Why is spacetime four-dimensional

[Fra]

5. In the beginning, It appeared that our degrees of freedom were limited to 2 and that we were organized so that we could only move from a cubic to a hex. pattern.

Roughly, the simplest way I imagine how 2D "spacetime" emerges from evolving discrete complexions is like this.

Consider an observer that has a finite information capacity (memory) that can distinguish only ONE boolean event. Consider a counter that simply encodes/stores the historical counts indexed by 0 and 1.

At each instant all there is, is a counter state.

At the high complexity limit when the counter structure becomes sufficiently complex, the limit of the state space of the counter converges fills [0,1]. So almost a real number (but the further construction can only be understood if it's acknowledged that the limit is never reached).

The state of this counter is constantly challanged by new events and when the counter is saturated, a decision problem appears: An existing count needs to be erased from memory in order to make room from fresh data. What is the optimal information update here? I conjecture that data is ereased randomly!

(This means the erased data is randomly distributed with respect to the emitter, but not necessariy with respect to the receiver; compare here to black body radiation and the information content of hawking radiation)

As the complexity of the observer increases (getting close to the continuum), more possibilities of reencoding the microstructure appears! For example one can consider histories of counter states, effectively considering a history of real numbers. This is the first dimension.

This can then be repeated. But clearly the stability of this higher dimensional records depends on the complexity. At low complexity, the idea is taht these are unlikely to appears, for statistical reasons. The are not forbidden at all, they just don't happen since they are unstable.

But in parallell to this simple cobordism type of genration of dimensions, there are OTHER maybe more interesting development, such as more complex recodings... cobordism is extremely SIMPLE. More complex things is formation of non-commutative strucutres such as a fourier-like transform of the first "string" of real numbers. This would encode the state of change, and thus increase predictivity and stability of the entire measure complex.

So dimensional creation and creation of non-commutative structures are really both just different types of recoding of the data. The selection of WHICH of these recodings that are most stable is the challange.

IF you start from the low complexity end, one can user combinatorics and look as things.

Also the cobordism type of development (histories of states by recursion) and the development of parallell non-commutative structures are in equilibrium since both processes are constrained by the same ocmplexity. Inflating higher dimensions is extremely complexity demanding, but even creating parallell non-commutin structures are... but at the same time this entire structure complexed is constantly challaged by it's environemnt... and if you picture an idea where ALL these possibilities are randomly tried, what emerges in evolution is the optimally fit decomosition of eternal dimensionality and internal non-commuting structures. There is some equilibrium condition we seek here. This is how I see it.

I'm working on this and, all along the guiding principles are no ad hoc actions, all actions are rational random actions. The point is that what is just a entropic dissipation in a simple microstructure, will generate highly nontrivial actions when you combine it with higher dimensions (ie more than one:) and non-commuting structures.

/Fredrik

 

[Fra]

1. the universe is confined to 10^-15m

Since I think you expected some informal associations, to spawn imagination, it's tempting to make also the following picture of confinement and the origina of quark mass.

The most obvious reason why you never see something in isolation, is because it's just one face of something bigger, right? There is always flip side, and they support each other.

If you compare some ideas from ST where quarks are associated with end of the string. Then combine that with the idea above that the string index is the [0,1]. Then confinement seems to be related to that it doesn't make senes to consider the upper limit of the state space unless there is an lower limit.

I mean the only way to separate the limits, is to split the index (ie SPLIT the STATE SPACE of the counter into TWO) which then corresponds to creating new pair of "ends". This is easier to understand if one understand that the string index is really just an index defined by the states of a counter. And of the history of this counter for somereason weakens the support of the index in the middle-states, then that effectively creates two new ends, and even the slighest fluctuation and random deletion of data (mentioned previously) risks breaking the link. In neither way does an isolated upper limit make sense w/o it's lower limit.

I think it's the fact that quarks are not seen in isolation, may make understading their mass values easier. The origin of the mass of the quarks might then always happen in the not one by one, but in the bound quark-systems. The bound system is created directly as a measure complex, and the quarks are just inseparable logical components of this.

This only way to really split them, is by creating more of them.

I hope no one is too offended by this baloney, but it is just another "mental image" that may explain make sense of this "counting picture" the thread is about. After all it's a subtle thing, to ask for hte physical basis of counting. All these visions are circling my head but there is indeed enourmous effeorts needed to develop this into a full blown theory. But acquiring some intuition and abstraction models is I think good, that doesn't mean there is any reason to mix these visions up with the full model. It's perhaps though, what it would take to UNDERSTAND such a model, once it's on the table. At least that's how I see it.

/Fredrik

 

[jal]

“Since I think you expected some informal associations, to spawn imagination”

I’m an amateur compared to you.

“So to attach my envisions construction into the standard big bang timeline, the starting points is somehow the Planck epoch. As early as this, is where the "discrete picture applies". When we get to the quark formation we first need to understand how the complexions separated out from gravity and how the continuum approximation is formed.”

... where the "discrete picture applies"

My understanding is that quarks are considered discrete.
If you make the assumption that discreteness originates at the Planck epoch then you are obliged to consider densest packing, (hex. or cubic) with the size of a dimension being reduced, (Not a new concept. String uses that concept).

CERN is on the verge of giving us some hints on discreteness of quarks and maybe the discreteness in the perfect liquid.

Should discreteness be demonstrated, in the perfect liquid, then my avatar would be good visualization and lattice, LQG, string calculations should lead to a mathematical description of what could be happening and what could have happened in the beginning.

jal

 

[qsa]

http://upload.wikimedia.org/math/b/2/5/b25919b3dd75b9248d07bc1e19056f89.png

only D=3 gives N=3. this might be very important, at least in regard to my own idea.

see higher dimensions

http://en.wikipedia.org/wiki/Euler_angles

 

[Fra]

I’m an amateur compared to you.

I'm definitely not a professional either, if I were I should have made far more progress than I have since I resumed this. The difference between trying to make progress in small time slots at weekends and nights and beeing paid to spend all days doing it is gigantic. (although of course, most professionals doesn't all days eithers as they need to often do part time teaching etc).

To look at the bright side of life, freedom of affiliation is also strenght, as it's easer to be faithful to your original ideas. Time is the only issue.

My understanding is that quarks are considered discrete.
If you make the assumption that discreteness originates at the Planck epoch then you are obliged to consider densest packing, (hex. or cubic) with the size of a dimension being reduced, (Not a new concept. String uses that concept).

You seem to always come back to this picutre of "perfect symmetry" etc.. I think you think in a different way. You seem to see the big bang from an external view. Ie. a perfect symemtry that is subsequently broken? something like that? this is an extenral picture.

I argue that an internal observer, would not SEE this perfect symmetry. The internal observer is just undecidable about almost everything. An internal observer can not infer a perfect symmetry - only an external observer can. This is the different I think between considering the conditions close to the big bang in a laboratory; where we DO have an external observer, and to SCALE the thery back to those proto-observer that did exists back then.

Of course, both perspective are valid! I just think that tha latter perspective has the simplest view (easiest to understand), this is the exploit I picture.

The quark masses for example, the external inference we have to day are experimental. But a good "checkpoint" would be to see if relations between the masses (and mass I associae to complexity), can be postdicted. The wrong postdiction would kill the reconstruction.

From the inferencial perspective, anything with mass is not elementary. This is why ALL mass needs to be explaind. Just explaining 95% of all mass as confined energy still leaves us with 5%.

/Fredrik

 

[jal]

With the assumptions of more than 3 spatial dimensions, then the definition of a closed system must be expanded to include those other dimensions.
Would this imply the redefining the role of a neutrino?
Does it take energy to open up a path to another dimension? Could neutrinos be that energy requirement?
What are the kinds of energies would can come into our 3 space dimension?
( dark energy?, gravity?, tachyons?, virtual particles or quantum tunneling?)
---
http://en.wikipedia.org/wiki/Neutrino
Neutrino

Wolfgang Pauli theorized that an undetected particle was carrying away the observed difference between the energy, momentum, and angular momentum of the initial and final particles.
---
http://en.wikipedia.org/wiki/Conservation_of_energy
The law of conservation of energy is an empirical law of physics. It states that the total amount of energy in an isolated system remains constant over time (is said to be conserved over time). A consequence of this law is that energy can neither be created or destroyed: it can only be transformed from one state to another. The only thing that can happen to energy in a closed system is that it can change form: for instance chemical energy can become kinetic energy.

 

[Fra]

Are you referring the universe as a "closed system"?

FWIW It's not how I see it. And more importantly I don't think it's how an inside observer can possibly see it: I do not see how an inside observer can much such an inference that the environment in which itself lives is closed. What does that even mean? I simply can't imagine the inference. What I can imagine is an expectation or illusion that it's closed. But the stability of such illusions remains undecidable. And if I understan you right, you seek to use this as a hard constraint. That logic is not sound to me.

To think of the universe from the outside as something that is closed, expands etc is to me somewhat of a fallacy due to applying the science we are known to apply to subsystems to the universe, where there always IS an effective external view. From the inside view, this external view is as I see it totally wiped out.

/Fredrik

 

[jal]

Are you referring the universe as a "closed system"?

No. It is limited by the event horizon.
However, only the universe of the proton, which is what is being considered, it is closed/confined. (10^-15m)

 

[Fra]

Ok, but I'm still not sure what you mean by closed. Even if one can not isolate quarks without creating other quarks around it, the entire complex (say proton, neutron) might be scalable. The origin and organisation of information in the proton, and how the proton responds to external perturbation is exactly what I think requires explanation. I can not imagine using this as a starting point. Then one has already missed some interesting steps.

With the assumptions of more than 3 spatial dimensions, then the definition of a closed system must be expanded to include those other dimensions.

In the way I mentally picture the discrete complexion picture above, there is no god given dimensionality at all. And different dimensionalities can exist without changing the complexity just by different ordering and grouping of discreteness.

I do not have a _visual_ picture of this at all, my own picture is just an abstraction in terms of a information processing/creating/storing observer that does a random walk in just a black swamp. The only map he has, is in his internal structure, acquired from the past. During equlibirium his internal map will not need revision and we have an holographic connection. But many systems aren't in equilibrium, it's just a special case.

Would this imply the redefining the role of a neutrino?
Does it take energy to open up a path to another dimension? Could neutrinos be that
energy requirement?
What are the kinds of energies would can come into our 3 space dimension?
( dark energy?, gravity?, tachyons?, virtual particles or quantum tunneling?)

These specific question I can't yet connect to. It's too early for me, but I think at some point they will be a handle on this.

Personally I picture some sort of unified quantum, from which the various quantums of the other interactions branch off as more complex observers emergg (starting from some basic Planck view, or below that, what do I know).

So in this perspective, a proton is indeed already a very complex observer.

A simple observer, then we're talking about perhaps a single massless bit or something fuzzy like that. So there would be an hierarcy starting from an almost trivial "observer, and then as you let the complexity scale run, stable-observer-complexes emerged along the way and serve as more complex building blocks for further bigger sturctures. Somehere in this hierarchy all the elementary particle must come up, or that's the idea.

And WITH THEN, implicit in their relations, also the selection of 4D spacetime.

/Fredrik