What can we know of reality?

[ldsoftwaresteve]

Jesus H. Christ. :phones:

 

Thanks Ansii. I appreciate the time it took to put it all down here. I have some shifting to do to get on the same page and that'll take some time. And I don't want to distract you guys.

 

I am very happy that someone else is talking to DoctorDick who can converse intelligently with him. I had the impression from day 1 that he had something important to say. And I felt absolutely horrible that I couldn't understand him. It wasn't his fault, it was mine. I had so many blindspots (and still do) in my worldview that conversation on this level wasn't and probably still isn't possible.

 

I may comment on some things but only to spur or trigger more clarity in a given area. Sometimes blindspots are a ***** to get rid of. And my brain always walks slowly and in random directions. :cheer:

 

One more thing. The 700 pound gorilla to me means 'now', the bleeding edge of experience, the current state of existence. Perhaps it would be more accurate to say that it is the invisible gorilla since we do not perceive the underlying activity except indirectly.

[DougF]

AnssiH

So let me restate with some more detail.

 

Good Post Anssi' date='

Thanks for taking the time to spell it out.

AnssiH

Yes, very annoying habit. "Naive realism" it's called. Almost no one thinks they abide to naive realism, yet most insist certain definitions in their worldview are also ontological things by themselves.

IMHO I think, you got this right.

[AnssiH]

Hi, sorry I haven't been able to use much time on this the past couple of days...

 

Notice that there are only two operators there. The issue is that those two operators are embedded in a collection of operators so what I really want to know is the exact form of the factor when the two are commuted. That is why I put in that term “(some junk B)”; in order to remind you that there were additional factors to the right of the two terms of interest.

 

I think it finally dawned on me what I was missing (while doing something else actually)...

 

It's that;

 

[math]\left[\frac{\partial}{\partial x_i}f(\vec{x}) + \left\{f(\vec{x})\right\}\left\{\frac{\partial}{\partial x_i}\right\}\right](B)[/math]

 

is the same as:

 

[math]\left\{\frac{\partial}{\partial x_i}f(\vec{x})\right\}(B) + \left[\left\{f(\vec{x})\right\}\left\{\frac{\partial}{\partial x_i}\right\}\right](B)[/math]

 

...which is somewhat what I was expecting to see... Yeah, it's my unfamiliarity with math that makes me miss the most obvious things, especially when I'm not sure what (and where) I'm supposed to look for :) So, did I get that right this time?

 

Still, about how [imath] \vec{\nabla}_i \vec{\Psi}_1\vec{\Psi}_2 [/imath] relates to [imath]\left\{(\frac{\partial}{\partial x})(f(x))\right\}[/imath] (or about me trying to figure out how does the "product rule of differentiation" help with the commutation of [imath]\vec{\Psi}_2^\dagger[/imath])

 

The first step here is to examine carefully exactly what the differential term looks like. The dot product, [imath]\vec{\alpha}_i \cdot \vec{\nabla}_i[/imath] was defined to be

[math] \left[\alpha_{xi}\hat{x}_i+\alpha_{\tau i}\hat{\tau}_i\right] \cdot \left[\frac{\partial}{\partial x_i}\hat{x}_i + \frac{\partial}{\partial \tau_i}\hat{\tau}_i\right][/math].

 

Now, if you remember the dot products between unit vectors (the answer is unity if they point in the same direction and zero if they are orthogonal) you will see that every term of this product is an alpha operator times a differential with respect to a specific argument.

 

I think I understand everything up to this point, but about this I have a question.

 

So I suppose the dot product essentially turns like this:

[math] (\alpha_{x1}\hat{x}_1)(\frac{\partial}{\partial x_1}\hat{x}_1) + (\alpha_{\tau 1}\hat{\tau}_1)(\frac{\partial}{\partial \tau_1}\hat{\tau}_1) + ...[/math] etc?

 

That is also what I would expect to see when looking at the dot product definition at Wikipedia: Dot product - Wikipedia, the free encyclopedia

(and your explanation of the same issue at #246)

 

But I feel a bit uneasy about this because when looking at that Wikipedia explanation, I do not understand why you mention the orthogonal unit vectors, as I don't understand when would orthogonal unit vectors ever get multiplied by each others... Or is that dot product "definition" at Wikipedia omitting the dot product of orthogonal vectors exactly because they'd amount to 0 anyway? I am really just guessing :I

 

Also I'm not quite sure why the unit vectors are indexed there... i.e. what's the difference between [imath]\hat{x}_1[/imath] and [imath]\hat{x}_2[/imath]. Just asking to make sure I'm not interpreting something wrong again.

 

So, what we really want to know is what is the consequence of that differential operator (it is the only operator which makes any difference).

 

So that is how I came to concern myself with commutation of that differential with the various functions. You must understand that the central issue is the integral over all arguments of set #2. In that respect there is no difference between commuting [imath]\vec{\Psi}_2[/imath] to the left and commuting [imath]\vec{\Psi}_2^\dagger\cdot[/imath] to the right. What is important is that we bring [imath]\vec{\Psi}_2^\dagger\cdot[/imath] [imath]\vec{\Psi}_2[/imath] against one another because that is a well defined expression.

 

So, if I'm getting this right, the [imath]f(\vec{x})[/imath] represents whatever the function that the index argument(s) have on... um, [imath]\vec{\Psi}_2[/imath]? (That's what [imath]f[/imath] means in post #194 then too?)

 

So is the issue here that you are effectively commuting [imath]\vec{\Psi}_2[/imath] to the left? No?

 

I'm really guessing here, the biggest hole in my understanding right now has to do with how does the product rule of differentiation actually aid in our goal of bringing the [imath]\vec{\Psi}_2^\dagger\cdot[/imath] and [imath]\vec{\Psi}_2[/imath] together... I mean I think I understand how the product rule is used as far as that example with [imath]\left\{(\frac{\partial}{\partial x})(f(x))\right\}[/imath] goes, but then I'm still not sure what the fundamental equation looks like by the time all the [imath]\vec{\Psi}_2^\dagger[/imath]'s are against [imath]\vec{\Psi}_2[/imath]'s. I don't think it was explicitly stated anywhere.

 

What I am getting at here is that the single most important factor is commutation of the differential operator with a function which is dependent upon the argument with respect of which that differential is being made.

 

This makes it sound like I might be on the right track with my assumptions on this post...

 

-Anssi

[modest]

If you know anybody in power, let them know that this LaTex in quotes is a bear. Other forums don't seem to have the problem so they ought to be able to fix it.

 

It's been passed up the chain-o'-command and it's in the works. :confused:

 

~modest

[Doctordick]

It's been passed up the chain-o'-command and it's in the works. :)

Thank you!

 

Hi Anssi,

 

You make me ashamed of myself with all the effort you are putting into this. After reading your post, I realize I need to put more effort into looking for errors in my posts.

Hi, sorry I haven't been able to use much time on this the past couple of days...

You owe me no appologies.

[math]\left[\frac{\partial}{\partial x_i}f(\vec{x}) + \left\{f(\vec{x})\right\}\left\{\frac{\partial}{\partial x_i}\right\}\right](B)[/math]

 

is the same as:

 

[math]\left\{\frac{\partial}{\partial x_i}f(\vec{x})\right\}(B) + \left[\left\{f(\vec{x})\right\}\left\{\frac{\partial}{\partial x_i}\right\}\right](B)[/math]

Exactly correct; as long as you remember that the left hand partial derivative with respect to [imath]x_i[/imath] operates only on [imath]f(\vec{x})[/imath] and not on (B) while the right hand partial derivative does operate on (B). The notation here is not very clear; that is why I keep harping on the issue.

 

Yes, I think you are getting it quite right. The real issue here is when and where we can commute these factors. As I have said a number of times the algebra being done in post # 194 in order to get to Schroedinger's equation is actually quite simple though you have to understand how these element commute.

If we left multiply the above equation by [imath]\vec{\Psi}_2^\dagger[/imath] (forming the inner or dot product with the algebraically modified [imath]\vec{\Psi}_2[/imath]) and integrate over the entire set of arguments referred to as set #2, we will obtain the following result:

[math]\left\{\sum_{\#1} \vec{\alpha}_i \cdot \vec{\nabla}_i + \sum_{i \neq j (\#1)}\beta_{ij}\delta(\vec{x}_i -\vec{x}_j)\right\}\vec{\Psi}_1 + \left\{2 \sum_{i=\#1 j=\#2}\int \vec{\Psi}_2^\dagger \cdot \beta_{ij}\delta(\vec{x}_i -\vec{x}_j)\vec{\Psi}_2 dV_2 \right. +[/math]

[math] \left.\int \vec{\Psi}_2^\dagger \cdot \left[\sum_{\#2} \vec{\alpha}_i \cdot \vec{\nabla}_i + \sum_{i \neq j (\#2)}\beta_{ij}\delta(\vec{x}_i -\vec{x}_j) \right]\vec{\Psi}_2 dV_2 \right\}\vec{\Psi}_1 = K\frac{\partial}{\partial t}\vec{\Psi}_1+K \left\{\int \vec{\Psi}_2^\dagger \cdot \frac{\partial}{\partial t}\vec{\Psi}_2 dV_2 \right\}\vec{\Psi}_1[/math]

 

This is the expression we are trying to algebraically derive from my fundamental equation. Notice that there is essentially no doubt as to what is being differentiated here; it is the intermediate steps which are difficult to express. Post #194 is the one we need to be getting through “one line at a time”.

Still, about how [imath] \vec{\nabla}_i \vec{\Psi}_1\vec{Psi}_2 [/imath] relates to [imath]\left\{(\frac{\partial}{\partial x})(f(x))\right\}[/imath] (or about me trying to figure out how does the "product rule of differentiation" help with the commutation of [imath]\vec{\Psi}_2^\dagger[/imath])

What you are missing is the vanishing of both [imath]\vec{\Psi}_2[/imath] and [imath]\vec{\Psi}_2^\dagger[/imath] in the first term of the equation I just quoted from post #194. You can see it either way: commute the [imath]\vec{\Psi}_2^\dagger[/imath] to the right or [imath]\vec{\Psi}_2[/imath] to the left. They are essentially the terms I refer to as (some junk A) and (some junk B). Notice that our product rule has produced a term (the differential of f(x)) where B is not differentiated.

 

Commuting the two terms together and integrating over all possibilities for set #2 then yields an answer of unity and the first term in that quoted equation arises. The other terms still have integrals to be done.

I think I understand everything up to this point, but about this I have a question.

And indeed you should! First of all you are absolutely correct, there should be no index on [math]\hat{x}[/math] or [math]\hat{\tau}[/math]. It is easy to get sloppy with LaTex, particularly when one is impatient and I get that way easily.

 

The dot product actually turns out like this:

[math] (\alpha_{x1}\hat{x})\cdot(\frac{\partial}{\partial x_1}\hat{x})+(\alpha_{x1}\hat{x})\cdot(\frac{\partial}{\partial \tau_1}\hat{\tau}) + (\alpha_{\tau 1}\hat{\tau})\cdot(\frac{\partial}{\partial x_1}\hat{x})+ (\alpha_{\tau}\hat{\tau})\cdot (\frac{\partial}{\partial \tau_1}\hat{\tau}) + ...[/math] etc?

 

If you then add to this the fact that [imath]\hat{x}\cdot\hat{x}=\hat{\tau}\cdot\hat{\tau}= 1[/imath] and that [imath]\hat{x}\cdot\hat{\tau}=\hat{\tau}\cdot\hat{x}= 0[/imath] then you get very close to what you wrote down: i.e.,

[math] \alpha_{x1}\frac{\partial}{\partial x_1} + \alpha_{\tau 1}\frac{\partial}{\partial \tau_1} + ...[/math] etc?

 

Orthogonal unit vectors yield a dot product of zero and parallel unit vectors yield a dot product of unity. I suspect Wikipedia is omitting the step I just laid out for you because it is usually taken to be obvious but, when you are doing involved algebra with many terms, leaving out steps can be dangerous.

...but then I'm still not sure what the fundamental equation looks like by the time all the [imath]\vec{\Psi}_2^\dagger[/imath]'s are against [imath]\vec{\Psi}_2[/imath]'s. I don't think it was explicitly stated anywhere.

It is explicitly laid out in post #194; the post we should be examining term by term.

 

I think you are very much on the right track. In order to make things a little easier, I am going to post a new thread called “Deriving Modern Physics from my Fundamental Equation”. I am going to open the thread with a copy of the essence of post #194. Hopefully the powers that be will allow such a thing. This thread is beginning to get a bit cumbersome.

 

To all those who are worried about a completion to this thread, I will answer the question, “What can we know of reality?” Modern physics is currently the best answer to that question.

 

Just so you understand where all this leads you should understand that by deriving Schroedinger's equation from basic principals, I have, in effect, shown that all conceivable universes may be seen as a three dimensional space occupied by objects which are required by definition to obey classical mechanics in the classical limit. What I have shown can be taken in two different ways. One can see the result as demonstrating that our classical view of the universe (a three dimensional space occupied by objects which obey classical mechanics) is entirely general and capable of representing any conceivable universe or one can view my results as demonstrating that the fact that classical mechanics is true by definition and that no classical experiment tells us anything about the universe except perhaps that our definitions are self consistent.

 

With regard to the second viewpoint, if one takes the position that the job of a research scientist is to search out the rules which separate the "true" universe from all possible universes, then no classical experiment can provide any guidance on the subject whatsoever. Classical mechanics is itself a tautology.

 

And this is just the opening salvo of my work; there is considerably more to come.

 

Wish me luck -- Dick

[AnssiH]

You make me ashamed of myself with all the effort you are putting into this.

 

Well I've made sure to spend plenty of time enjoying the (incredibly short) summer too :) Pretty soon it's going to become all cold and dark over here again :P

 

What you are missing is the vanishing of both [imath]vec{Psi}_2[/imath] and [imath]vec{Psi}_2^dagger[/imath] in the first term of the equation I just quoted from post #194. You can see it either way: commute the [imath]vec{Psi}_2^dagger[/imath] to the right or [imath]vec{Psi}_2[/imath] to the left. They are essentially the terms I refer to as (some junk A) and (some junk B). Notice that our product rule has produced a term (the differential of f(x)) where B is not differentiated.

 

Hmmm, well there are two things that confuse me at the above. The terms "some junk A" and "some junk B" did not end up next to each others in the example you gave in #265. Another thing is, am I supposed to see that term that the "product rule produced" (the differential of f(x)) somewhere in:

 

[math]\left\{\sum_{\#1} \vec{\alpha}_i \cdot \vec{\nabla}_i + \sum_{i \neq j (\#1)}\beta_{ij}\delta(\vec{x}_i -\vec{x}_j)\right\}\vec{\Psi}_1 + \left\{2 \sum_{i=\#1 j=\#2}\int \vec{\Psi}_2^\dagger \cdot \beta_{ij}\delta(\vec{x}_i -\vec{x}_j)\vec{\Psi}_2 dV_2 \right. +[/math]

[math] \left.\int \vec{\Psi}_2^\dagger \cdot \left[\sum_{\#2} \vec{\alpha}_i \cdot \vec{\nabla}_i + \sum_{i \neq j (\#2)}\beta_{ij}\delta(\vec{x}_i -\vec{x}_j) \right]\vec{\Psi}_2 dV_2 \right\}\vec{\Psi}_1 = K\frac{\partial}{\partial t}\vec{\Psi}_1+K \left\{\int \vec{\Psi}_2^\dagger \cdot \frac{\partial}{\partial t}\vec{\Psi}_2 dV_2 \right\}\vec{\Psi}_1[/math]

 

?

 

Because if I am, I don't recognize it...

 

I think I understand the rest of the post. And I'll be replying over to the new thread soon then...

 

-Anssi

 

EDIT: Oh, and good luck :)

[Doctordick]

Well I've made sure to spend plenty of time enjoying the (incredibly short) summer too :) Pretty soon it's going to become all cold and dark over here again :P

Yes, one of the problems with living in the far north. I was born and raised in rural Illinois outside Chicago; we had plenty of snow come winter time. I now live in Mississippi and to tell you the truth, I don't miss the snow at all. When I was a child, I had an uncle who lived in South Dakota which we used to visit occasionally so I know a little of their weather. I really couldn't understand how anyone could possibly want to live in North Dakota and the idea that there was a major city in Canada north of North Dakota (Winnipeg) was simply beyond me. Yeah, I know Helsinki is six degrees further north but at least you guys have mountains between you and the north pole. Canada is more like Siberia: just a flat plane between them and the Arctic ocean. Here in Mississippi, we can often barbeque a steak outside in a tee shirt on New Year's day.

Hmmm, well there are two things that confuse me at the above. The terms "some junk A" and "some junk B" did not end up next to each others in the example you gave in #265.

The answer to that difficulty is quite simple. You just need to recognize the fact that [imath]\frac{\partial}{\partial x}f(\vec{x})[/imath] is just another function of [imath]\vec{x}[/imath] and, as a simple mathematical function (you can think of it as a table where the value of the function is listed for every argument of interest) it commutes with any other such function. In the proof of the product rule (as I presented it) “some junk A” and “some junk B” can be anything (any kind of mathematical operators); however, in the case of interest (that first term in my explicit expansion) A and B are essentially the functions [imath]\vec{\Psi}_2^\dagger[/imath] (plus appropriate alpha operators) and [imath]\vec{\Psi}_2[/imath] so commutation is no problem (the order, right to left, of these terms, within the first term of my expansion, is immaterial). When I integrate over set #2, A and B, so defined, yield unity (plus the appropriate alpha operators) and vanish from the expression.

Another thing is, am I supposed to see that term that the "product rule produced" (the differential of f(x)) somewhere in:

[math]\left\{\sum_{\#1} \vec{\alpha}_i \cdot \vec{\nabla}_i + \sum_{i\neq j (\#1)}\beta_{ij}\delta(\vec{x}_i -\vec{x}_j)\right\}\vec{\Psi}_1 + \left\{2 \sum_{i=\#1 j=\#2}\int \vec{\Psi}_2^\dagger \cdot \beta_{ij}\delta(\vec{x}_i -\vec{x}_j)\vec{\Psi}_2 dV_2 \right. +[/math]

[math] \left.\int \vec{\Psi}_2^\dagger \cdot \left[\sum_{\#2} \vec{\alpha}_i \cdot \vec{\nabla}_i + \sum_{i \neq j\#2)}\beta_{ij}\delta(\vec{x}_i -\vec{x}_j) \right]\vec{\Psi}_2 dV_2 \right\}\vec{\Psi}_1 = K\frac{\partial}{\partial t}\vec{\Psi}_1+K \left\{\int \vec{\Psi}_2^\dagger \cdot \frac{\partial}{\partial t}\vec{\Psi}_2 dV_2 \right\}\vec{\Psi}_1[/math]

Not exactly, but it will reappear if the first term of that expansion is worked out in detail. The differential operator is contained in [imath]\vec{\nabla}_i[/imath] and, since there is but one function to the right of it in that term, the only function available to play the role of f(x) is [imath]\vec{\Psi}_1[/imath].

Oh, and good luck :)

I think we have good luck. It appears the powers that be are going to allow the new thread. Or, if you are referring to my cold, it's almost totally gone now.

 

Have fun – Dick

[Overdog]

This has been one of the most fascinating threads I have ever tried to follow. I'm glad the major points were explained in english!:)

 

Thanks!

[AnssiH]

If it's okay, I'll use this thread for a moment still to make sure I get this step right. If you think it's better to use the new thread, you can just place your reply there.

 

The answer to that difficulty is quite simple. You just need to recognize the fact that [imath]frac{partial}{partial x}f(vec{x})[/imath] is just another function of [imath]vec{x}[/imath] and, as a simple mathematical function (you can think of it as a table where the value of the function is listed for every argument of interest) it commutes with any other such function. In the proof of the product rule (as I presented it) “some junk A” and “some junk B” can be anything (any kind of mathematical operators); however, in the case of interest (that first term in my explicit expansion) A and B are essentially the functions [imath]vec{Psi}_2^dagger[/imath] (plus appropriate alpha operators) and [imath]vec{Psi}_2[/imath] so commutation is no problem (the order, right to left, of these terms, within the first term of my expansion, is immaterial).

 

Hmm, here we might be closing in to whatever it is that I just am not picking up. I do not understand here, how is it that the commutation is no problem once you've used the product rule, since there still is that differential operator [imath]\left\{\frac{\partial}{\partial x_i}\right\}[/imath] in there.

 

I.e. once the situation is;

 

[math](some\;junk\; A)\left[\frac{\partial}{\partial x_i}f(\vec{x})+\left\{f(\vec{x})\right\}\left\{\frac{\partial}{\partial x_i}\right\}\right](some\;junk\; B)[/math]

 

I just don't understand how that move made any good since it appears to me we still cannot move (A) and (B) together, since they are still separated by a differential operator operating on B...

 

Also, if I take a step back;

 

When I integrate over set #2, A and B, so defined, yield unity (plus the appropriate alpha operators) and vanish from the expression.

 

So we had this:

 

[math]\left\{\sum_{\#1} \vec{\alpha}_i \cdot \vec{\nabla}_i + \sum_{i \neq j (\#1)}\beta_{ij}\delta(\vec{x}_i -\vec{x}_j) \right\}\vec{\Psi}_1\vec{\Psi}_2 + 2\left\{ \sum_{i=\#1 j=\#2}\beta_{ij}\delta(\vec{x}_i -\vec{x}_j)\ \right\}\vec{\Psi}_1\vec{\Psi}_2+[/math]

[math] \left\{\sum_{\#2} \vec{\alpha}_i \cdot \vec{\nabla}_i + \sum_{i \neq j (\#2)}\beta_{ij}\delta(\vec{x}_i -\vec{x}_j) \right\}\vec{\Psi}_1\vec{\Psi}_2 = K\frac{\partial}{\partial t}(\vec{\Psi}_1\vec{\Psi}_2).[/math]

 

And through left-multiplying by [imath]\vec{\Psi}_2^\dagger[/imath], some algebra, and integration over the set #2, we get this;

 

[math]\left\{\sum_{\#1} \vec{\alpha}_i \cdot \vec{\nabla}_i + \sum_{i \neq j (\#1)}\beta_{ij}\delta(\vec{x}_i -\vec{x}_j)\right\}\vec{\Psi}_1 + \left\{2 \sum_{i=\#1 j=\#2}\int \vec{\Psi}_2^\dagger \cdot \beta_{ij}\delta(\vec{x}_i -\vec{x}_j)\vec{\Psi}_2 dV_2 \right. +[/math]

[math] \left.\int \vec{\Psi}_2^\dagger \cdot \left[\sum_{\#2} \vec{\alpha}_i \cdot \vec{\nabla}_i + \sum_{i \neq j (\#2)}\beta_{ij}\delta(\vec{x}_i -\vec{x}_j) \right]\vec{\Psi}_2 dV_2 \right\}\vec{\Psi}_1 = K\frac{\partial}{\partial t}\vec{\Psi}_1+K \left\{\int \vec{\Psi}_2^\dagger \cdot \frac{\partial}{\partial t}\vec{\Psi}_2 dV_2 \right\}\vec{\Psi}_1[/math]

 

So, can I see those "appropriate alpha operators" somewhere or did they also vanish, and if so, how? (Following your english explanation, I would expect to see them somewhere in;

 

I am also somewhat confused about the fact that the first part - [math]\left\{\sum_{\#1} \vec{\alpha}_i \cdot \vec{\nabla}_i + \sum_{i \neq j (\#1)}\beta_{ij}\delta(\vec{x}_i -\vec{x}_j)\right\}[/math] - looks exactly the same after [imath]\vec{\Psi}_2^\dagger[/imath] has been migrated through it. I was assuming the whole explanation about migrating [imath]\vec{\Psi}_2^\dagger[/imath] through a differential operator had to do with that first part since that is the only place where I see such a migration has happened (apparently). But then I would expect it to leave some marks behind. :/

 

...it is somewhat tricky to figure this out :/ Glad we are not in particular hurry :)

 

-Anssi

[Doctordick]

If it's okay, I'll use this thread for a moment still to make sure I get this step right. If you think it's better to use the new thread, you can just place your reply there.

I think that is what I will do.

 

Let us consider this thread as closed -- Dick

[AnssiH]

Recently I have been reading some textbooks on quantum chemistry and found the very interesting comments that I posted a few posts ago--that is, the conclusion held by more than just a few scientists that "the Schrödinger's Equation CANNOT BE DERIVED" ?! And this is not a view held by some high school student that happens to post on the internet--it is the view of Linus Pauling who was an EXPERT in quantum theory and perhaps one of the most intelligent scientists of the 20th Century. Well, I find this of interest, since here I have been reading for many months on this thread about how the Schrödinger's Equation can be derived, and then Linus Pauling telling me it cannot. So, why should I accept one option over the other. Either Linus Pauling is incorrect or DoctorDick is incorrect--or perhaps they use different concepts of what it means to 'derive' something such as an equation.

 

Then, I read the post of Qfwfq and he more or less indicates that Linus Pauling is incorrect--that the Schrödinger's Equation can be "derived" (whatever that means to him)...

 

Alright, if you are willing to make a serious attempt, I'll try to explain the essential point that needs to be understood here.

 

Those first quotes you pasted in #107 (In "Deriving Schrödinger's Equation..."), are suggesting that Schrödinger's Equation "just is" fundamental to reality, i.e. "just how world works". You see them comparing it to Newton's laws, also seen as "just the way reality is in an unexplainable manner". That is also an implication that they suppose reality is ontologically made out of objects that fly around in space, as most people intuitively do. The ontological correctness of that position cannot obviously be defended, if you want to remain completely objective.

 

When they say "it cannot be derived", that is obviously full of semantical pitfalls. Certainly there exists relationships from Schrödinger's Equation to all sorts of other established physical laws, and when people trace the logical steps from one of those laws to Schrödinger's Equation, they might call their work "a derivation of Schrödinger's Equation". Such is the case with the paper you linked; not really the "kind of derivation" that those first quotes were referring to. Also not the kind of derivation that DD is talking about.

 

Like I said, pay attention to "what" is "derived" from "where". You can't just think that "derivation" in all its possible meanings is impossible. (Additionally, Schrödinger certainly had some logical reasons that lead him to Schrödinger's Equation, and one could call that "derivation" as well. It's just semantics)

 

Now, to talk about DD's work, first you should understand that Newton's Laws can be considered "valid" only in so far that in your worldview you indeed do identify "objects" in the way that most people naturally do -> Once you have defined what constitutes a tennis ball, you have a way to think about its motion, and you can say its motion follows Netwon's laws of motion. And obviously this argument applies to the validity of Schrödinger's Equation as well.

 

So onto DD's epistemological analysis

 

DD's analysis begins from the point where we have absolutely no knowledge about the identity of any objects that we'll define as part of our worldview. It could be that we end up with such identifications where the defined objects follow Newton's laws, or perhaps we'll end up with something totally different...? Let's see what DD's analysis says about this, as it will give rather surprising answers.

 

All we know at the get-go is that some set of "persistent entities" will be defined as that is necessary for any predictive model of reality (As without any identification there's no way to "think about" the future of any entity, as no element would have any future).

 

Also we can say that the definitions of those entities are based on some "data patterns". I.e, a familiar pattern "x" becomes to be seen as a tennis ball, even when we don't know what is the underlying ontological reality behind that data pattern (i.e. we take into account that there is no actual, ontological information about any "identities of reality" even after we have arrived at some useful definitions)

 

So, in DD's work, conceptually this issue is handled by the idea of "undefined ontological elements"; these are simply some data points in the raw data we are working with; something that allow us to discuss - or mathematically handle - the idea of "patterns" at all. At this point you can think of this as patterns seen in the x,tau,t-space.

 

This is where those symmetry constraints step into the analysis. The shift symmetry for instance, is basically an argument that a specific data pattern, which gives you the expectation of "x will happen" in your final worldview, will give you that same expectation regardless of where it occurs in the x,tau,t-space.

 

You may be tempted to think that the context of where that data pattern occurs will have an effect to your expectations, but notice that the shift symmetry is referring to the entire universe; the context is shifted all the same. If you think about this, you will come to realize that the shift symmetry argument is really tautologous to the argument "our definitions of entities are based on 'patterns'". Or furthermore, tautologous to the argument that the specific chosen numbers for labeling the "data points" are immaterial and don't have an effect to what sorts of patterns between the data points can be recognized.

 

Now, it is very important that you realize, that this starting point makes absolutely no ontological assumptions. We are not supposing any specific form to reality at all. All we are working with are epistemological constraints, that is, constraints that exist simply due to the fact that we must define some entities based on some unknown data patterns.

 

This is the starting point, which leads to "Fundamental Equation" and further to Schrödinger's Equation. If you think about that, you realize that if indeed this relationship between the symmetry arguments and Schrödinger's Equation is valid, it means we can't really say "Schrödinger's Equation just is fundamental to reality", rather it is fundamental to our self-coherent and (prediction-wise) valid way to understand reality. Schrödinger's Equation can be seen as an elegant and incredible succint expression of the (purely logical) constraints that gave us means to define self-coherent set of "persistent entities".

 

The paradigm shift required here is from "Reality obeys Schrödinger's Equation and we don't know why" to "We defined reality in the way that the defined entities obey Schrödinger's Equation" to even more appropriate "Schrödinger's Equation is an expression of the constraints that must be valid for any given self-coherent worldview". (Given the approximations that DD talks about in the OP of "Deriving Schrödinger's Equation..."-thread)

 

So a succint answer to your confusion is, that this is not Schrödinger's Equation derived from more fundamental ontological concepts (which would be just as unexplainable themselves), it is rather Schrödinger's Equation derived from epistemological fundamentals.

 

And why is that significant...

 

If you think about that, you should come to realize that the significance of DD's work is not really so much in that it "derives Schrödinger's Equation which everyone thought is not possible". The significance is that it is an explanation for why reality seems to work in such an elegant fashion, and why at the limits of quantum physics reality is so eluding, and why relativistic time relationships are valid...

 

First of all it implies strongly that reality is not "given from the above" somehow the way we see it; it is not ontologically a slab of space where objects are floating around. Instead, the definitions that give us this newtonian picture, are just by far the simplest way to comprehend and predict the behaviour of fundamentally unknown reality.

 

Next, if you take reality as fundamentally something somewhat random, where familiar patterns are learned and then seen as predictably behaving entities (the probabilities entirely given by how we've seen those patterns working in the past), the "quantum mechanical relationships" that are uncovered imply that the quantum strangeness is in some sense a consequence of not really knowing the identity of the elements we are talking and thinking about. I think it is interesting to note that in quantum mechanical sense, we know what we saw only after we indeed saw it, and our ideas about the history of that observed element are based on the assumption that the element of interest did exist as exactly that element even before we saw it (i.e. it is thought of as an element with ontological identity, instead of something arising from our definitions on top of random data patterns).

 

If you take the position that random data patterns are seen as element "x" (judged by some specific context springing from the patterns in the raw data), you can see that it is entirely possible that there exists situations where a pattern seen as a "photon" or "electron" or anything at all arises at some semi-predictable manner. So, for instance in terms of Bell experiments, this implies that once you see the pattern identified as "photon with x polarity", then in terms of your defined worldview, that observation gives you a specific probability to expect a so-called "entangled photon with y polarity" to appear elsewhere. More fundamentally, that would be just "some associated observation occurring elsewhere".

 

The quantum mechanical prediction for the probability value is what is also experimentally found to be valid, and that is also the probability value implied by DD's work.

 

Holding onto naive realism too much will give you a problematic picture, because you are supposing the elements have real identity and they existed in specific state before the observations (incl. when they first interacted), and that idea will give you a different probability value to your expectations than what is observed.

 

Also, supposing some hidden/unknown relationships to exist between the entangled entities, will require that the information between the observations moves at super-luminal speeds. Under the common view of relativity (with ontologically relative simultaneity), that leads very trivially to incoherent picture of causality. (But to be correct, it is indeed possible to retain relativistic relationships even with the assumption of ontologically absolute simultaneity, but let's not get into that too much here)

 

Under DD's analysis, there is nothing that "moves" between the entangled entities, what we are talking about is simply the impact of "observation" ("knowing more about the situation") to our expectations regarding the state of the other photon. There is no "real" information moving from one photon to the next, nor did we ever have any ontologically real identity or ontologically real history of the defined entities (the "photons"), as they were just definitions of some data patterns. Hence, there are no problems with causality.

 

At this point, you can look at those quantum mechanically predicted, and experimentally proven probability values simply as a non-obvious consequence of having defined entities accordingly to those original symmetry arguments.

 

If that sounds immediately impossible, I think you are thinking about this from within a wrong paradigm. Just please re-think this whole logic chain; Symmetry arguments lead to -> sensically defined entities that obey quantum mechanical probabilities but have no real identity -> as a peculiar side effect of this, the expected behaviour of such defined entities is the same as quantum mechanical expectations in Bell Experiments, which is different from naive realistic view of real entities with real ontological identity.

 

I think that is why DD's said that Bell Experiment is basically an experimental verification of his work.

 

And, if his work indeed is valid, I'd say it is very significant (why do you think I put in so much effort to really understand the logical steps, even when my math abilities are next to nothing), and since you mentioned Nobel price, well I think they have been granted for less.

 

Btw, the above is still written with little bit shaky understanding of the exact logic (DD might correct me on some details), and also I did not pay very much attention to semantical clarity. I hope you can see over that and try not to get stuck into small nitpick issues. Instead try to look at the whole thing first and try to get a good idea about what DD's work is really about. I can only hope this post is helpful to you, and I hope you appreciate the effort... (Actually I'm hoping it might be helpful also for other lurkers who have been following these threads)

 

-Anssi

[lemit]

I hadn't noticed this thread before. As I started to read it, a question popped into my head, and I need to ask that question without having read the thread.

 

What if we can ask what reality is without all our intellectual underpinnings, all our intellectual claptrap? My training as a reporter included being willing to ask a dumb question. That's what I'm doing self-referentially and self-consciously here.

 

What is it like to be philosophically feral? What does the philosophically feral ask about the nature of reality? Possibly this has been addressed here. Now that I've asked, I'll go back and read the thread, although I'll probably get several headaches from it.

 

--lemit

[Rade]

Alright, if you are willing to make a serious attempt, I'll try to explain the essential point that needs to be understood here.

Thanks, I'll do my best to understand

Now, to talk about DD's work, ...So onto DD's epistemological analysis[/b]

Yes..

DD's analysis begins from the point where we have absolutely no knowledge about the identity of any objects that we'll define as part of our worldview

OK, we must start here, with the fundamental assumptions used by DD to arrive at his fundamental equation. For me to get into this, I must go step by step, but as you say I also must understand the forest for the trees. So, for now, I must completely understand this sentence you provide about where DD's analysis 'begins'.

 

A.1 To help me understand, I must dissect the sentence above into important words used, I find these to be in the order you present:

 

1. "analysis of DD begins"

2. "absolutely no knowledge"

3. "identity"

4. "objects"

5. "to define an object"

6. "form a worldview"

 

===

Now, Anssi, you must in your reply let me know where I deviate from your understanding of DD philosophy. I find that DD has absolutely no time to do this for me, too much water under the bridge between us, DD just tunes me out.

===

 

A.2 I would like to use some definitions to help me understand the words used.

 

Objects = what DD calls 'ontological elements'. Here I will use the symbol [Oi] for any specific ontological element. Ontological elements are the "physical things that exist" in our universe. I believe in his Fundamental Equation {FE} he uses the label A = set of all possible ontological elements that exist as physical things. Please correct me if I error.

 

Identity = the fact(s) of the individual objects [Oi] within the set of all possible objects, so identity also for me known as the 'thing-in-itself'. Identity would include things such as color, shape, mass, in quantum world spin, charge, etc. for any specific [Oi]. That each [Oi] must have an identity in the philosophy of DD is required by his assumption above that there are 'physical things that exist' in the universe, and to be a physical thing means there must be a physical identity for the thing.

 

Absolutely = with 100% certainty or 0.0 % error, that is, the Heisenberg Uncertainty Principle (HUP) does not apply if you claim to have absolute knowledge. When a person says they have 'absolute' knowledge of something, then they make a claim that is outside scientific investigation for the simple reason that science is defined as = uncertain knowledge.

 

Knowledge = ability of a living entity to grasp the fact(s) of some ontological element [Oi], that is, to grasp some aspect of the 'thing-in-itself", with some degree of uncertainty--that is, knowledge is never absolute. There are two differ ways to do this (1) via direct perceptual observation of some [Oi] ontological element or a group of [Oi] acting together, and (2) via an indirect process of reason based on the direct observation process in step #1. As stated above, scientific knowledge is NEVER absolute, there is always some degree of uncertainty, this is why the HUP is so useful, it gets to the essence of science which deals with humans gaining uncertain knowledge of fact(s) of individual ontological elements [Oi].

 

Define = a statement that identifies the essential characteristic fact(s) of a set of ontological elements [Oi] which as a unit are subsumed under what is called a 'concept'. Most likely only humans, of all the living entities, have the ability to define. Humans are very good at the process of concept formation and then placing definitions on them. So, first must come the process of forming a concept based on a set of similar [Oi], then comes the process of adding a definition to the concept. So, concept formation is always prior to definition and the two are not the same process, as different as night and day.

 

So, for example, the concept "bee" as a flying thing can be distinguished from the concept "bird' as a flying thing. So, I make a mental file folder for the concept "bee" but recognize that there are many different types (species) of bee, so I make sub-folders for each of these. I then put a label on the generic folder bee, and the words on that label are the generic definition of the concept bee, likewise I put a label on each of the sub-folders and these are the refined definitions for each species of bee. Within each folder are the fact(s) that represent the 'thing-it-itself' of the generic concept bee and each species of bee. These facts are part of what I can say I know about the set of [Oi] elements I have subsumed under the concept bee.

 

A.3 It is not clear to me the sequence of the logic of the six statements above where you explain how the 'analysis of DD begins". As you have the sequence of terms now, it seems to imply that the analysis begins with "knowledge", but this cannot be correct, that is, no valid philosophy can ever put consciousness prior to existence, first must be some "object" that exists, then comes "consciousness" which allows for knowledge of what exists. So, I will rearrange the six items above in what I view as the correct logic order required for a valid philosophy for DD to use to develop his Fundamental Equation.

 

1. "objects=undefined ontological elements" (formed as universe formed)

2. "identity=undefined fact(s) of the undefined objects"

3. "analysis of DD begins" (that is, DD born at a time and place in history of universe)

4. "absolutely no knowledge"

5. "to define an object"

6. "form a worldview"

 

I conclude (and I sure hope that DD agree) that the 'philosophy' of DD must 'begin' with a simple yet fundamental axiom, namely that objects or ontological elements [Oi] exist. Of course, since at this first step we are at the beginning of the process in the development of his Fundamental Equation, the individual [Oi] must be undefined and of course unknown. So, the philosophy of DD that leads to the development of his Fundamental Equation only requires one axiom, call it an assumption, and it can be stated as "existence exits", that is, there exists objects as ontological elements in the universe. We just take this as a given, it is not open to analysis or discussion, this is why it is called an axiom.

 

If this is not how the analysis of DD begins, then I need to know why.

 

So, I will stop here Anssi and wait for your reply.

[Doctordick]

Rade, after reading your post to Anssi, I think you need to be aware of my paper, “A Universal Analytical Model of Explanation Itself”, originally on my web site which is defunct. You can find what is essentially a copy of that document on WikipediA. Meanwhile, I think I have some important comments to make on your post.

Objects = what DD calls 'ontological elements'. Here I will use the symbol [Oi] for any specific ontological element.

First of all, “object” is a concept I define far down the road (after the derivation of Schrödinger's equation). I use the word “element” in the sense that “it cannot be reduced”: i.e., elements are fundamental entities (they are not “objects”).

Ontological elements are the "physical things that exist" in our universe.

No they are not! I will go along with the word “things” but I baulk at the adjective “physical”. Physical implies a classification of some sort and, before we begin, we have no means of establishing such a classification. Exist is another word I baulk at for essentially the same reason.

I believe in his Fundamental Equation {FE} he uses the label A = set of all possible ontological elements that exist as physical things. Please correct me if I error.

If I said such a thing, I apologize for I most certainly confused some important issues. First of all, when I introduce A the fundamental equation does not exist (it is yet to be deduced) and I use A as simply "What is to be explained."

Identity = the fact(s) of the individual objects [Oi] within the set of all possible objects, so identity also for me known as the 'thing-in-itself'. Identity would include things such as color, shape, mass, in quantum world spin, charge, etc. for any specific [Oi]. That each [Oi] must have an identity in the philosophy of DD is required by his assumption above that there are 'physical things that exist' in the universe, and to be a physical thing means there must be a physical identity for the thing.

This comment is simply “off the wall”. It presumes you already have an explanation of all these concepts you toss up with no thought. You are already “out of bounds” with regard to the issue being discussed.

Absolutely = with 100% certainty or 0.0 % error, that is, the Heisenberg Uncertainty Principle (HUP) does not apply if you claim to have absolute knowledge. When a person says they have 'absolute' knowledge of something, then they make a claim that is outside scientific investigation for the simple reason that science is defined as = uncertain knowledge.

This applies to your assertions, not to my presentation. I am presuming your [Oi] is intended to be my [b_i], “some element from A”. B is a collection of such elements and amount to the basis of your explanation: i.e., the underlying “valid” information which your explanation explains. (The "valid" is no more than a tag indicating that the information so tagged must be explained by all flaw-free explanations: i.e., there can exist other information which is merely presumed.)

Knowledge = ability of a living entity to grasp the fact(s) of some ontological element [Oi], that is, to grasp some aspect of the 'thing-in-itself", with some degree of uncertainty--that is, knowledge is never absolute.

You are defining “knowledge” to be something you understand. I am defining “knowledge” to be something you want to understand. There is a subtle but very important difference.

There are two differ ways to do this (1) via direct perceptual observation of some [Oi] ontological element or a group of [Oi] acting together, and (2) via an indirect process of reason based on the direct observation process in step #1.

Here you are presuming an understanding of “perceptual observation” and/or “direct observation”. You are once again outside the bounds being defined as the basis of the problem: i.e., you are presuming understanding of something.

Define = a statement that identifies the essential characteristic fact(s) of a set of ontological elements [Oi] which as a unit are subsumed under what is called a 'concept'. Most likely only humans, of all the living entities, have the ability to define. Humans are very good at the process of concept formation and then placing definitions on them. So, first must come the process of forming a concept based on a set of similar [Oi], then comes the process of adding a definition to the concept. So, concept formation is always prior to definition and the two are not the same process, as different as night and day.

 

So, for example, the concept "bee" as a flying thing can be distinguished from the concept "bird' as a flying thing. So, I make a mental file folder for the concept "bee" but recognize that there are many different types (species) of bee, so I make sub-folders for each of these. I then put a label on the generic folder bee, and the words on that label are the generic definition of the concept bee, likewise I put a label on each of the sub-folders and these are the refined definitions for each species of bee. Within each folder are the fact(s) that represent the 'thing-it-itself' of the generic concept bee and each species of bee. These facts are part of what I can say I know about the set of [Oi] elements I have subsumed under the concept bee.

You are so far outside the boundaries of the problem being discussed that I suspect you have no idea as to what Anssi and I are talking about.

1. "objects=undefined ontological elements" (formed as universe formed)

Presumes the universe “formed” a process which cannot be defined without the presumption of some kind of explanation of some sort. :naughty:

2. "identity=undefined fact(s) of the undefined objects"

Presumes these “objects” can be reduced to a collection of facts; that means that they are not elemental. :naughty:

3. "analysis of DD begins" (that is, DD born at a time and place in history of universe)

The only conclusion I can come to here is that you are so far out in left field (so to speak) that you have no comprehension of the problem being attacked. It is a total waste of time to comment on your delusions any further. I will nonetheless comment on one other thing you said:

So, the philosophy of DD that leads to the development of his Fundamental Equation only requires one axiom, call it an assumption, and it can be stated as "existence exits", that is, there exists objects as ontological elements in the universe.

No, that is not a necessary assumption. You may just as well presume nothing exists, that everything is no more than a figment of your imagination, just a random collection of meaningless information. If you are going to make up an explanation of that information and require that your explanation be internally self consistent, then that explanation can be interpreted in a way which obeys my fundamental equation. If you wish, you can take my opening axiom to be that logic is defined to be an internally consistent construct. :)

 

I am doing something very simple: I am carefully defining a way of referring to undefined elements and then creating a carefully constructed tautology which will “explain” those elements (an explanation being nothing more than a procedural mechanism which will predict expectations for information which is not part of the information on which the procedure itself depends).

If this is not how the analysis of DD begins, then I need to know why.

Why what? B)

 

Maybe Anssi can reach you -- Dick

[Rade]

Well DoctorDick, you are what they used to say in 1960s, a real trip.

 

Only because you insult me for the last time I comment here.

 

First, your comment about my use of the word, 'object'.

 

Well, you seem to have lost the understanding that I did not bring forth that term, it was a term used by Anssi in this sentence that I was responding to:

Originally Posted by AnssiH:

DD's analysis begins from the point where we have absolutely no knowledge about the identity of any objects that we'll define as part of our worldview

 

Do you now see the word..."objects" ? Do you see anywhere the word "element" ? So, what am I to conclude. First I have Anssi who was kind enough to try and help me understand what he says is how "DD's analysis begins", and he informs me that it begins from a point [of view] that no human can have knowledge of any sort (absolutely no knowledge) about the identity of any "objects"...

 

Did you read this sentence by Anssi before you sent off your diatribe, DD ? Do you not understand that the words I defined above are words used by Anssi to help explain your philosophy ?

 

Since it is now clear from your comments that your philosophy prior to the development of your Fundamental Equation has nothing at all to do with 'objects'--then your complaint with use of the word 'object' is with Anssi for so suggesting, not with me.

 

Sorry Anssi, I know you are trying to help, but you see, this is the type of BS that DD has been giving me for more than two years now. It also tells me Anssi that you cannot have a full grasp of what DD is saying--why would you use the term 'object' to help explain how the 'analysis of DD' begins when that analysis prior to development of his Fundamental Equation has nothing to do with 'objects' ? You more than anyone should understand this mental game DD plays with people that attempt to question his comments--he immediately attacks every word used. So, now, of course DD finds everything else I say to be wrong about your sentence Anssi, lol, everything else I say derives from the word 'object' ! Lol even more, the philosophy I hold is called Objectivism.

 

Now, let me continue. DD does make it clear that 'elements', not 'objects', are the 'fundamental entities' that he is trying to explain, that these are what he calls the 'things' that need to be explained. OK, fine. He does not call them 'ontological elements' but I know he has used this term many times, so, we can then conclude that the analysis of the DD philosophy begins with this assumption:

 

A.1 First assumption of DD philosophy used in development of his Fundamental Equation

 

1. Ontological elements are fundamental entities.

 

Great, an important first step. But, how is it exactly that DD reach this decision ? Seems to be part of his worldview, a fundamental assumption he makes, for, with no comments prior or logical reason, DD just makes the bold claim that 'ontological elements are fundamental entities' and off he goes to develop his Fundamental Equation.

 

But then DD goes off the deep end. He next immediately claims, after saying that ontological elements are fundamental entities that he accepts are 'things', that he also rejects that they (1) are physical and (2) that they exist. !! That is, the philosophy of DD begins with a first assumption that there are fundamental entities in the universe (his direct term) that are ontological elements as things, but they are NOT physical and they do not exist. Prey tell, what are they, what type of fundamental entity is present in our universe as a "thing" that is not physical and does not exist ?

 

Wow, but it gets better...Anssi, and now you will see that you do not have to feel so bad you not understand what DD is saying, because he also has no idea what he is saying from one moment in time to another-- because as we see here from his internet post titled his "Foundations of Reality" that he claims:

 

Comments of DoctorDick explaining his philosophy that he terms 'Foundations of Reality":

 

"So my mental image of the universe consists of three components: physical things which really exist, imaginary things which we dream up so our mental image will make sense and the rules we believe all these things must obey. The names I give to these three components are "knowable data", "unknowable data" and "rules". In essence, from an abstract perspective, all scientists make up "unknowable data" and "rules" in order to explain the "knowable data".

 

And, here then is why Anssi, I will never again have anything to do with this expert of thinking, this Ph.D. genius--for even the fool that I am can see clearly that somewhere within the fog of DD's brain is his mental image of PHYSICAL THINGS (recall a thing he just informed is his ontological elements as fundamental entities) WHICH REALLY EXIST that are in the universe, that he just had the insulting pleasure to inform me is a large plate of BS when it is I that so make the identical claim to him.

 

Please, no reason AnssiH to waste your time making any response--I will not allow this person to insult me ever again. I have no further interest in what DD has to say and will never reply to any post he ever makes on this forum.

[AnssiH]

Calm down Rade B)

 

If you get aggravated or just feel insulted, maybe wait for a day before you reply, you usually come to see the point of the other party clearer after a little while. You know, works for me anyway.

 

Anyway, I think you just made a small but very devastating misinterpretation regarding the meaning of "undefined ontological elements". Let me try and sort that out.

 

So onto DD's epistemological analysis

 

DD's analysis begins from the point where we have absolutely no knowledge about the identity of any objects that we'll define as part of our worldview. It could be that we end up with such identifications where the defined objects follow Newton's laws, or perhaps we'll end up with something totally different...? Let's see what DD's analysis says about this, as it will give rather surprising answers.

 

The first sentence means, at the starting point of this analysis, we make no presumptions as to what sorts of objects (yes, objects) we WILL end up having in our worldview (as a result of defining some patterns into "objects"). Could be those newtonian tennis balls, or perhaps something else.

 

Rather, we are planning to investigate what sorts of limitations or constraints there might exist to our definitions, due to the necessity of our definitions to be a self-coherent set (= a worldview cannot contradict itself to be considered valid), and due to the fact that we are not aware of the ontological meaning of the patterns we are trying to explain.

 

All we know at the get-go is that some set of "persistent entities" will be defined as that is necessary for any predictive model of reality (As without any identification there's no way to "think about" the future of any entity, as no element would have any future).

 

I said "persistent entities", perhaps for more clarity I should say "persistent objects". Whichever it is, the emphasis is on the word "persistent", because it is typical (actually necessary) for any real worldview that the objects it defines are indeed more or less "persistent through time". DD's talk about "what is, is what is" explanation is referring to the kind of form where each occurrence of each data point is considered a unique element of its own, only to disappear at the next instance and have a completely different element take its place. Any actual worldview that can exist in our minds, would be said to consider some of those occurrences to be "the same object persisting through time".

 

Also we can say that the definitions of those entities are based on some "data patterns". I.e, a familiar pattern "x" becomes to be seen as a tennis ball, even when we don't know what is the underlying ontological reality behind that data pattern (i.e. we take into account that there is no actual, ontological information about any "identities of reality" even after we have arrived at some useful definitions)

 

Here I'm pointing focus onto what will become a very important aspect of the analysis; that our definitions are based on some "patterns", and even after we have a worldview with tennis balls, we do not have any idea about any ontological identity of that tennis ball. It is a stably persistent pattern in some sense, but we do not know what sort of reality really gives rise to that pattern that we have defined as a tennis ball.

 

To give you a (somewhat sloppy) thought experiment, just imagine a task of sitting inside a brain, trying to understand what the electrical impulses from the sensory organs mean. When the eye "sees" a tennis ball fly across its field of view, what is the corresponding pattern like in the brain? That (reasonably large amount of data) would be the pattern getting defined as the "flying tennis ball", so to speak.

 

So, in DD's work, conceptually this issue is handled by the idea of "undefined ontological elements"; these are simply some data points in the raw data we are working with; something that allow us to discuss - or mathematically handle - the idea of "patterns" at all. At this point you can think of this as patterns seen in the x,tau,t-space.

 

Here's where you stumble a bit, and you know, when I was writing that, I first wrote something to the effect that "undefined ontological elements" can be a bit misleading way to talk about this issue and perhaps we should call them something else. But eventually scratched that part and decided to try and explain it the way I did. But just, let me re-emphasize what I've said there:

 

---

So, in DD's work, conceptually this issue is handled by the idea of "undefined ontological elements"; these are simply some data points in the raw data we are working with; something that allow us to discuss - or mathematically handle - the idea of "patterns" at all.

---

 

Try not to view these "elements" as real ontological elements that exist as some fundamental things in the universe. The essential issue that we are trying to solve here is "how do we express the idea of our definitions being based on some patterns, when we don't know what is the underlying reality behind those patterns"

 

Fortunately, the essential relationships that we are interested of will not have anything to do with what those elements actually are, but everything to do with the fact that we know something about the characteristics of the patterns that our definitions of objects will be placed upon. (The symmetry arguments)

 

That is what allows us to just refer to them as bunch of "undefined entities", but perhaps a less confusing way to refer to them would be "data points of unknown meaning, whose occurrences give us "some patterns", and specific patterns will become defined as "persistent objects" in the final worldview"

 

I don't really want you to get stuck here and try to question "so then data points exist?", as the main point here is just to have some way to discuss patterns coming from unknown source.

 

I believe all the rest of your questions revolved around the mis-understanding of this issue, so I won't comment on them more.

 

I also can't help but think that if you are interested of understanding the derivation of Schrödinger's Equation, perhaps you should stop nit-picking on details too much, and take a look at the logical steps from the symmetry arguments to Schrödinger. Then if you become convinced that such symmetry arguments really are tautologous to Schrödinger's Equation (with the necessary approximations), you might start to think about what that means, even if you are not yet convinced that the symmetry arguments are absolutely necessary. Even if you think they are just "sometimes" necessary, don't you think that a derivation of Schrödinger's Equation from them is somewhat surprising, and might mean something?

 

In the end, I would still like to comment on that paradigm shift that DD's work requires. I'm sure you've heard physisicst commenting something to the effect of "isn't it amazing that there are all sorts of fundamental parameters and laws of physics, fine-tuned to work together in incredible precision just right to give rise to stable matter and everything that we see around us".

 

To me, that has always sounded about as smart as saying "isn't it wonderful co-incident that there is ice at the north pole; otherwise the polar bears would drown!". A completely topsy-turvy way to look at the issue. And mind you, this was pretty much the mindset that almost everyone had prior to Darwin, towards all the "wonderful co-incidents" in nature.

 

I've really had this sort of super-darwinistic outlook on everything for quite some time, that all the "fundamental entities" are more properly just "stable systems" of some sorts, and they exist as products of their environment. Evolutionary mechanisms produce very fine-tuned systems (not just so-called "living organisms" but very large and very small stably persistent things also) and all their parts will be dependent on their environment, so yes, we should expect to be able to measure all sorts of parameters whose value need to be very accurate for things to work the way we see them working.

 

So, my perspective was not that far off from DD's, which probably allowed me to understand what he was talking about more readily. In DD's work, that perspective is in some ways even more explicit, as things are looked at from the epistemological perspective exclusively. We first need to define a coherent set of objects, before we can talk about any relationships or parameters that exist between those objects. That those parameters give us a picture of very fine-tuned universe, should not be a surprise to anyone.

 

Or, you can do what some people do and take it as a proof of God. Such a patient little tweaker that guy was!

The Universe IS Fine-Tuned By GOD

 

DD, I'll try to get back to Schrödinger tomorrow.

 

-Anssi

[lawcat]

Then, wouldn't DD's equation be of larger importance in Particle Swarm Behavior field? There, it could be tested without quantum constraints of charge, energy, field. (Why make it a point to derive Schroedinger, when the theory may have larger pertinence elsewhere?)