# String theory ~ the theory of physical theory?

Fra
In https://www.physicsforums.com/showthread.php?t=235006 there is a reference to Peter Woit's blog, which has one entry regarding the paper

“So what will you do if string theory is wrong?” by Moataz H. Emam
-- http://arxiv.org/PS_cache/arxiv/pdf/0805/0805.0543v1.pdf

I didn't want to inject the above thread with this sidetrack of mine, so I start a new thread.

This paper is a brief reflection that string theory may have a life of it's own regardless of physical relevance. But the the paper contains the following interesting and IMO ambitious view on string theory:

"I can imagine that string theory in that case may become its own new discipline; that is, a mathematical science that is devoted to the study of the structure of physical theory and the development of computational tools to be used in the real world. The theory would be studied by physicists and mathematicians who might no longer consider themselves either."
-- http://arxiv.org/PS_cache/arxiv/pdf/0805/0805.0543v1.pdf

If I read the author right, his view of string theory, is that string framework is in a fundamental way more fundamental than physical theory itself, and thus implicitly of higher generality? And somehow that the study of physical law, in a larger context (say such as evolving theories), would imply studying string theory.

Somehow that phrasing is very appealing to me and right in line with some of my thinking, but it's paradoxal that I can't see how the string framework could be a fundamental framework and strategy of sufficient generality to study physical law?

The fact that I want to understand the physical law in context, is why I find string theory speculative. I don't see how the string framework is the solution to the expressed quest?

Does most string theorists share the basic sentiment of this as expressed by Moataz H. Emam or is he in minority? or is he trying to make string theory something it's not?

/Fredrik

## Answers and Replies

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In https://www.physicsforums.com/showthread.php?t=235006 there is a reference to Peter Woit's blog, which has one entry regarding the paper

“So what will you do if string theory is wrong?” by Moataz H. Emam
-- http://arxiv.org/PS_cache/arxiv/pdf/0805/0805.0543v1.pdf

Hi Fra, you present a rather tenuous train of association
I grabbed Kea's comment off of Woit's blog. But I didn't mention Woit's blog or the article by M.H.Emam. That article must have been discussed in another entry, as you say. I don't recall any connection. So it really is a fresh topic.

As i understand it, Moataz Emam is a string theorist himself and presumably a devoted one. He seems enthused about string research. He may be unusual in that he is willing to contemplate hypothetically that string thinking might eventually not turn out to have much to do with nature.

Even then, says Emam, it is worthy to be pursued for its own sake. This represents, to my way of looking at it, an admirably dedicated commitment.

Personally I think i might have cautioned you not to broach the subject of Emam's paper because it is likely to spawn contention, or (if not two-sided contention) at least some one-sided expressions of outrage and contempt. A lot of people, it seems to me, simply don't care to contemplate as possible what he assumes hypothetically.

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Fra
Hi Fra, you present a rather tenuous train of association

Yes I figured from the context it wasn't your main focus, that's what I started a new thread. I am getting used to the fact that my associations are usually considered tenous, but that's all relative too I think and I can't help it But the article is mentioned i even in the title of Woit's blog-thread and the link to the paper is in the first scentence.
http://www.math.columbia.edu/~woit/wordpress/?p=684#comment-38202

Personally I think i might have cautioned you not to broach the subject of Emam's paper because it is likely to spawn contention, or (if not two-sided contention) at least some one-sided expressions of outrage and contempt. A lot of people, it seems to me, simply don't care to contemplate as possible what he assumes hypothetically.

I think I see you point, but to me, his view is interesting even is string theory is right. So my choice of focus is not to argue if string theory is wrong as such in some sense, it's been discussed already, no need to repeat that discussion. That isn't my intention.

It's rather to reflect over what string theory is. Is it a normal theory, or is it something else (in a way that is also discussed before, and IMO it's a kind of framework that constraints theory construction). I certainly don't mean it in a bad sense. If it was a theory or theories, then that would be excellent IMO. Sometimes I find some of the critics according to poppian thinking to be unfair. The poppian decsription seems to me slightly simplified and out of date, since the notion of falsify is more complicate when it comes to a learning strategy. Beeing wrong isn't a failure - failing to learn is, or failing to learn _fast enough_ in competition is (IMHO at least)

So I was curious on the logic within which this is seen as obvious, because I agree that it is an admirably dedicated commitment, in a deeper way, because IMHO history has taught us that things change. And theories change, therefor to study theories as evolving in larger context seems nice IMO.

/Fredrik

Fra
I guess what I did was, to find the most positive interpretation (relative to my view) of that paper.

If we try to make up a new discipline, which are to study the structure and evolution of physical law and physical theory, and from such an endavour try to learn something on practical models and strategies that can be used for real computational predictions, that sounds very nice IMO. Instead of considering theories that described the dynamics of observations, we add the level of self-reference that we are considering the dynamics of the theories themselves.

Questions like

1) what is a physical theory, and what is physical law?
2) How do they emerge and what are their physical representation (informationwise)?
3) What is the distinction between physical law, and the evolution of physical law, if there is a higher level law of laws?

Maybe I read too muhc out of that paper, but this is questions I ask, and if some string theorists think like this then perhaps they have failed to argue in favour of it?

I personally expect that questions like the above, considers also the physical nature of information, and information processing. And considering things like confidence, and howto distinguish a random lucky guess from a skill, we unavoidably touch the foundations also of statistics and probability theory.

Now if some string theorist share the same visions, and perhaps could elaborate the connection here I think it would have the potential to defend string theory from some of the poppian style critics. I also think these question may be relevant in trying to find a conceptual connection between the various approaches.

/Fredrik

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I recently read a bit of Nancy Cartwright. Heard her talk, a year or so ago, and was impressed, but didn't immediately follow up until now:
http://books.google.co.uk/books?id=...ct=title&cad=one-book-with-thumbnail#PPA10,M1

see if that will get you the introduction to her book "The Dappled World"
It might interest you.
I suppose it could be argued that Cartwright presents a more practical and realistic view of physical law than Emam seems to have.
I can't say this is a special interest of mine or that I know much about it, but since you think generally about physical law you might get something out of her introduction.

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I found something else that might interest you
http://books.google.co.uk/books?id=...r+galison&source=gbs_summary_r&cad=0#PPA40,M1
The disunity of the sciences
BTW the subtitle of the Cartwright book is "A study of the boundaries of science"
She's a department chair at the London School of Economics and recipient of a Macarthur (one of those so-called "genius awards").
A smart articulate empiricist. (that word even more than realist, pragmatist, practical real-world...is descriptive).
Empiricism making a comeback look at the program of Strings-2008 talks. Look at the 8 onehour review talks. Two of them are by Jos Engeler and Lyn Evans, who aren't string theorists-----the CERN CSO (chief scientific officer) and the head of the LHC project.
It's all quite natural given the time and context but nevertheless you can see the pendulum swinging.
http://ph-dep-th.web.cern.ch/ph-dep-th/content2/workshops/strings2008/?site=content/talks.html [Broken]

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Fra
I took a very quick peak at the first pages. Both of them seem to contain in some sense logical reasoning. But I couldn't see if they come to a "constructive suggestions" rather than only arousing sensations :) - did you read them?

I am very philosophical in my style of reasoning in that I am guided more by soundness of reasoning that beauty of mathematics (Although there may be good reasons why they sometimes coincide).

In despite of my philosophical angle, I am definitely looking for a mathematical formalism, that is computable. A theory can fails to come up with a computable (in reasonable time) algorithm is of limited utility. Also I rarely read philosophy litterature as such.

/Fredrik

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- did you read them?
...

I confess I did spend quite a lot of time this morning reading from Cartwright and that other guy. One reason their arguments can grab my attention is that their views are so different from mine (and I think yours.) It is important to be confronted by alien and conflicting trains of thought.

Cartwright is a worldclass expert who has directly addressed the issue of a physical theory-deciding machine, or to put it more vaguely a "theory of theories", and whether or in what sense such a thing is possible. Is there always a social element? Consensus as to what constitutes evidence? Actual personal battles and struggle at some level? Ultimately does science depend essentially on the functioning of communities, with ethos ethic status-ranking etc. Or in what way can it be abstracted and objectified?

I'm not saying that Cartwright is more sophisticated. I don't know enough to judge. It does seem to me however that she has made a brilliant career thinking about exactly what you are proposing to discuss (theory of physical theories) and that she has thought and written and talked and argued with a lot of other smart people about this for decades of year almost nonstop (that, and economic theory too). Intuitively there should be something you couild learn from her, if you had the time. But maybe not.

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Fra, you deserve some kind of response to your question and even though I may not be the most qualified person, I will, in the absence of other attempts, try. First notice that this forum is for Professionally researched theories that go beyond established models, it is not just limited to string brane loop---they just are symbolic examples of the kind of topic.

Nowadays Noncommutative geometry (NCG) is very strong because it reproduces the standard particle model simply from a picture of spacetime. That picture is NOT a differential manifold. It is an algebraic substitute for a smooth diff. geom manifold of the sort that Riemann invented in 1850.
String theory is based on differential geometry, on manifolds. That is another way to go.
Branes are differentiable manifolds, like Riemann invented.
Another strong contender is Causal Dynamical Triangulations (CDT) which is based NOT on differential manifolds but on a different idea of spacetime---piecewise linear, simplicial complexes, a limit of them, a Feynman path integral thru the set of them.

Then there are CATEGORIES AND TOPOI and things like that, that people like Grothendieck invented say around 1950 or roughly a hundred years later, and THEY give you a way of describing spacetime and geometry.

And there is whatever Witten is working on. In 2006 when I heard him give three 1.5 hour talks it wasnt string/M it was Geometric Langlands Program. He seemed to think that was more interesting. For the entire 4.5 hours he didn't mention string (somebody in the audience had to ask him about it at the end of the third talk.) So it is possible that THAT could form the basis of a new physical theory, or a machine for searching for theories. I shouldn't single Witten out. There are a lot of creative people nurturing new mathematical formalism and new approaches to physical theory. But he's one example.
================================

So what you are seeing is a battle of ideas to determine what will be the next mathematical formalism by which humans depict space time geometry motion and matter.
Some theories are still based on vintage 1850 differential geometry----smooth manifolds, worldsheets, branes, whatever.
some theories are based on other things, categories, topoi, simplexes, algebra like NCG uses to represent geometry, and other post-1950 mathematics.
the struggle between theories is essentially one to determine what is going to be considered the right formalism, for the time being.
================================

what comes out of this rowdy scuffle may have something to do with string formalism
or it may conceivably have nothing whatever to do with string formalism
we can't tell
research is the hardest thing to predict that humans do.
===============================

my own opinion is that it is foolish for someone to put all their bets on one particular mathematical formalism, at this point in the game

so I find what Emam proposed to be ridiculous. it is far too limited in scope.

but that is just my personal opinion.

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By coincidence, Fra, the same day I posted the above I saw this by John Baez
http://golem.ph.utexas.edu/category/2008/05/convenient_categories_of_smoot.html

since 1850 the european concept of continuum has tended to be the smooth manifold that Riemann invented, or something even simpler like Rn

what I'm telling you is that we are now seeing a brawl between different ways of advancing beyond that idea of continuum----we don't know which mathematical formalism will win out.

string worldsheets and branes are oldfashion smooth manifolds arising in a conventional Diffy Geom context like so much else in older physics, that formalism might prevail

or some other might prevail. it would be naive at this point to commit

BUT BAEZ HAS SOME REASONS WHY the oldfashion diffy geom. continuum is bad!

He shows us there are different ways to define what is a continuum or a smooth space or spacetime and he gives reasons why the vintage 1850 idea is unsatisfactory.

This is good. It is what you train and pay mathematicians for----to be able to see things like this.

Take a look.

So he and his buddy have joined the crowd of people looking for a better mathematical formalism for the continuum, and trying out various alternatives to the oldfashion smooth space idea.

what I'm saying is that ultimately if you want to theorize about the next physical theory, then you need a mental picture that includes alternative concepts of the continuum (not just the preserved Riemannian one you find pickled in so much conventional physics today)
David Gross occasionally says this. It comes across as a desperate outcry sometime: "We don't know what string theory is! We need a fundamentally new idea---fundamentally new ideas of space and time!..." and so on.
That is what they sound like when they need a new mathematical formalism. So take a look at what Baez writes in n-category cafe. He mentions Grothendieck (as I did earlier today). Maybe Baez doesn't have the right answer but he has something like the right SCOPE.

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Fra
Thanks Marcus for all your comments and sharing of views.

what I'm saying is that ultimately if you want to theorize about the next physical theory, then you need a mental picture that includes alternative concepts of the continuum (not just the preserved Riemannian one you find pickled in so much conventional physics today)David Gross occasionally says this. It comes across as a desperate outcry sometime: "We don't know what string theory is! We need a fundamentally new idea---fundamentally new ideas of space and time!..." and so on.

Maybe this drifted a bit from the original focus of having the more dedicated string theorists give their comment on Emamns article.

But I agree with a lot of what you say here. I have expressed my opinion in several posts that I fail to see the physical basis of the continuum. That's not to say that a discrete model can't be embedded in a contiuum model, but just that I see contiuum models containing uncontrollled unphysical degrees of freedom and that embeddding is thus non-physical, and we should shave off those degrees of freedom and get a more compact representation. My main objections are from the information point of view. You need a lot of information to specify a continuum , and well there is something that isn't right there IMHO. If I am not mistaken Smolin have argue along similar lines. So in short, I need no further compelling to question the concept of contiuum

Now I know some may interject here and point out the difference between a physical continuum and a continuum model. Many who work with continuum models seem to agree that ultimately it's a property of the model but not necessarily nature. That is true, but IMO that is not taking the models serious enough. I expect a better connection. From the effective view we already know continuum models are great in many cases. So that isn't the question.

This is very much related to the concept of counting we discussed before. Wether we are counting states of matter of states of the geometry. I think we should bring back a concept of distinguishability. We should count observationally distiniguishable things. One can still understnad why the continuum model is a good approximation to this, as a smoothed version of the real thing.

What I am trying to formalise is instead of a generator of say time on the level of universal law, I am considering a local(local with respect to the observers information) strategy for producing an expectation of the future. And this will have a complex feedback, that is sort of applied inductively. And somehow this induction and other feedback is processed in parallell, and the progress of all this is identified with local time evolution. The my aim is thus to put the notion of physical law and the notion of physical states, on the same level, with the only difference that they live at different levels of the induction and processing. And the notion of law have more inertia than the physical states - so although in principle - both are dynamical objects, the relative change of physical law in a small "time" window is small enough to distinguish between them.

Problem I have are how to represent information. There is a nonlinear feedback means that there is no universal way to distinguish the feedback from what it relates to. And this feedback is a process, that defines time. I've been thinking about this for some time now and I am making progress in small steps.

Meanwhile I like to see if other approaches distinguish the same questions, and how their solutions are lined out.

Anyway, this is why I found Emamns paper paradoxal. He gave a small hint of a grand vision - good. But then he suggests that string theory is the solution to that. I do not have to agree, but it would be enlightning to see if anyone that agrees with him, could expand on how you reach this conclusion.

/Fredrik

Fra
It is important to be confronted by alien and conflicting trains of thought.

I agree completely. To try to understand a disagreement can be very a enlightning process as it resolves to the problem of resolving a contradiction. Which I consider to be a key perspective in many ways.

Cartwright is a worldclass expert who has directly addressed the issue of a physical theory-deciding machine, or to put it more vaguely a "theory of theories", and whether or in what sense such a thing is possible. Is there always a social element? Consensus as to what constitutes evidence? Actual personal battles and struggle at some level? Ultimately does science depend essentially on the functioning of communities, with ethos ethic status-ranking etc. Or in what way can it be abstracted and objectified?

I will consider looking into her work! Right now I've other stuff piled up to "look into" where I'm lagging due to limited resources. So I usually want a very good reason why looking into this instead of that is more promising. Sure many things are potentially interesting, the only problem is that my brain has limited resources to process data with.

I see clear similarities with theory building in physics, as well as interactions in social, economical and biological systems. Game theory is one perspective where the above connections is there. This is all in line with my thinking, and the basic conceptual level here is somewhat clear to me. I am looking for how to exploit this.

The question of a physical theory-deciding machine, and wether such a machine can be universal? And what universal means, are interesting questions. My opinion is that each subsystem and observer is in an abstract sense a "theory-deciding machine". And I don't think there can be a universal one. From that point on, which seems rather hopeless, I ask how and why a local rules still emerge. And then to save us from chaos, these rules themselves are rated, which give them a kind of relative intertia.

From my experience with communicating with others, there seems to be two issues in communicating this.

The first is to convey the basis spirit of intent and the vision. I think this is best done in plain english, complemented by examples and analogies. But to understand this one needs a somewhat open mind.

The next issues is, once you are working within this spirit, to actually take it another step, towards something more formal, where you can induce a choice of mathematical or logical formalism, that will allow you to more constructively make quantitative models rather than conceptual models in words.

I have a conceptual idea on my own, and I sense a lot of that in the philsophical writings of Rovelli but also Smolin. So I really appreciate their world. But I don't quite understand or accept all of their current solutions to step 2.

Right now, I don't think I would benefit much from reading a step 1 book. I am looking for step 2 suggestions. So I have currently looked into rovellit en penrose and like parts of it, but still looking. My impression is that those(edit: the books you suggested above - rovelli is more precise but I feel he is jumping to fast into the chocies, without properly reflecting over it. I found his line or reasoning to be broken somewhere in his relational QM argumentation, although he started out nice) books doesn't contain stuff at that level? or does it?

If it does, I would definitely want to read it. Let me know what you think. If you think it contains such constructive formal ideas, I might take your advise and order it, and give it a closer look.

/Fredrik

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Fra
It seems a problem is to bridge the a sound somewhat philosophical basis for theory building and science with the more computational stringent formalism.

I find many papers to start right in the middle of some somewhat formal context, and the argue on. But that is lacking the continuous line of reasoning that has selected that formal system to start with. And if you think that the induction of something as per a particular line of reasoning, and also the choice of line of reasoning is part of the problems, such an approach which ignores the fundamentals and more or less arbitrarily chooses a formal framework is IMO a high risk one.

If one reads some of the original texts of founders of new disciplines, like Heisenberg and dirac and einstein, it's easy to see the significance of line of reasoning in the development of those theories. It is a clear guide. Extreme formalisations and axiomatisations are i think often post-constructions once the theory is mature. It's not always how real life progress is made as far as I can see.

/Fredrk

Pointy
It seems a problem is to bridge the a sound somewhat philosophical basis for theory building and science with the more computational stringent formalism.

I find many papers to start right in the middle of some somewhat formal context, and the argue on. But that is lacking the continuous line of reasoning that has selected that formal system to start with. And if you think that the induction of something as per a particular line of reasoning, and also the choice of line of reasoning is part of the problems, such an approach which ignores the fundamentals and more or less arbitrarily chooses a formal framework is IMO a high risk one.

If one reads some of the original texts of founders of new disciplines, like Heisenberg and dirac and einstein, it's easy to see the significance of line of reasoning in the development of those theories. It is a clear guide. Extreme formalisations and axiomatisations are i think often post-constructions once the theory is mature. It's not always how real life progress is made as far as I can see.

/Fredrk

To eleborate on this thought, a relevant entry on wikipedia's TOE page

Potential status of a theory of everything

No physical theory to date is believed to be precisely accurate. Instead, physics has proceeded by a series of "successive approximations" allowing more and more accurate predictions over a wider and wider range of phenomena. Some physicists believe that it is therefore a mistake to confuse theoretical models with the true nature of reality, and hold that the series of approximations will never terminate in the "truth". Einstein himself expressed this view on occasions.[15] On this view, we may reasonably hope for a theory of everything which self-consistently incorporates all currently known forces, but should not expect it to be the final answer. On the other hand it is often claimed that, despite the apparently ever-increasing complexity of the mathematics of each new theory, in a deep sense associated with their underlying gauge symmetry and the number of fundamental physical constants, the theories are becoming simpler. If so, the process of simplification cannot continue indefinitely.

There is a philosophical debate within the physics community as to whether a theory of everything deserves to be called the fundamental law of the universe.[16] One view is the hard reductionist position that the TOE is the fundamental law and that all other theories that apply within the universe are a consequence of the TOE. Another view is that emergent laws (called "free floating laws" by Steven Weinberg), which govern the behavior of complex systems, should be seen as equally fundamental. Examples are the second law of thermodynamics and the theory of natural selection. The point being that, although in our universe these laws describe systems whose behaviour could ("in principle") be predicted from a TOE, they would also hold in universes with different low-level laws, subject only to some very general conditions. Therefore it is of no help, even in principle, to invoke low-level laws when discussing the behavior of complex systems. Some argue that this attitude would violate Occam's Razor if a completely valid TOE were formulated. It is not clear that there is any point at issue in these debates (e.g. between Steven Weinberg and Philip Anderson) other than the right to apply the high-status word "fundamental" to their respective subjects of interest.

Although the name "theory of everything" suggests the determinism of Laplace's quote, this gives a very misleading impression. Determinism is frustrated by the probabilistic nature of quantum mechanical predictions, by the extreme sensitivity to initial conditions that leads to mathematical chaos, and by the extreme mathematical difficulty of applying the theory. Thus, although the current standard model of particle physics "in principle" predicts all known non-gravitational phenomena, in practice only a few quantitative results have been derived from the full theory (e.g. the masses of some of the simplest hadrons), and these results (especially the particle masses which are most relevant for low-energy physics) are less accurate than existing experimental measurements. The true TOE would almost certainly be even harder to apply. The main motive for seeking a TOE, apart from the pure intellectual satisfaction of completing a centuries-long quest, is that all prior successful unifications have predicted new phenomena, some of which (e.g. electrical generators) have proved of great practical importance. As in other cases of theory reduction, the TOE would also allow us to confidently define the domain of validity and residual error of low-energy approximations to the full theory which could be used for practical calculations.

Formalisation in the end cannot be a work-around around the determinism-approximation quandary of Einstein.

Pointy
The last lines from the TOE (physics) page

Theory of everything (physics) and philosophy

Main article: Theory of everything (philosophy)

The status of a physical TOE is open to philosophical debate. For instance, if physicalism is true, a physical TOE would coincide with a philosophical theory of everything. Some philosophers (Aristotle, Plato, Hegel, Whitehead, et al) have attempted to construct all-encompassing systems. Others are highly dubious about the very possibility of such an exercise.

The last lines from the Theory of everything (physics) talk page

Thank you for the clear insight. I think we both agree this pertains to TOE (philosophy). As such, that indeed has deep metaphysical issues. The only thing I can add to that is a quote from Albert E. himself;

"The eternal mystery of the world is it's comprehensibility", where one could in fact ask the question as to why, if it's not "REAL", why it all works out so beautifully? ( Not including any non-local theory ofcourse, this not being determinism)

So if Albert E. can't answer this question, I'm not even going to try :)

But the objection still stands, that instrumentalism and phenemologism are only metaphysically prefferred, if science can't explain everything. But as SR states, a new macroscopic theory should indeed help with many such problems, maybe all problems, and for sure with problems imagined unexplainable such as 'immediatism' and 'over-unity', and how there are shapes and sizes ( info on how matter relates to energy ) Why the link of logic and mathematics with 'realness' is not found is perhaps then more a problem of neuro-science, where conciousness and abstractability are closely related? —Preceding unsigned comment added by 83.134.83.20 (talk) 21:37, 2 June 2008 (UTC)

More to the point even is one of the last sentences on this TOE (physics) page,

if physicalism is true, a physical TOE would coincide with a philosophical theory of everything

Next to the fact that the author of SR is a software model engineer, and self-taught theorethical physicist, he is also a philosopher. One of the main physical implications of SR's correct metaphysical and mathmatical thought, is the non-existence of a vacuum. You know, a physical/metaphysical vacuum is where there is literally nothing there. One of the more famous metaphysically/mathmatically correct quotes of Mark Fiorentino is

"You cannot put something into nothing".

Think about that for a minute..

Thought about it?

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Pointy I have two comments on your two posts here.
One is not necessarily unfriendly, you may agree with it:

TOE is a really stupid term. It is media hype made up by John Ellis at CERN, who likes to talk to the media and TV and stuff. It is a distracting red herring.

I don't think anyone who is serious about the philosophy of science should bother discussing the TOE idea.

In naive credulous people it creates the fantasy of a UNIQUE ULTIMATE physical theory.
In fact over the centuries physical theory does become gradually more fundamental, more unified, more comprehensive in explanatory power.

But just because some joker on a TV program says TOE doesn't mean we are suddenly near the end of this process . We are nowhere near an end, and maybe there is no end.

So. I don't know, you may agree with this.

So why would serious people even be having a conversation about this phony idea?
=====================

My other reaction is critical, but not to make you feel bad. In your posts you don't SAY anything. You just copy/paste in stuff from like Wikipedia talk.

Quotes are supposed to illustrate something you yourself are saying. Or be quotes from some authoritative source or important scientist, that you are showing that this or that wellknown person had a certain opinion. And quotes can give context, so you arent just quoting ambiguously out of context. And you can use links.

But just pasting in anonymous Wikipedia talk text doesn't do anything. I find it hard to force myself to read a post that just pastes in verbiage by nobody in particular from nowhere special.

You know that Wikipedia physics articles themselves are not free from unreliable rubbish. So I would imagine that Wikipedia talk pages have even more stuff that one would naturally just ignore.

So I encourage you to say in brief what you are trying to say, and not merely paste in stuff.

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BenTheMan
I don't think anyone who is serious about the philosophy of science should bother discussing the TOE idea.

In what sense? Everything'' is typically taken to mean Standard Model + Gravity. If this is the definition, then I think only people who have no hope of reproducing the Standard Model + Gravity with their models have this opinion.

In naive credulous people it creates the fantasy of a UNIQUE ULTIMATE physical theory.

Or, of course, a landscape of possible theories. What's your point?

The only candidate for a theory of everything'' is string theory, which is perhaps why you hate the term, marcus. The efforts I've seen to get the standard model + a theory of quantum gravity fail pretty spectacualry---for example, Smolin's recent work in trying to get the standard model predicts 4 neutrinos (that, naively, are related by some symmetry operation), something that has been experimentally ruled out for a long time (neutrino mixing).

Inasmuch as I can tell, only string theory can claim to have a quantum theory of graviy + the types of mathematical structures needed to get real low energy physics out. The exact low energy physics depends on the compactified directions, of course, but quite generally string theory gives family replication, non-abelian gauge symmetries, chiral matter, etc. And note that you get all of this stuff for free---it's not lumped into some ad hoc stress energy tensor.

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To get back to the main topic
here is a possible position to take (Fra asks for our opinions)

1. string theory is not a candidate TOE
because of its multiverse of different possibilities it is looking these days more like
a theory of ANYTHING, any version of physics, not committed to anyone set of predictions
or a theory of NOTHING. This is the position that Larry Krauss took in debating Brian Greene at the Smithsonian in Washington. Krauss is a prominent physicist at Case Western, specialty cosmology.

besides which we are hardly in a position to discuss a TOE, we don't know what all physical phenomena are, more keep appearing, theory keeps on evolving. there is no sign of an end.
even if we were, string is enough of a failure that its pretty clear string would not be the answer. Krauss terms it a "colossal" failure. So that's one tenable position.

What Krauss says is not my position because I don't bother to criticize string. I am not a critic of string. What I focus on is reporting what is happening. If people don't like the news they may react with hostility, but they shouldn't confuse what I say with criticism of string thought or string math.

However I say that Krauss position is tenable. What I mean is he made his case and continues to hold it, and Brian Greene backed down. Tenable in a scholar debate sense.

In a recent interview at Edge, Brian Greene has backed off and said the erstwhile TOE talk was "youthful exuberance" from back in the 1990s. Now the hope is not that string be a comprehensive ultimate theory, but just that it say something about nature, be useful for something, in some sector. Paul Steinhardt, in the same interview, identified that as an "enormous retreat" (from the earlier string hype heard from Greene and others).

What came out of the Edge interview with Greene and Steinhardt is that the way to reduce tension is to stop the pretension. Greene was saying people should stop being mad at string just because of all the TOE hype in the 1990s. That was just "youthful exuberance". Now we don't make such claims. It's a way out. If the pretension and arrogance really does ease off.

So Krauss position is tenable. The Krauss's and the Steinhardt's have forced the Greene-like people to retreat. That is pretty much over and done, complaining about it is just whining.

A tactic on part of some string folks is to denigrate and scapegoat Lee Smolin. Smolin actually has little to do with all this. He is an advocate of support for background independent quantum gravity research. And generally been politely respectful of string research. The real critics Krauss and Steinhardt are not quantum gravity people. Nothing to do, either of them, with LQG, CDT, spinfoam, Smolin, Rovelli, Ashtekar. They are not making a case for the background independent quantum gravity program, as Smolin does.
So blaming Smolin and "the LQG camp" for the criticism is just a diversionary. It is not where the strong message is coming from.

===========================================================

2. string is not a candidate theory of physical theory
Stringy mathematics may well prove useful in modeling some sectors of physics. It may help with some aspects of nature. But I would argue that it is going in the wrong direction to be theory of theories.

The newer attempts to understand the nature of space, time, and matter are all manifestly and explicitly background independent** as classical 1915 General Relativity already was. But as quantum field theory is NOT.
They take background independence as a basic premise, that they are built on. There shall be no initially prescribed metric geometry on the continuum. Geometry is arrived at dynamically and emerges as a solution. It is not put in at the beginning.

String was not built on this premise. Traditionally it is background dependent. there is a hope that a manifestly background independent theory underlies string approaches but no one has spelled it out.

So string framework of ideas does not embrace the newer approaches. It is not comprehensive enough to represent and compare the theory directions where progress is occurring. So it is badly situated to serve as an overall mother framework.
============================================

3. string math may prove useful in limited ways to do various jobs
I think this is already occurring and I think it is splendid. Application of stringy math to quantum chromodynamics (QCD) calculations.
Hermann Nicolai had an article in Nature about this. He's an important European string theorist and I'm a fan of his since 2004 when the Max Planck division he directs put on a conference called "Strings meets Loops" at Potsdam.

Personally I admire string math, what of it I've been exposed to, and consider it great stuff. I don't criticize string research. What I do is try to report objectively on what is happening.
When Witten came out to Berkeley in 2006 he gave three talks each 1 and 1/2 hours. And I listened eagerly to all 4 and 1/2 hours (spread out over several days). He did not mention string theory or M theory at all because his research interest had changed to something more purely higher math which I thought was great.*

At the end there were questions and one person asked "what about string theory". Almost embarrassedly he said "Oh I still think that string theory will turn out to have something to do with nature."

Yes, and in a way that could be what Hermann Nicolai was talking about, a valid application of some mathematical techniques to make something easier to calculate. Useful applicability, not a Theory of Everything

footnote: * Witten was talking for nearly 5 hours about a grand generalized Fourier transform between not just signals or functions (like ordinary Fourier transform) but between higher mathematical structures. That is a goofy oversimplication. He was talking about what is called the "geometric Langlands program". I thought it was great. Several of my old math professors were there, happy as whitehaired clams. High powerful abstract math. No mention of string, which did surprise me.

footnote:** a good date for the newer approaches is 1998 because that was when Causal Dynamical Triangulations appeared, and spinfoam emerged about then, also Reuter's first Asymptotic Safety paper was 1998. Loop Quantum Cosmology appeared 1999 or 2000---the first big result was 2001 with the removal of the big bang singularity. So that is when a major movement got underway, I would think of the pre-1998 Loop stuff more as preparing the ground. One background independent approach up to that 1998 point became suddenly several others with more momentum. How I see it anyway

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Science Advisor
People get so confused about background independance. In many ways its a completely misleading term that is defined differently by different authors and pretty much synonomous with layman fog.

For instance, there is no sense in which Reuters asymptotic safety program is more or less background independant than String theory. In fact, probably quite less. Particularly in cases which are well under control (AdS/CFT) or with lots of SuSY present (where you will get explicitly emergent quantum geometry in certain nonperturbative regimes).

Also Lolls program is completely 100% background *dependant* in the sense that there is exactly one prescribed way to define her lattice parametrization, you have no choice in deforming around the 'man' made construct..

Also, its important to emphasize that it is most assuredly not a fundamental quality that a theories must possess. It is utterly trivial to formulate GR for instance in a way that explicitly breaks much of the diffeomorphism symmetry and makes explicit use of coordinates. It is still GR, its just been gauge fixed.

Science Advisor
Gold Member
Dearly Missed
For instance, there is no sense in which Reuters asymptotic safety program is more or less background independant than String theory. In fact, probably quite less. Particularly in cases which are well under control (AdS/CFT) or with lots of SuSY present (where you will get explicitly emergent quantum geometry in certain nonperturbative regimes).
...

You may have noticed that I did not mention Reuter's asymptotic safety program as background independent. "Probably quite less" is your conjecture. I simply don't mention it as exemplary that way.

As for your claim that Loll's CDT is 100 percent background dependent, you will really have to take that up with Loll.
It sounds ridiculous, the only way I can make sense is to suppose that you are reasoning by drawing analogies which Loll would simply not.
Conventionally, among nonstring QG folks, background dependence means you start with a manifold already provided with a metric. GR starts with a manifold without a metric. So does Loll. Therefore in the usual straightforward sense her approach is as B.I. as General Relativity itself. same spirit.
Trying to draw analogies and bend words around to make out it is not can only lead to semantic quibbling, I fear. Just go along and say what you want, Haelfix. there is no reason for me to wish to argue the point with you.

Science Advisor
"same spirit."

Which is semantics and not physics or mathematics. You can start with a given metric in GR just fine, and lo and behold, its still GR. No different than String theory. Alternatively, you can work in the worldsheet and leave the full spacetime manifold geometry unspecified and if you switch pictures you will see a fully dynamical quantity (the target metric field) fluctuating all over the place, and even changing its topology.

As for CDT...

*ALL* Lattice theories are 'background dependant' with the following definition: You input a starting *choice* of how you draw your lattice. It can be random, or it can be fixed. The details of this process, should drop out in the continuum limit assuming you have a consistent theory. So we will call a lattice theory 'background independant ' where the continuum, infinite volume limit is taken and all details of the choice drop out. We will further call such a choice consistent, if it encapsulates the correct semi classical limit, or in technical terms it is a relevant deformation of a renormalization group fixed point. When you do something on a computer, there is no such analytic process.. Thus it is background *dependant* by definition.

Now there is a further technical requirement in CDT, that is that all solutions derived by this method are topologically restricting. They all require a specific choice of foliation. Which is completely background *dependant* from the point of view of the path integral. You are essentially by hand, excising all topologies that don't have this particular property. In various other authors terminology, that is called 'quantum background dependance'

So the point is, just throwing words blindly around is vacuous b/c there are about 20different completely disparate concepts being thrown around into one catch all 'term' in the layman literature and on this board. It needs to stop.

Science Advisor
Gold Member
Dearly Missed
See https://www.physicsforums.com/showthread.php?t=238605
I've quoted Loll's abstract and highlighted where she says the approach is background independent.
I think I understand what she means and it makes sense.
It is correct professional usage among her colleagues.
I think you mean something else by 'background independent'. Unless you were to write one of the authors and get straightened out so you both mean the same thing, discussion is impossible.

I gather that there must be no one unique correct meaning. Since Loll says her approach is B.I. and Laurent Freidel says his is B.I. and Rovelli says his is B.I. and they would all agree among themselves. But you and many string theorists (apparently using the term differently) seem to disagree.

You suggest it is a term used by laymen, but I don't hear it much from laymen at all. I hear it recently a lot from QG professionals. The concept is evidently important, but not one that I can discuss with you because you attach different meanings to it.

Kea
But you and many string theorists ...

And many non String theorists ...

Careful
Now there is a further technical requirement in CDT, that is that all solutions derived by this method are topologically restricting. They all require a specific choice of foliation. Which is completely background *dependant* from the point of view of the path integral. You are essentially by hand, excising all topologies that don't have this particular property. In various other authors terminology, that is called 'quantum background dependance'

So the point is, just throwing words blindly around is vacuous b/c there are about 20different completely disparate concepts being thrown around into one catch all 'term' in the layman literature and on this board. It needs to stop.

I agree essentially with what you say. As for a definition of background independance (with respect ordinary differentiable manifolds M) : "A theory on M is BI (or simply covariant) if and only if the Lagrangian does not contain non dynamical-fields nor Lagrange multipliers".
With respect to your points on CDT: indeed, it is not an ordinary path integral since the geometries are GIVING you a foliation (it is not that you pick a coordinate system and evaluate for all geometries as the standard formulation would require). The real question is "what does it mean?". If it were simply a (partial) gauge fixing, then the relevant terms should be included in the action (but the problem is that nobody knows what gauge it is) and one should integrate out the Lagrangian multiplier and the time function (and obviously this would lead to an effective action different from Einstein-Hilbert). Since no such corrections are made, one concludes that an ad-hoc gauge dependent counter term has been added which would induce a preferred cosmic timelike field. Now, one could guess that (somehow) this slicing with clear geometric significance does not matter and drops out in the continuum limit - but I woudn't bet on it (since one would reasonably expect the lattice regularization to be a regularization of the modified continuum theory). That would indeed make the theory background independant, but it is clearly a highly non trivial thing (just like finding a needle in the haystack is) :-)

On the positive side, the theory is at least unitary which cannot be said of other "background independant" approaches.

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Science Advisor
"I agree essentially with what you say. As for a definition of background independance (with respect ordinary differentiable manifolds M) : "A theory on M is BI (or simply covariant) if and only if the Lagrangian does not contain non dynamical-fields nor Lagrange multipliers"."

Correct, but keep in mind different physicists will butcher this definition in many different ways. For instance, the full string theory is BI in the above sense, but not background independant in the LQG sense since there are metric fields that appear explicitly (and you really want something more like a connection variable), even though they are 100% varied in the action.

Point being, there is absolutely no one standard way across all programs where the term is uniquely defined. Its simply not the same thing to say a lattice theory is BI vs say a Hartle-Hawking path integral being BI vs a nonperturbative field theory being BI vs AdS/CFT etc etc.

Fra
I agree that the notion of TOE is a bit silly, if you see it as a thing, or static understanding that will one day be carved in stone.

I guess my view is more that the closest thing to a TOE is the process that is the journey of progress that may or may not result in a TOE, and I see no universal measure of progress and neither do I think the final desination or existence of destination of the journey is very meaningful to speculate about. And that might suggest to focus on ther process of progress, rather than speculation of what we may or may not come to find out. We don't know where we will end up, but OTOH I don't need to know that. All I need is the answer to me next question. And how can my decision progress on that matter be understood to emerge an evolve?

This is why I found this remark interesting

"I can imagine that string theory in that case may become its own new discipline; that is, a mathematical science that is devoted to the study of the structure of physical theory and the development of computational tools to be used in the real world. The theory would be studied by physicists and mathematicians who might no longer consider themselves either."
-- http://aps.arxiv.org/PS_cache/arxiv/pdf/0805/0805.0543v1.pdf

In this spirit it seems physical theory itself, is just a relative state, or result from a process.

I also think the notion of background independence in fuzzy. If it simply means not starting with a metric in a manifold, then i can help thinking of the manifold itself as a "background". I'd expect this manifold to also be explain in terms of something less complex.

With "the theory of physical theory" I really meant the opposite, that it might aim to describe the process of evolving theories, rather than just properties of a single TOE. And by consistency this reasoning should then be applied to itself, so that the theory of theories
is itself evolving.

Not that I see how string theory is that, but it was the question to ask if someone else can see that. I got the impression that was the ambitious vision Moataz H. Emam had of string theory. Which if true, would be even better than a old style TOE if it might describe the inductive and progressive step in "theory of theory", as it would describe the most non-trivial step, what to do what if your theory is wrong. Then you need a theory of the theory anyway, that guides you in revision.

So as I see it, the question of what the "TOE" is not interesting. It's how we, given our incompetence and limited brainpower, should make the quickest progress.

/Fredrik

Careful
Some clarifications (and more accurate wording) : I agree essentially with what you say. As for a definition of background independance (with respect ordinary differentiable manifolds M) : "A theory on M is BI (or simply covariant) if and only if the Lagrangian does not contain non dynamical-fields nor Lagrange multipliers".
With respect to your points on CDT: indeed, it might not be an ordinary path integral since the geometries are giving you a foliation and it is not clear where the latter comes from (that is, one should start from the full path integral, divide out the gauge degrees of freedom (in one way or another) and study the resulting effective action). The real question is "what might happen?". If it were simply a gauge fixing, then the effective action would probably differ from Einstein Hilbert (non trivial gauge dependent Jacobians). Since no such corrections are made, one could conclude that an ad-hoc gauge dependent counter term has been added which could induce a preferred cosmic timelike field (note moreover that physical gauge conditions often only exist locally and run into ton's of global problems - so one has serious reasons to suspect that something else is going on here). Now, one might guess that (somehow) such details of the path integral measure are irrelevant in the continuum limit (but this is extremely unlikely). That would indeed make the theory a quantized version of general relativity, but it is clearly a highly non trivial thing (just like finding a needle in the haystack is) :-) I would think people have thought about this issue but I do not know a reference from the top of my head.

So, one issue is whether CDT is the quantization of general relativity; another one would be wheter it corresponds to the quantization of some classical action at all (since as I said, it is not clear which gauge condition has been imposed). If the latter is not satisfied, then one could say it is not BI (but the first issue is much more pressing of course).

On the positive side, the theory is at least unitary which cannot be said of other "background independant" approaches. Moreover, one should try out something, right?

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Careful
"I agree essentially with what you say. As for a definition of background independance (with respect ordinary differentiable manifolds M) : "A theory on M is BI (or simply covariant) if and only if the Lagrangian does not contain non dynamical-fields nor Lagrange multipliers"."

Correct, but keep in mind different physicists will butcher this definition in many different ways. For instance, the full string theory is BI in the above sense, but not background independant in the LQG sense since there are metric fields that appear explicitly (and you really want something more like a connection variable), even though they are 100% varied in the action.

Point being, there is absolutely no one standard way across all programs where the term is uniquely defined. Its simply not the same thing to say a lattice theory is BI vs say a Hartle-Hawking path integral being BI vs a nonperturbative field theory being BI vs AdS/CFT etc etc.
I am not sure what you mean here; as far as I know the disagreement stems from wheter background dependent methods are adequate or not. I guess you would agree with me that CDT is background independent in a trivial sense (but that doesn't imply it is the quantization of a 4-D covariant field theory in the limit for zero cutoff - of course). Nevertheless, one can take the viewpoint that if low energy physics sufficiently agrees with predictions of GR and upon including matter (in the same fashion) there is sufficient overlap with the flat spacetime QFT standard model ; it is CDT which is fundamental and not the other way around.

Pointy
the determinism-approximation quandary of einstein

Dear Marcus,

I meant to differentiate beween

Quine's confirmation holism
and
Karl Popper's theories;

Popper noticed that two types of statements are of particular value to scientists.

The first are statements of observations, such as "this is a white swan". Logicians call these statements singular existential statements, since they assert the existence of some particular thing. They can be parsed in the form: There is an x that is a swan, and x is white.

The second are statements that categorize all instances of something, such as "all swans are white". Logicians call these statements universal. They are usually parsed in the form: For all x, if x is a swan, then x is white. Scientific laws are commonly supposed to be of this type. One difficult question in the methodology of science is: How does one move from observations to laws? How can one validly infer a universal statement from any number of existential statements?

Inductivist methodology supposed that one can somehow move from a series of singular existential statements to a universal statement. That is, that one can move from 'this is a white swan', 'that is a white swan', and so on, to a universal statement such as 'all swans are white'. This method is clearly deductively invalid, since it is always possible that there may be a non-white swan that has somehow avoided observation. Yet some philosophers of science claim that stringy science is based on such an inductive method.

=========

If there is indeed a TOE, which, in physics, is ofcourse only a measure to combine General Relativity with Quantum Mechanics, the kind of physicalism that Karl Popper clings to, does indeed state that a physcial theory also has to be a metaphysical theory (of everything).

In this view a physicalism-true TOE could go a little something like this;

Einstein and physicists and philosophers before and after him have spent a great deal of effort trying to explain how the Universe works. Scientists have spent the last 75 years or so trying to tie together all known phenomena to explain the nature and behavior of all matter and energy in existence.

Since physics has made little progress in discovering the Grand Unification Theory an interesting question arises. Why have the best minds of the past and present failed to discover the truth about our Universe.

Since the time of Isaac Newton who began the era of Classical Mechanics and modern day physics we have all been trying to unlock the secrets of how the Universe works. Many of the greatest intellects of all time have attempted to find a simple explanation for material existence and the central cause of force, action at a distance. The question of why so many great minds could not solve this problem eventually led the author of the theory to come up with a reasonble explanation for our failure to solve this great mystery. It seemed reasonable to assume that perhaps something might be wrong with our approach and that possibly a mistake was made somewhere in the past. The mistake would creat a paradigm shift that would take physics in the wrong direction.

If this idea is correct the only explanation that makes sense is that somewhere along the way we began to attempt to solve an inequality. In other words we switched onto a track that was a dead end, a red herring so to speak. What if for the past hundred years or so we have been trying to prove something, that is not true. What if we have been trying to prove that a=b and in fact a<>b. If we did not know this fact we could spend centuries trying to prove an incongruity.

=============

If there would be such a case as where the above is true, it might defy our many-worlds-interpretation itself. If such a case would exist in where there would be some sort of a complete quantum mechanics or some sort of super relativity, a many-worlds-interpretation would not be needed and invalidate the possibility of string theory being the theory of physical theory

Your question in fact reveals an important paradox, concerning such a string theory many-worlds-interpretation, as to the fact of the matter that if many worlds exists, all worlds have different physics theories. So indeed string theory would then perhaps be the theory of physical theory.

But such a case could be a self-fulfilling prophecy and might even be described as the paradox

In this it reveals exactly this dichotomy between Karl Popper and Quine (also see falisifiability)

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Fra
One difficult question in the methodology of science is: How does one move from observations to laws? How can one validly infer a universal statement from any number of existential statements?

Good focus!

Is there a way at all to by means of poolproof deductions find universal statements from existential ones?

If the answer is no, then to me, that suggests that more than ever changes the focus of the nature of law. And it my suggest an alternative quest.

The quest isn't to "find the universal laws of nature", it is to find out the nature and "dynamics" of law. This is the perspective I have personally adopted.

Inductivist methodology supposed that one can somehow move from a series of singular existential statements to a universal statement. That is, that one can move from 'this is a white swan', 'that is a white swan', and so on, to a universal statement such as 'all swans are white'. This method is clearly deductively invalid, since it is always possible that there may be a non-white swan that has somehow avoided observation. Yet some philosophers of science claim that stringy science is based on such an inductive method.

I guess the simple suggest is to argue that a certain amount of evidence support a conclusion to a given level of confidence. So you get a probability distribution of possible conclusions. But then the problem is that the probability is effectively just a rating of the conclusions, as per a particular logic. And I see no universal way to implement this rating system either. So the observed problem here, keeps getting back at each level like a torch in our behind.

But MAYBE in each particular case, there is a "preferred" logic that can be locally attained like a sort of local steady state equilibrium. And maybe we can related the structure of this logic to the structure of space-time and also matter. And maybe there is even a bound to the "set of logic". IF you consider logic as a set of rules from manipulating structures, then if the structures are limited in complexity then the logic that can live there may also be bounded. Maybe if we look at the simplest possible systems, we may not be left with a lot of choices, this is what I'm trying.

I am trying to ask these questions, like what is the logic in line with the above, of Einsteins Gravity. And what is the logic of the standard model of particle physics?

/Fredrik

Pointy
Good focus!

Is there a way at all to by means of poolproof deductions find universal statements from existential ones?

If the answer is no, then to me, that suggests that more than ever changes the focus of the nature of law. And it my suggest an alternative quest.

I could have an answer to your quest..

There is such a thing as the Curry-Howard correspondence which combines logicality with
mathmatical proof. From deduction we can see that physics/mathmatics and logicality/metaphysics could in fact be related.
As the Curry-Howard correspondence is the direct relationship between computer programs and mathematical proofs. Also known as Curry-Howard isomorphism, proofs-as-programs correspondence and formulae-as-types correspondence, it refers to the generalization of a syntactic analogy between systems of formal logic and computational calculi that was first discovered by the American mathematician Haskell Curry and logician William Alvin Howard.

And I see no universal way to implement this rating system either. So the observed problem here, keeps getting back at each level like a torch in our behind.

But MAYBE in each particular case, there is a "preferred" logic that can be locally attained like a sort of local steady state equilibrium. And maybe we can related the structure of this logic to the structure of space-time and also matter. And maybe there is even a bound to the "set of logic". IF you consider logic as a set of rules from manipulating structures, then if the structures are limited in complexity then the logic that can live there may also be bounded. Maybe if we look at the simplest possible systems (...)

I am trying to ask these questions, like what is the logic in line with the above, of Einsteins Gravity. And what is the logic of the standard model of particle physics?

/Fredrik

Curved space often refers to a spatial geometry which is not “flat” where a flat space is described by Euclidean Geometry. Curved spaces can generally be described by Riemannian Geometry though some simple cases can be described in other ways. Curved spaces play an essential role in General Relativity where gravity is often visualized as curved space. The Friedmann-Lemaître-Robertson-Walker metric is a curved metric which forms the current foundation for the description of the expansion of space and shape of the universe.

This curvature can be seen in many ways. Some logic suggests that logical 'spira mirabilis' are metaphysically and physically explainable.

A logarithmic spiral, equiangular spiral or growth spiral is a special kind of spiral curve which often appears in nature. The logarithmic spiral was first described by Descartes and later extensively investigated by Jakob Bernoulli, who called it Spira mirabilis, "the marvelous spiral".

Spira mirabilis is another name for the logarithmic spiral. Although this curve had already been named by other mathematicians, the specific name ("miraculous" or "marvelous" spiral) was given to this curve by Jakob Bernoulli, because he was fascinated by one of its unique mathematical properties
Logarithmic spirals are self-similar in that they are self-congruent under all similarity transformations (scaling them gives the same result as rotating them). They are also congruent to their own involutes, evolutes, and the pedal curves based on their centers.
The size of the spiral increases but its shape is unaltered with each successive curve. Possibly as a result of this unique property, the spira mirabilis has evolved in nature, appearing in certain growing forms such as nautilus shells and sunflower heads. Bernoulli eventually chose a figure of a logarithmic spiral and the motto Eadem mutata resurgo ("Changed and yet the same, I rise again") for his gravestone.

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Pointy
Next to curved space there's also KK

There are also some older standing theories about combining Einstein's relativity with quantifiable gravity.

There is the Kaluza–Klein theory, or KK theory, for short, which is a model that seeks to unify the two fundamental forces of gravitation and electromagnetism. The theory was first discovered by the mathematician Theodor Kaluza who extended general relativity to a five-dimensional spacetime. The resulting equations can be separated out into further sets of equations, one of which is equivalent to Einstein field equations, another set equivalent to Maxwell's equations for the electromagnetic field and the final part an extra scalar field now termed the "radion".

In the attempt to explain the Michelson-Morley experiment, Lorentz proposed that moving bodies contract in the direction of motion ( George FitzGerald had already arrived at this conclusion with length contraction.)
Length contraction, according to Hendrik Lorentz, is the physical phenomenon of a decrease in length detected by an observer in objects that travel at any non-zero velocity relative to that observer. This contraction (more formally called Lorentz contraction or Lorentz-Fitzgerald contraction) only becomes noticeable, however, at a substantial fraction of the speed of light; and the contraction is only in the direction parallel to the direction in which the observed body is travelling.
Lorentz worked on describing electromagentic phenomena (the propagation of light) in reference frames that moved relative to each other. He discovered that the transition from one to another reference frame could be simplified by using a new time variable which he called local time. The local time depended on the universal time and the location under consideration. Lorentz publications made use of the term local time without giving a detailed interpretation of its physical relevance. In 1900, Henri Poincaré called Lorentz's local time a "wonderful invention" and illustrated it by showing that clocks in moving frames are synchronized by exchanging light signals that are assumed to travel at the same speed against and with the motion of the frame.

By 1904, Lorentz added time dilation to his transformations and published what Poincaré named Lorentz transformations. It was apparently unknown to Lorentz that Joseph Larmor had used identical transformations to describe orbiting electrons. Larmor's and Lorentz's equations look somewhat unfamiliar, but they are algebraically equivalent to those presented by Poincaré and Einstein.
Lorentz' '1904' paper includes the covariant formulation of electrodynamics, in which electrodynamic phenomena in different reference frames are described by identical equations with well defined transformation properties. The paper clearly recognizes the significance of this formulation, namely that the outcomes of electrodynamic experiments do not depend on the relative motion of the reference frame. The '1904' paper includes a detailed discussion of the increase of the inertial mass of rapidly moving objects. In 1905, Einstein would use many of the concepts, mathematical tools and results discussed to write his paper entitled "Electrodynamics" known today as the theory of special relativity. Because Lorentz laid the fundaments for the work by Einstein, this theory was called the Lorentz-Einstein theory originally.

The increase of mass was the first prediction of special relativity to be tested, but from early experiments it appeared that his prediction was wrong; this led Lorentz to the famous remark that he was "at the end of his Latin."
The confirmation of his prediction had to wait until 1909 when Lorentz published his "Theory of Electrons" based on a series of lectures in Mathematical Physics he gave at Columbia University.

If one would apply one of the more recent postulates in relativity, a supposed super relativity, being 'Space' is not a void but is in fact a solid composed of variations of three fields; Gravitational, Magnetic and Electrostatic in an unconfigured format and it as such is continuous and unbounded; one could come to some different conclusion as to Lorentz's non-moving frame.
Einstein added that no kind of observation at all, even measuring the speed of light across your frame of reference to any accuracy you like, would help find out if your frame of reference was "really at rest". This implies, of course, that the concept of being "at rest" is meaningless. If Einstein is right, there is also no natural rest-frame in the universe

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Fra
I recently read a bit of Nancy Cartwright. Heard her talk, a year or so ago, and was impressed, but didn't immediately follow up until now:
http://books.google.co.uk/books?id=...ct=title&cad=one-book-with-thumbnail#PPA10,M1

see if that will get you the introduction to her book "The Dappled World"
It might interest you.
I suppose it could be argued that Cartwright presents a more practical and realistic view of physical law than Emam seems to have.
I can't say this is a special interest of mine or that I know much about it, but since you think generally about physical law you might get something out of her introduction.

As a note, I forgot you give feedback on this long time ago. I did order this book (several months ago) on your advice, and started reading it. I think what I supposed was her point (about the world not beeing unity, but rather "dapply" and that "looking for unity" may be a flawed guide etc) was more than clear from the foreword and in a sense I agree with her, but it's something about her writing style that I disliked and drove me nuts. So I dropped the book during the first chapters. I got the feeling that she kept repeating the same point over and over again and kept coming up with analogies, but I didn't see what I think would be the constructive thing, what does this insight suggest we do. It seems to me the book was trying to make a point (that I think she made early on), but I didn't see the constructive part.

Maybe I gave up too early, but her reasoning and writing style drove me nuts :)

Marcus did you read this, all of it? If so, what did you think?

/Fredrik