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by **friend** » Thu Jan 22, 2015 4:54 pm

friend wrote:
Ben6993 wrote:Hi Friend

Thanks for the interesting overview. Good luck in deriving the spacetime metric from logic.

This is my thinking so far: The metric of flat spacetime dx^2 + dy^2 + dz^2 - dt^2 = dtau^2 may be invariant under Lorentz transformation because of the result of some invariance principle of Gaussian distributions. Remember that the Feynman path integral was derived from the Gaussian of the form exp[-(x-x0)^2/delta^2], where delta^2 = 2ih(t-to)/m in order to give the denominator the same t-squared dependence as the numerator has with its distance-squared. See equations 24 and 25 of my derivation at logictophysics.com. For if we were to hold the exponent constant at, C^2, for some reason, then you could multiply this constant by the denominator, [2ih(t-to)/m]^2, and subtract it on both sides to get the flat spacetime metric in differential form equaling zero as it is for a Lorentz transformation. But why hold the gaussian exponent constant? Is it because this gaussian is more fundamental than any spacetime coordinates (being the representation of the material implication of logic which is more fundamental than a metric)? Or does that represent a process for which there is no loss of information?

If this invariance of the exponent holds up for some process, then this might explain the signature of the flat spacetime metric (-+++). I don't know yet why 3 space dimensions. But it may be that the space metric is locally Euclidean (x^2 + y^2 + z^2) because it might be necessary to keep the gaussian form of the distribution which allowed a derivation of the Feynman path integral. I like the way this is consistent with the idea that a manifold is locally Euclidean.

This makes me wonder if the exponent could generally have other quadratic cross terms such as xy + xz + yz. And does this place some restrictions on the spacetime metric that accounts for General Relativity?

If anyone has any insight into any of this, please share.

by **friend** » Thu Jan 22, 2015 2:27 pm

Ben6993 wrote:Hi Friend

Thanks for the interesting overview. Good luck in deriving the spacetime metric from logic.

This is my thinking so far: The metric of flat spacetime dx^2 + dy^2 + dz^2 - dt^2 = dtau^2 may be invariant under Lorentz transformation because of the result of some invariance principle of Gaussian distributions. Remember that the Feynman path integral was derived from the Gaussian of the form exp[-(x-x0)^2/delta^2], where delta^2 = 2ih(t-to)/m in order to give the denominator the same t-squared dependence as the numerator has with its distance-squared. See equations 24 and 25 of my my derivation at logictophysics.com. For if we were to hold the exponent constant at, C^2, for some reason, then you could multiply this constant by the denominator, [2ih(t-to)/m]^2, and subtract it on both sides to get the flat spacetime metric in differential form equaling zero as it is for a Lorentz transformation. But why hold the gaussian exponent constant? Is it because this gaussian is more fundamental than any spacetime coordinates (being the representation of the material implication of logic which is more fundamental than a metric)? Or does that represent a process for which there is no loss of information?

If this invariance of the exponent holds up for some process, then this might explain the signature of the flat spacetime metric (-+++). I don't know yet why 3 space dimensions. But it may be that the space metric is locally Euclidean (x^2 + y^2 + z^2) because it might be necessary to keep the gaussian form of the distribution which allowed a derivation of the Feynman path integral. I like the way this is consistent with the idea that a manifold is locally Euclidean.

This makes me wonder if the exponent could generally have other quadratic cross terms such as xy + xz + yz. And does this place some restrictions on the spacetime metric that accounts for General Relativity?

If anyone has any insight into any of this, please share.

by **Ben6993** » Wed Jan 21, 2015 8:59 am

Hi Friend

Thanks for the interesting overview. Good luck in deriving the spacetime metric from logic.

by **friend** » Fri Jan 09, 2015 9:14 am

Ben6993 wrote:Hi Friend
Have you applied your method of Logic to finding the laws of thermodynamics?...

Hi Ben,

Thermodynamics has to do with entropy which requires information which can only be derived from probability distributions. The very basics of a probability distribution is the ability to place a sample in a bin. From there it is just a matter of how many samples are placed in which bins and getting a distribution across all the bins. Samples in bins is another way of saying elements in sets or even points in a neighborhood of a topology. What I have done is to recognize elements in sets as a way of describing material implication of logic. This connects logic to sets to probabilities which results in information and entropy. It also connects logic to topology. What I have not derived yet is the metric of spacetime on that topology. If I could derive the metric of general relativity, then I might be able to connect gravity to thermodynamics.

by **Ben6993** » Wed Jan 07, 2015 10:04 am

Hi Friend

Have you applied your method of Logic to finding the laws of thermodynamics?

Note that Jay Yablon has a new thread (with a link to his very recent paper) here http://www.sciphysicsforums.com/spfbb1/viewtopic.php?f=6&t=138
which sets out a derivation of the laws of "classical thermodynamics from spacetime geometry".

Because of the above, I was reading the last chapter of Thermodynamics (1936) by Fermi, which treats thermodynamics wrt quantum mechanics, and came across some wording which immediately made me think of your method of logic's 'implications':
"The phase space is divided into a number of very small cells all of which have the same hypervolume ι; the state is then characterised by specifying the cell to which the point representing the state belongs." ... "This representation of the state of a system would evidently become exact if the cells were made infinitesimal".

Apologies if this is a red herring. As you well know, I very much like your method of 'implications' because I see it as closely fitting the wave function collapse and hence physically fitting what it is that happens (at least in my imagination) to particles at interactions.

Best wishes

by **friend** » Mon Jun 23, 2014 2:45 pm

minkwe wrote:It appears from quick glance at your website that what you are really doing is deriving different mathematical formalisms, starting from logic. That makes sense because mathematics, just like logic, is a framework for manipulation of information. But do not confuse that with having derived laws of physics. Hilbert space is a mathematical tool, and so is Dirac delta, etc. probably 95% of QM is purely mathematical manipulation of information (epistemology), only relevant to physics because the information happens to be information about physical things (ontology). The information itself and the frameworks used to manipulate that information are not physical things or laws of nature by themselves. Many have fallen down that abyss already. Do not let the same fate befall you.

Thank you. I'm sure I'll have to be careful. It's tempting to think there may be some sort of mind that does the derivation behind the physics that's derived. How can a logic that considers both true and false give rise to only true things that do exist? But the real argument is whether I've made a math error or a speculative assumption. We already use logic in math, set theory and its union and intersection that are involved with neighborhoods and topologies. What I seem to have done is to shrink to a point a set that forms a neighborhood which I use as a proposition in sentential logic in my math. Isn't this the usual way to turn union into conjunction and intersection into disjunction, like they do in DeMorgan's theorems (I may have gotten that backwards)?

by **gill1109** » Sun Jun 22, 2014 9:24 pm

Very perceptive remarks, Michel.

by **minkwe** » Sun Jun 22, 2014 8:01 pm

It appears from quick glance at your website that what you are really doing is deriving different mathematical formalisms, starting from logic. That makes sense because mathematics, just like logic, is a framework for manipulation of information. But do not confuse that with having derived laws of physics. Hilbert space is a mathematical tool, and so is Dirac delta, etc. probably 95% of QM is purely mathematical manipulation of information (epistemology), only relevant to physics because the information happens to be information about physical things (ontology). The information itself and the frameworks used to manipulate that information are not physical things or laws of nature by themselves. Many have fallen down that abyss already. Do not let the same fate befall you.

by **minkwe** » Sun Jun 22, 2014 7:48 pm

friend wrote:This is what I am attempting to do: derive physics from logic.

You are trying to mix ontology with epistemology, which is forbidden. A lot of the rubbish of present-day QM is precisely due to similar mixing. I'm afraid you won't make any progress with such ideas. A proper physical theory must assume that the real world (ontology) exists independent of our knowledge/imaginations and reasoning processes (epistemology/logic). Logic is simply a theory of consistent reasoning (manipulation of information/knowledge in our minds). Logic does not care or depend on the specific pieces of information we manipulate. Logic is only relevant to physics, to the extent the information/knowledge we are manipulating (epistemology) is about physical things we have assumed exist, or we have measured in an experiment (ontology). You can use logic to predict the existence of new/previously unknown physical things(ontology). But you can not derive physical laws purely from logic alone.

ET Jaynes, Probability: The Logic of Science wrote:Common language—or at least, the English language—has an almost universal tendency to disguise epistemological statements by putting them into a grammatical form which suggests to the unwary an ontological statement. A major source of error in current probability theory arises from an unthinking failure to perceive this. To interpret the ﬁrst kind of statement in the ontological sense is to assert that one’s own private thoughts and sensations are realities existing externally in Nature. We call this the “Mind Projection Fallacy,” and note the trouble it causes many times in what follows. But this trouble is hardly conﬁned to probability theory; as soon as it is pointed out, it becomes evident that much of the discourse of philosophers and Gestalt psychologists, and the attempts of physicists to explain quantum theory, are reduced to nonsense by the author falling repeatedly into the Mind Projection Fallacy
...
The belief that “randomness” is some kind of real property existing in Nature is a form of the Mind Projection Fallacy which says, in eﬀect, “I don’t know the detailed causes—therefore—nature does not know them.”

by **friend** » Sun Jun 22, 2014 9:26 am

gill1109 wrote: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.

If life is too short, then we don't have time to waste on unprovable, speculative ideas. What we want is a complete explanation of things ASAP. If we rely on one physical thing explained in terms of another physical thing, then we have just moved the goal post, having now to explain where the more fundamental thing came from. For example, when we explained protons and neutrons in terms of quarks, now we have to explain where quarks come from, and we can't really say that we are any closer to explaining things, we just have new things to explain.

There is no complete explanation until you explain physics from reason and logic alone. And if it is derived from logic, then you can't argue with it, unless you want to argue with the principles of reason itself.

This is what I am attempting to do: derive physics from logic. Prior to this, it was only considered a pipe dream and an impossible task. Philosophers considered logic too general to derive something as specific as the laws of nature. But now, I have had some very smart people review my work, and they are not saying I'm wrong. No one has found any point of speculation in my work. In order to continue the debate, they are forces to question the reliability of mathematics itself. You are invited to review it as well at:

http://www.logictophysics.com

by **gill1109** » Sun Jun 08, 2014 8:54 pm

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.

by **friend** » Sun Jun 08, 2014 4:04 pm

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

by **gill1109** » Sun Jun 01, 2014 12:16 pm

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.

by **friend** » Sun Jun 01, 2014 11:47 am

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

by **gill1109** » Sun Jun 01, 2014 8:00 am

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.

by **friend** » Sun Jun 01, 2014 7:13 am

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

by **friend** » Wed May 28, 2014 4:20 pm

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.

by **gill1109** » Mon May 26, 2014 10:29 pm

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).

by **friend** » Mon May 26, 2014 9:23 am

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.

by **friend** » Tue Apr 01, 2014 6:45 pm

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.

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