Dear Frederico

Very nice to see a fellow brazilian in the FQXI contest (I´m from Fortaleza). Your essay is impressive, clearly written and I think it touches on points frequently overlooked by physicists.

You have emphasized the relation between physics and language which is often tacitly understood . This is something I see with interest as well. There a paragraphs that are true gems.

''Our communication is limited by the degree of precision of our language and our concepts. Science is limited by the degree of precision of our words.''

Assuming this, what should we do? Should we insist on trying to understand the world using natural language? You might have heard about the idea of quantum logic, which tries to explain QM by proposing a new logic from the start.

Max Tegmark has adressed the problem you expose by stating that the universe is not merely described by mathematics, it IS mathematics. Tegmark´s proposal.

I have also thought for some time on your statement:

''It is the theory which should provide us the conceptual framework in which it

can be understood, not the existing worldview. The interpretation of quantum theory should provide us a new worldview, the worldview that makes quantum theory understandable, and where all paradoxes are dissolved.''

We cannot develop a theory without a a priori conceptual background. So suppose we have a theory suitable for the everday empirical experience which relies on easily-grasped and imagined concepts (like time, motion, objects). Then we find unexplainable empirical data that suggest a new theory (like QM). Now we may change the whole language we began with to make this theory more natural. And the process begins again. I wonder if an iterative proces could be possible. Language->physical theory->language->...

I believe however that we should not take our classic worldview as useless (our a priori conceptual background, or language we are confortable with) for one reason: it should be the classical limit of a more fundamental theory. If we play with ''the concepts'' we use at the classical level to describe the universe (objects, time, space) and find new conceptual ways to do physics, we may end up with a completely new theory (including its mathematical formulation). There is one very interesting fact which I´m sure you will find interesting. You might have heard of Mach´s philosophy and relational physics. Mach have tried to find the meaning of statements such as: ''the position of an object is (x,y,z)'' (make our worldview more closed). He has also attacked the concept of time. If everything in the universe had its speed doubled, including clocks, the flow of an invisible time parameter seems meaningless and useless. Time should be a concept defined from motion. Julian Barbour has implemented Mach´s philosophy and the result is impressive: Genreal Relativity is recovered!

So by making the classical worldview more semantically satisfactory, the whole gravitational physics pops out in a sense.

In my essay I propose the following question: what would we find if we tried to make the classical worldview COMPLETELY SEMANTICALLY SATISFACTORY? I propose that the concepts of time, motion and objcets could be defined upon each other, but these circular definition would not be a problem. I propose a category-theory approach to this. It had a very positive feedback from Julian Barbour himself and I think we can share many ideas. Here´s my essay Absolute or Relative Motion...or Something Else?

Boa sorte!

Daniel

    Dear Anton,

    Thanks for your comments. I believe when we have a consistent physical theory, and so a consistent mathematical formalism, a wrong assumption does not destroy all the results and application of the theory. Actually, when you find that an assumption you were using is wrong, the only thing that changes is the domain of validity of you theory. All the results are still valid, but with a smaller domain.

    This is precisely what happened with classical mechanics when relativity appeared. Classical mechanics is still valid, and the proof is that engineering works! All our buildings are based in this theory, and we can't say that it is completely wrong, but only that it is not valid when objects are moving close to the speed of light.

    In a sense, I think our fundamental theories are somehow permanent, well the most established ones. But only in a sense. The interpretation we give to our theories will change in the future, and the way they are formulated, but their essence will remain the same.

    The reason of that is the core of my essay. Closed theories are precisely the ones that are a permanent achievement. They cannot be modified. Any modification will probably give rise to a whole new theory. However, I argue that our theories are not yet closed theories. That's the point. Once they get to a point where there formulation is just like the formulation of what is ring in mathematics, then they are permanent and cast in stone.

    The examples of mathematics are perfect. If you change a single axiom from the definition o a ring, then it is not a ring anymore and deserves a new name. The same holds for closed theories

    Best Regards,

    Frederico

    Dear Daniel,

    I thought I was the only Brazilian here; it is good to know I'm not alone! I wish you "boa sorte"! And thanks for your comments. We have very similar ideas, and your comments really got into the point.

    Natural language is our first tool, and it is necessary in every beginning of a whole new theory. First you have to do something handmade, just then you can build a machine to do the same. The same holds for using natural language.

    In mathematics you can see it clearly. A new mathematical theory begins using a lot of natural language. At this point you say it is not formal. But then it becomes more and more formal and rigorous until the point it is completely formulated in formal language. Now, natural language is no longer necessary and we say that the theory is completely formal.

    A similar idea holds for physics. But now, we are not interested in removing natural language, but giving a formal meaning to it. But the meaning of natural language statement is the corresponding mathematical statement. So, a language with formal meaning is equivalent to mathematical language!

    How to do that? Simply using my concept of interpretation: the interpretation of a physical theory is what allow us "reading" its mathematical formalism. Therefore, the interpretation allows the translation from mathematical language to natural language, and vice versa. Then you can say the meaning of a sentence in natural language is the corresponding mathematical statement. Note that, doing this we also give a precise meaning to the used concepts.

    The set of statements in natural language we can unambiguously translate into mathematical statements are the ones that have complete precision. They define a subset of natural language with complete precision! What I claim is that, every physical theory can define a subset of natural language which has absolute precision.

    Once we find the closed formulation of our theories, all these problems are solved. For quantum mechanics, it will not only provide the right quantum logic, but also the right natural language, and concepts to talk about the theory! This will propose a new logic, and also a new conceptual framework. But then, the theory is proposing the conceptual framework in which it can be understood!

    I've been working on these questions, and I've proposed a new formulation and interpretation of QM that follows these guidelines. My approach provides anew logic for QM, but it is different from the original quantum logic school. In my manuscript, each result of the theory is formulated in mathematical language and in natural language, and one is simply the translation of the other!

    Our classical worldview is not useless; it is just not good enough for some things. That is, the concepts of our worldview are open concepts, and most of them are not very clear. For example, what is reality? what is truth? And I believe that physics has the potential for giving these fundamental concepts a precise meaning! And this is exactly making our worldview more closed!

    I don't know much about Mach's philosophy, but this is exactly my view. For me, the meaning of the statement ''the position of an object is (x,y,z)'' would be the corresponding mathematical equation in the formalism of some physical theory.

    That's great; you can see how making our worldview semantically satisfactory can be important for physics. I'm doing the same with quantum mechanics, but actually I'm working on a theory that is the basis for both quantum and classical mechanics. And you are right, in a sense; our classical worldview appears in a particular case of this theory.

    I'm not sure I've answered all your points, so fell free to ask anything again...

    Best regards,

    Frederico

    Frederico asked: "What is a wrong physical assumption?"

    Here is one:

    http://www.fourmilab.ch/etexts/einstein/specrel/www/

    "...light is always propagated in empty space with a definite velocity c which is independent of the state of motion of the emitting body."

    REDUCTIO AD ABSURDUM: If the speed of light is independent of the state of motion of the emitting body, then an arbitrarily long object can be trapped inside an arbitrarily short container, and the bug from the bug-rivet paradox can be both dead (according to one observer) and alive (according to another):

    http://math.ucr.edu/home/baez/physics/Relativity/SR/barn_pole.html

    "These are the props. You own a barn, 40m long, with automatic doors at either end, that can be opened and closed simultaneously by a switch. You also have a pole, 80m long, which of course won't fit in the barn. (...) If it does not explode under the strain and it is sufficiently elastic it will come to rest and start to spring back to its natural shape but since it is too big for the barn the other end is now going to crash into the back door and the rod will be trapped IN A COMPRESSED STATE inside the barn."

    http://www.quebecscience.qc.ca/Revolutions

    Stéphane Durand: "Ainsi, une fusée de 100 m passant à toute vitesse dans un tunnel de 60 m pourrait être entièrement contenue dans ce tunnel pendant une fraction de seconde, durant laquelle il serait possible de fermer des portes aux deux bouts! La fusée est donc réellement plus courte. Pourtant, il n'y a PAS DE COMPRESSION matérielle ou physique de l'engin."

    http://www.parabola.unsw.edu.au/vol35_no1/vol35_no1_2.pdf

    "Suppose you want to fit a 20m pole into a 10m barn. (...) Hence in both frames of reference, the pole fits inside the barn (and will presumably shatter when the doors are closed)."

    http://hyperphysics.phy-astr.gsu.edu/Hbase/Relativ/bugrivet.html

    "The bug-rivet paradox is a variation on the twin paradox and is similar to the pole-barn paradox.....The end of the rivet hits the bottom of the hole before the head of the rivet hits the wall. So it looks like the bug is squashed.....All this is nonsense from the bug's point of view. The rivet head hits the wall when the rivet end is just 0.35 cm down in the hole! The rivet doesn't get close to the bug....The paradox is not resolved."

    Pentcho Valev pvalev@yahoo.com

      7 days later

      Well, this is really a great paradox. I was not aware of this, and so is great to know another idea that blows our mind. However, I'm not an specialist on relativity so I cannot really discuss this paradox.

      Thanks for your reply!

      Dear Frederico,

      I read your paper with great interest. I think you are right with respect to your final conclusion, that the principle of excluded middle is - in a way - the main wrong assumption of physics.

      I am working on a Modern Metaphysics - in the belief, that it is the key to a final theory, because it is based on a truly foundational ground like the ONE.

      In introducing the ONE as a physical entity I have defined it explicitly of being INVISIBLE (= NON-VISIBILITY), whereas the UNIVERSE is explicitly defined of being VISIBLE.

      I found, that in a reality, that follows this dual conception, the ONE represents with respect to the UNIVERSE logically the Excluded Middle. But this logical status of the ONE does not disturb the universe in any way because the ONE being INVISIBLE is physically excluded from the VISIBLE universe!

      The ontological meaning of this self-referential conception of reality is actually astonishing: By the physical exclusion of the logical Principle of the Excluded Middle as it is represented by the ONE, the visible universe can make an unrestricted use of ALL possibilities that logic allows. It can indeed go to the outmost limits of logic - to a point, where a violation of logic cannot be avoided any longer, because its boundary conditions (at infinity) are becoming contradictory.

      I was quite surprised when I read Wittgenstein's tractus logico-philosophicus, in which he also described contradiction as the outer limit of propositions (5.143)

      In a previous contest I've sketched this Modern Metaphysics.

      see:The Taming of the ONE

      http://www.fqxi.org/community/forum/topic/502

      Good Luck for your Paper.

      Kind Regards

      Helmut

      P.S. I've seen you are also inspired by the work of C.F.v.Weizsäcker. His works were (and still are) a great source of inspiration for me.

        Dear Helmut

        Thanks for your reply. We might not agree in every aspects, but our deep motivations and inspirations are the same. Weizsäcker is someone who deeply inspired me, and there are times I feel like I was trying to continue his work. Wittgenstein also inspires me, I've read his Tracttatu several times, and the sentence you cite made me think for a while.

        I've also been working toward a final theory, and I really believe it is related to metaphysics, the true metaphysics. Actually, the definition I give to the final theory in this essay says that the final theory of physics is actually meta-physics! Follow my thought: what is in common to all logics but contains no logic at all? Meta-logic!

        What is in common to all mathematics but is not an ordinary mathematical theory? Meta-mathematics.

        What is in common to all physical theories but contains no physical theory at all? Meta-physics! The theory that goes beyond physics, and serves as foundation for it; in the same way meta-logic is the basis for many logics! The final theory is a metaphysical theory if not metaphysics itself! But metaphysics has too many enemies, that's why I avoid mentioning this relation. But this metaphysics is completely different from the old metaphysics is the sense it is just as rigorous and mathematical as physics.

        It is good to know I'm not alone. I've not yet finished reading your essay, but our ideas require a radically new worldview. I'll try to read it soon, but keep me updated. If you could, please rate me!

        And I suggest you reading my arXiv paper "On the Nature of Reality". There I propose some aspects of the final theory and also some metaphysical ideas. You may not agree with everything but It can give us nice discussions.

        "metaphysics could be the most challenging and revolutionary discipline of 21st century. It could change our view of the physical universe as well as our view of GOD."

        That is a belief I shall prove right. Or I'll die trying...

        Best Regards

        Frederico

        Dear Frederico,

        I agree mathematics is necessary to give a physical concept a precise meaning, but I am not sure whether it is an ultimate guide to a fundamental theory of reality, because mathematics itself is intrinsically limited. It has its own blind spots.

        Gödel's incompleteness theorem is certainly the most important one. It has shown that mathematics cannot be both consistent and complete. There are always some basic propositions that may be true but that are intrinsically not provable.

        You do not relate to this inner limitations of mathematics neither in your current paper nor in your paper "The Nature of Reality".

        Referring to this incompleteness theorem the physicist Roger Penrose has claimed, that there could be certain aspects of reality (i.e. consciousness) for which no mathematical resp. computational algorithm can be created.

        I am convinced that a modern metaphycis can meet this mathematical incompleteness by being a self-referential system of thought.

        Kind Regards

        Helmut

        P.S. I like to point to my current paper: Is the Speed of Light of Dual Nature? which might be an important piece of a complete quantummechanical description of reality you are looking for.

          Dear Helmut,

          I also wouldn't say that math is the ultimate guide for a fundamental theory of reality, but only that it is the language we should use. And I do agree that math has its own blind spots and most of them are precisely on the foundations of mathematics. A also believe math must be improved for being used in such a fundamental theory.

          About Gödel's incompleteness theorem, I think the point is about completeness. I do not want to make a theory that is complete in this sense, but consistent, useful and insightful. And this theorem may also affect any other formal language, every language has some limitations.

          A theory is complete when every formula in its language either is provable or its negation is provable. In other words "if it is consistent, and none of its proper extensions is consistent." But, a fundamental theory of reality must have proper extensions because every theory that describes an aspect of reality is an extension of it.

          Self-referential system can be very powerful, but they are also very dangerous. Well, you may find a consistent one, but most of the paradoxes of logic and mathematics were found in self-referential systems. So we need extra care when dealing with these systems. But I believe Gödel's incompleteness theorem represents no danger for metaphysics because of what I mentioned before. I think you don't need to worry about this theorem. Make your theory and if someone says it is impossible then simply show you have already done it!

          P.S. I'm taking a look on your paper. I'll rate it as an author; please rate mine.

          Dear Frederico,

          I am not quite sure whether we agree with respect to the role that mathematics is playing in physics.

          To discuss the case of metaphysics: In my view of a modern metaphysics all formulas without any exception have to fail, otherwise the metaphysical concept of TRANSCENDENCE does not have any physical meaning. This demand implies that we have to extend our theories to infinite values, f.e. to an infinite velocity, but just these values are usually regarded as a sign that the underlying concept is physically meaningless.

          What do you think about this? Are there infinite values involved in a truly fundamental theory of the universe?

          Kind Regards

          Helmut

            Dear Helmut

            My point is that math is a precise language, and any theory, when it gets enough precise and clear, it can be formulated in a mathematical language. Therefore, even a metaphysical theory can at some moment be, in principle, formulated in mathematical language. Can you already talk about transcendence using math? That's the question. However, not everything that can be described by a mathematical equation is a physical observable. In the theory I propose in "On the Nature of Reality", everything is described mathematically but there are many elements that are not physical observables. But can you explain what you think of transcendence?

            Well, I see no problem of infinities on physics. The problem is only with math which cannot hand infinities very well. Once our math could handle them properly and elegantly they will begin to appear on our physical theories.

            Best Regards

            Frederico

            Dear Hải.Caohoàng,

            Thanks for your encouraging comments. Definitely, to find a clearly defined basis for foundations physics is the greatest of all intellectual challenges; and we should work together to accomplish it.

            However I have to admit that I don't have much knowledge about the standard model and Higg's bosons. I have yet no opinion about these things and so I cannot answer your questions. I hope we could find something else to discuss. I'm reading and I will rate you essay as an author. Please rate mine.

            I believe no theory is simply correct or incorrect. Its correctness depends on where it is being applied, that is, if its assumptions holds in a specific domain, then the theory is correct on that domain, if the assumptions does not holds on that domain, then it is incorrect in that domain.

            Best Regards!

            Frederico

            Dear Frederico,

            transcendence is, of course, an epistemological term indicating that the most fundamental branch of reality (i.e. the ONE) cannot be described and observed in any way. Transcendence is the common feature of all religious systems.

            But to fill this purely epistemological term with a physical resp. metaphysical content you have to choose an ontological one. The most appropriate term in this regard is the term of INVISIBILITY, because something to which this property is ascribed, cannot be described or observed in any way. It is epistemologically a property of transcendent nature.

            Though the ONE itself being invisible cannot be described or observed -- the visible resp. observable Universe, of cource, can be described and observed.

            Now at this point I asked myself: How must the visible Universe be organized if it shall base on something invisible?

            Answer: It must have unavoidably a sort of radical non-dual conception.

            Argument: As the property of visibility (of the universe) depends on the existence of specific differences, something, that shall be invisible, must have solved all differences into ONENESS. Otherwise it would be visible.

            And just this general philosophical idea of ONENESS that is as old as Platon can physically be precised. I am calling this precised idea the --- radical non-dual conception of the universe ---. This metaphysical conception implies physical consequences that are provable from an empirical point of view.

            It implies f.e. the prediction, that at the outermost edge at the universe there must be a coincidence, otherwise the invisiblility of the ONE would not be secured.

            Such an empircial coincidence can actually be found at the edge of our universe. In modern physics it is known as Mach0. You can google this; choose the key word - Mach Principle -; there have been listed 10 versions of this principle. Mach0 is the first one: It is indeed the only one, that is explicitly expressed as a purely observational fact.

            Surprisingly this observational fact represents an ANOMALY within modern physics that cannot yet be explained convincingly. To my opinion it is - to make use of an Einsteinian metaphor - a Signature of GOD inside our universe.

            Kind Regards

            Helmut

            4 days later

            Dear Frederico

            your essay and associated paper are thought provoking and deep. It will take time to assimilate it. My main comment for the present refers to this statement of yours:

            "I have means to say that the main wrong assumption of physics is not

            a physical assumption, but a millenary logical assumption: the principle of excluded middle .. This principle says that a proposition is either true or false, in other words, either the proposition or its negation is true" I think that you might be saying that the truth or falsity of a proposition may depend on its context. That is very close to the concept of contextual effects that I discuss in my essay.

            George Ellis

              Dear George,

              Thanks for your comments and sorry for the late reply. Actually, what I mean by the violation of the principle of excluded middle can be understood when we think of a system in a superposed state. For example, when a cat is not in a superposed state, we can say that it is dead when the state is [math]|D\rangle [/math] or it is alive when the state is [math]|A\rangle [/math]. But then, when it is in a superposition [math]|D\rangle |A\rangle [/math], it is not dead but it is also not alive! It is in a superposition of dead and alive! But according to that principle, if it is not dead, then it is alive. Therefore, superposition means precisely violation of the principle of excluded middle! In the classical world there is no superposition, therefore the principle holds in a particular case. I hope it could make the idea clearer.

              Best Regards,

              Frederico

              Dear Frederico,

              i read your essay and you did a good job in examining the suspicious premises that are widly held high. Especially what you write about Commensurability is of interest for me, but i have to think about it some more time and also read your arxiv-paper. Nonetheless you struck me with your statement

              "There, reality becomes a closed and completely precise notion. Therefore, I have means to say that the main wrong assumption of physics is not a physical assumption, but a millenary logical assumption: the principle of excluded middle. It is the source of most of the paradoxes and misunderstandings about quantum theory and is precisely the assumption that gives rise to the classical world."

              For this statement alone you deserved - in my humble opinion - a positive score, nonetheless that my own usage of some exceptions to the principle of the excluded middle are more than epistemological in nature. My own interpretation is that there are ontological states that aren't anymore driven by this principle and i tried to explain this in my own essay. Especially i explain why the "collapse of the wave function" occurs, namely because at the point this does "happen", the causal structure of the system has consistently changed and the mathematical description of the former - unmeasured dynamics - isn't valid anymore. Indeed - as i believe - the schroedinger equation is just an illusion that mimics causality. It is no more than a mathematical tool, misinterpreted as an ontological dynamic process! I call that whole process of quantum mechanical mimics "physical retrodiction". If you like, i would be happy you could have the time to visit my essay and leave a comment.

              Its very easy to read, informative as well as entertaining (i guess) and you don't have to dive into some complex mathematics.

              Best wishes,

              Stefan

              Dear Stefan,

              Thanks for your encouraging comments. My arXic paper might be very interesting because it shows how the ideas proposed in the essay can be implemented. Well the principle of excluded middle is a hidden assumption that is part of the language we use. It is almost impossible to understand how it can be violated using only ordinary language, specially English. Try to say something like the cat is not (not dead)...

              I've explained this idea on a reply to George Ellis some topics before. Take a look and then ask me any questions. It'll be a pleasure to make this idea clearer. I've started reading your essay; I'll rate it as an author, please rate mine!

              The principle of excluded middle is deeply connected to the wave function collapse. The point is that, after the collapse, the principle of excluded middle becomes valid for the set of projectors you used for measuring! Think about it, as I said, most of the paradoxes are related to this principle, and the classical world is precisely where this principle holds.

              Best regards!

              Frederico

                Dear Frederico,

                thanks for replying to my comment.

                I read George Ellis' comment and yours and i agree with both comments.

                George states that classical information depends on the context. He uses the term "proposition" to indicate the premises we have built in to come to a certain conclusion about truth/false values. From the reference frame of a classical observer the opposite of the principle of the excluded middle (for convenience i will call it "non-ex") is the opposite of the principle itself (for convenience i will call it "ex"). So, "ex" and "non-ex" are opposites, and due to the logics and due to "ex", - both the governing-laws of the classical world ("ex" and its illusion of time, causal order and forces) and "non-ex" for us are contextual. Contextual in the sense that both principles are relative, they refer to each other and can be differenciated from each other only by referring to the othe principle. I think this is a hint that beyond the classical world there must be indeed a non-classical world - only due to logical considerations. QM is an indirect proof of this assumption, especially the feature of superposition.

                In my essay i assume the "cat" to be neither dead nor alive, rather than being dead and alive at the same time. I think this is a difference to common thinking about superposed states. I also avoid the conclusion of many worlds which could be constructed (by assuming an extended pure state for every mixed state by assuming the mixed state) is just an illusion due to our kind of thinking in a classical reference frame that assumes causality to be more fundamental than consistency. I think the latter is more fundamental and we should accept incompleteness of information in the classical world. Extrapolating the Schroedingers' wave function to be universally valid only leads to many-worlds; they may be complete in a certain sense and consistent, but the measurement problem for me seems to be not solved (the problem why the mathematical description of Schroedinger does "collapse" at the "moment" of measurement).

                At the weekend i will read your arxiv paper with great interest. I already gave your essay here a positive vote.

                After reading your arxiv-paper, i will give you another feedback on that and maybe you can profit from my points of view (i would hope so).

                Best wishes,

                Stefan

                Frederico,

                I think it's a rather bold conjecture that "The quest for giving a precise meaning to our fundamental concepts cannot be accomplished using natural language" ... without giving an example of a mathematical statement that cannot in principle be translated to natural language.

                So I'm in the uncomfortable position of agreeing with your conclusions while disagreeing with the way that you got there. It is surprising to me that you venture into meta-mathematics in your commentary without mentioning Chaitin's leading-edge research (particularly since he is a Brazilian Professor). For example, Chaitin's Omega gives a clear example of an algorithmic compression of a number that is uncompressible (the halting probability of a Turing machine). This example would seem to stand your conjecture on its head: an example of a meta-mathematical result whose natural language translation is straightforward: The number is algorithmically compressible IFF the halting probability of a universal Turing machine asymptotically approaches zero, regardless of the machine language by which such probability is calculated. With this extreme example, I am doubtful that your conjecture is true.

                Chaitin has extended his meta-mathematical program to life itself, with the recent publication of *Proving Darwin: Making Biology Mathematical.*

                Nevertheless, as a separate subject, I have to agree that what you call a closed theory (and which I would characterize as a closed logical judgment of a mathematically complete theory) is sine qua non -- not only to a final theory -- but to any scientific theory. Closed logical judgements, such as those in relativity, correspond to physical results that make the theory mathematically complete. I like your discussion of quantum theory interpretation, because it clearly exposes why anti-systematic analyses cannot impose a logically objective meaning. Quantum theory is mathematically incomplete. (I don't understand how you reconcile Wittgenstein's anti-systematic philosophy to your philosophy of science, though I would be interested to know.)

                Anyway, thanks for a great read and all best wishes in the contest. If you would like to see an information-theoretic take on the Schrodinger's cat problem, and which explicitly uses the excluded middle, please visit my essay ("The Perfect First Question.")

                Tom