Argument for discreteness of spacetime

  • Thread starter bcrowell
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  • #26
Fra
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Sorry to repeat myself, but I think a key question for this discussion is also how we view the notion of symmetry of nature.

Do we see the symmetries of nature as realist traits of nature? Without having to be observable, or follow from the result of observation?

If we do, noone can deny that the symmetries of nature we do talk about now are the result of an inference process we call "science". They are the result of human science. We can think that the analysis of the scientific process is more phsychology than physics, and maintain a "realist view" of the symmetries we have inferred from this process as "timeless facts of nature".

Or we can require that an observing subsystem, infers the symmetries of it's environment by physical processes on par with how it infers information about the STATE of it's environment by the measurement process (which in the case of subsystems is what QM describes). So instead of thinking that the "scientific process" is not interesting for fundamental physics, we can think that there is a yet not properly described process wherby a subsystem of the universe. infers symmetries of it's environment, and that this furthermore influences the first systems reaction on it's environment. And that THIS context may be the better way of seeing symmetries.

I of course subscribe to the latter view, but I suspect tha majority of others subscribe to the first view.

Is the first view really satisfactory? In either case I think the choice of attitude here strongly influences our reasoning also of the issue of for example lorentz symmetry.

/Fredrik
 
  • #27
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Your idea to compare LambdaQCD with the Planck scale does is not fully correct. The Planck scale can be deduced by purely dimensional arguments, whereas LambdaQCD emerges from a classicaly scale-free theory. That's why it makes sense to insist on the idea that new physics emerges at the Planck scale even if you are not able to derive this. In QCD it's fundamentally different: nobody knows about LambdaQCD before calculating beta functions, going through all the renormalization group stuff, and deriving scaling violation.


On the contrary. The reason that you can make a naive estimate of the Planck scale based on dimensional grounds is due to the dimensionality of Newtons constant. We know that gravity becomes non-perturbative once g=G E^2 ~1. So this suggests that this happens once E^2=1/G . However, just like in QCD, the coupling, in this case, G is itself is a function of the energy scale G(E). So it is case too in gravity that we do not know the E^2 =1/G(E) before we calculate the beta functions for gravity.
 
  • #28
tom.stoer
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I think you missunderstood. I simply want to say that there's difference how the two scales show up in the theory.

For the Planck scale you know from classical physics that there's a scale dependency: this is due to the dimension of the gravitational constant in the classical Einstein-Hilbert action. There is no question that gravity contains a fundamental scale - and we expect it to become physically relevant w/o knowing from an experiment that this is really the case. In QCD you cannot derive the scale based on dimensional arguments for the classical action because it is scale invariant. In contrast to GR you do not know that the theory contains a scale before you went through all the QFT calculations.

It is strange: in QG you are not able to go through all that stuff but you can construct - from the very beginning and w/o any calculation - a quantum gravity scale simply from G, c and the (quantum mechanical !) Planck constant.
 
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  • #29
qsa
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Discrete space has been proposed at Planck length. But has any other distance been proposed(studied), like near proton width.
 
  • #30
bcrowell
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Discrete space has been proposed at Planck length. But has any other distance been proposed(studied), like near proton width.
I think the diameter of a proton is definitely ruled out, because high-energy scattering experiments have probed distances a couple of order of magnitudes less than that.

In a theory of quantum gravity, there is only one length scale that you can build out of the relevant fundamental constants, and that's the Planck scale. Physicists already feel like there are too many arbitrary scales in physics, e.g., the electroweak scale; they don't want to add another one if they can help it.
 
  • #31
qsa
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I think the diameter of a proton is definitely ruled out, because high-energy scattering experiments have probed distances a couple of order of magnitudes less than that.

In a theory of quantum gravity, there is only one length scale that you can build out of the relevant fundamental constants, and that's the Planck scale. Physicists already feel like there are too many arbitrary scales in physics, e.g., the electroweak scale; they don't want to add another one if they can help it.

Thanks for the reply. I am familiar with the standard physics, but few months back I read something like that but I don't remember it any more. Of course when I meant near I meant a number of order of magnitudes( I know I was not clear).


In my own model (my profile), something strange happens when I make position discrete, then when I almost hit 355 strange things happen to the energies of the particles( it is like fixed points). It is known that if you compute 355/113 you get PI with six figure accuracy. Moreover, as I approach 4 all the energies cap to 1 in a similar behavior to black body radiation i.e. when energies are discrete the result becomes finite. But if I make my random throws on real line then all hell breaks loose and there is no stopping to the energies. For various reasons in my model it appears that 4 could represent a length of 1 to 1/1000 times the proton diameter. I am not sure; I have to find out or may be I am just calculating the wrong thing.


The other strange thing in my model is that if I don’t make space discrete I am simply not able to compute interactions (including gravity) properly and there will be ambiguities. But calculating energies is no problem the discrete and the real give me the same numbers that is above position 355.
 
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  • #32
qsa
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I think the diameter of a proton is definitely ruled out, because high-energy scattering experiments have probed distances a couple of order of magnitudes less than that.

In a theory of quantum gravity, there is only one length scale that you can build out of the relevant fundamental constants, and that's the Planck scale. Physicists already feel like there are too many arbitrary scales in physics, e.g., the electroweak scale; they don't want to add another one if they can help it.
here is a quote from a paper from this link

https://www.physicsforums.com/showthread.php?p=2721537#post2721537

Entropic force, noncommutative gravity and un-gravity

"Without loosing in generality,
but having in mind Noncommutative Geometry
as a specific tool for the description of the microscopic
structure of a quantum manifold, we start a revision of
Verlinde’s assumptions. Noncommutative Geometry encodes
the spacetime microscopic degrees of freedom by
means of a new uncertainty relation among coordinates
xμx  . (16)
The parameter  has the dimension of a length squared
and emerges as a natural ultraviolet cut off from the geometry
when coordinate operators fail to commute
[xμ, x ] = iμ (17)
with  = |μ|. In other words, the spacetime turns
out to be endowed with an effective minimal length beyond
which non further coordinate resolution is possible
.
This a feature of the phenomenology of any approach to
quantum gravity and it can be found not only in Noncommutative
Geometry (for reviews see [10]), but also
in the framework of Loop Quantum Gravity, Generalized
Uncertainty Principle, Asymptotically Safe Gravity
etc.. The scale at which the minimal length emerges is
not specified a priori, and it is kept generic saying that
at the most p < 10−16 cm, namely smaller than the
typical scale of the Standard Model of particle physics
.
Along this line of reasoning, we have to revise at least
two of the Verlinde’s assumptions."

I guess I was not too far off. PLS, see my earlier posts. But how does that relate to planck's length. anybody?
 
  • #33
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The Bekenstein bound says there's a limit on how much information can be stored within a given region of space.
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.
 
  • #34
tom.stoer
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The smallest amount of information is one bit. It can store the information whether it's zero or one. Something that is smaller than one bit would always always habe the information zero (no storage for more information :-), but this is no longer information.
 
  • #35
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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.
One of the arguments is the holographic principle. It states that our reality is just a hologram of the information contained on a screen. Therefore we observe the spatial object. Each point of the object is created of the product of the two or more information.
The maximum number of the information on a screen is equal Area/4 Planck length squared.
Therefore we can count the number of the information in our observable Universe.
If the number of the information is limited the spacetime has to be descrete too.
Holographic principle is developed by prominent physicists Hawking, Beckenstein , Verlinde, Smoot, 't Hooft and other. It is recently the most promising idea in physics.

As a curiosity:
(lp / l x ) * (lp / l y ) = -a Fg / Fe
where:
lp * lp – Planck length squared = hG/c3
l x , l y –Compton wave length of two interacting particles l= h/mc
a – alfa=ke2 /hc http://en.wikipedia.org/wiki/Fine_structure_constant
Fg – Gravitational Newton's interaction between particle m(x) and m(y)
Fe -Electrostatic Coulomb interaction=ke2 /r2

Each oscillation due to Compton wave causes electromagnetic interaction and a space curvature which we call gravity. The interference of the non-local information of the Compton wave length causes length contraction (space curvature) and time dilation.
This equation is possible if the space-time is discrete only.
http://www.cramerti.home.pl/ [Broken]
 
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  • #36
Fra
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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 realised even in principle.


/Fredrik
 
  • #37
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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 realised 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?
 
  • #38
Fra
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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
 
  • #39
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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.
 
  • #40
Fra
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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
 
  • #41
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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.
 
  • #42
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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?
 

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