LHC - the last chance for all theories of everything?

[tom.stoer]

I am still thinking about axiomatic systems plus a selection principle.

Let's make an example (we already discussed the exotic differential structures briefly; I think they can serve as a good starting point).

Assume that for some reason nature decided that its existence is based on manifolds. Now let's count manifolds (up to their symmetries). I guess we agree that we can count manifolds with respect to their dimension. Then I guess that for each dimension n we can count manifolds with respect to topological / geometrical building blocks (this is known in n=2, was conjectured by Thurston for n=3 and proven by Perelman: http://en.wikipedia.org/wiki/Geometrization_conjecture). In all dimension but 4 and we can count manifolds with respect to their differential structures. In n=4 the standard R^4 escapes counting as its family of non-diffeomorphic manifolds is uncountable (http://en.wikipedia.org/wiki/Exotic_R4).

At the same time most (all?) physical laws are local (differential equations), and locally all exotic R^4 spaces are diffeomorphic = physically indistinguishable.

Assume now that all those different manifolds exist in the sense as dicussed above: A mathematical structure is a universe. Therefore we have a countable set of manifolds w/o differential structure. Then we have a countable set of manifolds with different differential structures based on topologies different from R^4. And then we have an uncountable set of R^4 with different differential structures.

Now picking one manifold randomly will - with probability one - select an R^4 manifold. But as I said, locally all R^4 manifolds will be identical. Therefore we found a selection principle telling us that we are living in R^4.

I know this is not a perfect example, but it shows how a selection principle could emerge from deeper principles w/o using it as input. This is still my belief: Physical existence is based on mathematical principles. These principles allow us not only to describe what exists but to some extend to explain why it exists and why it is the way it is. Of course we have to use some axiomatic input (in my example it's the idea that nature is based on manifolds and that every manifold exists both in a platonic way and physically).

Remark: no version of the anthropic principle was required! Math alone was sufficient to explain why we live in an n=4 differentiable manifold.

 

[Fra]

I can symphatize with the desires to find constrainst to select away options. Given a choice of inference system, I think that one can certainly make an inference of some type.

Here is one way to connect my thinkg to Tom's thinking:

Assume nature is like THIS, then we might be able to find some constraints (deductive or inductive depending on the type of inference system) acting as a kind of "selection".

What disturbs me in general, is that the choice of inference system (axioms in your case) is ambigous. However I'm the first to acknowledge that this is unavoidable, since you need a current position, in order to make relative progress. The inference system is part of the position to me.

In a certain sense, I think any starting point must be valid as long as it, itself, is subject to selection and critics.

What I mean is that, consider 3 groups of scientists/observers...

One starts with an null hypothesis that the Earth is a flat pancake.
One starts with the null hypothesis that the Earth is a torus.
One starts with the null hypothesis that the Earth is more or less a sphere.

Once they put the hypothesis to test, two of the groups will be forced to revise their hypothesis, and in the end they will be in agreement.

Here the initial hypothesis isn't important, it's the scientific process itself that does the trick.

However, there is one important thing here which is that the initial inference system and hypothesis, must be able to be encodable with respect to the observers. In particular do I see it in a way that if you think of the inference system (the conjectured/hypotized law) as a computation, then computer is the observer. Clearly the complexity of the computer limits how complex algorithms you can compute.

Alot of the time when human scientists imagine, the inference machinery that are to apply to physical systems, the human limit is almost unlimited as what one can compare to say an electron. We can certainly ask questions that an electron can't.

So I try to ask myself like, what questions would I ask, if I were an electron? :) Quickly one can first post another question, what questions COULD I even FORMULATE if I were an electron?

Then I ask, what happens if I ask, what questions COULD a system x formulate, and then ponder what the limit complexity(x) -> 0 looks like. For sure then the options should be fed enough to possibly be finite.

There I have my starting point. This is principally as ambigous as tom's choice of more complex axioms, but I defend it with thta it's from my point of view, the smallest possible speculation that I have to do, to be able to make any predictions whatsoever.

Then I ask, what happes to this proto-inference system, as again complexity(x) -> grows.

/Fredrik

 

[tom.stoer]

Frederik,

don't focus so much on my (preliminary) axioms. I simply wanted to provide an example where one can see a physically viable selection principle emerging w/o the need to be put in by hand.

 

[ConradDJ]

Assume that for some reason nature decided that its existence is based on manifolds...

This is still my belief: Physical existence is based on mathematical principles. These principles allow us not only to describe what exists but to some extend to explain why it exists and why it is the way it is.

I understand why mathematical principles can seem more fundamental than physical ones – why again and again the quest is renewed to find a reason for the known physical principles in principles of math or logic. But in the first place, we’re always using physics as a guide to choosing a mathematical starting-point... which is otherwise arbitrary, from a purely mathematical point of view. Why manifolds?

And in the second place, what kind of success can we expect from this quest, and what would be accomplished if it succeeded? Suppose the original hope of string theory had proved correct, that there was only one mathematically consistent theory that was also consistent with all the complex symmetries in particle physics, including gravity? Or suppose it turned out there was only one mathematically viable formulation of quantum gravity. Something like that would at least give us a reliable starting-point for trying to understand why the world is built the way it is – but it would hardly be an answer in itself.

So I think it’s worthwhile to ask how we might expect to answer the fundamental questions, based on what we know about physics. One of the things we know is that the universe has changed very radically over 13+ billion years, and all or nearly all the physical structure of our world did not exist at the beginning. This in itself seems to point to something very different from mathematical principles, as a starting-point, and raises the possibility of an evolutionary explanation. We know from biology how powerful that can be, as a way of explaining why things are the way they are.

Another thing we know is that what things are and how things happen, in physics, has to do in some way with the complex processes by which information about things is obtained and communicated. Whatever happens in the “collapse of the wave-function” seems to be basic to the emergence of definite information in the physical world, but it’s not clear what if anything it has anything to do with mathematical principles, since it happens at random.

Fredrik’s project seems odd to me in some ways, but I’m rooting for him because he’s doing something that seems to me important – trying to develop an evolutionary approach that takes into account the information-capacity of physical systems. Mathematics plays a key role, but there are good reasons to think that what’s going on in the physical world – even at the foundations – involves more than mathematical consistency.

 

[ConradDJ]

In a certain sense, I think any starting point must be valid as long as it, itself, is subject to selection and critics...

However, there is one important thing here which is that the initial inference system and hypothesis, must be able to be encodable with respect to the observers...

So I try to ask myself like, what questions would I ask, if I were an electron? :) Quickly one can first post another question, what questions COULD I even FORMULATE if I were an electron?

Hi Fredrik –

Specifically, what seems odd to me in the way you explain your approach is that it focuses on the complexity of information a physical system (“observer”) can contain (“encode”) and process in some way (“inference”).

This makes sense to me as one part of the issue – but what doesn’t come into focus for me is the interaction-context... which not only communicates information to the observing system, but would also (I assume) be what poses the question the observer is trying to “infer” an answer to... and would also be the context for the observer’s “action” that results from the inference, which would presumably alter the environment for other observers.

I see the point of taking an “internal” view of the world... but it’s still a view of the world “out there” in which each system participates with others. So I’m trying to see what this informational interaction-context looks like. What would the electron’s “inference” be? What would the input be, and what would be its “action”?

I think what you’re saying is, that the basis for a TOE should be not just mathematical consistency per se, but what can appear consistently to a physical system in a particular context... which might then be the basis for a further (random?) search for possible consistencies. So mathematical consistency would be one aspect, and which sorts of mathematical consistency are physically relevant could change as the systems evolve.

 

[tom.stoer]

I understand why mathematical principles can seem more fundamental than physical ones ... Why manifolds?

It's hard to distinguish between mathematical and physical principles. I tried to explain my position a couple of days ago: usually you start with a physical principle and develop a theory out of it = develop a math framework. During the development the physical principle may be transformed into a mathematical one. Look for example at the principles in special and general relativity.
Why manifolds? I don't know. It is just a starting point for my example. The fundamental principle "manifolds ..." is not so interesting here. My idea was to demonstrate how from such a principle selection criteria may arise.

Or suppose it turned out there was only one mathematically viable formulation of quantum gravity. Something like that would at least give us a reliable starting-point for trying to understand why the world is built the way it is – but it would hardly be an answer in itself.

You are right; it wouldn't explain "why QG at all - and not game of life". So you would have to step back and think about your unique theory again. Hopefully you will find a hidden and more fundamental (physical) principle from which this uniqueness follows. At some point it may be appropriate to think about an evolution process, but as I said: I do not (yet) see a good starting point for an evolution process - and I still like the axiomatic approach more ;-)

... that the universe has changed very radically over 13+ billion years, and all or nearly all the physical structure of our world did not exist at the beginning. This in itself seems to point to something very different from mathematical principles, as a starting-point, and raises the possibility of an evolutionary explanation.

Not really. The standard model plus GR seem to explain the different structures on different scales (different ages) quite well. It's the same with evolution in biology: The fundamental laws (selection due to environmental pressure, survival of the fittest) and the building blocks (DNA, RNA) are static but nevertheless allow for a dynamic evolution process. That's for me a very good reason not to let everything become dynamic, emerging, relative and - hopefully not - arbitrary.

Whatever happens in the “collapse of the wave-function” seems to be basic to the emergence of definite information in the physical world, but it’s not clear what if anything it has anything to do with mathematical principles, since it happens at random.

I agree that the ontological interpretation of qm is by no means clear; but to take the wave function as a physically real entity is - if you ask me - not a very good choice.

... what’s going on in the physical world – even at the foundations – involves more than mathematical consistency.

Yes, but not less, either!
The biggest successes in physics were always backed up by mathematical consistency (Newton invented both his dynamics and analysis; Maxwell's theory = collection of known physical phenomena + partial differential equations; quantum mechanics = collection of known physical phenomena + Hilbert spaces etc.).
The current situation in physics is vexing: we are losing plausible physical input due to the fact that the domain of quantum gravity is hardly accessable by experiments. At the same time mathematical rigour fades away! As far as I know NO quantum field theory except the non-interacting ones are proven to exist mathematically. A couple of days ago I found a paperon arxiv (I have to post a link here) how rather clever people tried to construct 3- and 4-loop measure and amplitudes in string theory - a theory claiming since a quarter of a century that the perturbation series is well-defined and that no divergencies exist has not even started to define the n-loop amplitues for all finite n!

Why all this? Because I think that for a generation heading for a ToE I expect some carefulness before starting with multiverses etc. I have the feeling that we can learn much more from current physics if we study its phenomena carefully, take all facts into account and develop a sound mathematical system. After we succeed with this task it's time for the next meta-level.

 

[Fra]

Hello Conrad,

I see the point of taking an “internal” view of the world... but it’s still a view of the world “out there” in which each system participates with others.

We should distinguish between the view OF the outside (from the inside), and the view FROM the outside, I'm not sure what you mean here?

If we are talking about the view of the outside (from the inside), then that is still constrained to the complexity of the observer; since all we have is an IMAGE of the outside, but "painted" on the inside screen (very loosely put but I think you get the point). This IS the context of the inside view. From the inside point of view, the environment is like a "black box", whose actions and structure the observer is trying to predict.

I make this distinciton.

The the actions are independent on the external unknown black box. The actions depend only on evidence existing on the inside. The REaction from the environment OTOH is in principle unpredictable, and this is what generally makes the inference system on the inside revise. The inference system doesn't contain information to predict it's own evolution. Each inference system has a kind of "self-evolution" which is what to expect if no feedback is given from the environment.

This latter is a kind of correspondence to "measurement", and the self-evolution is the regular equations we would write down. IE. the schrödinger eq applies only in between measurements. If the schrödinger contained the information to predict the deformation needed at each measurement then it would contradict itself.

If we are talking about the outside view, then you have introduced another observer, and generally two observers are interacting.

In a certain sense it's obvious that to an inside observer, the environment is a black box, and if you think of the black box as the "context" to give feedback as to evolve the inference system then that's not know from the inside. The only way to get to know it, is to play the game, take an action and await the reaction, and revide your inference system accordingly.

If the inside observer could predict this entire evolution of himself then the entire discussion wouldn't be nessary. The fundamental problem, that I acknowledge is that generally we are forced to take actions based upon incomplete information. And of course the reaction is not deterministically predictable.

So I’m trying to see what this informational interaction-context looks like. What would the electron’s “inference” be? What would the input be, and what would be its “action”?

Of course, my approach isn't developed enough to answer this yet.

If I were to elaborate this it would probably take us even further away.

The "microstructure system" of the electron would have a representation here.
This representation implies an inference system. Each inference system contains a "natural action", which would encode the say "naked interaction properties" of the electron - what the interaction properties of the electron SEEMS to be, from an outside observer is still more complex. A kind of renormalisation would be built into this.

Hopefully the inference system, would explain why an electron say only responds to gravity and to EM fields: the idea is that this analysis should reveal WHY the other interactions are indistinguishble to the electron, and therefore it's action is invariant with respect ot them.

(Or of course, if this is just an approxiation, then any corrections to the action should come here)

So, I'm still trying to develop this idea. For example, in my approach, I have not yet even reconstructed something like the 4D spacetime, neither have I reconstructed any microstructure of matter, so I couldn't possibly have any postdictions of the properties of the electron yet.

I do start with some subjective assumptions that are the least speculative I can come up with, but these concern the revision of the inference systems; which is the direct physical analog of the scientific method; howto revise a hypothesis in the light of contradicting evidence. Not the exact makeup of them as such; that should follow from the design principle given a seed that could be chosen at random or at will.

/Fredrik

 

[moniker2]

The theory is reformulation of Albert Einstein 1905 work. It takes the mutual opposition of Lenard, 1910, and is written in terms of Isaac Newton’s idea of absolute space and time. It stipulates that space-time vacuum share similar properties to a non-Newtonian fluid causing particle polarities.

 

[Fra]

It's the same with evolution in biology: The fundamental laws (selection due to environmental pressure, survival of the fittest) and the building blocks (DNA, RNA) are static but nevertheless allow for a dynamic evolution process. That's for me a very good reason not to let everything become dynamic, emerging, relative and - hopefully not - arbitrary.

I have to object here. To call the DNA/RNA and the the relevant replication and synthesis machinery in a cell a "static" doesn't seem to nearly appreciate the depth of life. There was certainly a time where there was no earth, no DNA molecules, not even proteins, and not even atoms.

So I think it's clear that the static abstraction there fails.

/Fredrik

 

[tom.stoer]

I have to object here. To call the DNA/RNA and the the relevant replication and synthesis machinery in a cell a "static" doesn't seem to nearly appreciate the depth of life. There was certainly a time where there was no earth, no DNA molecules, not even proteins, and not even atoms.

So I think it's clear that the static abstraction there fails.

No, it doesn't fail. I agree that the structure of laws of physics and biology do match completely; but that's not the point here. My conclusion is that it is not sure that dynamic processes require dynamic laws. Far from it, progress in science tells us that in many cases the underlying laws of dynamic processes are static laws.

 

[Fra]

We seem to interpret current knowledge in different ways. You seem to think it supports your point, I think the other way :) Anyway, I understand your reasoning.

My conclusion is that it is not sure that dynamic processes require dynamic laws.

I agree, it's not certain, but neither is the opposite. My view doesn't say all laws HAVE TO change, it just says it's not certain, and just that the static cases are either special cases.

Far from it, progress in science tells us that in many cases the underlying laws of dynamic processes are static laws.

The question is what is cause and effect here? For sure, stable laws are preferred by the scientific method, for obvious reasons. So, are we discovering the static laws, or is the very interactions that creates/selects them?

If we look at the history of science the picture is dual. Yes, all laws of physics have usually been static, and timeless BUT these "timeless" laws nevertheless keep chaning the more we learn. The usual idea is simply that we had the "wrong" timeless laws, but that is exactly my point. Even a "timeless" law, that is not inferred to absolute certainty, are always subject ot possible negotiation in the future - so it's not really timeless after all.

/Fredrik

 

[tom.stoer]

What shall I say? As already explained your point of view seems to be "too subjective" - but you are right, both positions are allowed logically.

I do not say you are wrong, I just have the feeling that it's perhaps too early to start this kind of reasoning. My example with string theory goes exactly in this direction: there is still much we can learn from "ordinary" physics and sound mathematical frameworks. But of course that's not a dogma, it's only my private view.

Last but not least I don't want to insist on my view as it is not as elaborated as yours.

Tom

 

[Fra]

I do not say you are wrong

I might certainly be wrong of course, I like to think I'm sane enough to see the limits of my own inferences as well. If I thought I couldn't be wrong, I wouldn't even be selfconsistent Instead of beeing certain, I have a more modest requirement: I just need to be confident enough, to be able to place my bets and beware of the risks.

But it's interesting to see other peoples position and try to understand the logic of inference system. That's how I see this. Your inferences seems "rational" within your inference systemm, and your reasoning points out a little from others since you do somehow want to stick to the axiomatic systems, but at the same time you seem to acknowledge some issues with it. Alot of other people that do the static inferences, doesn't seem to reflect upon this as seriously as you did. I guess that's why your somewhat "structural realist" reasoning was different that those that doesn't seem to sniff the problems.

I'll probably be a little less active for a few days since I've got some more traveling coming up.

It was nice to argue with you.

/Fredrik

 

[tom.stoer]

But it's interesting to see other peoples position and try to understand the logic of inference system. That's how I see this. Your inferences seems "rational" within your inference systemm, and your reasoning points out a little from others since you do somehow want to stick to the axiomatic systems, but at the same time you seem to acknowledge some issues with it. Alot of other people that do the static inferences, doesn't seem to reflect upon this as seriously as you did. I guess that's why your somewhat "structural realist" reasoning was different that those that doesn't seem to sniff the problems.

I'll probably be a little less active for a few days since I've got some more traveling coming up.

It was nice to argue with you.

I would like to return that compliment. It was a very good discussion!

As I said: I am not so sure about my own position; it's still a moving target and therefore I appreciate conflicting but well-grounded ideas. The main problem is - as I already said - and this applies to my own ideas as well - that after starting to think into one direction, I always find very good reasons why it will NOT work that way or why I DON'T like it that way ...

 

[Fra]

The main problem is - as I already said - and this applies to my own ideas as well - that after starting to think into one direction, I always find very good reasons why it will NOT work that way or why I DON'T like it that way ...

I know the feeling.

I still remember my first reaction when I learned about QM. Before I seriously studied QM, I was pretty much a realist, and I still remember a moment during a class at my first QM course when I realized that the realist interpretation does not make sense and suddenly a light came on for me and my first reaction was that "all these years I have been scammed" and kept away from the light

/Fredrik

 

[tom.stoer]

For me it was different.

When I tried to understand QM and QFT I decided to become a positivist - just to make some progress and manage the maths. But over the weekend I was a realist and believed in a real world "existing out there".

 

[Fra]

It's certainly hard to be overly critical when you are supposed to study something from the practical point of view of study techniques. During the courses my approach was a mix of shut up and calculate and axiomatic view. To defend the choice of axiomatics temporarily the experimental success of the predictive machinery was my defense to reduce the frustration.

But from a more serious perspective (set aside the practical problem of managing and completing courses) this is just a pragmatic way of handling daily business.

But after that moment I was never realist, not even on weekends :)

/Fredrik

 

[Chronos]

Well, if the laws of nature are dynamic, the task of modeling reality is compounded. No model will ever be accurate because component information was derived at different points in time. Chicken soup consists of squawks past plus grain cubed, as my inscrutable grandmother was fond of saying.

 

[Dmitry67]

Sorry, I had missed a lot...

Just 2 cents about the binary existence.
I would say, there are 3 levels of existence:

Something exists and we can provide an example of such object;
Something does not exist and we can prove it

and between them:

Something exists in a sense that we can prove that statement

\vdash \exists Y : BlahBlahBlah(Y)

But no example of Y can be provided. Good example is Banach-Tarsky paradox, I wrote about it here: https://www.physicsforums.com/showthread.php?t=337197

 

[Dmitry67]

I agree to one part of the statement: 1) Everything that EXISTS must respect some laws of (binary?) logic and therefore correpsonds to some consistent mathematical system. But the other way round it's deep philosopophical statemet which I cannot accept w/o further discussion: 2) EVERY sound mathematical (logical) system EXISTS.

Ha! looks like I did not miss anything, because we were discussing exactly that - remember, I was talking about the informational interpretation of Ocamms razor?

 

[tom.stoer]

... looks like I did not miss anything, because we were discussing exactly that

You missed a lot regarding the emergence of physical laws from inference and "evolution" - but that's not really my position :-)

Regarding you levels of existence: sometimes I have the problem that currently all latex formulas are displayed as black boxes, so I can't read it (sometimes they are displayed properly). Do you know the reason?

You intermediate level is due to the non-constructiveness of proof of the existence. All proofs relying on the axiom of choice suffer from that issue.

 

[Fra]

Regarding you levels of existence: sometimes I have the problem that currently all latex formulas are displayed as black boxes, so I can't read it (sometimes they are displayed properly). Do you know the reason?

I have noticed the same problem.

In old threads, the latex pictures look fine (with my same browser). But since some time ago the new posts with latex are black and unredable. The picture is fine if I save it locally and view it in some image program. Then problema appears to be that my old browser (IE6; I have reasons for not having upgraded so far) for some strange reason fails to display this version of the png file.

I tried firefox and it works perfect. And older Opera also works fine. So it seems IE6 is the only one I've tried failing to display the pictures. About the newer IE I don't know.

/Fredrik

 

[Dmitry67]

I see formulas without any problems (IE8)

Well, may be I missed the "evolution" stuff, bu I really don't understand it.

How physical laws may change? If something changes over time (like Hubble 'constant') then it is just a part of more fundamental and constant law

I can believe that parameters of the Standard Model can be different in different 'bubbles' - but in that case there is common superstring background, with more fundamental laws, describing how universes with different parameters are created (branes colliding in high dimensional bulk space, different angles of collision create bubbles with different parameters, blah blah, something like that)

But in any case there MUST be fundamental TOE which is eternal and purely mathematical.

 

[Fra]

Well, may be I missed the "evolution" stuff, bu I really don't understand it.
...
How physical laws may change? If something changes over time (like Hubble 'constant') then it is just a part of more fundamental and constant law
...
But in any case there MUST be fundamental TOE which is eternal and purely mathematical.

I think we had some discussions on this before, and the conclusion as far as I remember is that you are far more of a realist, and I am much more subjective relative to your position.

We might not want to repeat everything, but I think have at least from my point of view addressed the questions you raise here - which are very typical realist objections to the notion of evolving law.

The core difference is that I am looking for an intrinsic measurement and inference theory. In that sense, it's not possible to arrive at an inference like you do: "there MUST be a fundamental TOE which is eternal". To me, such statement is more an expectation and vision, not a certain deductive inference, because I doubt you can prove it? :) The expectation and vision is rational, but expectations and visions change. The rationale for the acting as they are eternal, is because from the inside point of view their uncertainty is not distinguishable. This type of reasoning can not be understood in standard QM, it suggest a reconstruction of measurement theory, where QM is a special case.

But I think I've tried to argue several times but apparently the reasoning comes out as implausible to most.

/Fredrik

 

[BigFairy]

yeah you can kinda agree..

 

[friend]

The core difference is that I am looking for an intrinsic measurement and inference theory. In that sense, it's not possible to arrive at an inference like you do: "there MUST be a fundamental TOE which is eternal". To me, such statement is more an expectation and vision, not a certain deductive inference, because I doubt you can prove it? :) The expectation and vision is rational, but expectations and visions change. The rationale for the acting as they are eternal, is because from the inside point of view their uncertainty is not distinguishable. This type of reasoning can not be understood in standard QM, it suggest a reconstruction of measurement theory, where QM is a special case.

But I think I've tried to argue several times but apparently the reasoning comes out as implausible to most.

/Fredrik

I don't see how anyone can put any faith in evolving laws of physics, because then they would change in a way we can't predict, unless of course there is some more fundamental laws that govern how things change. So either you have faith that there must be some sort of constant fundamental law, or you have no faith at all, and you're just curve fitting the data from experiment.

 

[atyy]

I don't see how anyone can put any faith in evolving laws of physics, because then they would change in a way we can't predict, unless of course there is some more fundamental laws that govern how things change. So either you have faith that there must be some sort of constant fundamental law, or you have no faith at all, and you're just curve fitting the data from experiment.

Does every solution have a question (come from a set of equations)?

 

[tom.stoer]

... unless of course there is some more fundamental laws that govern how things change.

That's exactly my position when I compare Fra' ideas with biological evolution. Biological evolution is based on fundamental laws (DNA) which are not subject to the evolution process itself but provide a fixed, external system.

If physics behaves in a similar way than our job is to deduce these fundamental laws.

 

[friend]

Does every solution have a question (come from a set of equations)?

My belief is that there will always be questions and we will always be seeking equations until everything can be derived from logic itself. Are we really going to be satisfied with reducing things to some sort of particle and some sort of force? We might get smaller and smaller particles, and we might find symmetries in the equations. But that still leaves us asking why, why, why. But if things are reduces to logic itself, then the only thing left is to question reason itself. And the answer to why logic is the way it is is because either things exist or they do not, statements are either true or they are false.

 

[Fra]

Friend and Tom, your objection is clean and understandable! It's I would say the most expected objection to evolving law.

But there are subtle things that are the beauty in the approach that I have tried to elaborate on in several ways in several threads. I guess you require some concrete demonstration of the success of the principle to be see the point. Then I think more work is needed. I have revealed some of the conceptual and principles behind the reasoning, but the result of this in terms of a solving open problems in physics is of course still very much in progress.

I don't see how anyone can put any faith in evolving laws of physics, because then they would change in a way we can't predict, unless of course there is some more fundamental laws that govern how things change. So either you have faith that there must be some sort of constant fundamental law, or you have no faith at all, and you're just curve fitting the data from experiment.

Your latter choice is closer to my view, but you simplified it grossly when you mention curve fitting. But in a sense, a rational guess, is like a kind of rational inference in the sense of an probable extrapolation of the future, based on the past.

You can if you like call this a curve fitting extrapolation of the past, to the future. But the obvious problem is that the curve fitting is not unique. You end up with a landscape of possible extrapolations? In my view, there is a information divergence measure which guides the choices of "extrapolation parameters". It's in this space there is evolution as diversity and seleciton. The diversity is already there due to the uncertainty, but the important thing is that the diversity is constrained.

But a real inference machinery does not have all the history of the universe - it has only a reduced and compressed history to base the inference on; this inference leads to a rational action.

In this scheme, it's correct that there are things that are undecidable and unpredictable. But this does not preven us from making a kind of probable inference, or induction.

The real benefit of this approach is that one can make predictions, not as deductive inferences, but as uncertain inductive inferenes as to what the future will be, and this expectations yields a rational action of the inference system (matter system). IE. the mere conjecture that physical actions ARE involving a kind of uncertain inference, and that the inference machinery is bounded by a complexity, gives constraints on the effective fundamental action one would expect in nature.

IE. the uncertainty of the state of matters that insist on, does suggest a kind of associated action, that is construced from natural inference. This is why states, and states of laws (as implicit in physical actions) become comparable and it's not consistent to think of state of laws and configuration states as fundementally different if you take the measurement perspective; because then parts of the the laws are dismissed to background information, or background context.

I am not saything there is no context, I'm saying there is a context, but it's evolving. And at some point, there is a context whose evolution simply isn't predictable. To say that it could be predictable, but the predictions isn't made yet, just favours my point.

This is much deeper than just curve fitting. It also contains an reconstruction of information theory, that does not start with standard probability and continuums. But I obviously fail to convey what I mean. So we'll let this be some crazy mens opinon until some time later when maybe I get to make some progress, or someone else who is working in related directions are able to make some progress.

But any progress would be made against the collective opinion, rather than in line with. This is why the activation energy for this approach is extra high. Apparently it's hard to convey the reasoning, so that leaves only the hard concrete progress.

/Fredrik

 

[Fra]

And the answer to why logic is the way it is is because either things exist or they do not, statements are either true or they are false.

What is the meaning of beeing true, if it can not be proved from where you stand? the freedom to add another axiom saying it is? or what? Then ponder that the set of axiom is bounded in complexity; what do you do? You might need to erease one previous axiom to add a new one?

I see that you seem locked into this rigid realist type of logic, and I totally do understand that from your perspective evolving law simply makes no sense.

I think the type of motivation I would have to provide to prematurely motivate the reasoning behind evolving laws and physical action based on inductive inference, is that your way of reasoning risks getting stalled or run into a halt. It's not flexible enough. I think Tom was sniffing in this direction, but he still has not come over to the dark side, but I think in time he will

/Fredrik

 

[marcus]

... unless of course there is some more fundamental laws that govern how things [i.e. laws] change...

That's exactly my position when I compare Fra' ideas with biological evolution. Biological evolution is based on fundamental laws (DNA) which are not subject to the evolution process itself but provide a fixed, external system.

If physics behaves in a similar way than our job is to deduce these fundamental laws.

This sounds like a clear statement which agrees with our experience of the history of science.
Humans have repeatedly deduced patterns of regularity and formulated laws, and repeatedly they have then learned that these laws vary according to deeper laws. Can't we learn from that? Isn't it reasonable to expect this process to continue?

An example that comes to mind is Euclidean geometry. For many centuries it was a law of nature that the angles added up to 180 degrees and light traveled on straight lines, and everybody knew this. Galileo founded modern science based on such laws, and for centuries nobody questioned Galilean relativity either.

Then we found out what causes spatial geometry to be approximately Euclidean. Euclid is a temporary solution to a general equation governing the evolution of geometry. We now know why Euclid and we know not to assume that Euclid works in all times and places. There is a deeper law of geometry that explains the previous shallow law. We found that the geometry of the universe is evolving with time. And also our local geometry is evolving. According to a deeper law. Or if you don't like the word "law" then according to a deeper regularity or rule. It is our experience that law evolves with time.

Laws are just patterns of regularity that we notice and continually test, and they change. And happily enough (or because we've gotten good at the job), the human-noticed rules change only very slightly and slowly, so that we can get a lot of use out of them. We can treat them as reliable within some domain of applicability. Part of knowing the law is knowing the domain.
=====================
EDIT TO REPLY TO NEXT
Friend, "bottom up" and "top down" are idealizations, artificial constructs. It is not either/or. We humans arrive at laws however we do it, in whatever ways we always have done it. A method has never been accurately formulated, or universally adhered to, and even if one had been deduced from past practice it would not necessarily apply in the future. We do not entirely know how we have, and will, perceive test and formulate laws.
We only know that biological evolution has prepared us to figure out patterns and we are reasonably good animals at doing it, and it works seemingly pretty well.

You mentioned "faith" in your earlier post. I do not see how "faith" is involved. Beyond that of gradually learning from experience and doing what works.

In this next post you mentioned "debate" between different idealizations about how we do physics. I don't see the point of debate. There is a community with some written and unwritten traditions, an ethos, a social structure, it operates as it operates. At various junctions there is struggle. We do not know how it will operate in the future and our ability to affect how it will operate is limited.

 

[friend]

This sounds like a clear statement which agrees with our experience of the history of science. Humans have repeatedly deduced patterns of regularity and formulated laws, and repeatedly they have then learned that these laws vary according to deeper laws. Can't we learn from that? Isn't it reasonable to expect this process to continue?

I guess this brings up the debate between the bottom up or top down approach to discovering physical laws. Do we find the most fundamental of principles by interpreting equations that fit ever more accurate measurements? Or can physical laws be derived from principle alone? The former question leads us to ask if we can even possibly measure with enough accuracy. And I suppose this latter question brings up what fundamental principles do we start with and how much can we trust them.

It seems for certain we will not get there through measurement since we will never be able to achieve the energies high enough to test curve fitting theories. We'd have to recreate the big bang hundered of times over to see if we get the same laws of physics within a given probablity. But do we have any principles alone from which physics can be derived? I think we do. Whatever the question or theory proposed, we always end up asking whether it is true or false. So surely binary logic has to be at least part of the starting point. Surely, if we are trying to "prove" something, logic is involved. The question is how to proceed from logic to physics. How does math enter the effort? And how would we confirm that it is correct? Would it be sufficient if such an effort reproduced the mathematical structures of QM and GR? Or would we have to reproduce the SM?

 

[marcus]

...It seems for certain we will not get there through measurement since we will never be able to achieve the energies high enough to test curve fitting theories...

Aren't you making an artificial and useless distinction between "measurement" methods and the opposite (non-measurement?) methods?

Aren't you again making an artificial distinction between "curve fitting" theories, and some other (well defined?) type of theory?

How can you pretend to know in advance what patterns of regularity humans will or will not be able to test?

Surely not every approach to testing involves artificially generating high energies!
That is merely an illusion created by our recent experience with accelerators and colliders.
You look at 50 or 60 years of history and think that there is an iron law and it will always be this way.
People are already fitting their curves to the night sky, and they have only begun to watch the sky really intently.
Please cut your fellow animals some slack before you start making philosophical pronouncements about what we cannot do. We are just getting started.

 

[Dmitry67]

Fra, let's not repeat all arguments again. But Max Tegmarks hypotesis has several concrete and falsifiable predictions. Could you list any predictions of the theory you prefer? I have an impression (may be I am wrong) that if that evolving law thing is true, on our way to the ultimate TOE we will get dissapointed by our inability to build a formal system which describes the Universe. Trying to find the TOE we would understand that no TOE is possible. End of physics...

 

[friend]

Aren't you making an artificial and useless distinction between "measurement" methods and the opposite (non-measurement?) methods?

Aren't you again making an artificial distinction between "curve fitting" theories, and some other (well defined?) type of theory?

How can you pretend to know in advance what patterns of regularity humans will or will not be able to test?

...
Please cut your fellow animals some slack before you start making philosophical pronouncements about what we cannot do. We are just getting started.

Perhaps I've not considered well enough, but it seems to me that any measurement based curve fitting approach is inherently incapable of discovering the completion of physics. How are we supposed to know when there's nothing more to discover? When do we know that it's impossible to break up particles into smaller constituents? And how do we know the same laws of physics applies everywhere? We can't measure everything, so we can only guess that it's universal.

 

[Dmitry67]

Tom, I have a tricky question regarding the Occams razor thing we discussed before (everybody is welcome)

So, it is very likely that our universe is infinite. As we know, the expansion is accelerating, so there are cosmological horizons: we will never ever be in causal contact with some distant areas of our universe.

My question is: do these areas really exist?

I can open my cards, explaining why the question is tricky. Compare:

A1. Yes, of course, these areas exist! Why not? Yes, we will never be in causal contact, so what? Our mathematics and cosmological models tell us that these areas do exist!
A2. No. We will never be able to observer these areas. hence, they are just mathematical way to explain the curvature of space in our observable universe. If some object flies behind the cosmological horizon, then it ceases to exist. Occams razor dictates that there is NOTHING behind the horizon.

Of course, you would say that A1 is true, and A2 is weird. Now compare:

B1. All branches predicted by the Quantum Decoherence exist. Why not?
B2. No, only one branch exist. Other branches are cut by the occams razor.

Login in A1 is exactly the same as in B1, and in A2 as in B2. You can chose A1 and B1, or A2 and B2 to be consistent.

 

[Fra]

Could you list any predictions of the theory you prefer? I have an impression (may be I am wrong) that if that evolving law thing is true, on our way to the ultimate TOE we will get dissapointed by our inability to build a formal system which describes the Universe. Trying to find the TOE we would understand that no TOE is possible. End of physics...

I do not yet have a mature theory, but I can tell you what kind of "predictions" I expect out of such a program:

- effective unification of all interactions as the complexity of the inference system -> 0 - this would correspond to what in the standard language is the high energy limit. But there are some differences in that the normal high energy limit rather refers to the energy supplied from the context to the subsystem, my abstraction suggest that there is no unlimited source of energy, so the high energy limit gets a natural UV cutoff in way that is argued towards in a way that does not make use of black holes and other stuff. But I do expect a connection.

- A preferred way of breaking the unification as the complexity of the inference system increases from zero. This corresponds to going towards the low energy limit. Here is also a natural IR cutoff for each inference system, since the complexity is bounded.

- these cutoffs are rooted in the reconstructed measurement theory and has to do with resolution.

- A prediction of an action, can be done given an inference system, and thus the expected laws are system dependent, but the substantial difference from say string theory is that this approache should be immune to tragedies like the landscape issue because the diversity is constrained by the intrinsic information divergence.

- the selection principle of mutually consistent inference system should make predictions of the population of particular inference systems in nature; ie it should make predictionso of matter and particle contents and their actions, including their masses and so on.

- The relative masses and the hierarchy problem would I presume, be explained from the hierarchy of the information measures, and how it has evolved.

if that evolving law thing is true, on our way to the ultimate TOE we will get dissapointed by our inability to build a formal system which describes the Universe. Trying to find the TOE we would understand that no TOE is possible. End of physics...

If you think we will fail to fine and eternal TOE as a static thing like a fixed axiom systems, where we never have to remove or add axioms, I think you are right - it will fail.

But that's not a problem, because my focus is on understanding and making predictions of this evolving system.

In fact, IMHO, one key exploit here is that the reason for the action of the microstructure we see in the standard model of particle physics beeing what it is, is BECAUSE the particles participating in that interaction themselves don't have an ability to predict their own environment - this is reflected in their actions and INTERactions.

This is very far from end of physics, I rather think it would very much deepen our understanding of physics. Another level of "end of realism in physics" maybe, like we have seen suchs endings before with both Einsteins relativit and QM, we are still awaiting the next step I think :)

But I can't prove any of this of course. But it's just some of the expectations of such a program.

About other related predictions, Smolins CNS makes predictions on the maximum mass of neutron stars. Finding a neutron star more massive than the limit would falsify CNS.

/Fredrik

 

[Dmitry67]

thank you for your reply.
I have another question
Is there an effective way to distinguish
1. MWI (everything happens) + AP (Anthrophic Principle)
from
2. Cosmic Darwinism
and from
3. Evolving law?

 

[marcus]

Perhaps I've not considered well enough, but it seems to me that any measurement based curve fitting approach is inherently incapable of discovering the completion of physics. ...

It sounds like you are thinking about stuff that doesn't exist. I don't know of any purely curve-fitting approach to anything in physics. Ideas will always creep in
Could you be wrestling with a straw man named Mr. Curve-Fitting Approach?

I'm skeptical of your being able to find any branch of science where practitioners consistently follow any stated rulebook method, as if they were automata.

Maybe I shouldn't argue this anymore with you, Friend. You have your opinion about the Limitations of Science based on your own concepts and reasoning. I have a different set of aperçus. In the end all we could do is make predictions about, say, the next 15 years of research and (if we both survive that long) check later to see whose mental model was closer to the real world.

 

[marcus]

...About other related predictions, Smolins CNS makes predictions on the maximum mass of neutron stars. Finding a neutron star more massive than the limit would falsify CNS.
...

thank you for your reply.
I have another question
Is there an effective way to distinguish
1. MWI (everything happens) + AP (Anthrophic Principle)
from
2. Cosmic Darwinism
and from
3. Evolving law?

Dmitry, that's a beautiful clear question. As Fra already indicated Cosmic Darwinism (the usual version is Smolin CNS) does make predictions. It predicts that you will not find a neutron star with mass substantially greater than 1.6 solar. And various other specific things. The general prediction is that you will not be able to find a Standard Model number that is not "hilltop" optimized for black hole production in the sense of being better than its nearby neighbors.

Anthropery does not predict anything quantitative. Whatever you measure in the future, whatever Standard Model number, it will automatically be consistent with our having lived and with our having measured it. Any possible physics discovery is consistent with life having arisen and learned how to investigate physics.

CNS was developed partly for the very purpose of providing a testable alternative to Anthropery. To show that you could construct falsifiable multiverse hypotheses. It is very different from the typical stuff about ManyWorlds, or StringLandscape, or EternalInflation and suchlike colorful fantasies which give infinite food for imagination without solid quantitative predictions.

Science theories can never be verified, only falsified. But if they pass tests a lot, they get tentative acceptance. If you want to know if we live in a CNS universe, the way to get a handle is to try and disprove it. Try to find a change in any of the 30-some numbers that characterize our universe which, if it were somehow implemented, would have resulted in more black holes.

The other thing you ask is how to tell the difference from Evolving Law.
I don't know of any definite Evolving Law hypothesis that can be tested!
I think it is unscientific and irrational to assume that there are eternal immutable laws---because we have no proof of that. All the evidence is that our knowledge is only provisional and the patterns we see are subject to revision.
To claim that there are eternal unchanging laws would be to assert much more than we actually know.

But I could not deny that proposition either. How could I, on what basis?

To answer your question I need to have some specific Evolving Law hypothesis. Some law and some mechanism by which it evolves. The only specific I can think of is Smolin CNS.
It conjectures that a law (the standard models of particle physics and cosmology, given by the 30 dimensionless numbers) changes slightly and evolves towards reproductive success, so that you expect hilltop optimality. That is a case of Evolving Law. But it is not so interesting to just have one sole case.

How about you think up another example, a different reproductive mechanism, a different optimization for reproductive success. A different optimality prediction about how the numbers should be. Then we could test.

Maybe someone else can respond, but I don't see how unless you give me some specific Evolving Law mechanism to examine and compare.

 

[tom.stoer]

Tom, I have a tricky question ...

Dmitry67, I need time for the answer. In the meantime you can think about the following: Since God is all-powerful, can he create a stone too heavy for him to lift?

Tom

 

[Fra]

I can think of several ways to comment on this. Marcus already provided some comments but there are some more.

Note: The obvious example of evolving law, that Marcus makes and also that Smolins makes is that it's a basic observation to note that what we humans have thought was physical law, has changes over the years. Now, the typical realist objection to that would be that we are confusing physical law, with our knowledge of physical law. But that objection is inconsistent with another hypothesis of mine, namely that physical action depends upon the inference system and the information at hand only. Ie. every system responds/acts upon the information it has only.

Ie. it's exactly the view that you CAN distinguish between information about a fact, and the fact itself, that is the difference between a realist and a nonrealist IMO.

I am saying that the physical action of a system is invariant to which.

thank you for your reply.
I have another question
Is there an effective way to distinguish
1. MWI (everything happens) + AP (Anthrophic Principle)
from
2. Cosmic Darwinism
and from
3. Evolving law?

I'll try to write more later, on my way to work.

But in my view of evolving law, which is a little different than CNS, the viability should come from several components.

Diversity from uncertainty; uncertainty is bounded and so is diversity - there are no inflated landscapes of unconstrained possibilities.

The selection and evolution of an inference system is implemented by means of feedback from the environment (the unkonwn) as subjective times progresses, and this forces the inference system to either revise or to face destruction. A property of self-preservation selects inference systems by fitness. But this is environment dependent, and what is fit depends on the environment. Therefor some interaction of inference systems must be considered to find a probable distribution of inference systems in nature.

Time is subjective in my view, but I disagree with rovelli in that I do not treat the system-system transformations as realist elements. These transformations themselves are emergent as the system complexity increases. A given finite observer, has a limit to how well it can infere the symmetries. In practice he will infere the symmetry, but it will be fuzzy. IE. the symmetry transforamtion itself is uncertain.

This is different than how smolin argues. I interpret smolin to take a little more conservative approach by considering variation of some known parameters. But you have to start somewhere, and I see smolins CNS as an interesting first attempt at something little more concrete, but not necessarily the final implementation of the vision.

Antrophics is mostly an attempt to save situations where you are sitting in a landscape of possibilities and are lost. Then you try to shave of possibilities by saying that the inferences that doesn't lead to what you know, must be wrong. It's a sort of post-diction kind of reasoning. It's a little related to the evolution but the major difference is that my idea of rational action; suggest a way FORWARD, given the present, not just a way from some speculative past to the present. The further conjecture is that all physical actions are constructed this way, and this insight can also help us understand the action of the standard model - that there is a yet not acknowledged logic to it's construction, that is not just geometrical inspiration, it's rather inspired by a new inference model.

If you look at say the path integral, the association is clear that it seems that the physical action is construced by "considering" various options AS PER some specific inference system. I am convinced for more than the similarity reason that this is not a conicidence at all. There is something deep about inference and physical actions that is not yet acknowledged. For ME at least (not sure about smolin) I see this strongly linked to the concept of evolution of law, since the inference system itself is also subject to change. Picture the path integral or a generalisation thereof as a computation, then there is a computer (matter) and and action that is induced from the result of the computation (action) and a feedback from the environment (reaction) that gives feedback to not only the computation but also to the computer.

/Fredrik

 

[moniker2]

thank you for your reply.
I have another question
Is there an effective way to distinguish
1. MWI (everything happens) + AP (Anthrophic Principle)
from
2. Cosmic Darwinism
and from
3. Evolving law?

Here you go, but it comes from an unreliable source.

m = [f / {[(1/(1-(v ^2 /c ^2 )) ^1/2 ]-1}a
This makes many assumptions but the most intriguing is the imaginary units of mass.

 

[tom.stoer]

Tom, I have a tricky question regarding the Occams razor ...

So, it is very likely that our universe is infinite. As we know, the expansion is accelerating, so there are cosmological horizons: we will never ever be in causal contact with some distant areas of our universe.

My question is: do these areas really exist?

Dmitry67! yes, they exist - and again Ockham's razor is on my side.

First I have to explain what the principle of Ockham's razor really means: It essentially says that that "entities should not be multiplied unnecessarily; when you have two competing theories that make exactly the same predictions, the simpler one is the better": http://math.ucr.edu/home/baez/physics/General/occam.html
So it does not say that the theory that contains less entities is better, but the theory that provides the simpler explanation of known facts is better.

Now let's look at the expanding universe with horizons. A certain area of space which resides inside our horizon does exist (I hope we can agree on that). Now due to the (accelerated) expansion this area disappears beyond the horizon. The two competring theories are:

1) the area of space still exists but becomes invisible
2) the area of space ceases to exist

Both theories should be based on spacetime and should be compatible with the framework of GR; this means they have a common basis and are of the same complexity. Now the phenomenon of the horizon may add some new entities which are subject to Ockhams razor.

In theory 1) you have to explain what the horion is: it is a geometrical concept that is somehow build-in. There is no extra ingredient or entity besides the fact that you observe accelerated expansion. But that is not really new as it is derived from observation and not from theoretical constructions. The area of space beyond the horizon is no new ingredient, either, as it already existed before it went across the the horizon.

In theory 2) there will be one new ingredient or entity, namely an explanation how a certain area of space plus all matter, energy etc. can cease to exist. You have to provide a process, a formula or something which tells us what happens to all the stars, galaxies etc.

Look at a room with a huge library. Lock the door and throw away the key. Are the books still "there"? I would say "yes" ...

 

[Dmitry67]

Dmitry67, I need time for the answer. In the meantime you can think about the following: Since God is all-powerful, can he create a stone too heavy for him to lift?

Tom

Definitely God won't be able to lift such stone without help of Max Tegmark :)

 

[Dmitry67]

1
First I have to explain what the principle of Ockham's razor really means: It essentially says that that "entities should not be multiplied unnecessarily; when you have two competing theories that make exactly the same predictions, the simpler one is the better": http://math.ucr.edu/home/baez/physics/General/occam.html

2
In theory 2) there will be one new ingredient or entity, namely an explanation how a certain area of space plus all matter, energy etc. can cease to exist. You have to provide a process, a formula or something which tells us what happens to all the stars, galaxies etc.

1 Yes, we both agree on the definition of Occams razor. We don't agree on the definition of 'entity'. A HOLE or a VOID in substance - it is an ENTITY?

For me IT IS, because it breaks the symmetry and injects new information into syste,

2 Yes, definitely yes!
So you can apply the same logic to MWI branches - it is logical to say that they do not cease to exist. Once we accepted Level 1 and Level 3 multiverse, it is easier to accept Level 4 multiverse.

 

[Dmitry67]

It predicts that you will not find a neutron star with mass substantially greater than 1.6 solar.

Could you explain, why? My problem is that my disagreement with Smolin is so strong that I would hardly be able to read anything to the end.

 

[Fra]

Could you explain, why? My problem is that my disagreement with Smolin is so strong that I would hardly be able to read anything to the end.

You can read smolins papers, but the basic idea is that smolins conjecture is that our universe must be (or is highly likely to be) optimized for black hole production. The reason for this is that in Smolins CNS idea, a universe that produce no black holes would be steril and unable to produce "offsprings" (with or without variation).

Now smolin has argued that a universe that is so constructed, for optimal black hole production would not host arbitrarily massive neutron stars. "Ie. if the parameters of the laws of physics are so as to optimise black hole production, then there is a limit on neutron star mass."

I think that is the simple general idea. If you want to see the details, or verify that this is a correct inference I think you need to dig into Smolins papers.

But before you look at his specific CNS, I would suggest listening to his general arguments against eternal law first, because it's possible to have objections to CNS but still appreciate the general idea(http://pirsa.org/08100049). To jump into a specific suggestion before appreciating the general idea is I think harder.

I am not overly fond of CNS which I see as a first, probably simplest possible, attempt to realize the idea into something a little more concrete, but I share his general objection to eternal law.

/Fredrik

 

[Dmitry67]

Thanks. Why production of the Black Holes is so important?
Because he thinks that they give birth to other Unvierses, implementing the Cosmic Darwinism?

But if the Goal function is the number of universes/black hole, then it does not explain why do we exist. You can have a very successful 'universe factory', but all these universe can be strile. Say, no elements heavier then He, but manymany many black holes.

That idea would be much more interesting if the creation of Universe would require so rare conditions that it would require an intelligent life. That would be an alternative to AP. In the current form, it just explains why there are many universes, but you still need AP to explain, why at least some of them are life-friendly.