What caused the physical laws we have?

[AGlane]

Hi. I am new to this forum and was wondering if anyone can answer my question.

What caused the physical laws we have?
Have these laws always been in existence?
Is it true we may never know what the universe was lke before the BB?
Can a theory such as the multi-universe theory be proven?

If these have been asked before please direct me to their page.

Thank you still.

 

[gtring]

Wow. Those are grand and ambitious questions.

- There are different theories on how physical laws came into being. None have been proven. As far as we know, these physical laws that govern us today are the same laws that have been in existence since the Big Bang.
- It is true that we may never know what the universe was like before the Big Bang. Heck, we may never know who shot JFK, and that's a lot more local to us.
- Can a multi-universe theory be proven? Depends on your definition of "multi-universe". If communication is forbidden between different universes, then no, you cannot prove it. If communication is okay between different universes, then yes, you can prove it, but some might say that it's all in the same universe anyway since you can have communication.

 

[apeiron]

You could try some of the good books on the subject - Paul Davies' Goldilock Enigma is a decent recent on just these issues.

 

[marcus]

What caused the physical laws we have?

This is a reasonable question, but most fundamental physics research has not asked it. Instead the researchers have assumed the laws were there, and gone after them as a goal. As a rule they haven't asked are there really permanent laws, and if so why, and why are they these laws instead of others.

Here is a video lecture by Lee Smolin that does explore questions like that. It asks about the origin of physical law and why are the laws (and constants of nature) what they are rather than something else etc etc.

http://pirsa.org/08100049/
On the reality of time and the evolution of laws

He doesn't take the anthropic way out.
None of his analysis is like "well the laws have to be favorable to conscious life otherwise we wouldn't be here asking". He doesn't traffic in man-centered or mind-centered stuff, he tries to explain why these physical laws, independently of accidental detail like Earth life. It's a big challenge.

Smolin is writing a book about this with co-author Roberto Unger. Some of what is in the book comes out (in preliminary form) in this video lecture.
I don't know if they are going to finish the book. It is a hard project. It will take at least into 2010, I think.

No Goldilocks business in the book, or in the lecture. No talk about "if this or that constant were only 5 percent bigger or smaller then stars wouldn't shine or carbon atoms would decay and we wouldn't be here." The reasoning is not predicated on life as we know it. More trying to understand the universe on its own terms, whatever that means.

It may be the wrong approach! May not succeed. Anyway here is some more about it:
http://www.perimeterinstitute.ca/Events/Evolving_Laws/Audio/
These are 2005 audio files, not video.
Here is the agenda of the workshop on Evolving Physical Law
http://www.perimeterinstitute.ca/Events/Evolving_Laws/Agenda/

This may sound strange to you. Unger got tenure in 1976 at Harvard Law at the age of 29, the youngest or one of the youngest ever to get tenure.
He has won a lot of honors. In 2007 he was appointed to a ministerial position in the Brazil government and took over their Economic Policy thinktank. He seems to still be professor of law at Harvard. There is a world economic crisis. How can he also be writing a book with a physicist, Lee Smolin. He already has two demanding jobs: Brazil economic ministery, policy thinktank, Harvard teaching. Apparently a popular teacher:
http://www.thecrimson.com/article.aspx?ref=274071

Under the circumstances should we give up on the book and assume it is never coming out? The proposed title of the book is something like
Can the Laws of Nature Evolve?
Here's an earlier thread about it:
https://www.physicsforums.com/showthread.php?t=262171
What would Unger, a law professor, know about physical law? Human law and physical law are totally different, right?
The mind reels. On the other hand both Smolin and Unger are original thinkers and both very smart. It could be an interesting book if it ever makes it to the press.

 

[Chronos]

Our best observations strongly suggest the laws of physics have remained virtually constant for as long as the universe itself has existed. The most telling measure is variance in relationships between physical laws, like alpha. If alpha has varied over the age of the universe, the change is too small to measure thus far. Alpha is a key member among a group of values referred to as dimensionless constants.

 

[Fra]

Smolin is writing a book about this with co-author Roberto Unger. Some of what is in the book comes out (in preliminary form) in this video lecture.
I don't know if they are going to finish the book. It is a hard project. It will take at least into 2010, I think.
...
It may be the wrong approach! May not succeed. Anyway here is some more about it:
...
What would Unger, a law professor, know about physical law? Human law and physical law are totally different, right?
...
On the other hand both Smolin and Unger are original thinkers and both very smart. It could be an interesting book if it ever makes it to the press.

I like some of these ideas, the first link is a nice talk.

I don't know a lot about Roberto in person but from my perspective but I see no problem with the fact that he is a philosopher with sociological and economical systems (think game theory). On the contrary, if you question the notion of law from an abstracted information theoretic perspecive I think there is a lot in common there. Evolving information and expectations if you see it as an abstraction is not specific to physics. In economic and sociological theory these are also common abstractions, and I see no reason why the conventional physicists are necessarily the ones that understand this abstraction best.

After all it's a totally new suggestion of howto analyse physics and the nature of fundamental law that isn't part of physicists tradition.

/Fredrik

 

[Fra]

Our best observations strongly suggest the laws of physics have remained virtually constant for as long as the universe itself has existed. The most telling measure is variance in relationships between physical laws, like alpha. If alpha has varied over the age of the universe, the change is too small to measure thus far. Alpha is a key member among a group of values referred to as dimensionless constants.

An interesting point in this context, is that the very evaluation we have done, that suggest that the laws of physics has remained constant, has been made by scientists during say a very small part of late human history. And until we understand tha nature of law, how can we distinguish such a highly "local assessment" from the definition of law? Even though we observe light suppoedly from the early age of the universe, and conclude that it's consistent with constant laws, all that information processing has still been taking place in a very constrained part of the history of the universe.

Clearly, if we would have discovered that that laws did change, I'm sure we would quickly find an explanation for it so as to see that the real laws WAS constant. But this would require our knowledge of law to change.

If nothing else, our knowledge of law has for sure not remained constant. And if you combine that idea, into some supposed quantum gravity, then I think it is far from sure that these apparently reasonable assertions we have made will stand. This, due to the important of information in quantum theory. I think we must clothe physical law in terms of information, just like we do with states.

There is an inconsistency of reasoning in a few ways to distinguish information about initial states, and law. This is somewhat in line with Smolins reasoing I think, and I fully agree. I think he is absolutely right. It makes sense to me.

However Smolins the CNS, seems to be more consistent with thta hte physical law is constant throughout the universe, and mutate only when a black hole is formed. I think one can be more radical, and take Smolins logic further, which would suggest that variation of law is not constrained to black hole formation only.

/Fredrik

 

[Fra]

This is a reasonable question, but most fundamental physics research has not asked it. Instead the researchers have assumed the laws were there, and gone after them as a goal.

I see what you mean, but I think that even in this view, from the point of view of philosophy of science, the relevant question even within the idea of there existing eternal laws, and the philosophy that science tells how nature works, not why it works that way - is how an observers information/knowledge of law evovles, as a result of it's interaction history.

Because even if the laws of physical are fixed, the physical process whereby an observer informs himself about this remains to be questioned. Traditionally this has been the problem of the scientific method and belongs to philosophy of science.

But I thinkn a lot of this, suggest that this is more than just philosophy. In particular when you think about the lessons from quantum mechanics, where the apparently information is very fundamental, yet somewhat of a mystery. Why would information about law, in the generalized sense of a physical observer forming an "opinion" about the law, in the environment he exists, be an exception? I can't see a single good reason.

/Fredrik

 

[apeiron]

There is a lot of talk about "laws" - but what do people think they really are? Some rule laid down by a superior being that material objects must obey?

Laws are emergent statistical regularities. What is so likely to happen locally in a given global context that it becomes inevitable (with asymptotic certainty).

Then from this we can say that laws are downwards acting constraints. As said, it is the global context that determines what must (with the highest probabilty) occur at a locality.

If we forgot the word laws and just talked about global constraints, the machinery of physics would sound a lot less mystical.

And think about this. If we talked about global constraints, the interesting question becomes not can they change, but why they don't change?

You would need a theory about the universe's persistence rather than its existence (which is where dissipative structure theory and other modern thermodynamics would come into play).

 

[Fra]

Let me see if you interpret you right:

Laws are emergent statistical regularities. What is so likely to happen locally in a given global context that it becomes inevitable (with asymptotic certainty).

Then from this we can say that laws are downwards acting constraints. As said, it is the global context that determines what must (with the highest probabilty) occur at a locality.

Given the limited accuracy of the communication here, what you say sounds reasonable.

But to me the key is then the exact description of emergent statistics. If you apply this to a real observer, this process of emergent regularitues would then in principle yield a different "emergent pattent" depending on the choice of observer...

And think about this. If we talked about global constraints, the interesting question becomes not can they change, but why they don't change?

...which leads exactly to this question :) Agreed.

And IMHO, the route to an answer to the remarkable stability and consistency of laws (or if you call them statistical patterns) given the potential arbitrariness of the observer choice, likes exactly in that an evolution in the set of observers balances this. The large inertia of law, lies in the evolution of observers, which preserves and produces consistent patterns, which all observers ultimately agree upon as lawlike patterns. (as a limiting case, which btw, is never reached)

That's how I see it.

/Fredrik

 

[apeiron]

If you agree thus far in a general fashion, have you come across discussions of the model for emergent regularities?

As I see it, there are two general bodies of statistical modelling here - gaussian and powerlaw. Gaussian models the "laws" of static worlds (closed system perspectives like an ideal gas) and powerlaws model dynamic worlds (open, far from equilibrium, systems such as criticality, edge of chaos, renormalised, scale-free, fractal, etc).

So linear and non-linear phenomena. Inertial and accelerative frames.

The observer aspect needs to be considered as well. Again a choice. You can reduce the notion of the observer to some localised viewer (point-like within the system - and then choice of location becomes a big, (often relativistic), issue. Or you can expand observerdom to the global bound. Which is the event horizon approach. And the constraints approach in thermo/hierarchy theory.

So some choices that seem to split "law-making" into two broad classes of system-hood. Do you think static or dynamic, closed or open? Do you place your obsever at the local or the global scale?

Once we get to this point, the maths can begin.

 

[Fra]

If you agree thus far in a general fashion, have you come across discussions of the model for emergent regularities?

No, not yet any mathematical models that satisfy the requirements of my visions.

However, the precursor of a mathematical model is somethings a line of reasoning, from which a preferred mathematical formalism loosely follows. There are components of this reasoning present in the reasoning of several people.

1) Lee Smolin - Evolving law

2) Carlo Rovelli - Relational QM, with the key idea that observer can only compare measurements by means of physical interactions. Unfortunately he doesn't really change QM, which is my dissapointment. But there are some brilliant sections in his RQM paper that stand out even if the finish isn't what I hoped.

3) Ariel Caticha - Has the idea that the laws of physicse at some level conincide with the rules of inference as in reasoning based upon incomplete information, he is close to variou MaxEnt methods

4) Olaf Dreyer - with this "internal relativity", an point of view which aims to restores the largely neglected point of view of a physical inside observer. As I undestand it, his ideas are very young and is very much in progress. Time will show what he comes up with.

I have read some of what I've found from these people, and all of them has elements of reasoning that I think is extraordinary and keys. Yet, at the status of development they are, none of them has what seems to be a satisfactoty strategy. There are points in each of their reasoning which I do not share.

And since the reasoning of each of these persons, naturally leads to different formalisms, clearly if I don't share the founding principles, their formalisms are of little _fundamental interest_.

Now you may think that what these people are doing isn't what you all statistical modelling, but the general fashion in which I agree with you, is general. TO me key is the physical basis of the statistics, and in general, I do not accept the continuum probability theory as a basis. Instead, what I have in mind is mathematically a combinatorical starting point, where there are interactions between discrete structures, the continuum limit should be recovered as an effective description in hte large complexity limit, but the continuum does IMHO not have a place in starting assuptions. This is why, I have difficulty in adapting flatly all the standard statistics at this fundamental level.

So as for the choice of formalism, I am still looking for it. But I have some reasonable strong guidelines as to what I'm looking for, and in which general direction to find it.

As I see it, there are two general bodies of statistical modelling here - gaussian and powerlaw. Gaussian models the "laws" of static worlds (closed system perspectives like an ideal gas) and powerlaws model dynamic worlds (open, far from equilibrium, systems such as criticality, edge of chaos, renormalised, scale-free, fractal, etc).

So linear and non-linear phenomena. Inertial and accelerative frames.

The observer aspect needs to be considered as well. Again a choice. You can reduce the notion of the observer to some localised viewer (point-like within the system - and then choice of location becomes a big, (often relativistic), issue. Or you can expand observerdom to the global bound. Which is the event horizon approach. And the constraints approach in thermo/hierarchy theory.
...
Do you think static or dynamic, closed or open?

Given the previous comment, I think I have a more open and radical view, I am not constrained to current staistical modelling. But for sure it can not be a closed system model. It would rather be an open, evolving model, and most probably this is also reflected in the mathematical model. So it's more likely to be of a evolving algorithm-type model than it is to be a conventional static diff.equation model with static parameters. I hope there would be a minimum of parameters, ideally none at the fundamental scale, but at the effective human scale I think there will be, but then these parameters would be understood as evolved, and there would be no initial value problem.

Do you place your obsever at the local or the global scale?

Local of global with respect to what? Spacetime? That is one question I ask.

But even not answering that, my picture of the observer is that the observer could be any subsystem of the universe. And from the point of view of the observer itself, it's of course a local one. But an observer can of course sitll be distributed and non-local relative to a second observer. This does not present a contradiction as I see it.

I think of locality in terms of loose information geoemtric terms:

Two observers are close, if they have the same information.

Thus there is a direct tension is picturing two remote observers, having the same information. It doesn't make sense. Because it totally ignores the fact that spacetime is part of the information.

Sometimes the separation of spacetime and internal info is possible, but in the general case I don't see why it is even necessary. The separation, is rather as I see it related to the simultaneous emergence of spacetime and matter. Here Olaf Dreyer has presented similar arguments. He seems to think that artifical and ambigous separation of spacetime and matter at the fundamenntal level rather than helping, is part of the problem. I agree there.

Instead, the fundamental starting point is that there is no difference. Thus, the question is NOT how to patch matter models onto pure spacetime models. The question is how the separation of spacetime and matter degrees of freedom can be understood.

I similarly have the idea that the observer environment and the observed itself, evolving simultaneously. It's essentially an analogous problem to me.

/Fredrik

 

[apeiron]

Sounds like you should really take a look at Peircean semiotics and his bootstrapping approach involving firstness, secondness and thirdness. This is a general logical model of a system that could then ground the discussion of a particular world system, like our universe.

I probably should have talked about observers first, statistics second.

As you say, what we would be seeking is some fundamental, background independent, process of interaction (some relational QM type deal). We would have the "atom" of the system. Then we would allow this atom of interaction to express itself in every way possible and note the statistics of how it all turns out. So from many individual "observational events" or localised interactions would emerge the continuous whole, the general statistical ambience that is the global whole.

In modelling this way, we would be generalising our seed notion of the observer (or observational dyads - as it takes at least two to interact) to create a system-scale state of "observerdom".

This is Peirce's triadic logic precisely. Firstness = some initial impulse (out of a vagueness). Secondness = the potential for dyadic interactions that arise from the possibility of things existing. Thirdness = the global statistical regularities that result from all dyads being freely expressed.

This is the bottom-up causal view of the story. But there is also, in the emergence of a whole, the emergence of downwards acting constraints. So the whole is not merely a passive. It really is an "observerdom" in introducing a new top-down process of interaction.

This is why Peircean logic is a complex, hierarchical and holistic model of causality. You have the "horizontal" interactions between entities of the same scale, and the "vertical" interaction that run across scale, between the local and the global scales.

To sum up, many people are searching for observer-based or internalist logics with which to take the next step in cosmology/fundamental physics. But most are taking only simple, single scale, approaches. There exists some well-worked out hierarchical and holistic logics in systems science. With Peirce being the central cite.

Then having defined the generating mechanism, an internalist boot-strapping logic, we can crank it up and consider the statistical regularities that result. The output is lawful, regular.

To take a concrete example, we can think of the inverse square law for a force like EM or gravity.

A photon is an exchange between two particles separated in spacetime. So a dyad. But when all possible dyads are considered, we have the image of a sphere surface (a light cone). This is a global statistical picture which then leads to the inverse square law.

And is this law gaussian or powerlaw? Well it ain't gaussian.

 

[Chronos]

You don't need Peircean semotics to reach a statistical conclusion. I do not understand your point. No need for this to achieve a simple and readily affirmable understanding of spacetime. No model of spacetime requires gaussinity to my knowledge, it is merely a useful test for isotropy. Isotropy has not been disproven to date.

 

[Fra]

Sounds like you should really take a look at Peircean semiotics and his bootstrapping approach involving firstness, secondness and thirdness. This is a general logical model of a system that could then ground the discussion of a particular world system, like our universe.

I'm aware of Peirce as a philosopher, but I have never actually read a book or paper from him. It's true that what I described is a kind of bootstrap approach, but has Pierce actually taken this from philosophy to produce a mathematical model? The bootstrap I picture only makes sense in an evolving context.

I think it's important not to be afraid of philosophical angles, but the goal is to produce a physics model, not a philosophical writing. Do you have any pointer on a paper where he actually infers a mathematical model from his reasoning that might actually work in physics? If so I'd be glad to read it. From my point of view, that is problem now.

My reason for thinking that it's still worth to have these philosophical discussions is that some research strategies from my view, propagates as if they do not acknowledge the full nature of the problems.

As you say, what we would be seeking is some fundamental, background independent, process of interaction (some relational QM type deal). We would have the "atom" of the system. Then we would allow this atom of interaction to express itself in every way possible and note the statistics of how it all turns out. So from many individual "observational events" or localised interactions would emerge the continuous whole, the general statistical ambience that is the global whole.

I am still somewhat suspicious if you are thinking of this "global whole" as a birds view, or gods view. To me one key construction principle, is to at all stages, respect the physical inside view. There is no physical observer, can realizes the birds view. And therefor the birds view has no place in the bootstrap.

However, there are approximation to the birds view, when you consider multiple observers.

Most of my objections to some of the papers I've read is that they seems to want to implement at some level, a birds view. This fundamentally goes against the principle of intrinsic logic.

But from the little I know of Peirce, I would be surprised if he didn't think of this. He probably did. The question is if he made a mathematical model out of it. If you have an accesible pointer I woul appreciate it.

This is the bottom-up causal view of the story. But there is also, in the emergence of a whole, the emergence of downwards acting constraints. So the whole is not merely a passive. It really is an "observerdom" in introducing a new top-down process of interaction.

Oh I see. I think what you or Peirce (I still note that I have not read his work) call the downwards acting constraints would be the same as what I call the constraints of the prior. The current prior, implies an _expected_ action that is valid in the abscence in the absence of new information (like QM evolution is valid in between measurements). But in my view, this downward acting constraint is still living in a frog view. I do not see it as a global constraint. Although certainly the frog would see it as a global constraint! Because it's all it can see. But the point is that different frogs may have different views, as seen from a third frog, therefor I think it's in appropriate to call it a global view.

But I think that as the frogs interact, there will emerge a synchronization of their views, so a global view will be emergent out of this. I think this is what you mean as well. But this emergent global view, a limit, can not be used to influence the local action I think.

This is why I think of this emergent constraint as a evolving, not a fixed global one. The bootstrap evolving both the frog and the global constraints by a kind of induction. The frog pulls himself up by holding onto this vague expectations, the the feedback evolves the expectation accordingly.

Let me know if you have any Peirce pointers that may contain a mathematical construction of this. I wasn't aware of it, I thought of Peirce mostly as a philsopher.

/Fredrik

 

[apeiron]

You don't need Peircean semotics to reach a statistical conclusion. I do not understand your point. No need for this to achieve a simple and readily affirmable understanding of spacetime. No model of spacetime requires gaussinity to my knowledge, it is merely a useful test for isotropy. Isotropy has not been disproven to date.

Peirce did not predict any statistical story. As I said, two parts to this. Peirce is just a good cite for how to generalise the notion of observers.

Then we have two statistical/thermodynamic pictures, the regular one of gaussian bell curves and the more recently recognised case of powerlaw outcomes.

 

[apeiron]

but has Pierce actually taken this from philosophy to produce a mathematical model? The bootstrap I picture only makes sense in an evolving context.

Peirce was a logician primarily - which is prior to both philosophy and mathematics. A very enjoyable paper illustrating the mathematical depth of his thinking is this one by Kauffman which shows his handling of asymmetric dichotomisation...

http://citeseer.ist.psu.edu/rd/45492539%2C478038%2C1%2C0.25%2CDownload/http%3AqSqqSqwww.math.uic.eduqSq~kauffmanqSqCHK.pdf

As I say, the statistical story is subsequent to Peirce. It is what is under current discussion in the dissipative structure literature. And in hierarchy theory, particularly the work of Stan Salthe.

http://www.nbi.dk/~natphil/salthe/

A little social history. Peirce was drummed out of Harvard (where his father was a founding maths professor) and wrote a huge amount that was not published in his lifetime. He was so out on his own that he frankly can sound mad on first meeting. But over the past 15 years, he has been rediscovered, his writings gradually published in semi-orderly fashion.

There have now even been popular books like Menand's The Metaphysical Club which showed how he was part of the key trio of pragmatists philosophers, along with Dewey and James. And frankly, how Peirce was the central figure.

Smolin gave him a name-check in Life of the Cosmos (from memory) but just as a cite for the notion laws can evolve, not because Smolin had got into him properly.

Did Peirce turn his deep logical insights into concrete mathematical models of cosmology. No. He just laid some fruitful groundwork I am arguing. He created some valuable jargon, formalised some possible notation, sketched a plan.

Late in the 20th century, along came chaos theory, non-linear systems, scalefree networks - a bunch of actual mathematical models of open system statistics. And also along came Prigogine, hierarchy theory, dissipative structure theory. Most recently, have come Tsallis and others trying to enlarge the modelling of entropy.

Thermodynamics has long been treated as the dull country cousin of physics. Unlike QM or GR, we expect no surprises from it. Yet it does have this big surprise emerging. In my opinion anyway.

So 1) Peirce is a useful cite for the triadic logic that underpins a systems science approach to reality. And 2) open systems thermodynamics is the fundamental thermodynamics for cosmological modelling as a consequence. Not closed system thermodynamics.

I am still somewhat suspicious if you are thinking of this "global whole" as a birds view, or gods view. To me one key construction principle, is to at all stages, respect the physical inside view. There is no physical observer, can realizes the birds view. And therefor the birds view has no place in the bootstrap.

If you follow the arguments of Peirce and Salthe (particularly in Salthe's notion of the cogent moment), you can see that the global bound is the largest scale. There is no need for anything standing outside as the largest scale is doing the work.

As I say, the notion is equivalent to the event horizons now playing such a big part in thermo-inspired cosmology. Of course, physicists prefer to re-invent important notions rather than have to read about them elsewhere .

This is why I think of this emergent constraint as a evolving, not a fixed global one. The bootstrap evolving both the frog and the global constraints by a kind of induction. The frog pulls himself up by holding onto this vague expectations, the the feedback evolves the expectation accordingly.

One thing to note about global scale is that I am talking about spatiotemporal scale. So the downwards constraint acts not just from above, but from the past and the future.

From the past is not so controversial. Causal lightcones model the way the past constrains and therefore predicts what can be happening at the located spatiotemporal instant. But QM then forces us to accept that the future acts backward to constrain as well. We must have something like Cramer's transactional interpretation being take as "true". The future is also (in a nonlocal way) a context to what is happening now.

This is outrageous to ordinary philosophy/physics/logic. But is comfortably modeled in hierarchy theory.

 

[Fra]

Then we have two statistical/thermodynamic pictures, the regular one of gaussian bell curves and the more recently recognised case of powerlaw outcomes.

In the way I see this, I do not assume the form of some limit case distributions.

I envision a combinatorial approach first, and there are no continuous distributions. Continous distributions can emerge as a large number approximation though. And I don't see why a priori you see these two classes.

I think that if you believe in a unique birds view, then the form of that emergent distribution or pattern, could be used as a kind of constraint - I see the power of that. But to me, that kind of reasoning is not consistent with the intrinsic ideal, and I think there is a risk that such a reasoning leads in the wrong direction, because I fail to see how unique birds view can be inferred from an frogs view, which are the only views at hand.

This is why I see the inferred birds view, as the basis for the actions as seen from the inside, and the only way two observers can compare their inferred birds views, is to interact, and this interaction keeps evolving and converging the views.

The idea is that the strategy of a player in a game, is a function of this players view of a kind of birds view, that allows how to also "guess" the actions of the other players. But this very strategy is in principle constantly subject to change and evolution.

This is why the only constraining principle I have found, is that of the complexity bound.

No matter how mad action principles you have, in a discrete observer, the number of possible distinguishable actions are combinatorically limited. So that's where I look for starting points, and try to establish principles and handles for more advanced development. Then I try to picture how that pictures scales with complexity. As complexity increases, more advanced interactions become visible (from the inside), and diversity is produced. And I think the creation of diversity takes place far earlier than when the continuum approximation makes sense. But since there might be hierarchial structures, it may well be that the continuum approximation is ok at one level, it might be totally inappropirate at another scale.

/Fredrik

 

[wolram]

There must be some at least quasi stable states in the sub micro world, what is there to govern a state and keep it stable? some thing that can not change at least in any major way over the time we have been observing the U.

 

[Fra]

Peirce was a logician primarily - which is prior to both philosophy and mathematics. A very enjoyable paper illustrating the mathematical depth of his thinking is this one by Kauffman which shows his handling of asymmetric dichotomisation...

http://citeseer.ist.psu.edu/rd/45492539%2C478038%2C1%2C0.25%2CDownload/http%3AqSqqSqwww.math.uic.eduqSq~kauffmanqSqCHK.pdf

As I say, the statistical story is subsequent to Peirce. It is what is under current discussion in the dissipative structure literature. And in hierarchy theory, particularly the work of Stan Salthe.

Thanks for posting the reference! I took a quick look but I don't see how it helps specifially.

Perhaps you are encouraging philosophical reflection and reflection upon history. I think that is good. I have not studied philosophy per see, but I've read some stuff on philosophy of science, and also some of the history of probability theory etc. It's interesting, and it's interesting to see indeed, how some profound questions has been raised very very long time ago.

I agree it's important to ask the right questions, and in that sense some of these things can be useful.

http://www.nbi.dk/~natphil/salthe/

I'll check that later. Thanks.

If you follow the arguments of Peirce and Salthe (particularly in Salthe's notion of the cogent moment), you can see that the global bound is the largest scale. There is no need for anything standing outside as the largest scale is doing the work.

How can there be a fixed largest scale if it's not a closed system?

Also, there is the question of representation of information. It seems you are considering the whole as one inside observer, which is sort of fine with me. But then, there is still the question of how this complex observer can convey his information to a part of himself?

Are you suggesting something along the line that the information encoded in say an atom, is the same as the information encoded in the entire universe?

To me the practical basic problem, is how can a given inside observer make predictions and learn about it's environment. In a nutshell it's reasoning based on incomplete information, and even incomplete reasoning based on incomplete information. In that question, part of the problem is how to optimally learn from your mistakes, and revise your predictive engine.

/Fredrik

 

[Fra]

There must be some at least quasi stable states in the sub micro world, what is there to govern a state and keep it stable? some thing that can not change at least in any major way over the time we have been observing the U.

In all the madness discussed here, one might expect no stability, so I think it's a relevant question.

It's here I picture that inertia of the information state, in combination with an evolved synchronization betwee nearby observers is what keeps the stability of observations.

I think this synchronization of observers, so as to be resonably consistent, is even the informational basis of spatial separation. Ariel Caticha also suggested this. So that distance is simply a kind of measure of distinguishability between observers as seen by a third observer. The distance is a manifestation of that there at some level, a relative disagreement. The diversity in information define space. The usual idea that spacetime transofmrations leaves physics unvariant, implies that the other degrees of freedom has effectively decoupled from spacetime.

In the information view, clearly the amount of memory, or the number of microstates used to encode a particular information, provides a resistance to change, since each exposure to conflicting information needs to be negotiation, because even the inconsistent new information is not certain, so there is a relative confidence consideration between the disturbannce and the prior that gives stability.

A bit like bayesian updates. However, I think the strict bayesian update may not be flexible enough since it still assumes a kind of birds view of the proability space. so I think bayesian updates is a simplified and truncated version of what we are looking for.

/Fredrik

 

[apeiron]

In the way I see this, I do not assume the form of some limit case distributions.
/Fredrik

The argument is that the system is not stabily developed until it hit some equilibrium balance, some limiting bound.

In an ideal gas, that limit state is gaussian. The particles keep moving but cannot make the randomness of the system any deeper. Change ceases to be change.

Then in an open or freely expanding system, equilibrium is a powerlaw limit state. As modeled by scalefree nets for example.

The system has to be thermalised to be fully developed. And this is a limit. Once thermalised to the max ent, further change is no change.

 

[Fra]

The argument is that the system is not stabily developed until it hit some equilibrium balance, some limiting bound.

Ok, then I think I understand roughly how you envision this. But if this is what it sounds like I don't personally thinks such abstraction is ideal.

What about when this steady state approximation doesn't hold? When you speak of equilibrium I assume you acknoweldge that some timescale is involved, and on the cosmological scale, what is the meaning of equilibrium here?

I think we need an evolving description, rather that something that only makes sense in some hypothetic asymptotic case. I think this evolving description must not depend on the existence of future steady states. A proper evolving model, simply evolves. Why would it have to reference to some absolute steady state?

This sounds like the same principally flawed logic that you have in QM, where you assume the existence of a well defined state space, which is realized as the statistical distributions of infinite repeats of single experiments. It doesn't adress the fundamental point that the evolutionary laws supposedly address, at least in my opinion.

/Fredrik

 

[apeiron]

There must be some at least quasi stable states in the sub micro world, what is there to govern a state and keep it stable? some thing that can not change at least in any major way over the time we have been observing the U.

There certainly must. And that is what top-down causality provides. A weight of constraint shapes up what we find as quasi stable locations. As for example in the solitons of condensed matter physics.

We could even see this as the Higgs mechanism story - the jostling constraint that gives particles mass.

Or for a laugh, let's jump back 100 years to the Lorentz/Mie theory of particles...

"A new nonmechanical, electromagnetic view of nature began to emerge in the 1890s. One of the key people shaping this view was the Dutch physicist Hendrik Lorentz. His attempts to account for the results of the Michelson-Morley experiment led him to devise a radically new theory Of matter. In 1904 he proposed that the subatomic particles making up material bodies were not billiard-ball-like spheres distinct from the ether, but resilient wavelike excitations formed in the et her itself. Thus he conceived matter, like energy waves, to be basically electromagnetic in nature."

But as you stress, we don't have many people in physics theorising about the kinds of contexts that can persist to stabilise their locations. You have to go across to hierarchy theory - a realm of mathematical modelling - to find this kind of first principles discussion.

 

[apeiron]

How can there be a fixed largest scale if it's not a closed system?

Also, there is the question of representation of information. It seems you are considering the whole as one inside observer, which is sort of fine with me. But then, there is still the question of how this complex observer can convey his information to a part of himself?

/Fredrik

At some point you would actually have to devote some years to studying the literature. It is literally another way of thinking.

Anyway, the largest scale is not fixed - like the event horizon that is the visible universe, it constantly expands. That is why it is an open system model.

And on observers, small scale constructs, large scale constraints. One is event, other is context.

So two observers, as you put it, can construct an interaction. A multitude of observation over all scales becomes instead a constraining context. The causality changes sign going from addition to division with scale, in effect.

 

[apeiron]

What about when this steady state approximation doesn't hold? When you speak of equilibrium I assume you acknoweldge that some timescale is involved, and on the cosmological scale, what is the meaning of equilibrium here?

I think we need an evolving description, rather that something that only makes sense in some hypothetic asymptotic case.
/Fredrik

The argument runs a little differently.

In the beginning is your vagueness, a state of pure raw potential (let's assume as an axiom of this model).

The vagueness can only develop in ways that are stable, otherwise by definition the development is unstable and collapses.

In the logic advanced by Anaximander, touched on by Hegel, resurrected by Peirce, brushed up by systems science and hierarchy theory, it always takes two to tango. You must have two opposed tendencies which separate and then mix. Thesis, antithesis and synthesis as Hegel said - Hegel being about the only point of reference most people seem to have to any of this.

So your equilibrium is formed in the middle ground by the mixing of that which has been separated.

This analysis can be applied to any kind of self-organising system. But say we apply it to that very familiar and artificial system, the ideal gas. There is a global boundary set by the walls of a flask. There is the local kinetic motion of the gas particles. Then the mixing of these two things produces a gaussian equlibrium state.

Now the big trick is to understand how an open system, one without a fixed global boundary like a metal flask, one that instead in effect has to be its own container (as in an ever moving event horizon) can act as a constraining system.

Let's offer such an example drawn from physics. QM is non-local. The global scale can constrain. But nonlocality does not act over any distance in spacetime. Only from the current edge of the lightcone. So all is equilibrium (decohered) within. But there is always some largest scale. Nonlocality is not acting over infinite distance. What lies outside the lightcone cannot be part of the constraints acting on the local events.

 

[Fra]

You last response here makes sense to me. I think that it may be a matter of words and ways of expression. Relatively speaking, I think I share enough of your reasoning to say that we are close. But it could be that further arguments at this level doesn't help, perhaps the rest is in the details of how to implement the mathematical formalism here, and use it to solve some of the open problems in physics.

In the beginning is your vagueness, a state of pure raw potential (let's assume as an axiom of this model).

The vagueness can only develop in ways that are stable, otherwise by definition the development is unstable and collapses.

Yes, this makes perfect sense to me.

Now the big trick is to understand how an open system, one without a fixed global boundary like a metal flask, one that instead in effect has to be its own container (as in an ever moving event horizon) can act as a constraining system.

Ok, then it seems we are close. This also makes sense to me. However with one exception, I'm not sure the horizon is increasing. I can also picture it decreasing, as an observer looses complexity, But apart from that, the instant boundary if we call it so, can indeed act as a constraint on the actions. It's a critical part I agree. The logic here is exactly the same as to how a players knowledge limits/controls his own actions.

My objection was that I thought you suggested that this action is somehow constant and fixed. If we can agree that the horizon itself is also evolving then it sounds good.

If we are talking about an observer attached dynamica horizon then we are in agreement.

/Fredrik

 

[Fra]

As I say, the statistical story is subsequent to Peirce. It is what is under current discussion in the dissipative structure literature. And in hierarchy theory, particularly the work of Stan Salthe.

http://www.nbi.dk/~natphil/salthe/

I browsed the 12 online papers and none of them contains even a simple mathematical formula, except some brief reference to a powerlaw formula.

Just from the titles, I am sure that he has some interesting reasoning. Not that I deny the importance of reasoning, it's just that reasoning is something I have spent a lot of time on myself, for the reason that is IS important, and I feel that what I needed now is to take realize the mathematics, given the reasoning. Just more reasoning ad infinitum will not help.

Ariel Caticha has mathematics, he inferes the entropy measures from the cox axioms, and aruges along a particular line, to arrive at a information geometry formalism. But it's still not what I hoped for.

The only think I've seen from SMoling is some matrix model paper.

Carol Rovelli of course has his loop quauntum gravity, but while I love his start in the RQM paper, he lost me in a particular point. I first had high hopes for the spin network foramlism as a possible imeplementation of the combinatorics I referred to. But if that is to be realized, the interpretation of the spin networks seems totally different that what rovelli has in mind. So his particular development only confused me.

Olaf Dreyers work is still under process I think.

My abstraction currently is by combinatorical treatment of microstructures. This induces a sort of measure on "differential changes", and this acts as a sort of "constraint" if you like, that is used to negotiate conflicting information. The plain combinatorical model so far leads to a sort of transition amplitudes that depend on a complexity factro as well as the mass of the microstructure, and the mass of the incoming conflicting evidence as well as the Kullback-leibler entropy.

But then the complex parts are how to formalise the generation of mass, and how to separate internal and external degrees of freedom. There is a natural separation of the degrees of freedom representing the communication channel, And the area of this is bounded due to the limited complexity. Even the information divergence is limted since the probabiltiy space is discrete.

The evolution is effectively govered by an action principle which is implemented technically as a minimum speculation principle. the contraints, or prior info; implies an effective probability space; and then the expected action is the one with the largest transition amplitude.

anyway... there are no published papers on this I know of, and there won't be any for a long time... but I am hoping to come across someone that are working along thse lines...

There are a lot of reconstructions to make here... for example the general mechanism of activating dimensions, but this is also entangled with the generation of mass in my picture. I picture dimensions growing out of excitations of lower dimensions, due to information that out of consistency requirements maps out higher diemnsions. So the dimensions are also related in a measure-on-measure hiearchy. This is not too unlike some associations tostring theory you can make with some imagination. The difference is that, there is not strings, and no background space. It's instead the inside view that mapes out the dimensions, from the inside.

But there is still a long way from there to actually make an computations to see what relations between energy, mass and dimensionality this would predict.

The standard model would in this early phase simply be a "reality check".

/Fredrik

 

[Fra]

Even the information divergence is limted since the probabiltiy space is discrete.

I think I caused confusion on this point before so I add here: I don't just mean that the index is discrete (ie discrete samples), I mean that the probability value, usually [0,1] is discrete.

If we go back to say ET Jaynes nice attempt to argue that probabiltiy is the logic of science, he early in his book postulates that the degree of plausability takes the value [0,1]. This bold introduction of real numbers is very suspect. Instead, from this point I have different vision. The continuum is reconstructed from distiniguishable microstates. It effect it means that there is doubt to the physical basis of the continuum. The continuum is an abstraction. Everyone knows what a real number is, but before we introduce real numbers for counting or rating things like evidence some more thought is needed.

/Fredrik

 

[apeiron]

A few comments:

You say you are seeking some concrete cosmological model. That is the maths you want to see. My interest is in concrete models of systems in general, of which cosmological ones would be an example.

And it is early days. I take hierarchy theory to be mathematics. It is the geometry of systems, so to speak. But currently more at the descriptive than the calculating stage of development.

You want to see formula, well the formulas as far as they exist are mostly still in words and diagrams rather than notation.

There is some concrete modelling from another kind of source - neural network models. See the hierarchical ART models of Stephen Grossberg. He has exactly the kind of equilibrated bottom-up and top-down systems logic that I am talking about.

http://cns.bu.edu/~steve/

for a good overview of his work...
http://www.cns.bu.edu/Profiles/Grossberg/groASAttBra1995.pdf

 

[apeiron]

On the continuum:

The world, indeed all systems, are formed by symmetry breaking and so there is always a dichotomy. Discrete/continuous is one of those dichotomies. But in the systems science approach (which stresses mutuality, synergy, dyadicity) both aspects of a dichotomy must exist. It is not a binary choice. Instead, both aspects will be fundamental.

The standard metaphysical position of physicists is mondadic. The world must always be fundamentally a this or a that. And yet QM forced the dichotomistic on scientists (such as Bohr with his yin yang complementary talk). It is not either location or momentum but both.

So in my view, a successful cosmological model would contain both the discrete and the continuous as fundamental.

In fact, this is exactly what we find. We have a local model in QM that describes the smallest grain of being and a global model of GR that describes the global continuity of spacetime.

There is this project in physics to break-up GR and be left with only the little bits and pieces, the discrete atoms, of QM. It is called the search for quantum gravity. But a systems view says this cannot be possible or useful. The "real" theory would find both theories as its twin opposed limits - hierarchically speaking, its local and its global bounds (see Salthe's scalar hierarchy).

Yes, it should be possible to marry QM and GR - via their common dissolution into a vagueness. And this is why I like loop and spin network approaches. It is more a marriage of the two in a vagueness. But the monadic metaphysics demands that the globally continuous be broken into the locally discrete, And that cannot be possible.

To complete the story, the systems science and Peircean approach I am talking about always ends up with a triadic equilibrium structure as its stable outcome.

So where is the triad that emerges out of the dyad? Well between the hyperbolic spacetime of QM and the hyperspheric spacetime of GR we find the flat spacetime of classical Newtonian physics.

The full triad is QM (as the discrete local small scale model), classical (as the emergent flat middle ground that forms between two extremes, by the mixing of the two extremes), and then GR (the model of the warped, closed, global boundary).

In the systems approach, everything is dynamic rather than static, a process rather than a structure. And so all three levels of the system are in action. The QM smallness is always collapsing (decohering to its smallest achievable scale), the GR largeness is always expanding (collapse becomes a problematic issue, is it actually permitted?), and the middle ground is always equilibrating (becoming as flat as possible).

You can see how this dynamic systems approach which acknowleges the global scale can remove some standard problems of cosmology. It explains why universes must expand - that is what systems must do to persist. It explains why middle grounds are flat - that is what the action of equilibration achieves.

 

[Fra]

You say you are seeking some concrete cosmological model. That is the maths you want to see. My interest is in concrete models of systems in general, of which cosmological ones would be an example.

Actually I am also looking for general models. General learning models. It is how I think for most of the time. But probably my prime focus is physics.

The connection between learning models and physics is similar to Ariel Catichas, Jaynes and others ideas. That the laws of physics is somehow related to the logic of reasoning upon incomplete information. And if you put that into an evolving context, with feedback, that's what learning is. It's a game.

I am not specifically interested in only cosmology in physics. My main interest is unification of forces, with special attention to QM and GR domains, and to put this in a general information theoretic context.

What I mean with the quest for mathematics is that I want quantiative predictive models. And that normally means mathematics. But I fully agree that the constructing principels can well be described by general reasoning and abstraction. But the ambition must be a computable model, to establish a utility.

And it is early days. I take hierarchy theory to be mathematics. It is the geometry of systems, so to speak. But currently more at the descriptive than the calculating stage of development.

Yes, fair enough. The evolving approach in physics seems very young. So it's not surprising that much is open.

As I see it, there has been a trend to geometrize physics, but instead I wish to abstract it in a background indepedent information theoretic framework. And in that view, the physical interactions would be strongly related to rules of inference and evolutionary learning. The self-organisation is simply the constructive and self-preserving trait of learning and adapting.

Like you mentioned, the opposite would mean that observers failing to implement that, would self-destruct and simply not populate our world except in a transient manner.

My first inspiration was various Maxent methods, along the lines of Ariel. But I still realized something is wrong with that. And the founding key is how to "count evidence" and measure information, and here the continuum is confusing. Most MaxEnt methods fails in the sense that their choice of entropy measure is ambigous. the choice of measure, does constitute a background. Instead, my idea is that the definition and measure of information itslef, must evolve. Therefore, there is not universal measure of information. But this is exactly what the meaning of a background independent information theory means to me.

/Fredrik

 

[apeiron]

Had a swift zip through Ariel Catichas' approach. It seems in the same ballpark as Peirce, Salthe, Grossberg and Rosen (a logician, hierarchy theorist, neural networker and theoretical biologist!).

For example, Peirce's cosmology was based on the idea of learning. A world develops by a kind of self-discovery so to speak.

Grossberg's is a learning net approach. His ART systems predict the world they expect to see, then react and learn from that which has happened which was not predicted. This seems exactly Catichas' approach of global understandings only changing in the light of specific constraints.

Rosen's modelling relations theory is likewise all about models that anticipate and so minimise their need to change.

Applying all this to cosmology and entropy (using what some would call a pansemiotic approach) we could say there is a general drive for the universe to dissipate all gradients, all uneveness in terms of energy differences. So an uneveness would be one of the specific constraints that the general model must "learn" from in Catichas' view.

But the universe, as a context, is not just a passive learner, but an active flattener of uneveness, a dissipator of gradients. So really, I would want to say it is the general that constrains the specific.

Although this can also be phrased as saying the universe, as an example of a learning system, is seeking to become unconstrained by its local specifics. It wants to smooth out things to the point they are no longer locally troubling.

In mind science, this would be called the flow experience. Where everything is so perfectly anticipated, the global state of prediction needs no updating, no corrective learning.

This is getting us a long way from conventional notions of entropy as "disorder". But then entropy modelling is in want of a broader path.

Max ent for a system would be about reaching equilibrium - a state where there is nothing further to learn, nothing specific that could alter the global balance.

And this would be the heat death universe, an infinite cold void with all energy gradients flattened asymptotically to the limit.

 

[Fra]

Had a swift zip through Ariel Catichas' approach. It seems in the same ballpark as Peirce, Salthe, Grossberg and Rosen (a logician, hierarchy theorist, neural networker and theoretical biologist!).

I'm glad you see the general connection!

Max ent for a system would be about reaching equilibrium - a state where there is nothing further to learn, nothing specific that could alter the global balance.

And this would be the heat death universe, an infinite cold void with all energy gradients flattened asymptotically to the limit.

In my thinking, I bypass the general choice of entropy and just use combinatorics to defined a discrete conditional probability, which is effectively a transition probability. It is the probability for a given change, given the present. A differential form of transition probability. And here there is a MaxEnt kind of principle, which is closely related to a more information theoretic form of the least action principle.

In this, the KL divergence appears (relative entropy) appears naturally.
See http://en.wikipedia.org/wiki/Kullback-Leibler_divergence

One can say that the maxent principle defines a differential structure, that is valid until more information is received. This means that the entropy measure of the maxent is deforming during the process, which means that there is no global heath death.

But apart from this as I see it the abstraction contains also a kind of datacompression which I picture as several related memory structures, in the relation between these structures, non-commutativity will naturally emerge.

Another constraining principle is complexity, which means that a system om memory structures are still constraint by a total complexity, which imples that the probability for excitation of some structures depends on the complexity scale. Here a hierarchy is also present.

Also these communicating non-commutatuve structures further complicates the dynamics away from the simple dissipative style. The dissipative mechanism are defined in my thinking only in a differential-change-sense.

So I think the maxent reasoning applies to the general case, like flat spacetime refers to a curved global spacetime.

/Fredrik

 

[Fra]

Another complicatation yet is that since i do not picture infinite sequences of repeating experiements (this makes no sense since the measure are only define in a differential sense; it would mean you need to have infinite data before updating your opinion, which won't happen) different observes, having different information will in generall disagree upon their transition probabilities, because as I see it the utility of transition probabilities is that of odds, as basis for your actions.

So the "inconsistent" or disagreeing odds of the same event, suggests that they all act according to their beliefs. This is very strange if you have the frequentists interpretation of probability in the sense that it is verified by an actual infinite repeat of the same situation. I say that there is no way you CAN repeat the same situation without deforming you history and thus updating your information.

The frequentist interpretation is only an abstraction, where the sensible interpretation rather is more like a constraint for your actions. Instead the scientific approval of what probabilities that are "right" is simply the surviving acting strategy!

I think this is closely related to your thinking as well, and I think some form of probabilistic formalism will come in here, except I believe in a combinatorical one from start, where there is a system of interconnected "state spaces" rather than one. The difference is that the represent datacompression of actual history. Compression algorithms chosen, not to accurately mimic actualy timehistory, but to be of maximum utility for the future of the host.

Pretty much like some research suspect the human brain works.

/Fredrik

 

[Fra]

One can say that the maxent principle defines a differential structure, that is valid until more information is received. This means that the entropy measure of the maxent is deforming during the process, which means that there is no global heath death.

Another way to see this is that I am suggesting a unification of the Principle of maximum entropy, and he principle of least action. It is in fact, the one and same principle. The unification lies at information about states vs information about expected change. And if you insist on a transparent information picture the state space is replaced by a space of differential changes. so the MaxEnt principe implies a kind of principle of least action.

/Fredrik

 

[apeiron]

I've also argued that least action and MEP are the same - one is about the dissipation of histories (as in Feynman sum over histories) and the other about the dissipation of energy gradients.

 

[apeiron]

To wrap up - if laws are viewed as emergent regularities of self-organising systems, then we need three parts to the story.

We need the initial conditions, the unformed potential from which the system arose.

We need the selection mechanism or process which acts on this potential to develop it.

Then we need the statistics of the outcome - the regularities that persist because a system has gone to equilibrium.

This is a triadic story - which Peirce as a logician was trying to articulate.

And which part needs to be modeled as the mathematics? It could be just the end state.

You could perhaps throw away the mechanism and the initial conditions as excess metaphysical baggage, just use the emergent laws, or statistical regularities.

 

[Fra]

We need the initial conditions, the unformed potential from which the system arose.

We need the selection mechanism or process which acts on this potential to develop it.

Then we need the statistics of the outcome - the regularities that persist because a system has gone to equilibrium.

This is a triadic story - which Peirce as a logician was trying to articulate.

Philosophically we are close enough here.

I have structured the problem into three parts as well

1) what is the logic of guessing?
Which is the logic of choosing the action based upon the current info. Essentially this is a form of statistical inference.

2) what is the logic of correction?
Which is the logic of updating your information i nthe light of new, essentially bayesian but not quite. It's sort of statistical inference of change, based on differential structure of the former AND the fact that the statespace in general can change, expand or shrink. The logic of correction is what restores infomratio conservation.

3) The synthesis of the logic of a corretive guessing? which results in evolution.

I think I described parts of it very briefly in https://www.physicsforums.com/showthread.php?t=239414&page=3 some time ago.

And which part needs to be modeled as the mathematics? It could be just the end state.

IMO, all steps will be modeled quantiatively. Also all three steps are sort of intermingling. It's sort of a cycle. But it will be a mix of conenvtional analytic expressions, and algorithm type of models. As long as it's computable, it's quantitative. I have low hopes of fidning neat analytical solutiosn to this. It's far too complicated. Computer simulations is more likely, where near certain solutions effective analytical models can be found as approximations.

About the initial conditions as you say, I have come to the standpoitn that in principle the model msut work with ANY initial conditions. But that's an ambigouity that isn't possible to handle, so I have chosen to focus on the initial conditions in hte low complexity limit, simply because then the initial value problem becomes trivial, or vauge as you would probably call it.

Essentially the state space expands, and thus the initial conditions when the state space (abstractly speaing) is small, then there simlpy is no landscape of initial conditions.

But I sure don't have any answers yet either. But I expect to find them.

But we seem to share similar view on the nature of law in principle, and that it's a subtle concept.

/Fredrik

 

[apeiron]

I think the deep mathematical foundation here is to be found in "the geometry of symmetry breaking".

This is what underlies the modelling in all the different fields I've cited, from particle physics and cosmology, to hierarchy theory, Peircean semiotics, dissipative structure theory and neural networks.

So the target for mathematical modelling is the trajectory from max symmetry => max asymmetry.

Seeing as you want an information-based view of this, think of the trajectory from noise to signal.

Noise is the max symmetry initial conditions - the vagueness or pleni-potential. Then some operation (a symmetry breaking) isolates a signal. So we have the max asymmetry of an event standing proud of its (discarded) context. A 1 surrounded by a sea of 0s in Shannon's accounting system.

The max symmetry => max asymmetry trajectory would be a reformulation of the second law. It would be a higher level generalisation of the entropy of order => disorder story.

How does this square with cosmology?

In the beginning was a max symmetry in that the universe was plankscale. All distances and energies were vanilla the same and undifferentiated. Then the symmetry broke. At heat death, it will be max broken.

Again the outcome seems vanilla as everywhere (every location) is max cold. All gradients dissipated. But actually the situation is max dichotomised in that the universe is also max large and flat. So the universe is max divided into largeness and smallness with as little as possible existing in-between. A crisp outcome. A phase transition completed. A max ent in terms of a division between macro and micro states.

Dark energy and other issues would have to be reconciled to this picture. But the point is that second law thinking would seem the target of a fruitful generalisation towards concrete maths models. Intermediate stepping stone ideas like disorder, entropy, information, would be generalised to the fully geometric idea of symmetry (and symmetry breaking, and thirdly, asymmetry).

I have already been locked once in these forums for daring to suggest there is indeed a geometry of asymmetry, so I will leave it there.

 

[Fra]

I think the deep mathematical foundation here is to be found in "the geometry of symmetry breaking".

This is what underlies the modelling in all the different fields I've cited, from particle physics and cosmology, to hierarchy theory, Peircean semiotics, dissipative structure theory and neural networks.

So the target for mathematical modelling is the trajectory from max symmetry => max asymmetry.

Seeing as you want an information-based view of this, think of the trajectory from noise to signal.

Noise is the max symmetry initial conditions - the vagueness or pleni-potential. Then some operation (a symmetry breaking) isolates a signal. So we have the max asymmetry of an event standing proud of its (discarded) context. A 1 surrounded by a sea of 0s in Shannon's accounting system.

The max symmetry => max asymmetry trajectory would be a reformulation of the second law. It would be a higher level generalisation of the entropy of order => disorder story.

How does this square with cosmology?

In the beginning was a max symmetry in that the universe was plankscale. All distances and energies were vanilla the same and undifferentiated. Then the symmetry broke. At heat death, it will be max broken.

Again the outcome seems vanilla as everywhere (every location) is max cold. All gradients dissipated. But actually the situation is max dichotomised in that the universe is also max large and flat. So the universe is max divided into largeness and smallness with as little as possible existing in-between. A crisp outcome. A phase transition completed. A max ent in terms of a division between macro and micro states.

Dark energy and other issues would have to be reconciled to this picture. But the point is that second law thinking would seem the target of a fruitful generalisation towards concrete maths models. Intermediate stepping stone ideas like disorder, entropy, information, would be generalised to the fully geometric idea of symmetry (and symmetry breaking, and thirdly, asymmetry).

I have already been locked once in these forums for daring to suggest there is indeed a geometry of asymmetry, so I will leave it there.

Yes, we can finish the discussion here. Again your general reasoning above makes sense to me. So I have no obvious objections, except of course that we both admit that the exact mathematic model is still yet not on the table. So well have to keep working on that.

So back to the questions of post 1.

- What caused the physical laws we have?
- Have these laws always been in existence?
- Is it true we may never know what the universe was lke before the BB?
- Can a theory such as the multi-universe theory be proven?

I think we've now made our contribution to elaborate this. Which is also IMO partly well in line with Smolins reasoning that Marcus highlighted in post #4 when quoting his talk on the reality of time and the evolution of laws.

/Fredrik