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The present paradigm is simply to find math, by whatever means, that describes the measurements we see in experiments. We presently have a curve-fitting, trial and error, guesswork approach to the laws of nature that is subject to change upon further observations. Yet many put great faith in the results obtained by this method even though at best it is only provisionally correct and cannot be absolutely proven to be true. And it is an assumption of science that these laws apply everywhere at all time, though we really cannot observed that.

Quantum theory is particularly problematic. In classical mechanics we deal with forces that can be felt that satisfies intuition based on experience. And relativity is based on an assumption of the speed of light having a limit, which seems understandable. But Quantum theory as presently taught is a total curve-fitting exercise, with no intuition or reason for it. And this frustrates many students of physics.

I present a logical deduction of Quantum Theory based solely on the consistency of all things even at the smallest scale. I define existence to be the logical conjunction of all the things that exist. A conjunction of statements (each describing the smallest things) can be manipulated into a conjunction of implications between each fact and another. One can construct a path through all the implications, where the conclusion of one implication is the premise of another from some starting point to some end point. I go through a little effort to show how implication can be mapped to the mathematics of a gaussian distribution, conjunction can be mapped to multiplication, and disjunction can be mapped to addition. This allows the logical conjunction of paths to be mapped to the Feynman Path Integral of quantum mechanics. This is quantum theory, and the process can be iterated to give quantum field theory. It also explains where the symmetries of particle physics comes from.

See details at: http://www.logictophysics.com

friend wrote:See details at: http://www.logictophysics.com

Yes, this is a bit of a paradigm shift, to now think that physics can be derived solely from logic apart from experiment. But it assumes the same presuppositions, that all things must coexist in reality in a consistent manner, and that the laws of physics are the same everywhere at all times. Math is part of the sciences, so this is still a scientific endeavor. And any objection might be assuming that at some level it will be shown that reality is not consistent with classical logic. I don't think you can base an argument on the premise that reality can be inconsistent with logic. We can only prove that it is consistent (and therefore derived from) logic. The only question is how, and I think I've addressed that issue.

friend wrote:See details at: http://www.logictophysics.com

To derive something from logic suggests that it may be a logically complete system. But the Godel Incompleteness Theorem states that any system rich enough to do arithmetic is inherently incomplete. And so many think that just because physics uses math, then physics cannot be complete either. But geometry has been shown to be a complete system, and it uses math. So perhaps my derivation is a way to make physics complete in the sense that geometry is a complete system even though it uses math. I think the common point would be that the math is used only as a tool to describe the system; these systems are not an attempt to validate the completeness of math itself, but only to use parts of math.

friend wrote:

friend wrote:See details at: http://www.logictophysics.com

To derive something from logic suggests that it may be a logically complete system. But the Godel Incompleteness Theorem states that any system rich enough to do arithmetic is inherently incomplete. And so many think that just because physics uses math, then physics cannot be complete either. But geometry has been shown to be a complete system, and it uses math. So perhaps my derivation is a way to make physics complete in the sense that geometry is a complete system even though it uses math. I think the common point would be that the math is used only as a tool to describe the system; these systems are not an attempt to validate the completeness of math itself, but only to use parts of math.

I think the argument from Gödel is spurious. Gödel's theorem is a formal mathematical theorem about formal mathematical systems. The proof of Gödel's theorem relies on the fact that outside of the formal system, we do know whether a certain mathematical statement is true or not, in our intended application field! The incompleteness is only apparent, it is only relative. I think that whenever incompleteness would turn up with respect to mathematics intended to be applied to physics, we will be able to use intelligent reasoning about physics in order to decide the issue.

gill1109 wrote:

friend wrote:

friend wrote:See details at: http://www.logictophysics.com

To derive something from logic suggests that it may be a logically complete system. But the Godel Incompleteness Theorem states that any system rich enough to do arithmetic is inherently incomplete. And so many think that just because physics uses math, then physics cannot be complete either. But geometry has been shown to be a complete system, and it uses math. So perhaps my derivation is a way to make physics complete in the sense that geometry is a complete system even though it uses math. I think the common point would be that the math is used only as a tool to describe the system; these systems are not an attempt to validate the completeness of math itself, but only to use parts of math.

I think the argument from Gödel is spurious. Gödel's theorem is a formal mathematical theorem about formal mathematical systems. The proof of Gödel's theorem relies on the fact that outside of the formal system, we do know whether a certain mathematical statement is true or not, in our intended application field! The incompleteness is only apparent, it is only relative. I think that whenever incompleteness would turn up with respect to mathematics intended to be applied to physics, we will be able to use intelligent reasoning about physics in order to decide the issue.

Our theories of physics (and other sciences) must be incomplete. That is what we want. They shall not specify the problem they will be applied to, they
shall not specify initial conditions. Those shall be provided as additional information and shall be different according to particulars of each application.

Mikko wrote:Our theories of physics (and other sciences) must be incomplete. That is what we want. They shall not specify the problem they will be applied to, they shall not specify initial conditions. Those shall be provided as additional information and shall be different according to particulars of each application.

What provides the information of initial conditions? Are you suggesting that the universe as a whole is incomplete? Are you suggesting that there is something that truly exists outside the universe? Or are you suggesting that there is a source of information outside the universe that determines it initial conditions? This sounds like Intelligent Design. I would have to think that the universe is self-contained by definition. And so the laws that govern the evolution of the universe are complete, not depending on something outside or more than the universe. If it did, then we would include that something as part of the universe.

friend wrote:Are you suggesting that the universe as a whole is incomplete?

No, that would make no sense. The universe is not a complete theory. It is not an incomplete theory, either. Other meanings of "incomplete" are not relevant here.

Whether or not a theory is "complete" depends on what you decide should be covered by the theory. EPR famously attempted to define what was *real*. They then characterized a complete theory as one which describes everything which is real. Finally, they showed that QM was not complete, according to their own definition of what was real.

Many worlds theorists get out of the problem of completeness (or not) of quantum mechanics by denying the reality of any particular quantum branch. For them the only thing that is real is the collective of all possible paths. For them, whether or not the cat is alive or dead is not part of reality. There are paths with dead cats and paths with alive cats and only the collective of all paths is real.

I am saying that what we mean by "the universe as a whole" depends on what we mean by "reality", and actually it is a theoretical concept.

The universe is the universe. It is not a theory. A qualifier like "complete (yes/no)" can't be applied to the universe.

It is hard to say what is real without having some kind of theory, and it is hard to say whether a theory is complete or not, without having a theoretical notion of what is real and what is not real. If you accept the idea that irreducible randomness could be a fundamental (bottom level) feature of reality, then quantum mechanics can be considered complete. It describes everything that there is. If you don't accept the idea that irreducible randomness could be a fundamental (bottom level) feature of reality, then you have a problem (if you think that the empirical predictions of QM are close to true). You'll have to accept non-locality or worse (conspiratorial super-determinism).

Mikko wrote:No, that would make no sense. The universe is not a complete theory. It is not an incomplete theory, either. Other meanings of "incomplete" are not relevant here.

Reality can be defined as the collection of all facts in it. There cannot be any facts outside the collection of the whole universe. Completeness is having each and every fact imply each and every other fact in the universe. There are no facts outside the universe that have any effect on any fact in our universe. Each fact cannot go unaffected by any other. Every fact has an effect on every other.

gill1109 wrote:Whether or not a theory is "complete" depends on what you decide should be covered by the theory.

The term "complete" was introduced to this discussion by friend with a reference to Gödel's incopleteness theorem. There it means that a theory is complete if it can prove or disprove every sentence of its language. Equivalently, a theory is incomplete if there are two models of the theory so that some sentence is true on one and false in another. This kind of completeness is not desirable in theories of physics.

Mikko wrote:The term "complete" was introduced to this discussion by friend with a reference to Gödel's incopleteness theorem. There it means that a theory is complete if it can prove or disprove every sentence of its language. Equivalently, a theory is incomplete if there are two models of the theory so that some sentence is true on one and false in another. This kind of completeness is not desirable in theories of physics.

What kind of completeness do you suppose David Hilbert had in mind when he posed the challenge to complete physics back in the late 1920's? We may be agreeing together that Godel's Incompleteness is not applicable to physics.

I think I understand your point that the laws of physics don't specify the situations to which they can be applied. But my question is whether the mathematical laws could be proven on principle alone without resort to physical interpretations. Can what we regard as the mathematical laws of physics be derived from logic alone. I tend to think yes.

It seems now all we have is a mathematical description of observations - a curve-fitting of the data. But can this really be considered an explanation for why reality is the way it is? Or does this only lead to more questions as to why this math and not another? Sure, that may be sufficient for engineering purposes. But my contention is that questions will not stop until we manage to derive physics from logic alone. For then the only thing left to question is reason itself. I've managed to derive the principles of quantum mechanics from logical considerations alone. See

http://www.logictophysics.com

But I don't have the principles of relativity yet. I need to make connections to the defining concepts of a manifold. I've described the logic of material implication in terms of set inclusion. And I've assumed that there exists at every point in the quantum mechanical space a set which includes each point, that set shrinking to a point. This is very similar to the concept of the Hausdorff property of a manifold. Therefore, this begs the question as to whether every manifold automatically admits quantum mechanical constructions. And I wonder what other principles of a manifold are included in my quantum mechanical derivations. How can I derive a metric on this space, and how would I get curvature? Is there a hidden spacetime symmetry lurking about in my efforts that determine a metric field equation? Any help would to appreciated and acknowledged.

I tried to read your proposal but I cannot make much sense of it. You say you have "derived" the principles of quantum mechanics from logical considerations alone but it seems to me that you only "connected" one of the principles of quantum mechanics to logic. You know there is a big field called "quantum logic" which had exactly the same research programme as yours. It has been stagnating for many years (it produced some generalized abstract nonsense but no insight into physics, as far as I know).

gill1109 wrote:I tried to read your proposal but I cannot make much sense of it. You say you have "derived" the principles of quantum mechanics from logical considerations alone but it seems to me that you only "connected" one of the principles of quantum mechanics to logic. You know there is a big field called "quantum logic" which had exactly the same research programme as yours. It has been stagnating for many years (it produced some generalized abstract nonsense but no insight into physics, as far as I know).

First of all, consistency among all the facts in existence is a physical consideration. Since they all exist simultaneously, no one fact can prove any other false. Secondly, consistency is also a logical consideration. So this already proves that there must be a connection between logic and physics.

As for "quantum logic" that is a effort that is the total reverse of mine. They are trying to derive logic from the starting principles of quantum mechanics. I think it is a blatant logical fallacy. For quantum logic supposes the breakdown of the distributive law so that the following is not true:

p^(q v r) = (p^q) v (p^r)

But remember that ANDs and ORs can be broken down so that any logical statement can be equated to statements with only negation, parenthesis, and implication (for example). And so to assert the breakdown of the distributive law is to assert the validity of parenthesis, negation, and implication in some circumstances, but deny it in others. That's called special pleading, and it's a logical error.

To connect logic and physics requires one to consider facts. And we can consider the universe to be a collection of facts. This things exists and that thing exists, these are facts. To talk about the universe in terms of numbers mean we must count things. And we do that all the time. What is not usual is to go from logic to numbers. How does one introduce numbers in logic? I believe the key to this is the Dirac measure which basically results in 1 if an element is included in a set and otherwise results in 0. So numbers are mapped from set inclusion. And set inclusion can be thought of as a description of the material implication of propositional logic. A proposition implying another is like a set implies it's members. If a set (of propositions) is true, then this implies that it elements (of propositions) are also true. If any of the elements are false, then so is the set. If the element is not included in the set, then the implication is false. This type of reasoning has lead me to derive QM from logic alone.

See: http://www.logictophysics.com

friend wrote:To connect logic and physics requires one to consider facts. And we can consider the universe to be a collection of facts. This things exists and that thing exists, these are facts. To talk about the universe in terms of numbers mean we must count things. And we do that all the time. What is not usual is to go from logic to numbers. How does one introduce numbers in logic? I believe the key to this is the Dirac measure which basically results in 1 if an element is included in a set and otherwise results in 0. So numbers are mapped from set inclusion. And set inclusion can be thought of as a description of the material implication of propositional logic. A proposition implying another is like a set implies it's members. If a set (of propositions) is true, then this implies that it elements (of propositions) are also true. If any of the elements are false, then so is the set. If the element is not included in the set, then the implication is false. This type of reasoning has lead me to derive QM from logic alone.

See: http://www.logictophysics.com

Numbers are derived from logic in the foundational works on mathematics. As soon as the notion of set has been defined, one can talk about the empty set. We could even call it "zero". Now one can define the set containing only the empty set. We could even call it "one". Now define the set which contains only "zero" and "one". Call it "two". And so on.

So we already know very well how to build mathematics from logic.

If you want to go from mathematics to physics you have to build a bridge between abstract mathematical concepts and our sensory perceptions and/or intuitions. Our brains are already "hard-wired" with notions of (usual) 3D geometry, time, motion, cause and effect, objects and agents, number. This is called "systems of core knowledge" in neuro-linguistics, people in artificial intelligence call it "embodied congnition". I am afraid that we do physics by combining three things: logic, intuition/instinct/inborn insight, and sensory perception. It will be a difficult job to separate these things. I found your derivation of QM by logic alone a lot of hard work which gave only a tiny bit of QM while making a lot of jumps of faith (ie jumps not carried by logic). I do not see the point of it. Especially since we learn from Bell's theorem that QM actually defies our intuition of space, time and causality. What people think should be "logical" turns out simply to be false, in some situations.

gill1109 wrote:Numbers are derived from logic in the foundational works on mathematics. As soon as the notion of set has been defined, one can talk about the empty set. We could even call it "zero". Now one can define the set containing only the empty set. We could even call it "one". Now define the set which contains only "zero" and "one". Call it "two". And so on.

Yes, I've seen that before. But it does not make any sense to me. It seems to be a ever more complicated reference to nothing, the empty set, and sets of sets of the empty set. It seems to me that if you are going to do any counting, then you have to be referring to something other than the empty set. And so what's wrong with using the Dirac measure to assign 1 if a set includes a element of interest? That seems very intuitive to me. Even babies will claim to have found 1 when they pick up a colored stone on the beech. The set being the beech, the stone being the element in the set.

gill1109 wrote:If you want to go from mathematics to physics you have to build a bridge between abstract mathematical concepts and our sensory perceptions and/or intuitions. Our brains are already "hard-wired" with notions of (usual) 3D geometry, time, motion, cause and effect, objects and agents, number. This is called "systems of core knowledge" in neuro-linguistics, people in artificial intelligence call it "embodied congnition". I am afraid that we do physics by combining three things: logic, intuition/instinct/inborn insight, and sensory perception. It will be a difficult job to separate these things.

The whole point of physics is to makes sense of it. You wind up asking whether the theory is correct or not. Does it represent the truth? I don't think it is sufficient to simply find a formula the fits the data. That's engineering, not explanation. The questions will always come up, why this math and not something else. And that question can not be ended until you have derived physics from reason itself. So some way or another we will want to derive physics from logic. It's just a matter of how.

gill1109 wrote:I found your derivation of QM by logic alone a lot of hard work which gave only a tiny bit of QM while making a lot of jumps of faith (ie jumps not carried by logic). I do not see the point of it. Especially since we learn from Bell's theorem that QM actually defies our intuition of space, time and causality. What people think should be "logical" turns out simply to be false, in some situations.

I hope you are able to recognize that you've really not posed an argument or a question. Yes, it's about a 2 hour read. But it really does not involve any hard conceptual math. I think even an advanced highschoolers could understand it. I've not shown every single construction of quantum mechanics. But what I think I've shown is where the wavefunction comes from to begin with, where the Born rule comes from, and why nature would prefer the symmetries of U(1)SU(2)SU(3). In other words, I believe I've derived the conceptual foundations of quantum mechanics from logical considerations alone. I think this is much better than to try to construct logic from quantum mechanics. That can only lead to obvious logical inconsistencies by definition.

http://www.logictophysics.com

Sorry, so many other people have claimed to have done what you have done, and it is always much more than a two hours read, and in the end it rather disappoints. Have you read Inge Helland's papers, by the way? He has a similar program to yours, gets further ... I understand that Mauro d'Ariano has also got very far with a very logical very axiomatic approach.

BTW I am not proposing to construct logic from quantum mechanics. I see it this way: from logic we get mathematics, and with mathematics and logic we describe and understand the world. It turns out to be a pretty amazing place and no amount of logical derivation is going to change that.

So sorry: I am not going to do that two hours read. I took a quick look and decided that for me, life was too short.

Starting from nothing rather from one was a great conceptual step forwards (the contribution of the Arabs, who maybe got it from the Indus civilization?). The invention of "0" was a really important step forwards. And the insight that from "0" you can get a set {0} = 1 of just one element, and then a set {0, 1} = 2 of just two elements, is pure genius.

If it has not been proven that physics cannot be derived from logic, then I don't think it is warranted to reject the idea out of hand.

www.logictophysics.com

I am not rejecting your idea out of hand. But I have some other ideas which for me are more pressing to explore. Life is short.