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...

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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

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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...

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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

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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...

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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

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Minor corrections to my latest post:

instead

"by assuming an extended pure state for every mixed state by assuming the mixed state"

please read

"by assuming an extended pure state for every mixed state"

i wrote

"Extrapolating the Schroedingers' wave function to be universally valid only leads to many-worlds; they may be complete in a certain sense and...

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Minor corrections to my latest post:

instead

"by assuming an extended pure state for every mixed state by assuming the mixed state"

please read

"by assuming an extended pure state for every mixed state"

i wrote

"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)."

i would add

It's not only the moment of a "collapse" that is problematic (in many worlds the "collapse" does not exist and therefore is not a problem), but also the fact that for every binary decision i make, another "me" realizes the other alternative. The question here is if this alternative "me" existed before *i* made my binary decision or is it somewhat "cloned" by the Schroedinger equation? I assume that the two branches arising out of *my* decision aren't symmetrical in the sense that the other branch (the alternative "me") is forced to decide between *my* binary decision and gains exactly the "opposite" of *my* decision. Here the question arises why there should be multiple quantum experimentalists within a Schroedinger equation that branches those experimentalists in a non-deterministic manner. Not enough, where is the borderline between a classical decision and a quantum decision? A quantum decision surely seems to be random, but the Schroedinger equation says it is deterministic. So even *my* own decisions (for example my decision to write this post) should seem to be as random as single quantum events seem. An interpretation of QM as strictly deterministic does not alter the mystery why *i* got entangled such that i had to write down this comment. It further does not elucidate that human behaviour in most cases is consistent and makes some sense. Although this could be due to past entanglements, but nothing in the whole QM theory and the Schroedinger equations neccessitates that human behaviour should make sense and shouldn't be non-sensical when averaged over the whole human population.

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Dear Frederico,

i now read your arXiv-paper. Although i must confess that i did not check every part of your statements to be reasonable or not, my main interest was to look at what you have to say in your plain text.

You wrote

"The importance of the distinction between pure and mixed states, and the fact that only pure states can be associated with a vector (ket) is...

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Dear Frederico,

i now read your arXiv-paper. Although i must confess that i did not check every part of your statements to be reasonable or not, my main interest was to look at what you have to say in your plain text.

You wrote

"The importance of the distinction between pure and mixed states, and the fact that only pure states can be associated with a vector (ket) is dismissed. The distinction show totally different mathematical properties and meaning of each of them. We say that the pure state [ψ] is something objective, actually that it represents reality itself. And the mixed states ρ represents something

epistemic, that they are the state of knowledge of some observers. This two elements are not, however, completely independent, there is a condition for a density operator to be considered a possible state of knowledge. However, the state of knowledge is not totally defined by reality, and that’s why we say that it is subjective. We can say that this theory is a theory of knowledge and truth, and this the explanation of why there are elements of this two natures: epistemic and ontic."

As i understand this, it is not possible to unambigiously assign some reality to the "time" between two measurements?

I think this would be difficult, because in the case of Schroedingers Cat (if one leaves decoherence processes out of the discussion) you write

"Note that we have propositions that are neither true, neither false; and that is something new, because according to classical logic, a proposition is either true or false."

In the time in between the measurement of the Cat's state, there must be some "time" elapsing, i guess. In my own interpretation, with the help of some ideas of decoherence, i tried to interpret what's the meaning of the "time" between those two measurements.

It is true that classical logic leads to either true or false values, but if we consider the opposite of the classical logics to return neither true or false values, we cut out a huge part of reality, if we take this new logics to be a passive negation of the classical logic. We can interpret that as the subjective lack of knowledge (the epistemologic part), but this interpretation in my opinion is not sufficient to understand why QM is the way it is, this interpretation is only sufficient to illustrate why QM *itself* cannot give the answer why it is how it is. That's an important difference.

My own interpretation assumes a meta-physical (meta-physical in the sense that classical logic is only a special case of a logic that isn't anymore bound to causal thinking - but nonetheless to reasons - and to physical time) level of reality where the *reasons* for the non-classical logic reside. In my opinion this level has no classical timeframe, but only conistent interdependencies. Therefore no assumption are needed in this realm and all answers to questions are rendered senseless because questions in a timless, interconnected realm don't make anymore sense.

Maybe we are not so far apart from each others point of views, except that i speculate about what's beyond the classical logic and epistemological knowledge, and you seem to not do this.

Thanks again for an exciting essay and an interesting arxiv-paper!

Best wishes,

Stefan

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Hi Frederico,

You write, "Try to read the equation F=ma. In the context of classical mechanics you would say the total force equals to the product of the mass and the acceleration. But out of context, or better, without any interpretation, you cannot say it."

If you mean only that I have to expand the shorthand symbols to natural language, such that I should write, "Force equals mass...

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Hi Frederico,

You write, "Try to read the equation F=ma. In the context of classical mechanics you would say the total force equals to the product of the mass and the acceleration. But out of context, or better, without any interpretation, you cannot say it."

If you mean only that I have to expand the shorthand symbols to natural language, such that I should write, "Force equals mass times acceleration," then I don't really think that constitutes either context or interpretation. The symbols, after all, mean the same things whether one's native language is Portuguese or English, or any other. Mathematical symbols are universal; we learn this "alphabet" of symbols in learning the artificial language of math, yet the symbols are themselves derived from natural language.

Suppose you mean, though, that to understand how to interpret the way in which these symbols correspond to personal experience, such that we are assured the symbols are indeed universal -- we resort to comparing the symbols to objects, exactly the way one learns natural language. "Mass" one can understand as identical to weight, by balance measurement. "Acceleration" is exactly why Newton invented the calculus, to explain acceleration as the rate of change of the rate of change -- can this be explained by direct comparison to an object? -- yes, if one sees the difference between uniform motion described by a straight line, and acceleration described by a curved line, which is the visual basis of the calculus. Then corresponding experience informs one that a hammer head "weighs" more when accelerated toward the nail head, than when resting on it uniformly. We call that increase of mass-energy by the name "force."

"The problem of natural language is that it is not as precise as math, and there are too undefined concepts or open concepts. For example, define reality? Define proposition? Define truth? These concepts are very hard if not impossible to define in natural language. I cannot prove you it is impossible to define these concepts in natural language, but if you look to a dictionary you will see that some definitions are at most circular and you cannot remove the circularity.'

Sure. However, I *can* prove that it is possible to express every mathematical statement in natural language, even though it is impractical, unnecessary and exceedingly tedious. Formal proofs rely on logical judgments derived from a given set of axioms -- they do not necessarily tell us what is true; in fact, the common way of conveying the meaning of Godel's theorem is in the statement: "Truth is stronger than proof." In other words, there exist true statements derived from any set of axioms that cannot be proven from that set, no matter how many or how few axioms the set comprises.

A dictionary is no help here, and in fact we can prove it! Your set of questions above asking to define terms can be reduced to "Define definition." The answer: "Definition is defined by the set of all definitions in the dictionary." Is that useful? -- it is, if one is a mathematical realist (Platonist) as Godel was. Roger Penrose is another example of a modern Platonist. To such a mathematician, there exists a universal "dictionary" -- pure perfect mathematics, in fact, is only a set of self consistent statements. In fact, Godel used to refer to proofs he found particularly elegant as having come straight "from the Book."

Science as a whole, though, conventionally follows the logic of Tarski (correspondence theory of truth) adapted by Popper to correspondence between logically closed mathematical judgments (theory) and experimental results. That's an even longer discussion.

"Really, I was not aware of Chaitin's work." Try his site . I know you'll be interested.

"I liked the way you characterized a closed theory, although we need to take with the meaning of mathematically complete, because if it is understood in the sense Godel then we have a problem with his incompleteness theorem."

I hope I covered that sufficiently above. "Mathematically complete" I take from the EPR definition: every element of the mathematical theory corresponds to every element of the physical reality.

"I've read his book but I'm not a specialist on Wittgenstein philosophy, and so I cannot really answer how my ideas are in relation to his philosophy. If you have something more specific ..."

This is a longer discussion still. Maybe later.

"I'll visit you essay. Thanks for visiting mine, and pleas rate me if you haven't! I wish you all the best in this contest, and that we could keep our talks beyond this scope."

I'd be delighted to engage further ... and of course will award your essay a deservedly high rating.

All best,

Tom

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Hi Tom,

You wrote:

"Hi Frederico,

You write, "Try to read the equation F=ma. In the context of classical mechanics you would say the total force equals to the product of the mass and the acceleration. But out of context, or better, without any interpretation, you cannot say it."

If you mean only that I have to expand the shorthand symbols to natural language, such that...

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Hi Tom,

You wrote:

"Hi Frederico,

You write, "Try to read the equation F=ma. In the context of classical mechanics you would say the total force equals to the product of the mass and the acceleration. But out of context, or better, without any interpretation, you cannot say it."

If you mean only that I have to expand the shorthand symbols to natural language, such that I should write, "Force equals mass times acceleration," then I don't really think that constitutes either context or interpretation. The symbols, after all, mean the same things whether one's native language is Portuguese or English, or any other. Mathematical symbols are universal; we learn this "alphabet" of symbols in learning the artificial language of math, yet the symbols are themselves derived from natural language.

Suppose you mean, though, that to understand how to interpret the way in which these symbols correspond to personal experience, such that we are assured the symbols are indeed universal -- we resort to comparing the symbols to objects, exactly the way one learns natural language. "Mass" one can understand as identical to weight, by balance measurement. "Acceleration" is exactly why Newton invented the calculus, to explain acceleration as the rate of change of the rate of change -- can this be explained by direct comparison to an object? -- yes, if one sees the difference between uniform motion described by a straight line, and acceleration described by a curved line, which is the visual basis of the calculus. Then corresponding experience informs one that a hammer head "weighs" more when accelerated toward the nail head, than when resting on it uniformly. We call that increase of mass-energy by the name "force." "

Tom, quoting you: "If you mean only that I have to expand the shorthand symbols to natural language, such that I should write, "Force equals mass times acceleration," then I don't really think that constitutes either context or interpretation."

Your statement appears to me to be dependent upon interpretation. The equation f=ma before interpretation says only that 'something' equals 'what' times acceleration.

Quoting you: " "Mass" one can understand as identical to weight, by balance measurement. "Acceleration" is exactly why Newton invented the calculus, to explain acceleration as the rate of change of the rate of change -- can this be explained by direct comparison to an object? -- yes, if one sees the difference between uniform motion described by a straight line, and acceleration described by a curved line, which is the visual basis of the calculus. Then corresponding experience informs one that a hammer head "weighs" more when accelerated toward the nail head, than when resting on it uniformly. We call that increase of mass-energy by the name "force." "

In other words the 'what' from my statement above is identical to a different 'what'? What is either 'what' without interpretation?

Acceleration has no need for interpretation.

Quoting you: "We call that increase of mass-energy by the name "force." "

In other words: We call that increase in 'what_1' dash 'what_2' by the name 'something'. Or perhaps you are saying that the results of interpretation can be used to explain a 'something' without needing to interpret that 'something'? :)

Can you please say more about your view of the meanings of 'not interpreting' and 'interpreting'?

James

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:) in all humility of course,This theory has been found by a young belgian of 37 years old.

Of course it is irritating for a lot of scientists. Just due to the potential of this theory of spherization. Indeed I have found dear sciences community. Of course there are a lot of jealousy and envy. Just due I am repeating to this potential at shot middle and long term. Of course several...

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:) in all humility of course,This theory has been found by a young belgian of 37 years old.

Of course it is irritating for a lot of scientists. Just due to the potential of this theory of spherization. Indeed I have found dear sciences community. Of course there are a lot of jealousy and envy. Just due I am repeating to this potential at shot middle and long term. Of course several academicians are going to try just for the funds. But in fact.These persons are not really academicians but simply false scientists.Indeed they do not imrpove, they just decrease the real evolution. Their hates in general are proportional with their frustrations. Of course their credibility is on a sad road if I am recognized. So of course probably that they are obliged to be very bad in their strategies. The irony at its paroxysm above the cries of desesperated frustrated. I suggest that they learn real searchers and real generalsits. But of course their vanity and their taste of opulences imply that they have no times for the real learning , general and foundamental.Me I am a real generalist. Them, no !

ps the incompleteness is rational and the serie is finite and precise. We are just far of our walls separating this light without motion and the light with motions, so the physical universal sphere in 3D and its 3D quantum spheres and cosmological spheres. If the systems of informations is encoded , it rests rational.Not need of extradimensionalities and multiverses where we have different laws. I beleive that a lot of scientists become very irrational there !!! The problem is that we cannot utilize monney without wisdom and universal consciousness. The hour is serious, we have real global probelms and we are near several chaotical exponentials.We must harmonize this earth with a pure harmony. The rest is vain. If the scientists are not able to solve the problems, so they are not scientists. If they loose their time with pseudos extrapolations, so it is very bizare.We return about a simple evidence, this money and the vanity and the frontiers. It desreases the speed of evolution spherization. Each governments must take its responsabilities. The china must take its responsabilities, the USA also, the Russia and europa and the others. The scientists , rational must have responsabilities in their countries. The solutions exist in respecting the sciences and the road of optimization.We have the tools, so what is the problem? the monney, the unconsciousness, what? the stupidity? what ? it is time to create a global earthian commission of quick optimization. the governments of big countries must act quickly together !!! China: take the 2500 best scientists, general and universal of your country and give them powers of acting. USA make the same, take your 1000 best scientists with solutions and act also.Europa :make the same, africa also ....it is essential for our earth , it is now or never you know dear responsibles of governments. We are in a very bad global situation. The solutions exist.

Regards

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Dear Frederico,

I am interested to see your "closed formulation" of part of quantum theory. I take it that is your reference 1?

Regarding Godel, I'm not an expert on undecidability, but I think that Godel's result applied to systems like the natural numbers is rather clear intuitively. The following isn't a proof, but it shows intuitively what an absolute miracle it would be if...

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Dear Frederico,

I am interested to see your "closed formulation" of part of quantum theory. I take it that is your reference 1?

Regarding Godel, I'm not an expert on undecidability, but I think that Godel's result applied to systems like the natural numbers is rather clear intuitively. The following isn't a proof, but it shows intuitively what an absolute miracle it would be if Godel's theorem were wrong. Take the natural numbers. You have a system which is defined by means of a finite set of postulates, yet it has an infinite number of elements, and you can make an infinite number of different statements about it, each of which may be true or false. (I am assuming, for the sake of the theorem, that it is consistent.)

Now suppose you have a statement that IS true, meaning that whenever you substitute natural numbers into it, you will get an identity. How could you PROVE this? Well, you could test it number by number, but you would never finish because there are an infinite number of numbers. So you have to fall back on the axioms. A certain chain of reasoning using the axioms might prove the result true for a certain infinite subset of natural numbers (for instance, multiples of 3), but might not work for others. So you could use a different chain of reasoning for another subset, but there might still be numbers left out. Once again, you might never arrive at a proof.

You can see that to prove this true statement, you would have to be very lucky: a finite number of finite chains of reasoning would have to suffice to prove a statement about an infinite number of numbers. This statement might be true for some numbers for entirely different reasons than for others. "Most" true statements about the natural numbers are undecidable in this sense. Intuitively, this is similar to the fact that "most" real numbers are not rational; to be rational, the decimal expansion must terminate or repeat in a finite number of steps. You have to be very lucky for this to occur.

I agree with what you said about item 2; that's why I prefer to call these "versions" rather than "interpretations." They do generalize differently.

I haven't rated most of the essays yet because I have not finished reading them all. But I won't forget to rate yours! Take care,

Ben

P.S. For the view of Godel's theorem you mentioned; it's a good way to think about it, but one must be sure that the word "extension" means the same thing you intend it to mean in the context of physics!

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