LHC - the last chance for all theories of everything?

[tom.stoer]

Hey Tom, I didn't you also liked exotic smoothness. Right?

What do you mean exactly?

 

[MTd2]

What do you mean exactly?

You said "The continuum hypothesis may be artifical, but homeomorphic, non-diffeomorphic manifolds may very well be physically interesting!"

In 4 dimensions, that is exotic smoothness. Google for it! :) This is the topic that I like the most, and I think it is at the very core of every 4 dimensional theory with fractal dimensions, like Horava gravity, LQG, Loll's universe, Asymptotic Safety, and the likes.

This is also closely relateted to the classificantion of smooth 4-dimensional manifolds. The simple connected case has not classification, and it is also related to the question if the generalized poincare conjecture is true or not in 4 dimensions. That is, about the existence of exotic smooth sphere. Hendryk Pfeiffer paper above is related to all this.

 

[RUTA]

To repeat Dicke's famous response, "Well boys, we've been scooped." The search for the unified force is over:

http://www.theonion.com/content/node/39512

Damn, I had my money on LQG.

 

[Fra]

Honestly speaking I expected something like that!

I came to the conclusion that insisting on inference and at the same time relying on axiomatic methods would cause big trouble for you approach. It would rely on consistency w/o being able to prove or disprove it.

I think you are starting to see the logic I tried to convey.

I still see problems with that approach:
1) I still have the feeling that there is "something" in your approach that is NOT subject to evolution and that is NOT immune regarding the following argument:
2) I think that you can change perspective again and map your approach into a kind of axiomatic system or a member of a family of axiomatic systems.
3) Then you are trapped again because now you have to deal with inconsistent axiomatic systems - not a very nice idea.

I guess it is possible to try to map this into a kind of sujbective axiomatic approach, but then to keep the spirit, the set of subjective axioms would sort of constitute the DNA of the inference system, and those actual systems encoding in their actions a particular inference system, would still be subject to challange/selection, and one could say that the inference system implicit in a set of axioms, can have varying degrees of "success" of actually making inferences that MATCH the actual future, and here there is a selection for the axioms, so that axioms can be lost, like genes can be lost, and new axioms can come.

So if we insiste on a axiomatic approach, and still insist on keeping the spirit of reasoning here, then the axioms are still subject to evolution. One one is faced with the problem of understand the logic behind going from axiomatic system to another.

That might make sense to me, but it doesn't make the problem easier, it's just putting it in different words. IT's still very different from the ordinary axiomatic approach, which is more like an accumulative buildup of an axiomatic system. This does not match what I envision because the "choice of axioms actually contains information" about what's fit and what's not. And the axiomatic system are still bounded in complexity in my view, since it's encoded by a finite inside observer.

So the really ordinary axiomatic method (without this evolving stuff I talk about) does not as I see it match this.

/Fredrik

 

[tom.stoer]

In 4 dimensions, that is exotic smoothness. Google for it! :) This is the topic that I like the most, and I think it is at the very core of every 4 dimensional theory with fractal dimensions, like Horava gravity, LQG, Loll's universe, Asymptotic Safety, and the likes.

This is also closely relateted to the classificantion of smooth 4-dimensional manifolds. The simple connected case has not classification, and it is also related to the question if the generalized poincare conjecture is true or not in 4 dimensions. That is, about the existence of exotic smooth sphere. Hendryk Pfeiffer paper above is related to all this.

Yes, you are right, this is exactly what I am talking about. The paper provides a fresh view on PL manifolds which could be used as "diffeomorphims-invariant triangulation". This is a very interesting idea.

I am not so sure if exotic smoothness for R^4 is the very core of 4 dim. physics. Pfeiffer explicitly excludes topologogically inequivalent manifolds, but I would expect that different topologies will matter as well. (I've seen some statements in this regard in the CDT context, but I can't remember the details ...)

 

[tom.stoer]

I guess it is possible to try to map this into a kind of sujbective axiomatic approach, ... ... and here there is a selection for the axioms, so that axioms can be lost, like genes can be lost, and new axioms can come.

So if we insiste on a axiomatic approach, and still insist on keeping the spirit of reasoning here, then the axioms are still subject to evolution. One one is faced with the problem of understand the logic behind going from axiomatic system to another.

That might make sense to me, but it doesn't make the problem easier, it's just putting it in different words. ...

No, it's not just putting it in different words.

1) If you succeed with this reformulation you will have an axiomatic approach which describes how axiomatic systems can evolve. It describes (sets the rules) how axioms can be lost and how one can go from one axiomatic system to another. It will be very interesting to learn if this meta-level is again an axiomatic system, if it is subject to evolution, if it can be constructed explicitly or if you can only prove existence, what about my "next stage ..." reasoning etc.

2) If you fail you will hopefully learn from failing if your approach is richer than the purely axiomatic one; perhaps failing with the construction will be a success for your approach ...

So you will learn if your approach is immune to my criticism - and if this is a feature or a weakness (weakness in the sense that self-immunization may be non-scientific; refer to arguments against the anthropic principle).

 

[Fra]

No, it's not just putting it in different words.

1) If you succeed with this reformulation you will have an axiomatic approach which describes how axiomatic systems can evolve. It describes (sets the rules) how axioms can be lost and how one can go from one axiomatic system to another. It will be very interesting to learn if this meta-level is again an axiomatic system, if it is subject to evolution, if it can be constructed explicitly or if you can only prove existence, what about my "next stage ..." reasoning etc.

2) If you fail you will hopefully learn from failing if your approach is richer than the purely axiomatic one; perhaps failing with the construction will be a success for your approach ...

So you will learn if your approach is immune to my criticism - and if this is a feature or a weakness (weakness in the sense that self-immunization may be non-scientific; refer to arguments against the anthropic principle).

I thikn I see what you mean.

Do you mean wether it's possible to describe what I propose - the evolving axiom system - again as a *fixed* objective larger axiom system?

I think that is not possible - it would in fact not be very conceptually consistent with the spirit of the idea. What I think is possible OTOH, which also part of the idea here, is that it IS possible to describe the evolution of axiom systems, RELATIVE to another axiomsystem. But there is no objective universal axiomsystem which we can see in a realist view.

I figure you also think it's weird that if there are no objective, or non evolving structure, how can this possibly get predictive? The idea is that I view this as a game, and all we can do is play.

One might compare this again to Gödel stuff in that the consistency of one system could be provable from another axiom system (normally larger), and the correspondence of this in my view would be how one observer inferes the action of parts of it's environment.

But there is as far as I have analyzed this, always more questions that you CAN NOT answer, but you can insist on asking them - this is in my mind related to evolution and also at a different level in the hierarcy time.


/Fredrik

 

[Fra]

It will be very interesting to learn if this meta-level is again an axiomatic system, if it is subject to evolution, if it can be constructed explicitly or if you can only prove existence, what about my "next stage ..." reasoning etc.

I'm not sure my response made sense to you but what I mean to say, is that to predict one axiomatic system or inference system, you need another inference system. (observer2 observes observer1) This could I think probably we realized at least effectively if we consider the inference system we discuss when we do particle physics. Because then we can make inferences of this inference system, relative to the environment which in a way is a much larger inference system.

This is I think possible, but the larger context is itself evolving, and there simply is no external axiom system, much like there is no external space which the universe is expanding INTO. Neither do I think there is an objective configuration space for the universe which describes multiverses.

That's quite analogous to the problem of inference systems.

I THINK you are wondering if what I suggest can be phrased in terms of a possible larger fixed axiomatic system that plays the rold of meta law. If so, I do not think that so, and neither do I at least see it as a problem. It's probably the natural way you'd want to see it, when coming from the traditional view: To try to axiomatise, the axiom evolution, or to describe the evolution by law by a meta law. This is not how I see it. But like I tried to convey, there ONE correspondence to "meta law" I do see, is still constrained to an inside view which is usually bounded (the size of the genome is bounded), there is no external context where it can be, unless you do take on a structural realist view, THEN it makes sense, but I don't. And it also introduces an enourmous ambiouity - massive landscape of possible "master inference systems". And I think others have made that mistake before, and I don't intend to repeat it :)

/Fredrik

 

[tom.stoer]

Do you mean wether it's possible to describe what I propose - the evolving axiom system - again as a *fixed* objective larger axiom system?

I think that is not possible - it would in fact not be very conceptually consistent with the spirit of the idea.

Yes. I am not convinced that your approach is right, but IF it is right, this must be true, of course.

What I think is possible OTOH, which also part of the idea here, is that it IS possible to describe the evolution of axiom systems, RELATIVE to another axiomsystem. But there is no objective universal axiomsystem which we can see in a realist view.

Again my question is how these laws of evolution become subject to evolution.

Let me present you one argumentation which demonstrates why and how your approach will fail - or at least why you fail in explaining it to us:

Assume for a moment that you were able to figure out how it works, that you were able to explain in detail and that finally we all agree. Wouldn't that mean that your approach became a somehow fixed system of rules and statements? Wouldn't that mean that it is no longer subject to evolution? Wouldn't that mean that your meta-program became an "axiomatic system"?

If you have to admit that the answer is "yes", there are two possible conclusions:
If you accept this reasoning, you have to admit that your approach has failed.
If you insist on the success of your program the only way out is to accept that you will never be able to figure it out completely and explain it to us.

If you say that the answer to the above raised questions is "no" there is only one conclusion, namely that the approach is somehow inconsistent or incomplete as we agreed to accept it,but at the same time we concluded (right now!) that it is not fixed but subject to change and therefore we have to withdraw our acceptance unless you have finished your work.

A last way out would of course be to abandon the theory (at least partially) and admit that the theory itself is immune to this discussion - or that these self-referential constructions must be excluded due to consistency. But that of course means that it's no longer a ToE but that its domain of application is in some sense limited.

 

[Fra]

I see and acknowledge your question. I've certainly thought about this but I need to think a bit on how to phrase it to be more clear. Part of the ambigouity is that this is my own reasoning ie. it's subjective. So this is indeed only as per my own inference system and "educated guess".

Am I CERTAIN that this program will succed? Of couse not! But - here is my subjective basis - I see NO better option. It's the most plausible idea I have. If you have a better one and are able to convince me, I am open.

Similarly, I fully understand that it's not trivial to convey and abstract idea to anyone else. I do not expect you to easily get it. This is why like I said before, the ultimatey argument will be if and when I succeed. But most probably the first publication will not be on here :)

But for sure the argument I present now and here are not meant to be definitive arguments at all for my approach. It is only plausible arguments as part of a sound discussion.

I'll see how I can make this clearer, but I apparently need a different way to putting.

More later

/Fredrik

 

[ConradDJ]

But the thing is, our world is much more than a body of fact. Among other things, it's a system that makes its facts physically meaningful -- i.e. observable and definable in terms of other facts, that are also physically observable and definable.

Mathematical systems seem to work very differently -- they're logical structures built on undefined basic elements / operations. These basic elements are meaningful to us, because we live in a physical world that has analogues to them. But there seem to be very basic features of the physical world that we haven't yet tried to account for in our theoretical models.

Can you give me examples?

Yes... the key example is just this business of measurement. If you have a physical fact -- say the mass of a particle -- there is also a physical context of interaction that allows its measurement. This context involves other kinds of physical facts -- to observe the mass of a particle, you need to be able to measure space/time intervals, etc. Another way to describe this: the world is not only a set of facts, but is also a system that physically communicates those facts... by means of other kinds of facts, that are observable in the context of other facts. Our current theories aim to be mathematical models of the fact-structure, but I don’t know of anything that models the structure of the communications system.

I tried to describe this kind of functionality in another thread –
https://www.physicsforums.com/showthread.php?t=332292"

But there are other “basic features of the physical world” that – so far as I know – haven’t been modeled mathematically. Our laws of physics obviously support more or less stable structures – atoms and molecules, crystals, all kinds of material objects. How does this work? It all depends on the functionality of the basic “building-blocks” – but atomic structure is very complicated, dependent on several apparently unrelated principles, e.g. electromagnetism, the exclusion principle, and whatever the laws are that keep nuclear particles stable.

So our world clearly provides highly functional “building-blocks” – but is there a theory that tries to explain what kinds of physical principles are required to do this?

Then too there’s the “calculation problem”. Obviously, in our world, physical systems obey dynamic laws, to a remarkable degree of precision. Yet we know that even in such a simple case as Newtonian gravitational dynamics among three point-particles, the equations have no analytic solution. Very clearly, physical systems do not have to compute their dynamics... so how does this thing of “obeying laws of physics” actually work? How does the physical world constantly create precise real-time “solutions” to problems that are mathematically intractable?

Basically I’m responding to your idea that we need a radical new paradigm, by saying – there are basic things we take for granted about the physical world, that haven’t yet been addressed in physical theory. If you’re taking seriously the question – why are things the way they are? – maybe these other aspects of “how things are” need to be considered, to get the complete picture.

 

[MTd2]

I am not so sure if exotic smoothness for R^4 is the very core of 4 dim. physics. Pfeiffer explicitly excludes topologogically inequivalent manifolds, but I would expect that different topologies will matter as well. (I've seen some statements in this regard in the CDT context, but I can't remember the details ...)

Exotic smoothness exists for an infinite type of different topologies! What I said about exotic sphere it is that it is the most difficult one is the the one case in which there is homomorphism to a sphere, thus, an exotic sphere. There are exotic spheres in several dimensions, but in 4 dimensions it is unkown. But if there is, it will be one that has infinite non-diffeomorphic kinds. In other dimensions, the number is merely finite.

 

[tom.stoer]

Exotic smoothness exists for an infinite type of different topologies!

All I wanted to say is that before different differential structures for one fixed topology become interesting, different topologies will be important. Look at strings: there you do not have several differential structures but its the basic topology of the world sheet that matters.

But I agree, exotic smoothness is a fascinating discovery.

 

[tom.stoer]

I see NO better option. ... If you have a better one and are able to convince me, I am open.

I certainly do not have a better one :-)

I am still thinking about the (ontological) relation between mathematical structures and physical entities. I am thinking about criteria for a candidate-ToE. I would say that a rather direct relation between mathematics and physics is obvious - otherwise it's magic why mathematics describes our world in a very accurate way. But I am not willing to accept that mathematics IS reality = IS physics.

Mathematics cannot answer questions regarding existence. THINKING about new axioms for set theory in order to overcome the axiom of choice and the riddle regarding the continuum hypothesis is neither equivalent to CREATING corresponding universes nor is it equivalent to DISCOVERING these (already existing) universes. Therefore there is a missing link between physical existence and mathematical truth.

I am still more conservative in the sense that I believe in rather fixed physical laws which do not change in time or which emerge from a deeper structure. If the latter would be true I would immediately try to get hands on this deeper (but then again fixed) structure and take this as a more fundamental law. And I am conservatice in the sense that I do not like anthropic reasoning as it seems to me to be a collection of excuses only.

Later I will try to explain in more detail how my proposal could look like. Unfortunately currently I am only able to tell you how it does NOT look like.

 

[MTd2]

Look at strings: there you do not have several differential structures but its the basic topology of the world sheet that matters.

You do have exotic structures in string theory. Actualy, Witten was the first one to write about exotic structures, although in 8 dimensions.

http://math.ucr.edu/home/baez//week141.html

Edward Witten, Global gravitational anomalies, Commun. Math. Phys. 100 (1985), 197-229.

http://projecteuclid.org/DPubS?service=UI&version=1.0&verb=Display&handle=euclid.cmp/1103943444

But I rather study the most complex ones, infinitely more, which are in 4 dimensions, and it also happens to be the dimension we live in.

 

[Fra]

Wouldn't that mean that your approach became a somehow fixed system of rules and statements? Wouldn't that mean that it is no longer subject to evolution? Wouldn't that mean that your meta-program became an "axiomatic system"?
...
If you say that the answer to the above raised questions is "no" there is only one conclusion, namely that the approach is somehow inconsistent or incomplete as we agreed to accept it,but at the same time we concluded (right now!) that it is not fixed but subject to change and therefore we have to withdraw our acceptance unless you have finished your work.

My answer to the above would be the no option.

I follow your reasoning but I think your expected logic is too rigid to be fit for the quest we face, and I think the explanation might be a difference in focus here. I used to think like that - I didn't always like the concept of evolving law - but I changed my mind. I think your rigid thinking is connected to your "traditional view" of fixed laws, that's how it was for me. But the more I thought about this the more did I see that this really isn't what I see, it was just what I expected to see.

So what is the problem at hand? To find and capture the TOE? No, not in my mind. The problem is that we want to increase our understanding as much as possible as fast as possible as rational as possible. the point is that even if a TOE is a goal, the ROAD to the TOE is the more immediate goal. Thus the goal is to infere the immediate future, not the end of time. And by construction then the inference system is present "now", is different from the one present in a definite future.

At no point in this process, must the fact that we are still on a journey, or the fact that our inference system can improve, inhibit us from actually doing so. I have a feeling thta your quest for "perfection" or ultimate consistency, ambitious as it may be, is actually inhibiting. You almost run into a halt. Nature don't do that. I'm just projecting here my own path from where I was to where I am. But my hat would go off if you can capture the perfect eternal consistency between the palms of your hans, but I couldn't do it, and I don't see how it would even make sense. My attempt of TRYING, lead to my my current strategy. So I did consider the rigid inference system, but I can't make sense out of it. Thereof my position.

I'm repeating myself here but I think your resistance against accepting evolving inference systems as an actual best descriptio nof nature (rather than a fixed on) is similar to Einsteins original resistance against the evolving/expanding universe. At first he tried to make it static, because he didn't first know that the universe ISN'T static.

Look around, does the inference systems we can distinguish in nature seem fixed? Not as far as I can see.

/Fredrik

 

[friend]

Mathematics cannot answer questions regarding existence. ...Therefore there is a missing link between physical existence and mathematical truth.

The only representation we have of the states of existence or non-existence is binary logic with its algebric manipulation of true and false. Here true represents what exists, and false represents what does not exist. We always consider true those statements that describe what really is, and visa versa. So any ToE that proports to determine what is, as opposed to what is not, would have to be based in logic. Can you imagine a theory of physics which does not comply with logic? I think logic is a ToE since we assume it applies to everything physical. The question is how do we extract laws of physics from this.

It may not be that hard. Whatever the tiniest constituents of reality are, it's fair to assume they can be describe with statements or propositions. And it's fair to assume that every little part co-exists with every other little part. That means reality is described as a logical conjuntion of all the propositions for every little part. I would assume that there is an infinite number of porposition required to describe all of reality. And in order to distinguish each little part, every proposition would have to be assigned numbers, or coordinates to keep track of them.

Any mathematical law of physics by definition has to describe how things go from one state to the next, how one set of propositions necessarily implies the next. These laws, like any function, describe how given one state what the next state will be, and given that what the next state will be, and given that what the next will be, etc. We could use a variable, say, t, to parameterize which step along the path you're at. And since all the facts co-exist together, there is no preferred path in the way one proposition implies the next, and every path would have to be considered. So maybe this conjunction of propositions can be manipulated into a combination of paths of implication and somehow integrated using the assigned coordinates to give us something that looks like a physical law, say something like Feynman's path integral or something.

 

[tom.stoer]

My answer to the above would be the no option.

At no point in this process, must the fact that we are still on a journey, or the fact that our inference system can improve, inhibit us from actually doing so.

OK, now you position is clear. You include in the process not only nature's evolution of laws but also our quest for these laws. My feeling as that it becomes al little too subjective, but that's my position - and I don't want to repeat it here.

I have a feeling thta your quest for "perfection" or ultimate consistency, ambitious as it may be, is actually inhibiting. You almost run into a halt. Nature don't do that. ... My attempt of TRYING, lead to my my current strategy. So I did consider the rigid inference system, but I can't make sense out of it. Thereof my position.

Yes, you are right. As I just said I can only tell you how it does NOT work (what a pitty). If it is this what you mean by "halting" then I agree.

Looking at the dilemma we face, there are two very different options.

You have chosen to search for evolving laws - and you somehow adapt your search strategy accordingly. You are like Achilles running after the turtle. You never overtake the turtle, but you are coming closer and closer - and perhaps this is the best you can do.

I have chosen (together with other traditionalists) to look for deeper levels of understanding and laws. It's a layer model, where uncovering the next layer immediately raises new questions. Here it doesn't matter if the layers are fixed and static or if they are evolving, because in this picture the laws for evolution would somehow be located at the next layer, so it fits into the picture.

If we focus in your picture more on the process of science, then we more or less agree; it's just a special description of philosophy of science. My new layers are paradigm shifts or revolutions (I think Kuhn wrote something like that).

If we focus on the nature and existence (or emerence) of laws then we disagree - but that's the interesting point here :-)

 

[tom.stoer]

The only representation we have of the states of existence or non-existence is binary logic with its algebric manipulation of true and false. Here true represents what exists, and false represents what does not exist. We always consider true those statements that describe what really is, and visa versa.

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.
(I hope that is the meaning of your "vice versa")

So any ToE that proports to determine what is, as opposed to what is not, would have to be based in logic. Can you imagine a theory of physics which does not comply with logic? I think logic is a ToE since we assume it applies to everything physical. The question is how do we extract laws of physics from this.[/QUOTE

Very good starting point.

... every proposition would have to be assigned numbers, or coordinates to keep track of them.[/QUOTE

Then you face the usual trouble with natural numbers, Gödel etc. Binary logic alone seems to not powerfull enough to do the job; using natural numbers may lead to inconsistent or incomplete systems w/o any chance to prove or disprove it.

Let me ask some questions to get a better understanding of your second statement:

Do you believe that natural numbers exist?

Do you believe that this is not only a platonic existence, but that there is a level of mathematics (say the natural numbers) that IS physically EXISTING = fundamental physical entities (which we haven't discovered so far).

Do you believe that you can somehow construct physical laws (which rely on more than logic) from logic itself? That means do you think that natural numbers, real numbers etc. emergy somehow from logic alone?

Or do you think that if we uncover the ultimate laws of science those concepts fade away as purely approximate descriptions and we are faced with a system of logical automata interacting with each other?

 

[ConradDJ]

The only representation we have of the states of existence or non-existence is binary logic with its algebric manipulation of true and false. Here true represents what exists, and false represents what does not exist... So any ToE that proports to determine what is, as opposed to what is not, would have to be based in logic... I think logic is a ToE since we assume it applies to everything physical. The question is how do we extract laws of physics from this.

It may not be that hard. Whatever the tiniest constituents of reality are, it's fair to assume they can be describe with statements or propositions...

Friend -- The point I was trying to make above (#149, 186) is that this binary representation of physical existence isn’t adequate. For a proposition “A exists” to have any meaning, it must be possible for something to determine something about A through interaction, within some particular frame of reference.

The very essence of classical physics is the assumption that these conditions under which something can be meaningfully determined have nothing to do with the nature of physical existence itself – a thing “just is” what it is, regardless of the conditions under which it can make a difference to anything else in the world. The essence of QM is the discovery that this is not the case.

Likewise the logical proposition “A=A” is fine, but has meaning only insofar as you can actually identify a determinate “A” and distinguish it from and compare it with other things. Because our physical universe gives us many, many ways of doing this, logic seems to apply to everything, as you say, a priori.

But again, the classical assumption is being made that the functionality that let's the existence of things be physically meaningful to each other, is irrelevant... that is, the complex conditions under which things can make a definite difference to each other, and under which propositions can be meaningfully true or false.

I'm not arguing against the use of logic, of course. I'm arguing that there are other aspects of physical existence that need to be considered. To reduce physics to logic is much the same as reducing human language to logic, assuming all the conditions of meaningful communication are irrelevant.

Logic and mathematics are abstractions supported by the complex functionality of language. I think the logical and mathematical aspects of physics are likewise abstractions from "physical existence" -- a complex functionality that we generally take for granted.

 

[friend]

Let me ask some questions to get a better understanding of your second statement:

Do you believe that natural numbers exist?

Do you believe that this is not only a platonic existence, but that there is a level of mathematics (say the natural numbers) that IS physically EXISTING = fundamental physical entities (which we haven't discovered so far).

Do you believe that you can somehow construct physical laws (which rely on more than logic) from logic itself? That means do you think that natural numbers, real numbers etc. emergy somehow from logic alone?

Or do you think that if we uncover the ultimate laws of science those concepts fade away as purely approximate descriptions and we are faced with a system of logical automata interacting with each other?

No, at this time I don't believe numbers in and of themselves have any physical meaning. Propositional logic and numbers and math are only a human contrivance of language to help us better describe reality. There are no fundamental particles that have a "1" or a "2" written on them. We can just as easily count them in a different order.

I don't know how numbers can be derived from logic alone. I understand Whitehead and Russel wrote a book doing just that. They also attempted to proved the completeness of math, but failed.

However, I do believe that the laws of physics can be derived from principle alone, without the need for measurement. Although, we might need measurements in order to check the math. For example, I've seen derivations of the path integral from logic alone. It's not on the arXiv yet, so I'm not allowed to publish here. PM me if you are interested in seeing it.

 

[friend]

Friend -- The point I was trying to make above (#149, 186) is that this binary representation of physical existence isn’t adequate. For a proposition “A exists” to have any meaning, it must be possible for something to determine something about A through interaction, within some particular frame of reference.

Yes, binary logic may not be sufficient, we do end up using numbers to quantify things.

But when you say, "it must be possible for something to determine something about A through interaction", I'm understanding material implication from that; we need some sort of B to prove A. Yet this is part of binary logic as well.

 

[Fra]

I think we're starting to reach a mutual understanding of positions.

OK, now you position is clear. You include in the process not only nature's evolution of laws but also our quest for these laws. My feeling as that it becomes al little too subjective, but that's my position - and I don't want to repeat it here.

Yes. I also understand why you think my position is a subjective - it is. The question where we differ, if it's avoidable or not - does the real world fit into a static description?

Yes, you are right. As I just said I can only tell you how it does NOT work (what a pitty). If it is this what you mean by "halting" then I agree.

Yes something like that is what I mean.

You have chosen to search for evolving laws - and you somehow adapt your search strategy accordingly. You are like Achilles running after the turtle. You never overtake the turtle, but you are coming closer and closer - and perhaps this is the best you can do.

That analogy seems a bit odd :) but it's true that I think the point is the quest for best performance. The perfect performance might be impossible.

Implicit in my reasoning is indeed a special view also of the philosophy of science. I use the very same abstraction to describe the scientific method & process, as I use to describe physical law and physical processes.

If we focus on the nature and existence (or emerence) of laws then we disagree - but that's the interesting point here :-)

Yes, I think this is where from my point of view, I would classify you as a kind of structural realist, enough though you currently seems to be in a process of finding out the problems of this approach and it seems, like you say yourself that you've at least partially found out what does not make sense.

I'm curious to see what your understanding eventually evolve into :)

/Fredrik

 

[moniker2]

does the real world fit into a static description? I think so...if you look at the world in terms of frames of time.

friends, I would like to bring up a theory I read two years ago. It's starts with the idea that LHC will not find any Higgs Boson particle, and it looks at the idea of quantum inertia. I think it's seven equations in total, but I'm not sure.

 

[tom.stoer]

I don't know how numbers can be derived from logic alone. I understand Whitehead and Russel wrote a book doing just that. They also attempted to proved the completeness of math, but failed.

I think set theory was required as well.

 

[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.