Is an infinite series of random numbers possible?

Chronos

Cantor already did this.

*Loren Booda*

Quote by chiro

I've got to fly (classes very soon), so I'll and try and look at this later tonight and give my thoughts tomorrow.

If you have to, just wing it. Hoping you find relationships between classes.

chiro

Quote by Loren Booda

[Speculation]The Bell experiment implies that their are three types of "communication" -- censored, probabilistic and informative. The first allows no exchange of radiation, the second allows exchange of thermal energy, and the third, communication exchange.

An "internal observer," relative to its black hole, sees numerous particles of many kinds, as we see the microwave backround radiation. A "surface observer" sees many particles, but all as a Hawking blackbody. They are produced in pairs across the event horizon finite energy barrier, some infalling and fewer infalling/outgoing. The latter are like local pairs produced in radioactive decay for an EPR experiment.

The Bell EPR "non-local observer" experiment does not allow faster-than-light signaling. It does, however, allow patterns of data to be transmitted faster than light speed, but effectively only one-way. My own explanation is that signaling from the original decay travels both in our non-local macroverse and in local microverses central everywhere to the macroverse. This allows a relatively sub-light (macro) signal to reinterfere with a relatively super-light (micro) signal.

This is the thing I was hoping to imply with regard to experimental testing regarding a general Bell-Theorem scenario in the way that you would statistically test firstly a) that some non-local communication exchange was going on and b) whether it was bound by known constraints (the obvious one being the speed of light).

Again the thing is that our understanding of physics is unsurprisingly physical and this is not meant as a derogatory statement, but rather as a statement to allow for the possibility that we have communication happening that is not locally spatial.

If you wanted to incorporate this physical idea of thinking you could simply use the idea of space-time structures where points could join at will when they need to, to actually model this using the standard calculus techniques we use to model phenomena in terms of local changes (as represented by the derivatives and partial derivatives of physical equations in the classical sense).

This kind of thing of having a dynamic manifold that allows this is of course not a new concept and has been studied extensively in gravitational theory for quite a while. All I'm suggesting is to instead of interpreting in this context, you treat it more or less as a general information system with general communication exchange and then place the constraints on the information and the communication mechanism in that context.

What this ends up doing is that you don't try and think about communication in terms of particles and force-carriers in a physical sense like you would when you think about the situation where you have two billiard balls on a snooker table where you hit one and it hits the other and the communication exchange is basically a 'physical' thing.

Again this is just my perspective and I don't really think about communication requiring a local mechanism like you would expect if you thought about it in a physically intuitive context.

The short answer that I would speculating with regard to your question, but if you wanted to know what I would do personally I would develop the theory in this context where you don't use specific local models of physics, but rather ones of a non-local nature and then find either contradictions or support for non-local behaviour of any sort. You could almost think of this as some kind of cellular automata but with even less restrictions on the communication mechanism itself.

What this means is essentially looking at generalized models that don't rely on differentials but something broader and I know that I would cop a lot of flak for this, especially from the physics community because it seems overly complex and perhaps un-necessary: the point is that with a framework like this in combination with statistical analysis that is tailored for inference in this type of problem: you can get the data and rule out (at least with some measure of confidence) whether you get this happening or not and instead of putting your theorems in terms of simply local properties: you put them in non-local ones.

Another reason this is hard mathematically is that we have to introduce analyses that correspond to this: with dx/dt or dy/dx we only think of local changes, but with a non-local framework, the scope is a lot more broad.

Like I said I am not a physicist, but if I put the physical laws in this context with a lot of effort (I know that physics is not an easy endeavor), I would see it in a way that would make sense to me both computationally, statistically and information wise. This would take a lot of effort, but then again the results could be fruitful.

http://en.wikipedia.org/wiki/Planck_mass The minimum energy needed to produce the (smallest) Planck black hole is 2 x 10^-5 gm=2 x 10¹⁶ ergs= 10²⁸ electron volts.
__________

Regarding "information content"

http://en.wikipedia.org/wiki/No-hair_theorem
". . . More generally, every unstable black hole decays rapidly to a stable black hole; and (modulo quantum fluctuations) stable black holes can be completely described at any moment in time by these eleven numbers:

mass-energy M,
linear momentum P (three components),
angular momentum J (three components),
position X (three components),
electric charge Q.

These numbers represent the conserved attributes of an object which can be determined from a distance by examining its gravitational and electromagnetic fields. All other variations in the black hole will either escape to infinity or be swallowed up by the black hole."

The next thing you would do is to convert this to an entropy measure itself. We have entropy in terms of the states of 'stuff' itself (like the particles), but the next thing to do would be to express the 'structure' in terms of an entropy.

The reason for this is that you would something in a way that you can deal with universally. Once you have the entropy of the information and the structure for a system, you can treat it in a common way. In terms of the entropy for the structure, this will depend on the information content of the structure itself.

This is why I think information theory is important because most people, if they ever consider entropy, they consider only the entropy of the realization of bits of information that have a particular structure, class, or classification and because of this, you can't say if you have 100 particles (bosons, whatever) treat them in a true unified way.

What typically happens in my own reading, is that the theories kind of 'glue-stuff' together using for example group structures. In a situation where you treat any structure in the same context, you overcome the shortcomings of this problem.

Of course, it's not simply that easy. Firstly you have to be able to move back and forth between entropy, algebra, the realizations of your information in a fluid manner.

What currently happens is that in mathematics we have numbers and for the most part, the information content of the numbers let alone the algebras that are associated with system descriptions is completely left out. We don't think of this and as a result when it comes to understand the real information (and thus entropy) of the entire system, we have these two frameworks that are not compatible with each other.

Like the previous question, this again would require a lot of mathematical development that would incorporate again computer science, information theory, mathematics and statistics in a highly developed way.

http://en.wikipedia.org/wiki/File:St..._Particles.svg [Speculation] Enjoy the profound symmetry. That particle matrix may have a fundamental information content associated with it. There also might be a limit to the number of resonances (excited particles) possible.

Energy is a conserved quantity, symmetric to invarience under time translations. (See http://en.wikipedia.org/wiki/Noether...tion_of_energy .) As I mentioned before, the second law of thermodynamics may not be a law at all. Will the universe eventually approach heat death or entropy death?

This is just in line with my thoughts earlier in this thread, but I think that the universe as a whole will not reach either total chaos or total staticity but globally remain in a state between those two spectrums. If I'm wrong, I'm wrong, but I will say that this is a prediction by me (I know there is no data or mathematics), but my reasoning for this is the same as before: with any chance of staticity you will get your entropy death which means any kind of dynamics of the system is destroyed and thus it can not evolve. Subsequently too much chaos will result in a system that ends up growing ever so unstable until the point where order can never be restored thus making the system go beyond a point of 'no return' so to speak.

While you can reach these situations, for the same reasons above I predict that you will not be able to globally create a situation where you create entropy death or heat death.

As for sub-regions, this would have to be investigated theoretically and mathematically and I can't really comment on the specifics of this because frankly I don't know.

http://en.wikipedia.org/wiki/Geon_%28physics%29 "In theoretical general relativity, a geon is an electromagnetic or gravitational wave which is held together in a confined region by the gravitational attraction of its own field energy. They were first investigated theoretically in 1955 by J. A. Wheeler, who coined the term as a contraction of "gravitational electromagnetic entity.

Since general relativity is a classical field theory, Wheeler's concept of a geon does not treat them as quantum-mechanical entities, and this generally remains true today. Nonetheless, Wheeler speculated that there might be a relationship between microscopic geons and elementary particles. This idea continues to attract some attention among physicists, but in the absence of a viable theory of quantum gravity, the accuracy of this speculative idea cannot be tested."

[Speculation]I call the former an Electronic Black Hole (EBH). "A gravitational black hole abhors a 'naked' mass singularity, but allows it the observable property of charge, with correspondent electromagnetic field. Similarly, the horizon radius r for "electronic black holes" (where m_ec²=e²/4πε₀r, r=2.81 x 10^-13 cm) limits what we may eventually know about the electromagnetic structure of a charged particle. An electronic black hole (E.B.H.), typical below the scale of a proton, has a particular charge whose electrical potential magnitude equals its associated rest mass-energy. E.B.H.'s are entities so gravitationally bound against electric repulsion at a given radius as to be reproduced by the energy of attempted E-M measurement. As with strong force quark isolation, charge singularity (i. e., E.B.H.) observation itself denies direct ("naked") E-M information.

Might the E.B.H.s have less entropy than similar particles from the Standard Model?

The thing about the speculation of these black-hole scenarios is the same that I wrote about previously in the context of things like the Penrose-Process.

In the Penrose Process that you mentioned earlier about extracting energy from black-holes, this question reminds me of the same kind of scenario in that in these situations you are able to explicitly control the process of energy (and hence information) distribution in a very controlled manner.

If it ends up that you have the Penrose-Process, the process where you can have naked singularities or similar kinds of processes, I don't think it will be an easy thing because again doing these kinds of things is equivalent to controlling energy, since if the black-hole scenario represents the maximum entropy situation and the process itself is just an energy distribution mechanism in the forms of stabilization, then to me it suggests that the fact that this happens happens to make sure things don't screw up and because of all effects going on in this situation, the only way you could achieve these scenarios is if you could control it in any kind of semi-certain way.

Like I said before, for the most part, we are still boiling water through coal and we use nuclear energy and in my mind it is ridiculous but at the same time I am unfortunately glad because if we had the ability to control energy like we would do with something like a black-hole, then the fact that human beings would be behind this terrifies me.

Figuring out the black-hole scenario in absolute death to me is the equivalent of being for lack of a better word 'God'.

In terms of your question though, again it depends on the information and any communication that is happening (potentially) between it and anything else.

Again with black-holes we think that just because it is a black-hole and just because light can't theoretically escape it, then apart from your situations with Hawking radiation, there must be no communication going on.

This is an assumption using classical intuition of billiard balls and from a scientific point of view, I would rather test it from a general non-local statistical inferential analysis over using a local one.

I tend to think that it's best to start with the idea that everything is potentially talking to everything else because from that you can be sure that at least from the statistical point of view that there either is evidence for this to be a general principle or for it to not be general.

If it wasn't general and the data was reliable, then ok that's how it is but I would want to see data from a high energy environment that is similar to the characteristics of a black-hole mechanism.

[Speculation]Given the wrong circumstances, most people would be obediant enough to carry out the Milgram experiment to its completion. http://en.wikipedia.org/wiki/Milgram_experiment "[/QUOTE]

Personal responsibility, or more properly put, the lack of it, is the thing that lets evil breed. People lie to themselves everyday thinking everything is ok and when you have a situation where you have group or social reinforcement, then this makes it a lot harder.

When people take personal responsibility for themselves it means they think long and hard of what they are doing. It also means that people will acknowledge their faults, their wrongdoings, and their ugly side.

It's unfortunately a lot easier to just lie to themselves even though they know better and again it's no better when everyone thinks the same way which ends up establishing the social norms that create the chaos we have.

Anyone that chooses to deny personal responsibility at any level will become the perfect Milgram experiment participant and in a situation where you have what the participant thinks is a 'norm', then it becomes a lot harder due to the characteristics of our social makeup and how social situations affect us.

Most people call this peer pressure and other words, but usually it boils down to usually a personal security issue of some sort and the fact that choosing to be the Milgram candidate enforces some kind of gaurantee for said security.

It's hard to think by yourself and it's hard to act that way when you see the rest of the world acting in the complete opposite manner.

[Speculation]Stability and staticity exist relative to chaos and astronomically accelerating dynamics.

Chaos theory I think would be the best way to study this formally in terms of statisticity and also through chaotic bounding.

It would be interesting to take into account the acceleration of the universe (is this what you're asking) with respect to what that does for chaos in any finite subregion.

If you had things shrinking, then I see the situation for chaos becoming more imminent due to the kind of argument you get when you consider a standard statistical mechanics problem if you put matter in a box and the box shrunk with the matter itself being conserved (I know I'm using the physical intuition here so forgive me ;)) assuming we are talking situations where you have this pattern (which is a lot of situations).

By having acceleration, you actually do the reverse: you create a situation where it becomes harder to create an unnecessary chaotic situation which means that you create a great chance of things becoming a lot more ordered and I think it's a good thing to favor ordered scenarios as opposed to chaotic scenarios.

[Speculation (from post #67)]
http://en.wikipedia.org/wiki/Hidden_variable_theory -- (regarding encoded information), Bell's theorem would suggest (in the opinion of most physicists and contrary to Einstein's assertion) that local hidden variables are impossible. Some have tried to apply this to entangled states straddling the black hole horizon, that is, to pair production of particles and whether entangled states can stay so with one having infallen. Communication of this third kind is based primarily on entanglement, with the "non-local observer" (above). They are more constrained with observation than an "surface observer." Thus if the "non-local observer" respects entanglement, so does the straddling "surface observer."
[Speculation]A black hole, in the classical sense, obeys

GM_EH²/R_EH=M_BHc²

That is, M_EH=R_EHc²/G

Where G is Newton's gravitational constant, R_EH is the event horizon radius, M_BH is the black hole mass, and c the speed of light.

A quantized approximation yields the number of quanta on the event horizon: R_EH²/L*², where L* is the Planck length. R_EH/L* is the root mean square.

M_EH ± ∆m_q(R_EH/L*)=R_EHc²/G ± (h/c∆r_q)(R_EH/L* ),

where ∆r_q is the quantum uncertainty of length, h is Planck's constant, and ∆m_q is the quantum uncertainty of mass.

The order of the quantum tunneling distance to the event horizon radius for a solar-mass black hole is approximately (R_EH/∆r_q)=(hc/G)^1/2/L*=1

I will answer this in the next post.

chiro

Also just thinking about your acceleration question, the entropy constraint that I would test would be based on isotropic ideas.

In other words, the idea is that you would isotropic properties through space for the chaos and staticity constraints as a first basis for a model and then see how the forces affect this and adjust for this.

If the universe really did 'stretch' as a function of time, then it would make the staticity and chaotic requirements a lot easier (tending to favor more order than chaos) and this property of expansion would make this situation a lot easier.

In terms of specifics, this would require analyzing how combinations of things affect entropy and thus chaos and staticity, but again just using the statistical mechanics analogy above, if you apply the idea isotropically through space then it makes this a hell of a lot easier.

micromass

This thread has gone waaay of topic. It now deals with physics and not with mathematics anymore, so it is not suitable for this forum. Furthermore, I can see lots of speculation happening which is not allowed here.

Thread locked.

If you two want to keep talking, you should probably PM each other.

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micromass Blog Entries: 8 Recognitions: Gold Member Science Advisor Staff Emeritus	This thread has gone waaay of topic. It now deals with physics and not with mathematics anymore, so it is not suitable for this forum. Furthermore, I can see lots of speculation happening which is not allowed here. Thread locked. If you two want to keep talking, you should probably PM each other.