Physics from reason alone

[friend]

The theory of everything, the ultimate truth, the end of physics, the final theory... What would this even look like?

As it is practiced today, physics is just a clever attempt to match the data gained from experiment to the equations of math that we can then use to make predictions that we can further test. In essence it is a reverse engineering effort at curve fitting the data. Especially in quantum mechanics! Ever since Max Planck inserted Planck constant, h, into the black body power spectrum as a desperate attempt to find a curve that matched the data, quantum mechanics has become a curve fitting exercise. And it will remain so until a better explanation can be found for quantum theory.

Now, when theoretical physicists try to advance unification efforts or to connect quantum field theory (QT) and general relativity (GR), these efforts don't even begin to try and justify quantum theory from foundational math principles. So they are not even sure they are dealing with final theories of QT or GR to begin with. For all they know, they may be working with effective theories that are only validated provisionally, provided that they are not falsified by the next experiment. There is no "proof" of these laws of physics. Proof only exists in the realm of logic and math. But these theories are only curve fitting equations, clever as they may be. So any unification they may achieve can only be seen as coincidental. If we find another particle for dark matter, for example, then we don't know if the symmetries of quantum theory will remain the same. And we don't know that QT will continue to remain unified with GR in these new theories.

We except the present laws of physics based on the inductive method of proof, that if enough experiments do not contradict our equations but seem to confirm them, then we have more confidence that they are correct. And we see in our equations smaller entities and design experiments to detect them. We describe larger structures in terms of ever smaller ones, atoms, then a nucleus and electrons, then protons and neutrons, then quarks and gluons, then who knows what else. And we are always left wondering why these smallest things exist. But where does it all end?

We can always keep asking questions about the nature of reality until everything is derived from reason itself. Then the only questions could be what reason is and why it is the way it is. So the final theory must be one based on principal alone. We are looking for laws of physics derived from the principals of logic alone. But until now this has only been a philosophical dream with no clear path to its realization.

I have a derivation of quantum theory completely from logic alone, without recourse to any data from experiment. This explains quantum theory on principle alone. Some may think that this is just a mathematical trick. But I use the formulation to derive its particle content, and it seems to match the Standard Model of particle physics. Not only is QT justifiable, but so are the various particles. And the math is relatively easy, integration of complex exponential functions. The website is at: logictophysics.com. Let me know if you have and questions or comments.

[FrediFizzx]

My question would be; can you put that site all in one PDF file for download and printing?
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[friend]

My question would be; can you put that site all in one PDF file for download and printing?
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I understand your concerns. I'm in the process of converting it to PDF, but it's difficult to configure the math equations for printing. I can't get them all within the margins. However, the website (http://logictophysics.com/QMlogic.html) has been designed to make it easy to review. When I make a reference to a previous equation, that reference can be mouseover'd to view the equation it refers to. That way you don't lose your place when you scroll back to find the reference. Just mouseover the reference to see the equation itself. Hyperlinks are opened in a new tab so the original tab is undisturbed. And I also use cookies to keep track of your place in the document so you can come back to it to resume where you left off. So please try to read the website and let me know if you have any problems with it. In the mean time I'll work on the PDF version. Thanks.

[FrediFizzx]

My question would be; can you put that site all in one PDF file for download and printing?
.

I understand your concerns. I'm in the process of converting it to PDF, but it's difficult to configure the math equations for printing. I can't get them all within the margins. However, the website (http://logictophysics.com/QMlogic.html) has been designed to make it easy to review. When I make a reference to a previous equation, that reference can be mouseover'd to view the equation it refers to. That way you don't lose your place when you scroll back to find the reference. Just mouseover the reference to see the equation itself. Hyperlinks are opened in a new tab so the original tab is undisturbed. And I also use cookies to keep track of your place in the document so you can come back to it to resume where you left off. So please try to read the website and let me know if you have any problems with it. In the mean time I'll work on the PDF version. Thanks.

It is just too much for me to read on the computer but looks interesting. For this stuff, I like to print out and read whilst lying on the sofa (I'm a real old-timer ). Then I can also make notes in the margins.
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[friend]

It is just too much for me to read on the computer but looks interesting. For this stuff, I like to print out and read whilst lying on the sofa (I'm a real old-timer ). Then I can also make notes in the margins.
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OK. I have a PDF file available at: http://logictophysics.com/QMlogic.html. Just click the PDF icon at the top, left. I had difficulty converting it from html to a Word document; much of the formatting did not translate, and I had to fix a lot of it. So I would very much appreciate it if you let me know if you find any mistakes or if you have trouble understanding what I've written. I will try to fix it immediately. The math is at or below the sophomore level, but some of it can be a little tedious in places because I wanted to be as complete as possible. If you're having trouble with a section, try that section at the website. I created mouseover text to give some shortcut tips to help understand what I'm doing there. Otherwise, just ask, and I'll try to help you with any problems. Thanks.

[FrediFizzx]

Thanks for that. I'm reading it now. Probably will take a while.
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[jreed]

Thanks for putting that PDF file on the system. I'll go through it also. It looks interesting.

jreed

[friend]

Any questions, yet? Did you get stuck anywhere? Do I need to put more or less information in some sections?

[FrediFizzx]

Any questions, yet? Did you get stuck anywhere? Do I need to put more or less information in some sections?

Doesn't all of mathematics come from logic anyways? I believe that is what my logic course said more than 50 years ago. I think I still have that textbook around here somewhere. More information is always good. Still reviewing what you have done. Got sidetracked a bit with revising a paper.
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[friend]

Any questions, yet? Did you get stuck anywhere? Do I need to put more or less information in some sections?

Doesn't all of mathematics come from logic anyways? I believe that is what my logic course said more than 50 years ago. I think I still have that textbook around here somewhere. More information is always good. Still reviewing what you have done. Got sidetracked a bit with revising a paper.
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Russel and Whitehead tried to prove that all arithmetic is derived from logic. But Kurt Godel proved that arithmetic is incomplete (assuming it's consistent). I only have a passing familiarity with the effort of these gentlemen. So I'm not completely persuaded yet. Still, I don't think Godel's incompleteness theorem will prove any of our present math statements wrong, only that there may be other theorems that are true, though not provable with our present math. So what does that mean for us? Are there math statements lurking close by in construction to our present math theorems that are true though not provable by us? Do we have any other choice but to describe physics using math? I think the only relevant question is why we should use this or that math in our physical theories. And perhaps I made some progress in that regard.

[FrediFizzx]

"...proved that arithmetic is incomplete." What does that even mean? Why does it have to be complete? And what does that even mean? Anyways, not sure what that has to do with math is derived from logic and math is used to describe physics thus you automatically have logic --> physics. I see the sense in that.
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[gill1109]

Any questions, yet? Did you get stuck anywhere? Do I need to put more or less information in some sections?

Doesn't all of mathematics come from logic anyways? I believe that is what my logic course said more than 50 years ago. I think I still have that textbook around here somewhere. More information is always good. Still reviewing what you have done. Got sidetracked a bit with revising a paper.
.

Russel and Whitehead tried to prove that all arithmetic is derived from logic. But Kurt Godel proved that arithmetic is incomplete (assuming it's consistent). I only have a passing familiarity with the effort of these gentlemen. So I'm not completely persuaded yet. Still, I don't think Godel's incompleteness theorem will prove any of our present math statements wrong, only that there may be other theorems that are true, though not provable with our present math. So what does that mean for us? Are there math statements lurking close by in construction to our present math theorems that are true though not provable by us? Do we have any other choice but to describe physics using math? I think the only relevant question is why we should use this or that math in our physical theories. And perhaps I made some progress in that regard.

Gödel proved that you can’t prove that mathematics is consistent; and also that it can never be complete, because you can always create new mathematical statements about infinite sets which you could take axiomatically to be true or false, just as a matter of taste. Or as a matter of physics intuition! But still I think it is correct to say that *pure* mathematicians is “just” logic. Or vice versa. In pure mathematics one can go for absolute truth but on the other hand those absolute truths are mere tautologies.

[Joy Christian]

In pure mathematics one can go for absolute truth but on the other hand those absolute truths are mere tautologies.

That is exactly right. A fine example of that is Bell's theorem. It is tautologous. It assumes (in a different guise) what it wants to prove, in order to prove it. Nice mathematics, bad physics.

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[friend]

Nice mathematics, bad physics.

And what if physics can be made a branch of mathematics? Some may have philosophical objections to that. But I think my efforts may be a start in that direction. I have yet to hear any mathematical objections to it.

[jreed]

Any questions, yet? Did you get stuck anywhere? Do I need to put more or less information in some sections?

I wouldn't say I'm stuck, but I"m having difficulty seeing what you are trying to get at. After several pages of Boolean algebra, you come up with the Kronecker delta. Then go on to integrating Dirac delta functions. These are well known in physics and used extensively. This expression is manipulated by adding time, imaginary numbers, and notation until you come up with something that looks like a path integral. Would you have obtained this form without knowing what a path integral should look like? I don't see Boolean algebra adding anything, since when physics is done logic is normally followed.

[friend]

I wouldn't say I'm stuck, but I"m having difficulty seeing what you are trying to get at. After several pages of Boolean algebra, you come up with the Kronecker delta. Then go on to integrating Dirac delta functions. These are well known in physics and used extensively. This expression is manipulated by adding time, imaginary numbers, and notation until you come up with something that looks like a path integral. Would you have obtained this form without knowing what a path integral should look like? I don't see Boolean algebra adding anything, since when physics is done logic is normally followed.

I'm trying to justify every step of the way. It's rather easy to get the path integral from the iterative property of the Dirac delta function. From equation [22] I use the exponential form of the Dirac delta function and replace the variance parameter with equation [26]; the path integral follows immediately. But why then the Dirac delta function? For that matter, why an integral? Why the exponential form of the Dirac delta function? Why use a complex number in the exponent? The Website is the story of how to justify the use of these forms to get to the path integral. The details may be a little tedious, but the payoff is extreme.

From the framework developed in this document, it becomes possible to define space as the entanglement of "virtual particles" connecting all the points of space. It also becomes possible to define mass and energy in terms of these virtual particles. And the various particles of the Standard Model seem to simply fall out of this construction. There are other Webpages in the TOC that address all this. And at this point I'm beginning to think that the theory of everything can be derived from all this.

To be honest I would not have been able to derive the path integral without first knowing what it looked like. There are some subtleties that would not have been obvious. And I would not have known what I was trying to prove or where to stop. So I would not say that anyone before Feynman should have been able to easily come up with all this even though the pieces of the puzzle were there.

You wonder why I had to go all the way back to propositional logic (Boolean algebra). If I had not done so, then questions would be left hanging as to why I used this form of math and not some other, especially if I don't resort to some sort of physical intuition. What should be recognized is that the Dirac delta equation [22] can be mapped from the logical equation [7]. It has the same iterative properties needed to construct the Feynman path integral. But then some means has to be developed to map the parts of the logic to the parts of the math. So the first part of the article justifies the effort to map logical conjunction to multiplication, logical disjunction to addition, implication to the Kronecker delta and then the Dirac delta in the continuum. Hopefully this give an easy perspective into all this.

[friend]

It seems the modern paradigm of quantum theory is build on reverse engineering, ad-hoc, curve fitting. Max Planck introduced "h" into the equations as a desperate attempt to find a curve for the black body power spectrum. This is the definition of curve fitting. And it's ad-hoc because he followed no method to get this curve; he simply guessed at it and used it because it worked in this situation only - that's the definition of ad-hoc. Others who followed may have used cleaver means to derive results. But we will always be left with questions until physics can be derive from the principles of reason alone.

Yet, logic has to do with propositions, and physics has to do with the numerical value of measurements. So the question is how to go from logic to math. Of course a number can be defined as the cardinality of a set, the number of elements in a set. And the most basic numbers are 0 and 1, where 0 is the cardinality of the empty set, and 1 is the cardinality of a set with only one element. In order to go from logic to math, then, we need a function that we can use to map the logic of true and false to the math of 0 and 1. This is accomplished by the Dirac measure which is equal to 1 if the Dirac set has one element and 0 if it is empty.

So I use the Dirac measure to map logic values and operators to math values and operators. I go through all the details to justify this map. Or at least that is what to look for when reading this paper. In the end, it turns out that the wave function of quantum mechanics is a representation of the material implication of logic. Again, the website is at: logictophysics.com

[friend]

Some are amazed as to why mathematics should be so effective at describing the laws of physics. And the question is always there as to why we use this kind of math and not some other. I no longer have these questions. It's not even a mystery why logic is so applicable in the world.

Logic deals with what is true or false, and physics deals with what exists or not. Both are binary systems with an excluded middle. So binary logic is used to understand what exists or not. We have the correspondence principle that what exists can be described by propositions that are true. And we assume that everything in the universe is logically consistent with everything else.

And so the math used to describe physics should also be derived from this binary logic. The Dirac measure seems to provide a means to develop the math needed for physics. The Dirac measure gives us a numeric value of 1 if the set of Dirac measure has the required element; it has the value of 0 if that set is empty. This is a binary algebra, for a set can only be empty or not. So it can be used to represent the binary states of True and False. It can also be used to represent implication. For if a set (of the Dirac measure) can be said to exist, then we know that the elements of that set exist. But just because an element exist somewhere does not mean it exists in that set. So the set implies its elements but elements do not imply a set.

So the Dirac measure gets us from logic to math, but it does not yet get us to physics. We can get to physics, however, if we map the right logical equation to the right mathematical equation. But what is the right logical equation? What unequivocal truth can we say with absolute certainty about all the facts in the universe? One thing is for sure, all the facts that exist in the universe coexist in logical conjunction with each other. Even every point in space exists in conjunction with every other point in space. So if we use a different proposition for each individual point in space, we can construct a logical equation; each region of space can be defined as the conjunction of all the points in it.

Then since a conjunction of things logically implies an implication between them, the implication between all facts (or points) can be used to derive a mathematical equation for physics. If the Dirac measure is used for every implication, the wave equation of Quantum mechanics can be derived. The derivation is not difficult, though it might be a little tedious. See all the details at: logictophysics.com

[jreed]

Friend, you are certainly a persistent person. I did a search for quantum physics from logic, and found you, or someone else, promoting these same ideas on several physics blogs for about the past 10 years. If these theories haven't caught on yet, I don't think there's much to be gained by continually posting them.

[friend]

Friend, you are certainly a persistent person. I did a search for quantum physics from logic, and found you, or someone else, promoting these same ideas on several physics blogs for about the past 10 years. If these theories haven't caught on yet, I don't think there's much to be gained by continually posting them.

You realize, of course, that's no reason to reject or accept a new theory. To say, "I won't consider it because no one else has" can only come from a bandwagon mentality, someone not really interested in truth, someone only interested in community support. Or it may be that it is too much of a paradigm shift for professional peer review. It might be that this requires too much skill in the foundations of mathematics for physicists to consider. Or the implications may go too deep and be too far reaching for their comfort.

I'm not a PhD and I'm not affiliated with a university. So I can not get it published on the arXiv.org. Perhaps if I were rich I could pay a doctor to look at this theory. Or maybe by chance there are PhDs here who may wish to comment under a pseudoname.

But every now and then I make some progress that I get excited about, so I feel compelled to share it. That's what this forum is for, right? I'm so sorry you are not able to offer any relevant comments.