Physics from reason alone

Foundations of physics and/or philosophy of physics, and in particular, posts on unresolved or controversial issues

Re: Physics from reason alone

Postby jreed » Tue Jun 23, 2020 10:34 am

friend wrote:
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.


I have a PHD in physics, in theoretical quantum scattering. I suggest you put together a simple example of how your theory solves the quantum mechanics of the two slit experiment. Doing that would make it easier for physicists to understand. I would like to see an understandable interpretation of quantum mechanics. There are now many, but none that are truly believable. Feynman said "Nobody understands quantum mechanics.". I believe that is still true today.
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Re: Physics from reason alone

Postby friend » Wed Jun 24, 2020 6:14 pm

jreed wrote:I have a PHD in physics, in theoretical quantum scattering. I suggest you put together a simple example of how your theory solves the quantum mechanics of the two slit experiment. Doing that would make it easier for physicists to understand. I would like to see an understandable interpretation of quantum mechanics. There are now many, but none that are truly believable. Feynman said "Nobody understands quantum mechanics." I believe that is still true today.

I appreciate your interest, but I'm surprised you don't recognize what I'm trying to do. The fact that you are asking about the two slit experiment tells me you are looking for more basic motivations for my work. I find myself wondering in what terms you would like me to explain. So I have to ask where did I lose you? Were any of my recent posts helpful in regard to motivating my article? Have you even tried to read my article (at logictophysics.com/QMlogic.html)?

What I’m trying to do is show where quantum theory came from to begin with, why the universe is quantum mechanical. This is not an attempt to debunk modern theory; it is an attempt to justify it completely. It is an attempt to derive physics from the foundations of mathematical logic. If such is successful, then physics no longer depends on observation, but becomes a tautology, necessarily true from the start. This would have an effect on every philosophical discussion about math and physics. Gone would be every claim that physics is basically just curve fitting. It might even open the door to thinking that self-reference in math leads to consciousness in reality.

I can see why it would be difficult for PhDs in physics to join such a conversation. There really is no PhD in foundations of physics. They are not really trained in the foundations of math which is where this conversation leads.
So I will continue to ask questions in this forum hoping someone out there may have some insight.
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Re: Physics from reason alone

Postby jreed » Thu Jun 25, 2020 9:45 am

friend wrote:I appreciate your interest, but I'm surprised you don't recognize what I'm trying to do. The fact that you are asking about the two slit experiment tells me you are looking for more basic motivations for my work. I find myself wondering in what terms you would like me to explain. So I have to ask where did I lose you? Were any of my recent posts helpful in regard to motivating my article? Have you even tried to read my article (at logictophysics.com/QMlogic.html)?


Yes I read the PDF you generated. As I said before, there's a lot of Boolean algebra that doesn't seem to add much to the discussion. The real derivation of the path integral starts at equation [24], the representation of the product of two delta functions. That equation goes through a lot of curve fitting, as you like to call it, to get to the expression for the path integral, equation [30].

I don't think further comments by myself will add to this discussion. Good luck with your efforts.
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Re: Physics from reason alone

Postby friend » Thu Jun 25, 2020 8:34 pm

jreed wrote:Yes I read the PDF you generated. As I said before, there's a lot of Boolean algebra that doesn't seem to add much to the discussion. The real derivation of the path integral starts at equation [24], the representation of the product of two delta functions. That equation goes through a lot of curve fitting, as you like to call it, to get to the expression for the path integral, equation [30].

I don't think further comments by myself will add to this discussion. Good luck with your efforts.

But of course I can't start with equation [24] for no good reason. I think it would seem more odd if I were to just pull that equation out of the air and call it my starting point. So in order to avoid appearances of being arbitrary, I go through all that Boolean algebra. I thought an obvious starting point was that all the facts (or points in space) coexist in logical conjunction with each other. But perhaps it seems strange to use an abstract notion like conjunction, disjunction, and implication as secretly containing the math of physics.

Although I do see your point. There might be lots of different ways to get to equation [24], so why do I have to go through all those logical manipulations? However, the logic really shines when I start deriving the particles of the Standard Model, as shown at: http://logictophysics.com/StandardModel.html

Here, since a conjunction of points implies a conjunction of implications both way, and an implication gets mapped to a wavefunction, then there are two wavefunctions, one in each direction of time. This can be seen as the electron and the positron. Each iteration of this procedure seems to account for the number and charges of the other particles of the Standard Model. The first iteration gives electrons and positrons, the next iteration gives the weak particles, the next iteration give quarks, the next iteration gives gluons. This is utterly amazing; it cannot be a coincidence.
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Re: Physics from reason alone

Postby friend » Sat Jul 11, 2020 12:54 pm

It should not be surprising that the hypothetical of a logical implication should be used to construct the ultimate theory of physics. Every theory of physics is a hypothetical, given some circumstances as a premise, this implies that another set of circumstances will result as a consequence. And of course, you can always insert intermediate states where the intermediate state is the consequences of a prior starting circumstances. But then that intermediate state also serves as the premise for the next hypothetical that concludes in the end result. And if you insert more and more intermediate states, then the process of going from one state to the next serves to construct a trajectory or path from start to end. Notice also that a state can be labeled as both a premise and a conclusion. And it is only time that determines which hypothetical in the chain is active at any time. The function representing a hypothetical would be zero for all times other than the time it is active. But there is an active hypothetical for any time along that trajectory/path, and the next hypothetical function is active in a consecutive sequence along the path. This is what we should expect of any valid physical theory, and this is what I’ve constructed. See the article at: http://logictophysics.com/QMlogic.html

The only questions left are how to mathematically represent a hypothetical so that we can get some math out of the logic. And is this math unique? I’ve used the Dirac measure to convert a hypothetical implication to a function of math. It seems to be the simplest function possible; it’s equal to 1 if there is an element in a set and 0 otherwise. And it can represent an implication in that a set implies its elements, but an element does not imply a set.

But any sort of path can be constructed. One path might go through point 1 before point 2. But another path might go through point 2 before point 1. In the Dirac measure the set implies its element. In a path the prior point implies the next point as a consequence. So the set must somehow relate to a first point and the element to the next point. Yet the role of first and next can be reversed in a different path. So the question is how to get a set to represent what is otherwise considered to be an element. Then when the roles of premise and conclusion are reversed in the logic, the roles of set and element can also be reversed when needed. It is easy to represent an element as a single point in space. But can a set be uniquely labeled by a single point as well? If so, then the roles of premise and conclusion can be represented by set and element, which can then be represented by the first point and the next point in a path. And there is no problem when the roles are reversed in a different path, since a point can represent either a premise or a conclusion, a set or an element, a prior point or a next point.

I resolved this by considering that in the definition of a set in the Dirac measure, there is no limit on the size of a set. So I choose to shrink the size of a set down to the size of a point, or at least smaller than any point next to it that you might consider. Then any point you might pick can represent either a set or an element. In doing this the Dirac measure can be converted to the Kronecker delta function, which is equal to 1 when two points are equal and 0 if they are not equal. This allows me to map logical conjunction to multiplication and logical disjunction to addition and implication to the Kronecker delta itself.

However, this shrinking a set down to a near point brings up mathematical questions that perhaps some here are able to answer.

1) Is the assigning a set with the label of a point a use of the axiom of choice?

2) Does this use of the Dirac measure specify that the paths are continuous? If going from one point to the next requires the Dirac measure to be 1, which requires points to be equal or near equal, then does this mean that there must be an infinite number of Dirac measures, all infinitesimally close to each other?

3) Does this use of the Dirac measure shrinking down specify a manifold? It seems this procedure is the same as that described for the Hausdorff property which is required of a manifold.

4) How similar or different is the Dirac measure to the definition of completely regular spaces? Both go from 0 to 1 from a point to a set.

I'd appreciate any insight anyone would care to add. Thanks.
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Re: Physics from reason alone

Postby gill1109 » Wed Aug 12, 2020 6:59 am

friend wrote: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.

Friend: you don't *derive* the path integral. You just notice an analogy. You don't derive Born's law. You just say that conscious beings need to calculate probabilities! But that is nonsense. Unconcious computer programs are very good at guestimating probabilities by doing statistics. Conscious beings then have to point out that such predictions are unfair and even illegal. Conscious beings bring in issues of morality and of ethics and of aesthetics. The physical world is teeming with probability.

You also mention that a certain property *requires* Gaussian distributions because you haven't been able to think up anything else which would do the trick. Well, as a professional probabilist, I can think of lots of other things which could do the trick.

So I think you are seeing patterns, which you can see because of your own background in mathematics and physics, but you are not proving anything or deriving anything.

Which is not to say that I don't admire your research program. Keep it up!
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Re: Physics from reason alone

Postby friend » Wed Aug 12, 2020 4:05 pm

gill1109 wrote:You just say that conscious beings need to calculate probabilities! But that is nonsense. Unconscious computer programs are very good at guestimating probabilities by doing statistics. Conscious beings then have to point out that such predictions are unfair and even illegal. Conscious beings bring in issues of morality and of ethics and of aesthetics. The physical world is teeming with probability.


It certainly seems that conscious being (humans) are the only entities aware of probabilities. Apart from our intelligence, physical objects do not calculate the probabilities to determine their course. They simply interact or not with other objects. And the overall average direction of very many interactions may determine its course. Rocks and trees and bugs and frogs do not consider how likely it is things will happen. They just automatically respond to simulation. No, it seems the only use probabilities can have (the knowledge of likelihood) is to confirm or negate a theory some intelligence may have. Computers can be programed to calculate probabilities and take action based on that. But that's just an extension of human knowledge. So I take probabilities as metaphysical. Probabilities of themselves are not physical; they are about physical things. And only intelligence is concerned with metaphysics.

gill1109 wrote:You also mention that a certain property *requires* Gaussian distributions because you haven't been able to think up anything else which would do the trick. Well, as a professional probabilist, I can think of lots of other things which could do the trick.

Yes, I'd very much like to see other forms of the Chapman-Kolmogorov equation, eq[24] in my article, besides the exponential form.

gill1109 wrote:So I think you are seeing patterns, which you can see because of your own background in mathematics and physics, but you are not proving anything or deriving anything.

Perhaps you are referring to the fact that I have not proven the uniqueness of my derivation. I take notice of this "iterative property" common in the logic and in the Dirac delta function and in the exponential Gaussian. But I don't claim that the Dirac delta is a unique representation of the logic or that the exponential Gaussian is a unique representation of the Dirac delta function. So my derivation is not unique and therefore not a proof. Is this your position?

Perhaps if I introduce as a premise that the Dirac delta function is a representation of the logic, and introduce as a premise that the exponential Gaussian is a representation of the Dirac delta, then have I constructed a "proof"? As I recall, all that is required of a proof is that the premises be true that requires the conclusion to be true.
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Re: Physics from reason alone

Postby friend » Fri Aug 14, 2020 6:28 am

gill1109 wrote:Friend:... You don't derive Born's law...


You're right, though. I don't actually derive the Born rule. I just show how it fits naturally into my framework. The Born rule does not tell us what the probability of an event is. It tells us what the probability of an event is given a particular cause. So you need there to be a conjunction of both the setup and the possible results.

What I attempt to show is that the wave function is a representation of material implication. Given a cause the wave function tells us the possible outcomes. The complex conjugate of the wave function represents the reverse implication. Given a particular outcome it tells us what the possible causes are. When the cause is in conjunction with the outcome, this implies that the implication is in conjunction with its reverse implication. Since conjunction is mapped to multiplication (as I show), the wave function is multiplied by its conjugate, which gives us a probability density.

How did Born come up with the Born rule? Was it a derivation or a guess?
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Re: Physics from reason alone

Postby friend » Fri Aug 14, 2020 4:27 pm

friend wrote:You're right, though. I don't actually derive the Born rule. I just show how it fits naturally into my framework.


Keep in mind I did not derive numbers from logic either. I simply use the validity of math as another premise in the process of my derivation.
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Re: Physics from reason alone

Postby gill1109 » Sun Aug 16, 2020 9:25 am

friend wrote:
gill1109 wrote:Friend:... You don't derive Born's law...


You're right, though. I don't actually derive the Born rule. I just show how it fits naturally into my framework. The Born rule does not tell us what the probability of an event is. It tells us what the probability of an event is given a particular cause. So you need there to be a conjunction of both the setup and the possible results.

What I attempt to show is that the wave function is a representation of material implication. Given a cause the wave function tells us the possible outcomes. The complex conjugate of the wave function represents the reverse implication. Given a particular outcome it tells us what the possible causes are. When the cause is in conjunction with the outcome, this implies that the implication is in conjunction with its reverse implication. Since conjunction is mapped to multiplication (as I show), the wave function is multiplied by its conjugate, which gives us a probability density.

How did Born come up with the Born rule? Was it a derivation or a guess?

Born *guessed* the Born rule. In fact he wrote it down as a footnote which he added while correcting the proofs of a big paper on quantum mechanics. The big guys had already come up with wave mechanics and matrix mechanics but nobody had explained how the formalism was connected to laboratory measurements. Sure, they derived expressions which perhaps should represent ensemble averages of important dynamical variables. But there were no probabilities or probability distributions or measurements. In fact 30 years later Schrödinger wrote that no one should imagine that the theory applies to a single particle. It was, to him, as ludicrous an idea as the idea of recreating a living Tyranosaurus Rex. (This was some time before Jurassic Park). He also wrote that he found it all a terrible theory and he wished he had never had anything to do with it.
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Re: Physics from reason alone

Postby friend » Sun Sep 27, 2020 10:50 am

Perhaps I've not emphasized this strongly enough. So I'd like to do so here. Modern physics does not say where the subatomic particles come from or why they obey the rules of quantum mechanics. But from the framework I've developed, it can be seen that the particles are perfectly logical. It's amazing how simple it is. The full disclosure is at: logictophysics.com/StandardModel.html.


1st Iteration: electrons, positrons

Spacetime consists of infinite many points, all coexisting in logical conjunction with each other. And a conjunction implies conjunction of material implications, as shown in the following expression. The website links to a truth-table calculator that proves this relation.



But the relation of subsets, , can be used to represent material implication. If exists, then also exist, but the existence of does not guarantee the existence of . The relationship of set inclusion can be represented in math by the Dirac measure, , which equals 1 if , and is 0 otherwise. Here, math enters the picture. And then if we let these sets shrink down to the size of points, then implication can be represented by the Kronecker delta, , which is equal to 1 if and is 0 if not, and where and are numbers given to each point in space. In the continuum, the Kronecker delta becomes the Dirac delta function, .

If we represent the Dirac delta function with a Gaussian exponential, we get:



If we let the variance be:

,

we get the Dirac delta in this form:

.

And this is equivalent to the transition amplitude of a particle:

,

where the antiparticle would be the complex conjugate of this.

We see from this that if a material implication, , can be represented as a transition amplitude of a particle, then the reverse implication, , would reverse the time coordinates and create the complex conjugate. So it would be represented by the antiparticle.

Graphically, a positron can be represented as an arrow between points in space. (Italics are used to indicate my interpretation of my framework.) The direction of the arrow indicates which point implies the other, as shown below.

Image

The electron would have the arrow in the opposite direction.

Image


2nd Iteration: W, Z bosons

But now this entire procedure can be iterated. The first iteration above comes from the expression,

.

The second iteration is then,



A second iteration particle can be graphically represented as shown below.

Image which is the same as Image

This graphic can represent the term, . But we don't know whether is an electron or a positron. Likewise we don't know whether is an electron or a positron. Thus the notation . And we also have a forward implication term and a reverse implication term.

So the forward implication, , represents 4 possibilities. It can be either , , , or . The reverse implication simply repeats these possibilities.

Notice that has a positive charge of positrons, has a negative charge of electrons, and both and have a zero electric charge. The question is whether and are distinct particles or are they the same. The space and time differences are determined in the and . But the implication between and is independent of space and time. So there is no distinction noticeable in spacetime between or ; they are indistinguishable.

So we have three particles in the 2nd iteration. The , representing , The , representing , and the , representing or . These are graphically shown below.

Image , Image , and Image .

So far, the particles derived here appear to have twice the electric charge that their Standard Model correlations have. But if we divide by the number of distinct absolute values, |+/-2| and |0|, or in this case divide by 2, then we get the expected +1, -1, and 0 expected electric charge for the W and Z bosons. This trick works for the quarks as well.

The particles of the Standard Model are considered fundamental and do not have any substructure. But here Weak-bosons and quark are constructed of different elementary particles. This may account for the ways in which the subatomic particles interact and decay. It's not as though you can break them up arbitrarily, the higher iteration interconnections will need to be maintained and accounted for in some way. More on this at my website.


3nd Iteration: the quarks

If we iterate again we get,





.

This is represented graphically below.

Image

We can simplify this as shown next.

Image

And we can simplify further to,

Image

And as before, we can count how many different quarks there are by seeing how many unique ways one can be connected to another. We have what appears to be the Up quark, constructed as shown below. It appears to have the charge of 2 positrons.

Image

Then we have the Anti-Up quark with the charge of 2 electrons, shown below.

Image

We have the Down quark with the charge of 1 electron, as shown below.

Image

And we have the Anti-Down quark with the charge of 1 positron, as shown below.

Image

This accounts for the first mass generation quarks. However, there are a few others. These have 0 electric charge, shown below.

Image

I label it a ζ, which is the Greek letter sigma used at the end of words. I only use this symbol because it somewhat looks like a fancy Z for zero charge. These particles are beyond the Standard Model. However, some have suggested that perhaps dark matter could consist of quarks with 0 electric charge. (ref available at website)

So the list of quarks obtained from this framework are the , , , , and the , with charges +2, − 2, +1, −1, and 0, respectively. If I use the trick from the previous section, I should divide these charges by the number of different absolute values. There are 3 of them, |0|, |±1|, |±2|. So if I divide these charges by 3, I get +2/3, −2/3, +1/3, −1/3, and 0. And this matches the electric charge for the quarks of the Standard Model.

Yet quarks are also supposed to have a color charge of red, green, blue, or anti-red, anti-green, anti-blue. Can we find 3 configurations and their reverse hiding in each quark of this framework? It turns out that we can. For there are different ways to connect the electrons and positrons that make up a quark of a given charge. For example, an Anti-Up quark can be constructed in the following ways using the same electrons.

Image , Image , Image

This shows how the same electrons can be connected in different ways to form the same quark. It would be arbitrary as to which of these configurations is assigned to be the red, green, or blue color charge. The anti-color charge would depend on whether there is a head or tail of an arrow connecting it to another quark. The particles that bind or connect one quark to another are gluons.


4nd Iteration: the gluons

Following the same pattern, the 4th iteration can be depicted as shown below. (I will spare you the logic for this.)

Image

We can arbitrarily label this as a red-antired gluon. It's red on the left side because (arbitrarily) it has a tail on the gluon connection. The right side is anti-red because it has a head of the gluon connection. And there is other connections possible. Below is a green-antired gluon, and below that, a blue-antired gluon.

Image

Image

So there are 3X3=9 possible color-anticolor combinations of gluons. But three of these leave the color charge of a quark unchanged; the red-antired gluon, for example, would leave the color of a red quark unchanged. A red quark would annihilate with the antired color charge and leave the red color charge as before. All of this is specified by the Standard Model of particle physics.


In Summary

What I've shown is that the number of particles and the various charges of the Standard Model of particle physics can be accounted for on purely logical considerations. No complicated mathematics is necessary. A simple iteration of the conjunction-to-implication principle is all that's required.

Here I've only addressed the first generation of particles. But on my website I detail how the other generations of particles can be obtained. I also address the construction of photons and neutrinos. I also begin to address interactions and decays. There I show how the math can be iterated as well. For those interested, the website is at:
logictophysics.com/StandardModel.html.
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Re: Physics from reason alone

Postby gill1109 » Mon Sep 28, 2020 1:02 am

Nice! The standard model is derived by playing with symmetries of solutions of fancy systems of differential equations. The Dirac equations. So it is plausible that some of its features come from playing with symmetries of much more simple objects. I hypothesize that that is what you are doing. I hope the experts will take notice.
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Re: Physics from reason alone

Postby friend » Tue Oct 06, 2020 3:28 pm

gill1109 wrote:Nice! The standard model is derived by playing with symmetries of solutions of fancy systems of differential equations. The Dirac equations. So it is plausible that some of its features come from playing with symmetries of much more simple objects. I hypothesize that that is what you are doing. I hope the experts will take notice.


As far as the Standard Model symmetries are involved, I believe I found some parts and pieces that might help. I go through the math here rather quickly. So if I made a mistake, please correct me.

The Standard Model has the symmetry of U(1)XSU(2)XSU(3). The U(1) symmetry describes the electromagnetic interaction. The SU(2) symmetry describes the Isospin symmetry of the Weak Interaction. And the SU(3) symmetry describes the Color symmetry of the Strong Interaction. See page 2 of https://uw.physics.wisc.edu/~himpsel/449group.pdf.

However, U(1) is described by the the complex numbers. And SU(2) is described by the quaternions. And SU(3) is described by octonions. See these references. If you know of any better references, let me know.
https://en.wikipedia.org/wiki/Symmetry_in_quantum_mechanics#U(1),
https://en.wikipedia.org/wiki/Representation_theory_of_SU(2),
https://golem.ph.utexas.edu/category/2020/07/octonions_and_the_standard_mod.html.


hypercomplex numbers

The quaterions and octonions are hypercomplex numbers that can be derived from the complex numbers using the Cayley-Dickson construction. See https://math.ucr.edu/home/baez/octonions/node5.html. This construction is achieved by an iteration process that's similar to the iteration process used in my efforts.

Very briefly, the hypercomplex numbers can be achieved by re-inserting complex numbers into the definition of a complex number that exist in a higher dimension. So, start with a complex number in general such as , where .

Then to create a quaternion number let, and . And we insert these into , where is another complex number different than . This gives us,

, or,

or,

,

where , and , and where , , and .

Notice that since , for example, the quaternions no longer commute under multiplication.

The quaternion also have a matrix representation, with

Image, Image, Image, Image. Seehttps://mathworld.wolfram.com/Quaternion.html.

These are called the Pauli matrices used in QFT for the Weak interaction. And they have the same multiplication properties as . Notice that these matrices also have the complex numbers inside them.


And then to create the octonions, we can insert quaternion numbers into the definition of a complex number. So let and be the quaternions: , and let . And insert these into the complex number , where is a different complex number other than . This gives us,

, or

, or

,

where . The multiplication table for the octonions gets a little more complicated and can be seen here with a change of notation: https://en.wikipedia.org/wiki/Octonion. The translation to the notation used here is: , , , , , , , .

But notice now, for example, in the notation used here that . So the octonions no longer have the associative property of multiplication.

And the octonions also have a matrix representation in the form of the Gell-mann matrices used in QFT for the Strong interaction, see page 24 of http://people.oregonstate.edu/~drayt/MTH679/handouts/notes06.pdf, and see page 3 of https://arxiv.org/pdf/1907.12520.pdf. See also, http://benasque.org/2011qfext/talks_contr/2034_Bisht.pdf. Notice that the Gell-mann matrices for octonions seem to contain the Pauli matrices for quaternions.


I'm sure you are aware that, . This is because can be expanded into a power series, and any power of a complex number is also a complex number. So likewise, I take it that , and . And since is unitary, I take it that and are likewise unitary.

So we can express this iterative process in terms of exponents as,

,

,

.


SU(2) Weak bosons

And this all fits nicely into the iteration process I use in my thesis. See my previous post in this thread for more details. But in summary of my framework, I start with the principle that a conjunction implies both a forward and reverse implication,

.

I describe each point in space with individual coordinates. And I then mathematize logical implication by going through set theory, then using the Dirac measure to get the Kronecker delta, and then getting the Dirac delta function from that. I use the Gaussian exponential to represent the Dirac delta. But the assignment of coordinates to each point is arbitrary. And one implication should not be considered more important or weighted any differently than another. So in order to ensure no preferential treatment of one implication over another, and to maintain coordinate independence, I assigned the exponent of the Gaussian representation of each implication to be a complex number. That way the absolute value of each implication is the same; the only difference is a phase. All of this enables an implication to be mapped to a transition amplitude of a particle.

.

And the reverse implication is the complex conjugate of this and represents the antiparticle. There are only two possible conjugates in the complex numbers; so they would account for the electron and positron. And we see that this exponent to a complex number gives us the U(1) symmetry of the electromagnetic interaction.

Then to iterating we apply the conjunction to implications principle again to get,



All I did was insert and implication into each proposition. In the math, since the transition amplitude is a function of and , this means I would iterate by replacing these by transition amplitudes themselves. Then I will have amplitudes inside amplitudes, exponents inside exponents. So I make the following substitutions:

, and

.

This gives us,

(If you cannot see all of the math in this picture, use ctrl-mouse-wheel to decrease the size of text.)
Image.

This is of the form , which makes this a quaternion. And this gives us the SU(2) symmetry of the Weak interaction.

There are four possibilities with the equation above. What is shown is a positron connected to a positron as indicated by the plus sign in the (s,r) exponent and the plus sign in the (u,t) exponent. So this would represent a boson. But there are three more possibilities. We could have an electron with a minus sign in the (s,r) exponent and a positron with a plus sign in the (u,t) exponent. Or we could have a positron with a plus sign in the (s,r) exponent and an electron with a minus in the (u,t) exponent. But since the difference between these exponents is squared (the purple 2), there is no mathematical difference. They are the same particle. They have zero electrical charge, since the electron charge cancels with the positron charge. So this would be the boson. And lastly, we could have an electron with a minus in the (s,r) exponent and an electron with a minus in the (u,t) exponent. This is a different particle than the other two and would be the boson.

The next question is whether it makes any difference if the j is conjugated all by itself. In other words, is the forward implication the same or different in this second iteration. I assume that if we were to derive a real value from a quaternion (for example, an expectation value), then the quaternion conjugate would reverse the sign of the j and then be multiplied by the original. This would cancel the quaternion out of the result. So the expectation value would be the same for both forward and reverse implication in this iteration. So in essence the forward particle is identical to the reverse particle in the real world.

Before moving on, let's employ some abbreviations for simplicity. With the A's and B's and the W defined appropriately, the previous equation can be expressed as,

Image.

This allows us to see the complex numbers without the clutter of unneeded math.

SU(3) quarks

In the next iteration, implications of implications are substituted for each proposition in an implication. The conjunction rule then give us,




.

In the math, this means I would substitute two instances of the previous math equation into the definition of a transition amplitude. I abbreviate with the added C and Q to get,

(If you cannot see all of the math in this picture, use ctrl-mouse-wheel to decrease the size of text.)
Image.

We have an exponent inside an exponent inside an exponent. This is of the form, , and so it is an octonion, which give us the SU(3) symmetry of the Strong interaction.

And now there are five unique, possible configuration since because of the square (blue 2) a (+W1,-W2) is the same as a (-W1,+W2). These are (+W1,+W2), (+W1,0W2), (-W1,-W2), (-W1,0W2), (+W1,-W2)=(-W1,+W2)=(0W1,0W2), and these correspond to the first mass generation quarks. The zero quark (the last 3 in the list), is not part of the Standard Model and has yet to be observed; perhaps it is dark matter.

So let's take a moment to consider what happens when you have exponentials inside exponentials. In the first iteration we have wavefunctions in the form, . This is just a sinusoidal waveform; it propagates forever as does the EM field. However, in the second iteration, we have wavefunctions in the form, . When is small this would propagate like a normal wavefunction. But as gets large, the wavefunction will no longer propagate as usual; it will break apart. Since this is meant to represent the propagation of the Weak bosons, this might be why these bosons do not propagate very far before breaking up. And in the third iteration, we have wavefunctions in the form, . These don't propagate very well at all before breaking up. I have to wonder if they break up by becoming other quarks.

Before moving on, it should be noted that the real, complex, quaternion, and octonion numbers each form a normed division algebra. This means that multiplication and division have unique values. But as we iterate the Cayley-Dickson construction, we lose multiplication properties. I've already shown that the quaternions no longer commute under multiplication, thus neither do the octonions. The octonions lose the associative property of multiplication. And if we were to iterate again we would get the sedenions, but these do not form a division algebra since multiplication can form zero-divisors. This means we lose the property of multiplication altogether, which means we can no longer represent logical conjunction with multiplication. So my formalism stops with the octonions.

gluons

But there might be a way of connecting quarks without iterating to sedenions. If we were to iterated again, we would get,

,

where and is one of the many bases of the hypercomplex, sedenion numbers. But note that, . So the above becomes,

, which is equal to,

.

Here, the are for the amplitudes of the quarks that have exponentials inside exponentials inside an exponential, with leading factors included.

Now, if , then there would be no and no sedenions to consider. The connection between quarks, the gluons, requires that,

.

Or, the two quarks in a gluon must differ by a plus or minus factor of , then quarks can interact. Or if the term were to be zero, then there would be no quark terms connected to the sedenion term, .This would be yet another type of gluon to connect quarks. So there are three possible values that a gluon can have. Could this possibly account for the red, green, blue color charge of a gluon? This sedenion exercise only supplies a restriction in the octonions in order to make a connection. So the gluons belong to the octonion SU(3) symmetry. Here, there is no counting how many gluons have various electric charge. So these gluons do not have an electric charge.

What I think I've shown is that the normed division algebras of real, complex, quaternion, and octonion numbers can be used to explain the particles of the Standard Model and why they have the symmetries they have. Since any further iterations give zero divisors in the multiplication, the formalism stops with octonions. As I will try to show in another post, this may explain the reason that there are only 3 mass generations as well.

Feel free to comment as you please on substance or style. Thanks.
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Re: Physics from reason alone

Postby gill1109 » Wed Oct 07, 2020 8:08 am

If you could get someone at a university or with a PhD interested, you could write a paper together and put it on the arXiv. If you can find a couple of “establishment” people who will support you, then you can get on arXiv without an academic affiliation. There are fora like this, and there are repositories like viXra. So everything is not hopeless.
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Re: Physics from reason alone

Postby friend » Thu Oct 08, 2020 9:35 am

gill1109 wrote:If you could get someone at a university or with a PhD interested, you could write a paper together and put it on the arXiv. If you can find a couple of “establishment” people who will support you, then you can get on arXiv without an academic affiliation. There are fora like this, and there are repositories like viXra. So everything is not hopeless.


Yes, I'm sure I need an education in the requirements to get on the arXiv. As I understand it, the arXiv is a place for preprints before publication in journals. It seems to be there in order for authors to get some preliminary review in case they made some mistakes. I think it is also there to record your efforts so that no one else can claim publication before you. So it is there to prevent plagiarism.

Although, I'm not aware if it's possible to publish on the arXiv someone else's work as long as they have permission to publish from that author. What if I were to include on my website an explicit statement giving anyone permission to publish on the arXiv, could any qualified person do so as long as they give appropriate attribution? Thanks.
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Re: Physics from reason alone

Postby Heinera » Thu Oct 08, 2020 12:47 pm

You need someone with endorsement rights for arXiv to endorse you for publication there. Google "arxiv endorsement" to find more. There are many endorsers, but most of them keep a rather strict quality requirement since they otherwise risk loosing their endorsement rights.

If the paper is spectacularly good, there is really no need to publish elsewhere since arXiv will suffice, especially in the field of mathematics. For instance, Grigori Perelman put three papers on arXiv for which he was promptly awarded the Fields medal, without trying to submit them for publication in a journal.

He declined the medal.
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Re: Physics from reason alone

Postby friend » Thu Oct 08, 2020 3:13 pm

Heinera wrote:You need someone with endorsement rights for arXiv to endorse you for publication there. Google "arxiv endorsement" to find more. There are many endorsers, but most of them keep a rather strict quality requirement since they otherwise risk loosing their endorsement rights.


It seems this endorsement ability is used mostly for post Dr's or at least those who are in a PhD program.

A couple of roadblocks to that: I don't even have a masters degree. Although I have had some graduate courses in mathematical physics where I learned to manipulate exponentials. Has anyone ever endorsed an undergrad?

I think I'm in a territory where no one has gone before. And you're supposed to get an endorser who has some experience in what you're writing about. But since I'm deriving things from scratch, and only scratch, some may suggest that it is not even physics.

Besides, I prefer to keep my anonymity, at least until I get endorsements.
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Re: Physics from reason alone

Postby gill1109 » Fri Oct 09, 2020 8:54 am

friend wrote:
Heinera wrote:You need someone with endorsement rights for arXiv to endorse you for publication there. Google "arxiv endorsement" to find more. There are many endorsers, but most of them keep a rather strict quality requirement since they otherwise risk loosing their endorsement rights.


It seems this endorsement ability is used mostly for post Dr's or at least those who are in a PhD program.

A couple of roadblocks to that: I don't even have a masters degree. Although I have had some graduate courses in mathematical physics where I learned to manipulate exponentials. Has anyone ever endorsed an undergrad?

I think I'm in a territory where no one has gone before. And you're supposed to get an endorser who has some experience in what you're writing about. But since I'm deriving things from scratch, and only scratch, some may suggest that it is not even physics.

Besides, I prefer to keep my anonymity, at least until I get endorsements.

As long as you are anonymous, nobody can endorse you. I could endorse you on some sections of arXiv if I knew you better. You don’t need formal qualifications. You need to be producing interesting work and following academic standards such that your papers would have a good chance of being published in decent journals
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Re: Physics from reason alone

Postby friend » Fri Oct 09, 2020 2:22 pm

As long as you are anonymous, nobody can endorse you. I could endorse you on some sections of arXiv if I knew you better. You don’t need formal qualifications. You need to be producing interesting work and following academic standards such that your papers would have a good chance of being published in decent journals


I suppose I don't mind a few professionals having my personal information. But I have to wonder how much of that do I have to make public in any paper on the arXiv. Is a first name and obscure email address sufficient? After all, I would not be asking for endorsement of first papers, and then afterward I can publish without endorsement. I don't think that is appropriate for an amateur to have in any case. I my case I would prefer to get endorsement (thus some sort of first order review) for anything I would submit. Perhaps an endorser could publish my material in his own name with explicit acknowledgement of the original author.
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Re: Physics from reason alone

Postby friend » Fri Oct 09, 2020 4:20 pm

If the whole purpose of my framework is to justify physics as we have it today, then I will have to reproduce the QFT that we have. Presently we have various fields expressed in terms of raising and lowering operators. So now I'm going after the raising and lowering operators. And I could use a little help.

The transition amplitude for a particle to go from x to x' can be written as,



The transition amplitude for this particle to have momentum at position can be found by taking the Fourier transform of this to get,

.

The details of the transform are given at: http://logictophysics.com/themath.html#Momentum. Please check this. For clarity, the exponent of the last equation is,



since , this can be written, . If we let and , then the first term of the above changes to give,

.

If we let , where is the frequency, then the above becomes,

.

Although I think I'm missing a factor of 1/2 in the first term. Assuming I find it, the about is the energy of a harmonic oscillator. And since it is in the exponent of an amplitude that gets integrated over all possibilities, it is the Hamiltonian operator of a harmonic oscillator. Then the raising and lowering operators can be derived from this as usual,

,

and



See for example, page 3 of https://faculty.washington.edu/seattle/physics227/reading/reading-22-23.pdf.
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