entanglement is used in quantum cryptography. It is not possible to send an information faster than light but we may construct a quantum code and send the coded information. We have the code and our fried has the same code. If sombody want to see the information he change the quantum code and we know about it then.
It is 100% secure transmission of the information.
http://en.wikipedia.org/wiki/Quantum_cryptography