Chaos theory and the uncertainty principle?

[Daecon]

Is it possible to use predictions from chaos theory to compensate for quantum uncertainty?

 

If something small can have exponential repercussions, could those large-scale observations be extrapolated backwards to determine the initial state, at the same time as directly observing the initial state of another property?

[fredrik]

Is it possible to use predictions from chaos theory to compensate for quantum uncertainty?

 

If something small can have exponential repercussions, could those large-scale observations be extrapolated backwards to determine the initial state, at the same time as directly observing the initial state of another property?

 

If you are referring to the heisenberg uncertainty principle, say between x and p, and wonder if this uncertainty could be due to missing initial information, and due to an unknown causal chaotic relation, then I personally think this path alone is unlikely to be fruitful.

 

The reason for the uncertainty is not unknown interactions, it's because there exists a relation between x and p - they are not really independent. In general, if you are given two variables. There is no a priori reason to assume anything about their relations or non-relations, all assumptions should IMO be traced to the path of observations.

 

The notion of adding information "x and p" does not follow the normal rules of statistics and classical probability. Exactly why this is so, may be analysed in different ways. Normally, it follows from the operator definitions in QM, or postulates, depending on how you line out the theory and the axioms. But of course this is unsatisfactory and clearly a cheap way, because if it's just a matter of postulates and definition, the question still remains why this fits so well with observations, and it make the scientific progress itself the interesting part! One can still question the process that leads to this CHOICE of definitions.

 

I guess until it's all understood, there is no need to close any doors. But I ask myself questions like, given that we measure only position, how can the measurement of momentum, be understood to emerge as a result of a dynamica process? Ie. can new "operators" be understood to be a result of unpredictable interactions involving prior operators? Then all measurement process are related. This is the relation system I wish to find. This is in line with the intrinsic thinking popular from GR - when new phenomena appear, I'd expect them to be constructible from information at hand, and most probably as deviations/exceptions from the current expectations, rather than pulled out of the sky.

 

The question is if a answers arises spontaneously to a question that you never asked, or if the is first goes via exceptions from expectations based on current questions, then the deviations induces a new question. I imagine that this is how measurement operators may appear, and perhaps an analysis of this process explains from more first principles their relations. So that we can reduce the number of free constants, postulates and definitions.

 

/Fredrik

 

The reason for the uncertainty is not unknown interactions, it's because there exists a relation between x and p - they are not really independent.

 

When I think of this, it's of course possible to view this "relation" as a type of interaction as well. I guess it depends on how you see it. Words are easily wrapped around.

 

Pehaps, to avoid bending words, it would be more interesting if you could expand what strategy your idea would use. How would this extrapolation be implemented physically and how are you to get information about this

exponential repercussions?

 

/Fredrik

[foodchain]

Pehaps, to avoid bending words, it would be more interesting if you could expand what strategy your idea would use. How would this extrapolation be implemented physically and how are you to get information about this

exponential repercussions?

/Fredrik

 

I could only think entanglement?

 

I mean there is no way to do QM without some kind of observation involved. Its sort of funny to me because you have to use it to study itself in some way, so you have to be able to basically I would think then understand the interaction which has a whole list of words. I like the superselection one, simply because I can sort of make sense of it. I mean the whole idea about where the classical and quantum separate never made sense to me, more so when in all reality you have to use such to study the evolution of the universe currently.

 

I mean in an observation something seems to reduce and trap a probability amplitude of some discrete unit of energy that could probably be anywhere and most likely is:D So what is reducing the probability on observation? Is it more or less like some liquid of little energy Lego pieces reacting to each other and producing an environment? My best guess is simply conservation laws but I have no idea how you would prove if those are truly fundamental or if just currently listed as such. I mean could that produce laws of physics based on time or history? Such as why we have atoms?

[fredrik]

I could only think entanglement?

 

I don't understand what you mean here. How do you envision that entanglement, reduce the uncertainty that's due to incompatible observables? I'd expect a prescription, defined from the point of view of an incompletely informed observer.

 

One difficulty in thinking about this is to not try to use information we really don't have in possession, in order to explain something. Sometimes we have incomplete information about somthing, and this can be used for systematic reasoning, if we at the same time can measure the confidence in the premises. Then our conclusion can be given an estimated probability of "beeing" right.

 

It's easy to loose track of what is going into the inductions, and one ends up with a possible conclusion without any accompanying measure of plausability whatsoever.

 

For example, in many decoherence treatments, there are two views. The inside view, and the global view. The global view, can explain the constrained view, given that we assign a border, and reduce information. But that is answering a question that wasn't the original one. The global view, having information about the entire "universe" really isn't a physical view, as it does not represent a true inside observer.

 

Decoherence is interesting, but it does not provide the complete answer. It rather makes up another question, which it answers. But that other question is not a physical one, in the inside-view sense. That's how I see that.

 

/Fredrik

 

I mean there is no way to do QM without some kind of observation involved. Its sort of funny to me because you have to use it to study itself in some way

 

I mean in an observation something seems to reduce and trap a probability amplitude of some discrete unit of energy that could probably be anywhere and most likely is:D So what is reducing the probability on observation?

 

In one perspective, a probability distribution in the first place is an expression of uncertainty. I recall some philosophical paper where someone reflected over what a question is and made an interesting abstract association between "a question" and a "probability distribution" (PD).

 

A PD can be taken to be a well defined meaning of a question, at the indexing defines the possibilities, and the weight at each index explains the odds. So the implicit question: what event will we observe next, is complemented by an _expectation_ of the answer. The expectation contains the SET of possibilities, and a weight for each possibility.

 

Now if you actually get an answer, in general, this SET and this set of weights are updated. So the result of answering a question, is a new question.

 

This is how I see QM.

 

An objection to this is that the notion of "information" is unclear. What are talking about physical reality here, and thus it's a justified question to ask what the correspondence is between "information", "questions" and "answers" in terms of something physical?

 

The way I see it, the physical microstructure of an observer, itself, encodes the prior information, which also contains all current "questions".

 

So the PD:s IMO have a physical correspondence in the observers microstate.

 

This also suggests that the abstract "game" of questions and answers, really correspond to the observers microstructure physically interacting with the environment.

 

So the collapse of the wavefunction, IMO corresponds to a physical change of the observers internal microstate. We call it names like perturbations, excitations etc. One can also classify these perturbations as rotations, translations, and other types of excitations.

 

One interesting thing here is to distinguish between microstate and microstructre. The mictrostructure defines the degrees of freedom, and their inter-relations. The microstate OTOH is simply state of and given microstructure.

 

But in the above reasoning it's clear that in principle BOTH the microstate, and the microstructure may change!

 

Changing of microstates is IMO a simpler type of information exchange, evolving the microstructures is more sophisticated and IMO may not always be unitary in the traditional sense. Of this unitarity and conservation of information is an ideal of modern physics, but I think we might be open to question everything in a scientific spirit, because as we speak of relational information, it's not trivial to define WHICH information is conserved. Because information, always refers to a real inside observer, and the notion of information is DEFINED relative to "inside measurements" this observer makes.

 

But here my understnading of physics is incomplete.

 

I think many feel the smell, but we're all trying to see where it comes from

 

/Fredrik

[Country Boy]

Are you clear on what "Chaos Theory" is? It has nothing to do with uncertainty or chance. In a sense, Chaos Theory is the opposite of probability. In probability, we have individual events that happen purely arbitrarily but "in the long" run, may turn out to be very close to determined- as in the famous demonstration where you drop beads on to nails so that each on bounce left or right at random but the mass of beads come right up to the "bell curve" already drawn on the glass.

 

In Chaos Theory, every step is given by a specific algorithm- but the algorithm is so complex, that "in the long run", very very tiny differences are expanded to where, unless you are absolutely perfect in your initial conditions, you can have no idea what the result will be.

[foodchain]

 

I think many feel the smell, but we're all trying to see where it comes from

 

/Fredrik

 

Thanks for the reply. I don’t have what it takes to make it through a physics education, I need picture books with animals, and plants, and stuff during class to keep interested, that being said I find QM terribly interesting.

 

Your point about the observer makes a lot of sense to me I think. If I get the information bit coding would just be current state or pointer states?

 

-------------------------

For the thread in general.

 

"The study of the implications of chaos for a system in the semiclassical (i.e., between classical and quantum mechanical) regime.

 

In quantum chaos, trajectories do not diverge exponentially because they are constrained by the fact that the entire evolution must be unitary."

 

http://mathworld.wolfram.com/QuantumChaos.html

[fredrik]

Thanks for the reply. I don’t have what it takes to make it through a physics education, I need picture books with animals, and plants, and stuff during class to keep interested, that being said I find QM terribly interesting.

 

The most interesting parallell and also challange I personally see between physics and biology is to unify the biological evolution of life supporting structures and later on cellular based life and ultimately multicellular organisms which may even grow brains.

 

IMO, I think of this starting at a very fundemental level - at which level the principles of physics and biology etc are necesserily the same.

 

I've got a university physics & math education, but not an formal bio one. However I've studied some of that on my own, and it was very enriching to me, and one of the most fascinating perspectives IMO, is to try to understand the inside view. In biology for example, how does "life" look like, from the POV of a single cell? What does the every day problems look like? I found out that the inside view is possibly quite similar to the every day issues of a human. I need to do alot of things. Find food so I can generate free energy, sometimes I need to make choices - which choice is most benefitial to me? I need to fight problems, repair the cellular structure, get rid of toxic waste/by products. Maintain a functioning logistics to make sure all of these tasks are working. If any of this fails, I will waste valuable energy, and possibly even die.

 

So in a way a cell is an "observer" of it's own environment, whos task is to survive. Survival takes make forms, many complex regulations, reproduction of course.

 

It is this "inside view" that I think is the realistic view, and in this inside view, I think the "logic" takes it's cleanest form! I think the many "strange" things in QM, and strange logic arise because of this.

 

Your point about the observer makes a lot of sense to me I think. If I get the information bit coding would just be current state or pointer states?

 

Perhaps something like that, but what I think is at least one of the important keys, is that while we can, by reducing information, understand the inside view, relative to the big view, that really isn't a completely satisfactory treatment!

 

To make an interesting parallell. In GR, one considers "curved spacetime". One can understand this curvature if one considers the world embedded in higher dimensions. But the interesting parts is to try to define the inside experienced curvature, without using external structures.

 

There is an analogy here to QM. Intrinsic information vs the external birds view information. The analogy certainly isn't clean but I see it at least.

 

And from the intuitive point, and since hte problem of quantum gravity is exactly how to unify QM and GR, I find this choice of analogy particularly nice.

 

The usual idea on howo keep unitarity is to imagine a bigger information context, where the originally non-unitary deviations are adapter. But I think care should be taken when this is done, because one can not just increase the information capacity just like that. It's not physical. IMO at least.

 

/Fredrik

[foodchain]

It seems a lot of what you are talking about is apparatus related as if all we could know in physical is the apparatus. I have to agree but how does that work out in regards to thought or encapsulation of the information. In that sense then it would seem people could only ever understand up to the uncertainty principal, in that physically from an insider view we cant know that percent of data. From an outsider view as in reality outside of human observation, or conscious observation that reality itself will also always physical operate to the percent of uncertainty.

 

So it would seem that would be a base line for explaining physical phenomena. If you could reduce to that say an item rolling down a hill, or being pushed up. Yet in reference to larger cosmological ideas how do you equate not only that but entanglement into theory?

 

As a side question if you want can you relate entanglement to uncertainty at all? Or has such been tried?

[fredrik]

Some quick initial comments.

 

It seems a lot of what you are talking about is apparatus related as if all we could know in physical is the apparatus.

 

Yes, that's loosely speaking close to what I personally think. I should still add that this is my personal expectations, there may be others who think differently. But given that this is a "discussion" I'll continue

 

I have to agree but how does that work out in regards to thought or encapsulation of the information.

 

That's an excellent question and it's where current formulation of QM is IMHO not making complete sense. In QM, one can start by postulating the existence of operators, which corresponds to measurements, which corresponds to projecting information. But the point you raise here, is how much information that can be encapsulated by a particular observer? In normal QM, there is no limit to this as long as the measurements are compatible. This raises the issue of information capacity! This is a very important point. And IMO, this is most certainly also part of the cause of divergences. But the divergences aren't "real", but neither should they IMO need to be removed by ad hoc tricks, they simply shouldn't be there in the first place.

 

What I'm saying is that MAYBE(nonone knows yet) this is related to the excess information capacity in our models.

 

The way I envision this in principle, is that measurement apparatus itself encapsulates the information. In fact, what I wrote in the other thread is that I think that the reason for emergence of incompatible observables can be understood to be a related to this info issue. I sure can't prove this yet but I'm working on it.

 

In that sense then it would seem people could only ever understand up to the uncertainty principal, in that physically from an insider view we cant know that percent of data.

 

IMO, it's worse than that, since we don't even know to that percentage is

But the good part is that I think this might make sense anyway. The nice part is to explain why the concepts still stick togethre and actually make sense, while we at the same time suggest that there are no solid references anywhere.

 

This task is very similary to the task Einstein faced. But instead of talking about 4D "spacetime events", we are talking about distinguishable events with no fixed prior structure of dimensionality. And the task IMO at least is to understand the mathematical connections here that may suggest some epxectations on what the elmementary structures are in this world, ie, what can we say of them? this is an open question, no dense assumptions involved except the principles lined out. And what are the principal interactions that we can expect to be distinguished between these structures?

 

So, what I'm suggesting is that the measurement apparatus is sort of, loosely speaking, part of the encapsualted information. So the encapsulation of information is taken seriously.

 

But where do you start? It's easy to get the feeling in the sea of uncertainty that "anything goes". What is the resolution to this "paradox", because clearly it's not the case that anything goes? IMO, you can say anything goes, but anything does NOT go with equal plausibility. So what could create stability and order out of this complete chaos, is the generation of a relationally and observer relative, defined plausability(think probability) measure.

 

I think this can be done. And the challange is to find out how. This will of course be a mathematical formalism, but I don't think it can be overstated that the core problem is not technically a "mathematical problem", it's a physical problem. Mathematics and logic is just the best human language we have to describe it with.

 

/Fredrik

[foodchain]

That’s just the thing to me. How much study have we done with the uncertainty principal in relation to all the various subatomic particles? I am not sure but I don’t think a single quark of any flavor has been exhausted in regards to study, and on a theoretical side we have concepts like string theory which as far as I know also escape serious testing. I wont pretend like I understand the math involved but for the sake of argument its somewhat pointless to me. The math of any idea alone does not have to work and can be flat out false even if derived from mathematical frameworks that do allow for understanding, or work with the real world. Math and prediction or the physical test going hand in hand I just feel currently that physics is at a great impasse really. So I guess the LHC will be the next step?

[fredrik]

Math and prediction or the physical test going hand in hand I just feel currently that physics is at a great impasse really. So I guess the LHC will be the next step?

 

As an outsider judging from the apparent progress the last 50 years or so that might seem to be the case, however, first of all science to me isn't a job, so I couldn't care less about things that a professional HAVE TO care about in order to stay in business. I'm a lucky fool

 

But from my subjective POV, I am not going to work at LHC, and I also currently enough problems to solve that at leat will keep ME personally busy for a few more years. I am interested, not only in "models of physics" as in static modelling, I'm interesting in the modelling itself, as a dynamical phenomenon. I personally feel that an analysis of this is needed. And deep inside me, I think that this may also unravel some of the keys to solving some of the current conceptual problems in physics. I have a feeling that alot of the "observations" of these issues, ie. the logic of the scientific methods and modelling used in physics, are rarely analysed because it's supposedly meaningless. Here I see alot of DATA that is simpyl not analysed. This data will keep at least happy morons like me busy until LHC or the next generation of accelerators start to produce surprises.

 

I think future of physics will be very exciting. I expect the new physics to come out of a new layer of abstractions that also renews the scientific method.

 

/Fredrik