A Simple Geometric Proof With Profound Consequences

[Doctordick]

Or maybe three dimensional form is just "enough" for survival, and more would be a wasted effort. But I can't analytically prove any of this, it's just thoughts I'm having.

Well, it is quite clear that a single rotating simple polygon in an n dimensional space would display all the relationships conceivable in a three dimensional space sort of says that, if we could comprehend the phenomena possible in that projection, we could understand everything. It is clearly just something beyond our comprehension. We just don't have the mental prowess to use the picture: i.e., we have to fall back onto mathematics.

 

Well if you think it might have any value, you could still just lay the math down for easy reference of any educated physicist who might stumble across this post in the near or distant future.

Actually the procedure is quite simple for anyone with a decent education in quantum mechanics. The procedure for laying out those solutions is first year graduate study common to any class in angular momentum. But I will comment that a lot of the graduate students I knew didn't really understand what they were doing. It is not a trivial exercise.

 

What do "l" and "m" stand for here?

“l” is the angular momentum quantum number and “m” is the projection on a specific axis. The position of an object in a three dimensional universe is described by three arguments (x,y and z in rectilinear coordinates or “r”, theta and phi in spherical coordinates) only the angular coordinates end up being quantized. The two can be quantized at the same time.

 

Why "n+1 pieces of data"?

A couple of paragraphs earlier, I held “r” out as quite different from the angular variables yielding “n” as the number of angular variables to be analyzed.

 

You are using a language that I am not very familiar with, but I believe I understand what you are saying. That your result implies, that the 3 dimensional representation of information that we are using, has one additional "momentum quantized dimension" worth of information embedded to each element. And as I well know, you are using the concept of tau-dimension with infinite uncertainty to position to represent that information, and that it just so equals exactly to the modern physics definition of mass if you make the appropriate approximations to the solutions of the fundamental equation.

Also note that in the n (or n+1) dimensional system, tau is no longer necessary as everything in the universe is represented by one point and the idea of two points being the same vanishes.

 

It's quite interesting, I really hope there are more people than just me who understand what you are saying there.

That would be nice but I suspect it is very rare for truly thoughtful people to read these forums; the overwhelming volume of thoughtless posts just blocks interest in reasonable discussion. You are a very unusual find in that you are willing to put up with the baloney. On the other hand it is entirely possible that there are actually some thoughtful people reading this stuff.

 

Indeed. And if I'm capable of understanding this thing, I'm sure there are plenty more out there.

Oh, I am sure there are some intelligent people out there but I think they have better things to do with their life than read these forums. There are aspects of the standard forum structures which essentially bury intelligent conversation. I have thought about that quite a little and am often tempted to make some comments about it to Tormod.

 

I have a strong feeling that it would improve things considerably if some forums were controlled by a committed monitor. Someone who had the authority to edit and/or move off subject and idiotic replies to alternate threads. Essentially leave the forum with some seriously controlled threads which anyone could read but which contained only coherent comments. Sort of analogous to educational class rooms with controlled participation.

 

I haven't made any such suggestions because it reeks of authoritarianism which I am violently against; however, something analogous to Socrates' walks in the garden (his academy) with limited participation seems very reasonable. Something anyone could read but only a handle-able few could participate. The rest could talk amongst themselves outside of “class”. If I were allowed to clean them up a bit, my threads could almost satisfy that requirement now.

 

If you really want me to show you how to solve that hyper-spherical representation of my fundamental equation, I could go through it (and I think you could follow it) but it would be a lot of work for both of us.

 

Have fun -- Dick

[AnssiH]

A couple of paragraphs earlier, I held “r” out as quite different from the angular variables yielding “n” as the number of angular variables to be analyzed.

 

Ah right that's what you were referring to.

 

That would be nice but I suspect it is very rare for truly thoughtful people to read these forums; the overwhelming volume of thoughtless posts just blocks interest in reasonable discussion. You are a very unusual find in that you are willing to put up with the baloney. On the other hand it is entirely possible that there are actually some thoughtful people reading this stuff.

 

Well yeah maybe one day in the future. It will stay around for quite some time for future reference.

 

I haven't made any such suggestions because it reeks of authoritarianism which I am violently against; however, something analogous to Socrates' walks in the garden (his academy) with limited participation seems very reasonable. Something anyone could read but only a handle-able few could participate. The rest could talk amongst themselves outside of “class”. If I were allowed to clean them up a bit, my threads could almost satisfy that requirement now.

 

I guess the systems where users vote junk posts (to be hidden by default) and promote good posts (to be highlighted) are fairly close to what you are thinking, probably the only addition needed would be that the vote of the OP would weigh more than the rest.

 

Anyway;

 

If you really want me to show you how to solve that hyper-spherical representation of my fundamental equation, I could go through it (and I think you could follow it) but it would be a lot of work for both of us.

 

Well, I would probably learn something, but certainly it would take some time since it's not a subject I'm very familiar with. I don't have a good understanding of that post #50 either, I just skimmed it through to get the gist of it. If you don't mind laying it down, we could see how far we get if I just start asking questions again.

 

On the other hand, if you have ideas as to how to improve the presentation on the universal explanation, that might be time well spent as well.

 

-Anssi

[Doctordick]

Well yeah maybe one day in the future. It will stay around for quite some time for future reference.

Yeah, but I won't get to see it.

 

I guess the systems where users vote junk posts (to be hidden by default) and promote good posts (to be highlighted) are fairly close to what you are thinking, probably the only addition needed would be that the vote of the OP would weigh more than the rest.

Well, I don't really trust a lot of “users”. I think the author of the opening post of a thread should have the power move what he considered troll posts to a subsidiary category which anyone could chose to ignore. If they don't want to ignore them, they could simply not chose to ignore them. If a sufficient number of users complain about the main thread, the monitors should be able to lock the main thread (and perhaps, leave the subsidiary thread open). That doesn't close down discussion in any way not chosen by either the readers or the monitors. Seems fair to me and it shouldn't be difficult to implement. :shrug:

 

Well, I would probably learn something, but certainly it would take some time since it's not a subject I'm very familiar with. I don't have a good understanding of that post #50 either, I just skimmed it through to get the gist of it. If you don't mind laying it down, we could see how far we get if I just start asking questions again.

I will lay it out in a new thread I'll call “A Closed Solution to the Universe”. It's really not difficult, just long and involved algebra with a little first year calculus. I will try to check my work carefully so don't expect it to be fast. ;)

 

On the other hand, if you have ideas as to how to improve the presentation on the universal explanation, that might be time well spent as well.

I have no ideas on how to improve the presentation because, to improve the presentation, you have to understand the reader and I have utterly no comprehension of what is going on in their minds when they read my stuff.

 

Have fun -- Dick

[Qfwfq]

Clearly, since we have only one knowable point and our fundamental equation is valid only in the center of mass system, the probability function which represents our event must be symmetric about the origin (or we can move the origin to make the statement true). The unknowable data can be viewable as forming a potential well which constrains our point to the origin: by simple symmetry it cannot depend on any angles. The interesting thing about this model is that the radial function, the only part where any variation is possible, is totally unimportant. Clearly, any solution for the entire universe must be dimensionally scalable and we only have one linear dimension: i.e., "r". In this view, the fundamental equation of the universe (seen as a point in an n+1 dimensional sphere, n angles and one radius) becomes

 

[math]

\left\{\vec{\alpha}\cdot\vec{\nabla}+\beta g®\right\}\vec{\Psi}=k\frac{\partial}{\partial t}\vec{\Psi}=ikm\vec{\Psi}

[/math]

 

where we have explicitly inserted conservation of energy. Consistent with previous practice, we may use the implied operator identity [math]\vec{\alpha}\cdot\vec{\nabla}+\beta g®=ikm[/math] to generate the n-dimensional Laplacian equation

 

 

[math]

\left\{\nabla^2+2g^2®\right\}\vec{\Psi}=-2k^2m^2\vec{\Psi}=-K\vec{\Psi}

[/math]

 

Note the two arises because of the fact that [math]\alpha^2=\frac{1}{2}[/math].

 

The curious thing about the equation above is that the angular part, the only significant part, admits of solution in closed form.

So, you choose a representation in which the universe is like a hydrogen atom in many, many dimensions, with some pure radial dependence of the potential. A cute idea. Although I wasn't 100% sure of the equivalence (with a purely radial potential) before I thought more in detail about it, I was assuming you had ascertained it very carefully over the years. I was only wondering what great new Truth you intend to draw from it but, when I did think more carefully about the radial potential, I only became much less certain.

 

At that point I figured out a counterexample and of course one is sufficient. In the traditional worldview of [imath]n[/imath] particles, even just three are sufficient and even with the familiar old Coulomb type potential, especially if we allow two opposite signs of charge. To enhance things, place three points along a stright line, with the one charge in between the two of like sign. Start with it being much nearer to one than the other, then consider a new configuration in which it is yet much nearer and the one at the other end is moved so the single scalar [imath]r[/imath] remains unchanged. This can be done with the sum of potentials differing from the previous configuration, even handsomely, despite the same sum of distances squared. It can't really be a potential then, can it?

 

Then, as I chose what to quote, reading the above part carefully I realized that it would be highly paradoxical anywise...

[Doctordick]

At that point I figured out a counterexample and of course one is sufficient. In the traditional worldview of [imath]n[/imath] particles, even just three are sufficient and even with the familiar old Coulomb type potential, especially if we allow two opposite signs of charge. To enhance things, place three points along a stright line, with the one charge in between the two of like sign. Start with it being much nearer to one than the other, then consider a new configuration in which it is yet much nearer and the one at the other end is moved so the single scalar [imath]r[/imath] remains unchanged.

:huh:

I have utterly no idea as to what you are talking about here. Are you discussing three points in a one dimensional universe (which would correspond to one point in a three dimensional universe)? If that is the case, where does that Coulomb type potential come from? (That is, if there are no other points to consider, there are no hypothetical bosons to implement the supposed potential.) I am only talking about the mathematical representation of the relevant information and have no mental picture of what is being displayed, merely the fact that such a mathematical transformation of the underlying information is possible.

 

Have fun -- Dick

[AnssiH]

So, you choose a representation in which the universe is like a hydrogen atom in many, many dimensions, with some pure radial dependence of the potential. A cute idea. Although I wasn't 100% sure of the equivalence (with a purely radial potential) before I thought more in detail about it, I was assuming you had ascertained it very carefully over the years. I was only wondering what great new Truth you intend to draw from it but, when I did think more carefully about the radial potential, I only became much less certain.

 

At that point I figured out a counterexample and of course one is sufficient. In the traditional worldview of [imath]n[/imath] particles, even just three are sufficient and even with the familiar old Coulomb type potential, especially if we allow two opposite signs of charge. To enhance things, place three points along a stright line, with the one charge in between the two of like sign. Start with it being much nearer to one than the other, then consider a new configuration in which it is yet much nearer and the one at the other end is moved so the single scalar [imath]r[/imath] remains unchanged. This can be done with the sum of potentials differing from the previous configuration, even handsomely, despite the same sum of distances squared. It can't really be a potential then, can it?

 

Then, as I chose what to quote, reading the above part carefully I realized that it would be highly paradoxical anywise...

 

Just related to the discussion at the other thread, I think these comments again just clearly reflect your misconception about what DD is talking about. I really very much doubt that you said the above with any kind of abstract information format in mind. I am quite certain that you are referring to physics concepts, are you not?

 

DD was talking about the equivalence of some information being embedded to the distribution of n points, or to the angular positions of an n dimensional sphere. How the defined entities (and the particular circumstance) that you are referring to would translate to either format, I don't know. I very much doubt you have either, surely you were just thinking of the points themselves as directly reflecting the entities defined by modern physics?

 

Just remember, quite many approximations would still stand between the FE and those modern physics definitions.

 

I'm sorry if you feel that's a stubborn response, but right now it's the only response I can give...

 

-Anssi

[Qfwfq]

I have utterly no idea as to what you are talking about here.

The exact same thing you were talking about Dick, the exact-f'ing-same-f'ing-thing. Ehem, apologies to all for the lewd language, my effort to keep it in could go no further than those apostrophes.

 

Uh, Dick, the only difference between what you and I were talking about is that the sin I committed is the exact same one that you committed (just as usual). I used a few typical words of physics for some of the abstract terms in your pure math, according to formal analogy. And, what's more, guess what, this time around it was the exact same words you appeared to be attaching to the same mathematical terms!!!!!!!! In the very part I quoted!!!!!! You talked about a potential well and mentioned the radial function, invoking "simple" (spherical?) symmetry to justify the step.

 

Were you or were you not referring the above talk to [imath]g®[/imath] and its formal role in the rest of the equation? A straight Yes or No answer to this question would be highly suitable, pls. & thnx. After that, tell me if my trouble is because I need to know some secret magic trick about how [imath]g®[/imath] comes to appear at all. Is it some conjuration?

 

I really very much doubt that you said the above with any kind of abstract information format in mind. I am quite certain that you are referring to physics concepts, are you not?

Seek the answer to this in my above reply to Dick, perhaps in his reply to me, and likely it could go on ad nauseam as usual... But, if it is your free choice to fall for his sleight of hand, I will make no further attempt to avoid you such misfortune.

[Doctordick]

Once again, Qfwfq appears to respond to posts without ever taking the trouble to read them.

 

Uh, Dick, the only difference between what you and I were talking about is that the sin I committed is the exact same one that you committed (just as usual). I used a few typical words of physics for some of the abstract terms in your pure math, according to formal analogy. And, what's more, guess what, this time around it was the exact same words you appeared to be attaching to the same mathematical terms!!!!!!!! In the very part I quoted!!!!!! You talked about a potential well and mentioned the radial function, invoking "simple" (spherical?) symmetry to justify the step.

And exactly what does that have to do with anything you said?

 

In the traditional worldview of [imath]n[/imath] particles, even just three are sufficient and even with the familiar old Coulomb type potential, especially if we allow two opposite signs of charge. To enhance things, place three points along a stright line, with the one charge in between the two of like sign.

So what? You want to point out how you intend to convert that information into to a hyper-spherical coordinate system? If you can't, you are omitting some information somewhere. All the relevant data must first be transformed from many points in a 3-dimensional coordinate system into a single point in an n-dimensional Euclidean coordinate system. Then that coordinate system has to be transformed into a hyper-spherical coordinate system before it is represented by the hyper-spherical representation of my equation. Anyone who can't comprehend the existence of such a transformation is wasting their time reading my stuff.

 

And that [imath]g®[/imath] appears only because eliminating it would require some additional arguments I chose not to put forth and its existence has little to do with the angular issues I am discussing. Any such underlying angular functions must vanish in the solution because of symmetry issues. I can give some decent arguments which would require [imath]g®[/imath] to vanish also but, at this point, it is rather immaterial. Leaving it in there happens to bring up some interesting questions down the road (extensions on what is being shown here). But I doubt you will bother to make an intelligent investigation of anything that matters.

 

But, if it is your free choice to fall for his sleight of hand, I will make no further attempt to avoid you such misfortune.

 

Well at last a ray of hope from the Grand inquisitor!

 

Have fun -- Dick

[Qfwfq]

And exactly what does that have to do with anything you said?

And exactly what does that have to do with anything you said?

 

Anyone who can't comprehend the existence of such a transformation is wasting their time reading my stuff.

Dick, I did not cast the slightest shade of doubt on the existence of such a transformation. I actually was reasoning according to it and I was assuming that you should be able to follow.

 

And that [imath]g®[/imath] appears only because eliminating it would require some additional arguments I chose not to put forth and its existence has little to do with the angular issues I am discussing. Any such underlying angular functions must vanish in the solution because of symmetry issues. I can give some decent arguments which would require [imath]g®[/imath] to vanish also but, at this point, it is rather immaterial. Leaving it in there happens to bring up some interesting questions down the road (extensions on what is being shown here).

Well, that's a relief. Thanks for clarifying the matter. It would have seemed more rational if you had made it clear from the onset. OK, keep expecting people to follow you and have no trouble understanding you...