Argument for discreteness of spacetime

[Fra]

How can you be sure that information has a lower limit for scale? Maybe information can occur in infinitely smaller forms, allowing infinite amounts to occupy any given region.

First, I think of these information bounds not in a realist since, but in the sense that the amount of information _as see from the outside_ (from the other side of the boundary) is limited. Ie. the information the observer HAS, about this region, indicates that a certain amount of information is hidden

But note that even before bekenstein, I don't know anyone that claimed that a finite region holds infinite information. The special thing is that the bekenstein bound scales with the area of the boundary or scree, rather than volume. But in either case, it would be bounded! The only question is, does it scale as volume or interface area or something else?

Infinite information in a finite region in a realist sense just doesn't make any sense to me in the first place.

The only think that makes sense to me is wether the outside observer can _infer_ that the amount of information about the mictrostructure of that region he is missing is infinite. Now I think that's impossible for any given fixed observer, because I think no finite observer can encode and relate to an ifinite amount of information. That along is IMO an argument that makes the concept of infinite information useless, non-computable and lacking connection to something that could be realized even in principle.


/Fredrik

 

[brainstorm]

First, I think of these information bounds not in a realist since, but in the sense that the amount of information _as see from the outside_ (from the other side of the boundary) is limited. Ie. the information the observer HAS, about this region, indicates that a certain amount of information is hidden

Why does it matter which side of the territorial boundary the observer is looking from? Why does it matter whether information is hidden, or how much? It comes down to deciding if there is a lower limit on information-size which would limit the amount of information that could be contained in a given unit volume. A post above mentioned "bits." What is the smallest physical entity that can be used to represent a "bit?" A quark? Do quarks have an absolute minimum volume?

But note that even before bekenstein, I don't know anyone that claimed that a finite region holds infinite information. The special thing is that the bekenstein bound scales with the area of the boundary or scree, rather than volume. But in either case, it would be bounded! The only question is, does it scale as volume or interface area or something else?

Did they mention lower limits on bit-size?

Infinite information in a finite region in a realist sense just doesn't make any sense to me in the first place.

Because infinite smallness of particles or energy-patterns is implausible to you for some reason?

The only think that makes sense to me is wether the outside observer can _infer_ that the amount of information about the mictrostructure of that region he is missing is infinite. Now I think that's impossible for any given fixed observer, because I think no finite observer can encode and relate to an ifinite amount of information. That along is IMO an argument that makes the concept of infinite information useless, non-computable and lacking connection to something that could be realized even in principle.

So you are willing to claim that because something is unobservable it's possible existence can be excluded from consideration? How can you make absolute claims about something you can't observe?

 

[Fra]

I think the original question was just to response to your objection that there is a bound (regardless of how this bound looks like; I don't think bekensteins bound is the more general form yet to be discovered, it has too much baggage, but that's a different discussion I thikn)

Your further comments reveal that we either have vastly different views, or that you didn't get the logic of my points, but here are some more comments on how I would choose to address the new objections you raise, some of these things are open issues where poeopl hold different views. There is no established consensus on this.

Why does it matter which side of the territorial boundary the observer is looking from?

Because to me we're discussing a mesurement/inference theory, and it is not a priori clear that the result of and inference or measurement is independent of the choice of observer. I'd even say it's reasonably clear that it is not.

So the relation between the observer, and the system under consideration is a critical component in this analysis IMO, because the question you pose, can only be "formulated" but the observer itself.

It makes no sense to isolate the measurement from it's context.

It comes down to deciding if there is a lower limit on information-size which would limit the amount of information that could be contained in a given unit volume. A post above mentioned "bits." What is the smallest physical entity that can be used to represent a "bit?" A quark? Do quarks have an absolute minimum volume?

It sounds like you think of "bits" in an objective realist sense - that is not how I see it. The "bit structures" is IMO just the smallest distinguishable parts, and the concept of distinguishability only makes sense in the context of an observer - therfore, it's important to pay attention to where is the observer and where is the "region" which we want to estimate the information content. Because it's not IMO a priori obvious that there exists "bits" in naive realist sense. I think the nature of these bits are far more subtle.

Did they mention lower limits on bit-size?

Before we discuss this one has to be clear what we mean by bit. Clearly we can not think of bits as we do classicaly. I would say that bit size, can be observer dependent, and it's not entirely clear yet how two observer can compare their bit assessments. Altough my hunch is that the assessment of each observer, constrains their ACTIONs, and the deviation from objectivity here, is exactly what's introducing interactions between the observers. So consistency may be recovered by renaming the deviation to a new force. That's one possible idea of hte scheme, but it's yet an unsolved probllem.

My main point is just to argue that even the maning of a bit, only makes sense in an observer context, where it's operationally defined in terms of the smallest distinguishable resolution. To other observers, this is then revealed in the action of this observer.

Because infinite smallness of particles or energy-patterns is implausible to you for some reason?

It's because what you say, makes sense operationally, ONLY to an observer with infinite resolution power. And that itself, just doesn't make sense. Because it's not possible to make an computation with infinite information. So this picture seems to me "sterile".

How can you make absolute claims about something you can't observe?

I can't and I don't. This is exactly the point I take very seriously, which leads to my position. I think you must misunderstand me.

But claims are results of an inference process, therefore I can make relative claims about something I don't observe - see below.

So you are willing to claim that because something is unobservable it's possible existence can be excluded from consideration?

No no. What I claim is that it's not rational, resonable or sensible, for the decidable part of the the action of an observer to depend on things is unobservable.

I hope you see the importan distinction here.

It is still possible, that things that's currently unobservable, to become observable in the future. But we must not loose focus of what the core question is. The core question to me, is to decided what actions to take, given the current state of information. This is all that is rational. To try to determine an action based on unavailable information is just irrational and undecidable.

There is always an undecidable part of evolution, this is what I adhere to a view that considers evolution of laws.

/Fredrik

 

[brainstorm]

No no. What I claim is that it's not rational, resonable or sensible, for the decidable part of the the action of an observer to depend on things is unobservable.

But now you're talking about some form of practical instrumentalism. The issue was whether infinite increases in smallness of information is possible that allow for infinite amounts of information to exist within a given area/volume.

It's because what you say, makes sense operationally, ONLY to an observer with infinite resolution power. And that itself, just doesn't make sense. Because it's not possible to make an computation with infinite information. So this picture seems to me "sterile".

I will give you that any given instrument with limited resolution power will have a lower limit to the size of information it can recognize, which will put an upper limit on the amount of information possible within a limited amount of volume. But the question is whether there are infinite amounts of information taking place at sub-observable levels, or whether there is some natural limit to the scale of particles/energy. It seems to be a purely theoretical question to me, since you simply can control particles beyond a certain size to observe them.

 

[Fra]

But now you're talking about some form of practical instrumentalism. The issue was whether infinite increases in smallness of information is possible that allow for infinite amounts of information to exist within a given area/volume.

I'm still talking about theoretical abstractions. But part of my point, is that I personally take the operational implementation seriously. A theoretical consideration, that ponders something that is not practically realisable even in principle, doesn't make much sense.

My point is that the only way to give meaning to things like "amount of information existing in a system", is by the process wherby you would infer it.

If you reject this, then you probably subscribe to some form or realism, where you imagine in some sense that the information has an objective existence regardless of verification or measurement.

I will give you that any given instrument with limited resolution power will have a lower limit to the size of information it can recognize, which will put an upper limit on the amount of information possible within a limited amount of volume. But the question is whether there are infinite amounts of information taking place at sub-observable levels, or whether there is some natural limit to the scale of particles/energy. It seems to be a purely theoretical question to me, since you simply can control particles beyond a certain size to observe them.

It's not just about resolution of instruments or communication channel, it's also about the information capacity of the memory record (storage).

Since information can be coded in different ways, it's still possible that one observer can observe and encode the amount of information, even theough the information itself is hidden. This means that the information is not hidden, since some macroscopic qualities are still observable.

(*) Another question is when and why different observer would AGREE on the amount of information stored in a certain region of space. This is a harder question, and I think to undertand that the origina and makup of space needs to be understood.

/Fredrik

 

[yoron]

What a nice thread. I have some arguments for why I think of it as a 'smooth' continuum. The first is that a discrete always need 'joints', you can't use the idea of 'discrete bits' without assuming that somewhere they must join. Then the question becomes, how do they join? And what is it where they 'join'. To me a statement involving 'joinings' always imply a 'space extra', in where something joins to something else, a background. I know that Smolin speaks of spin networks that don't need a background, but as long as it isn't one undividable 'string' creating it, and us all, there seems to exist seams to me. And if there is seams, or a 'background', would that then be smooth, or will that too become 'joinings', add infinitum.

A smooth start takes care of that problem, recently I've started to wonder about indeterminism, not virtual particles but indeterminism itself. Could that hold a mechanism by which everything becomes a smooth phenomena? We call it a 'superposition' sometimes. Then Plank scale, some see it as a construct, but I think at it as a 'border' of sorts, just like 'c' is to me, although I'm not sure for what, well except the obvious, that we can't make any sensible predictions past it. I doubt we ever will be able to look into the Planck scale, and as indeterminism seems to come into play at a larger scale? I'm not sure, but HUP is very strange to me, and interesting.


Integral challenges physics beyond Einstein.

 

[friend]

What a nice thread. I have some arguments for why I think of it as a 'smooth' continuum. The first is that a discrete always need 'joints', you can't use the idea of 'discrete bits' without assuming that somewhere they must join. Then the question becomes, how do they join? And what is it where they 'join'. To me a statement involving 'joinings' always imply a 'space extra', in where something joins to something else, a background. I know that Smolin speaks of spin networks that don't need a background, but as long as it isn't one undividable 'string' creating it, and us all, there seems to exist seams to me. And if there is seams, or a 'background', would that then be smooth, or will that too become 'joinings', add infinitum.

Or in other words...

If spacetime is not continuous, then at that level you'd loose the connection between cause and effect. How is some discrete thing over here going to have any effect on some other thing over there if there is no medium of exchange?