What can we know of reality?

[Doctordick]

Hi Anssi, as per usual, I think you understand almost everything I am presenting. Again, you are mixing a number of different issues. It is best that these issues be kept distinctly in mind because the whole is quite dependent upon the validity of the proof and the extensions (once the proof is totally understood) are actually far beyond what you have currently comprehended. Going over your post I find three very specific issues being brought up and I will try to alleviate your feelings of misgivings.

 

The three issues I want you to keep separate are: first, the deduction of my fundamental equation; two, the algebraic demonstration that most all of modern physics is nothing more than approximation to that equation; and finally the interpretation of result (i.e., what it has to do with your world-view). The third issue should not really be approached until the first two are understood. Think of it this way, as Buffy has commented, the first is purely logic and has absolutely nothing to do with reality. The second is also nothing more than pure algebra and also has nothing to do with reality. However, by construction, these first two steps are applicable to absolutely any collection of information (that is why I keep referring to it as a “data compression mechanism”). I call it a “paradigm” because it is a convenient way to “look at” absolutely any collection of data and a “paradigm” is generally defined to be “a way of looking at things”.

 

The big issue (embedded in issue number three) is our paradigms. I am not inside your brain and I have no idea as to what your “paradigm” actually is; however, I do know that, if my proof is valid, there exists an exact translation from your paradigm into the one being presented here. It makes utterly no difference what your world-view is; if you try to explain it to me, I can interpret your explanation is such a manner that it is perfectly consistent with my paradigm. That, in itself is a very powerful fact. When we agree, it does not mean we have the same paradigm; what it really means is that we have managed to find a perfect translation between the two. This has very profound philosophical consequences but we cannot go into those until the proof is understood.

 

So, I've been really scratcing my head on this part, and it's hard to pick it up. Initially a "present" was unordered sets of labels, and to be able to see the change in between "presents" as "momentum" requires one to interpret the situation in some context sensitive way I suppose.

Your problem here is that you are stepping off into issue number three. I transformed the “past”, the information available to you to create your “world-view, into a collection of points in an abstract x,tau,t space (tau was required to allow multiple occurrences of specific x to survive this transformation). The “future' was defined to be “what you do not know” which resulted in “the present” being the boundary between the two. I then stated that the past can be seen as a collection of presents (changes in what you know). What we have at that point is the “fact” that everything you know (or think you know) can be seen as a collection of “presents” (changes in the information available to you).

 

The issue at that point becomes “what are your expectations”. What I proved is that there always exists a set of “invalid ontological elements” (noumenons, unknowable data, fictional events ... whatever you want to call them) which will constrain that known past to exactly what you think you know. Now simple symmetry requirements absolutely demand that (if we use numerical labels for “what we know”) there alway exists a function [imath]\vec{\Psi}[/imath] which will yield those expectation and that the function must obey my fundamental equation. If that function does not exist, we cannot have any expectations.

 

So, what do we have? We have our past (the set of points in that x,tau,t abstract space) and we have our expectations (a measure of which set of points in that x,tau,t space we find most probable). This is clearly a set of points in an x,tau space which change with time. What I showed (in deducing Schroedinger's equation) was that the “time” behavior (time being defined as a parameter indicating what you know) of individual points in this picture would obey Newtonian mechanics. This says that the fundamental elements of your explanation will obey Newtonian mechanics (if your explanation is flaw-free and the proper approximations are valid).

I mean I'm not sure how the difference between two sets of "unordered labels" can be seen as containing the information of momentum without interpreting or assuming some sort of identity to some elements (which are the "x,tau"-points or specific patterns?)... I.e. I'm looking at the "momentum" term, but I'm not sure what does it mean to say that a specific element is "changing at a constant rate" (or what would that look like in the x,tau,t mapping)

The identification of those elements requires “an explanation”. The issue is that it does not matter what your explanation is, it must be built of fundamental elements which can be seen as obeying Newtonian mechanics. They either stay the same, change in the same manner as they did in the “past” or have a behavior which is being altered by the current context (i.e., those fictional elements introduced to explain their behavior).

Or are you making such a shift in perspective in this interpretation that the x,tau,t point is not seen as a label but as a position, and if so, what's the mechanism that says which element in one "present" is which in another "present"

As soon as I transform the information into a collection of points in that x,tau,t space, it should be clear to you that the perspective becomes a st of points whose positions are changing in time. It should be clear to you that it is your explanation which defines which element in one “present” is which one in another “present”.

I hope you can pick up what I'm trying to ask here :P

I think I understand exactly what you are trying to ask. The important question is, do you understand my answer?

But it seems there's just one irritating complication; what I was referring to was any experiment where Bell inequality is violated.

I think you misunderstand the “Bell inequality”. The issue in the “Bell inequality” is that quantum mechanics predicts results which require information to be propagated from point A to point B at speeds in excess of c (the speed of light). To quote the reference you gave, “It appears most of these experiments produce results which agree with the predictions of quantum mechanics”. That agreement requires information to be communicated between A and B at velocities well in excess of c. In fact, this is exactly the same issue raised by the “simultaneous collapse of the wave function everywhere”: that collapse violates the whole structure of “relativity”. From the perspective I am putting forth, quantum mechanics (as it is currently presented in this presentation by Schroedinger's equation) is a fundamental truth required of your explanation. It certainly takes precedence over “relativity”. As I told you earlier, in my paradigm, relativity comes in in quite a different manner than it does in conventional modern physics but it is none the less a fundamental requirement of any “explanation”. Don't worry, I will resolve the conflict in a very logical manner.

...and we'd probably always be free (for a large part) to choose what.

Not nearly as free as you think you are.

 

Have fun -- Dick

[AnssiH]

Hi Anssi, as per usual, I think you understand almost everything I am presenting.

 

Heh, I have the same feeling, emphasis on the "almost" :D

 

Again, you are mixing a number of different issues. It is best that these issues be kept distinctly in mind because the whole is quite dependent upon the validity of the proof and the extensions (once the proof is totally understood) are actually far beyond what you have currently comprehended. Going over your post I find three very specific issues being brought up and I will try to alleviate your feelings of misgivings.

 

I wouldn't say I have feelings of misgivings, and I think I have a decent idea about what your fundamental equation is and what it isn't. Whatever the reality behind some data, a self-coherent model of it can be mapped as such that it obeys the differential equation. I will not confuse ontology and epistemology very easily, if ever you're worried about that.

 

Also the third issue, I realize that your equation being meant to apply to produce logical expectations from any unknown data at all (i.e. we are not just talking about physics), all the talk of dust motes and what have you are a way to see the differential equation. I am little bit jumping back and forth between the issues 1 and 3 just in order to get a better handle of issue 1; I'm trying to imagine the dynamics of the differential equation in some sense with hopes I can understand the meaning of the math better. I think its working but I still need to stare at the equation and look at the earlier posts more.

 

The issue at that point becomes “what are your expectations”. What I proved is that there always exists a set of “invalid ontological elements” (noumenons, unknowable data, fictional events ... whatever you want to call them) which will constrain that known past to exactly what you think you know. Now simple symmetry requirements absolutely demand that (if we use numerical labels for “what we know”) there alway exists a function [imath]vec{Psi}[/imath] which will yield those expectation and that the function must obey my fundamental equation. If that function does not exist, we cannot have any expectations.

 

Here's one issue that I feel I "almost" get but not quite. Essentially after the inclusion of the invalid elements, the x,tau,t-space is filled with elements, right? I am not quite sure what that means in terms of that differential equation. If these invalid elements were not added to the soup, what would happen to the differential equation. You already tried to explain that; it was essentially the term dubbed "interaction" term, and you said without it it's as if the "dust motes" do not interact at all. That comment by itself makes perfect sense to me, as does this;

 

They either stay the same, change in the same manner as they did in the “past” or have a behavior which is being altered by the current context (i.e., those fictional elements introduced to explain their behavior).

 

...but my lack of experience with differential equations and math prevents me from seeing that clearly from the fundamental equation directly.

 

I think you misunderstand the “Bell inequality”. The issue in the “Bell inequality” is that quantum mechanics predicts results which require information to be propagated from point A to point B at speeds in excess of c (the speed of light). To quote the reference you gave, “It appears most of these experiments produce results which agree with the predictions of quantum mechanics”. That agreement requires information to be communicated between A and B at velocities well in excess of c. In fact, this is exactly the same issue raised by the “simultaneous collapse of the wave function everywhere”: that collapse violates the whole structure of “relativity”.

 

Yes I am well aware of the issues behind so-called "simultaneous collapse of the wave function everywhere", but that is not at all the problem I am trying to refer to. And no I do not think a simultaneous collapse is a solution to the problem at all just because there are those complications you are referring to. I hope you won't assume too much about why I'm asking this, and can pick up exactly the point I'm wondering about, I'll try to pinpoint what I'm thinking;

 

I don't concern myself with the issues behind a wave collapse, instead I'm taking one step backward and I'm referring to - if we talk about the experiment described at that web page - the fact that Alice & Bob score +1 some 87% of the time when they should logically score it 75% of the time. The uncomfortable issue being that that higher percentage is what you'd get if you assumed (among a plethora of other assumptions) that the measured property perfectly aligns itself to whichever way it was measured as it is measured, as oppose to having that measured property with it all along. One might say "the expectations between epistemological collapse and ontological collapse are different with this experiment".

 

I myself do not see such Bell experiment as an indication of an "instantaneous collapse of a wave function" at all, but I see it as a challenge to explain because there's no straightforward way to suppose the measured property existed for both entities, because if it did you should score +1 75% of the time.

 

That's why I did not ask you if you had a comment about "instantaneous wave function collapse" as I understand that is not what is being observed. I asked if you have a comment about the unexpected correlation between measurements. Slightly different issue.

 

Also I did say it is a side-issue since I understand that before anything can be seen as a "correlation between measurements", a large number of assumptions about reality must first exist (I realize I make a lot of assertions above that are mere assumptions, and I happen to think the answer lies in manipulation of those assumptions... ...that's an issue outside of this thread). IOW, that seems to imply, the explanation to the unexpected correlations does not lie in the differential constraints but in some specific [math]\Psi[/math], doesn't it?

 

However...

 

From the perspective I am putting forth, quantum mechanics (as it is currently presented in this presentation by Schroedinger's equation) is a fundamental truth required of your explanation. It certainly takes precedence over “relativity”. As I told you earlier, in my paradigm, relativity comes in in quite a different manner than it does in conventional modern physics but it is none the less a fundamental requirement of any “explanation”. Don't worry, I will resolve the conflict in a very logical manner.

 

...that is very interesting comment and I was about to ask you about that in the previous post. It's interesting because one road to explain the "too high correlation" is to interpret relativity slightly differently than it usually is (actually yielding ontologically absolute simultaneity without changing any observable properties). I do not yet understand how it all works in terms of your differential constraints, but hopefully I will soon... ...it could be the constraints do imply something about the too high correlations after all.

 

Ps, I hope you do not get the feeling that you've got from many people before me, that I'm just trying to find a logical problem in order to exit the topic as quickly as possible. I don't see any logical problems with the differential constraints at all.

 

-Anssi

[Doctordick]

Hi again. I was surprised to find your response to last nights post this morning. That was quick. Sorry I didn't answer as quickly; I had some things to do around the house today.

 

Let us first go to Bell's theorem. Essentially, it is “instantaneous collapse of the wave function” which is the source of the conflict. If you read that reference carefully, there are a number of sentences which are solid clues as to what is going on in Bell's world view. First note those two assumptions:

 

The desire for a local realist theory was based on two assumptions:

 

1. Objects have a definite state that determines the values of all other measurable properties, such as position and momentum.

 

2. Effects of local actions, such as measurements, cannot travel faster than the speed of light (as a result of special relativity). If the observers are sufficiently far apart, a measurement taken by one has no effect on the measurement taken by the other.

 

The first expresses the idea that the quantum mechanical solution is that ”real” states can be mixtures of eigenstates. (Eigen is the German word for “real” so an “eigenstate” has ended up being the name applied to the state seen when a measurement is made. Some circumstances can be seen combinations of different equivalent eigenstates depending on what is being measured; spin being one of these type situations. Linearly polarized states can be seen as combinations of circularly polarized states. Now that is once again getting into physics so I don't want to be teaching that.) One can create states where two different entities have correlated eigenstates (this is what is being referred to when people talk about “entanglement”) When a measurement is made, that mixture of states collapses to whatever the measurement was.

 

The second is no more than confidence that special relativity is exactly correct. Try and tell people that the problem is there and you'll have a fight on your hands. Today, asserting that Einstein was wrong gets about the same reaction as asserting Aristotle was wrong in 1300: they would burn you at the stake if they could.

 

If Alice and Bob take measurements on “entangled” entities when they are far apart, quantum mechanics says they will obtain the same correlations which would exist if the measurements were made in the same place. If the thing being measured is “real” then the information about the measurement has to get from Alice to Bob instantaneously and that violates relativity. To quote the wikipedia reference, “Bell's theorem seemed to put an end to local realist hopes for QM. Per Bell's theorem, either quantum mechanics or local realism is wrong.”

 

Down the page you will find the sentence, “Bell test experiments to date overwhelmingly show that Bell inequalities are violated. These results provide empirical evidenceagainst local realism and in favor of QM.”

 

If you understood my presentation you should understand that QM is correct (I have derived it from fundamental logical principals). That is to say, the quantum mechanical calculations have to give you the correct expectations for any experiment you perform as the fundamental relationships required by the mathematics is exactly what a flaw-free explanation must produce. It follows that, in the two assumptions made above, the second has to be in error. If you look at my derivation of my fundamental equation, you will see that I have made no presumption concerning the concept “local”. Those indices, [imath]x_i(t)[/imath], are mere numerical labels and no relationship as to their selection has been specified. As I said to Qfwfq quite a while back, you cannot talk about “local effects” without defining “local”. I have not yet defined the term in my paradigm so the concept “local realism” is still a meaningless concept.

 

Again, the only way to view what I have presented is to see it as a data compression mechanism for keeping track of what you know or think you know. I may have reproduced quantum mechanics as the correct way to calculate your expectations but I have certainly not even suggested that these functions [imath]\vec{\Psi}[/imath] constitute “real” waves propagating through the universe. Your expectations are in your head and no where else. The “collapse of the wave function” amounts to no more than, “you now have more information and you need to change your expectations to accommodate that new information”. Since the simultaneity exists only in your head you should comprehend that your comment is on point: “(actually yielding ontologically absolute simultaneity without changing any observable properties)”.

Here's one issue that I feel I "almost" get but not quite. Essentially after the inclusion of the invalid elements, the x,tau,t-space is filled with elements, right?

Well close but not really accurate. What I said was that, no matter what the “valid ontological elements” were one could always conceive of a set of “invalid ontological elements” such that a rule [imath]F=\sum_{i \neq j} \delta(\vec{x}_i - \vec{x}_j) = 0[/imath] would constrain the “valid” elements to exactly what they are. If the valid ontological elements (or the numerical indices representing them) are known exactly then, yes, the x,tau,t space would have to be filled with “invalid ontological elements”; however, if there is any uncertainty in the correct values of those reference indices, one can omit an “invalid ontological element” for any possibility which is to be left open for a valid ontological element. In that case, the rule above would allow a range of values instead of just one single value. The existence of uncertainty in what we know requires uncertainty in that index assignment.

I am not quite sure what that means in terms of that differential equation. If these invalid elements were not added to the soup, what would happen to the differential equation.

Since, in order to assure that the rule remain valid all the way to infinity, it was necessary to require the solution to be antisymmetric with respect to exchange of “valid” ontological element labels. Now please note that this does not mean that antisymmetry is a sign of “validity”; there can be no way of establishing the validity of any ontological element; however, if your explanation requires no “invalid ontological elements” then [imath]\vec{\Psi}[/imath] must be asymmetric with respect to exchange of any pair of indices. In that case, [imath]\sum_{i \neq j} \delta(\vec{x}_i - \vec{x}_j)[/imath] will always be zero as [imath]\vec{\Psi}[/imath] will exactly vanish if any two indices are identical and the rule is unnecessary. The “interaction” term can be simply dropped and the equation is separable as I suggested in the previous post. The solution is totally equivalent to a universe consisting of a collection of non-interacting dust motes. Not a very interesting problem to consider.

You already tried to explain that; it was essentially the term dubbed "interaction" term, and you said without it it's as if the "dust motes" do not interact at all. ... but my lack of experience with differential equations and math prevents me from seeing that clearly from the fundamental equation directly.

I think it would be beneficial to carry my post to Bombadil (that would be post #203) one step further. That is the post where I give him the exact form of f generated by left multiplying by [imath]\vec{\Psi}_2^\dagger[/imath] and integrating over all the indices in set #2.

[math]f=\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 + \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\}[/math]

[math]-K \left\{\int \vec{\Psi}_2^\dagger \cdot \frac{\partial}{\partial t}\vec{\Psi}_2 dV_2 \right\}[/math]

 

There are three terms there. A close examination of the second term will reveal that all arguments are integrated out thus it becomes a mere number multiplied on [imath]\vec{\Psi}_1[/imath]. Once you understand that the right hand side of the fundamental equation has been defined to be the energy of the system (a conserved quantity) this second term is nothing more than an adjustment to that energy due to the energy which is to be associated with set #2. The final term I have already discussed elsewhere. It provides a time variation of the energy of the universe required by time variation of the rest of the universe: i.e., it yields a time variation in that potential well which turned up in the Schroedinger equation I deduced. The first term is the one I want you to think about. It is a sum over both i taken from the “valid” set under consideration and j taken from the “invalid” set. First of all, any part of the invalid set which is antisymmetric with respect to exchange with the “valid” set yields exactly zero as the arguments of that Dirac delta function can not be the same. We are only interested in the contribution from the symmetric portion of set #2 (that would be bosons). Let us look at a single term of that sum:

[math] \int \vec{\Psi}_2^\dagger \cdot \beta_{ij}\delta(\vec{x}_i -\vec{x}_j)\vec{\Psi}_2 dV_2 \equiv \beta_{ij}\int\vec{\Psi}_2^\dagger \cdot\vec{\Psi}_2 \delta(\vec{x}_i-\vec{x}_j)dV_2 [/math]

 

It is being integrated over all arguments. So long as the integration is over an index not in the Dirac delta function, the integral will be exactly unity. It follows that the only contribution is from the integration over [imath]\vec{x}_j [/imath]. At this point you need to comprehend what happens when you integrate over a Dirac delta function. The Dirac delta function is zero everywhere except when the argument [imath](\vec{x}_i-\vec{x}_j)[/imath] is zero. When that occurs the value of the function goes to infinity; however, it goes to infinity is a very specific way. The integral across that value is defined to be exactly unity. That is,

[math]\int f(x)\delta(x)dx = f(0)[/math]

 

In our case, the function being integrated is [imath]\vec{\Psi}_2^\dagger \cdot\vec{\Psi}_2[/imath] evaluated when the argument of the Diract delta function is exactly zero or, when [imath]\vec{x}_i\equiv\vec{x}_j[/imath]. That means that the result is a function directly proportional to the probability that the invalid ontological element (that exchange symmetric "invalid"ontological element, a boson referred to as [imath]\vec{x}_j[/imath]) is at the point [imath]\vec{x}_i[/imath]. In other words, (since the terms in the differential equation have been defined to be "energy") the potential energy well seen by the valid ontological element is exactly modeled by the probability density of these invalid ontological elements. In essence, we are looking at boson exchange forces. Instead of quantizing a force field, we generate a force field from the quantized entity (our reference label).

Ps, I hope you do not get the feeling that you've got from many people before me, that I'm just trying to find a logical problem in order to exit the topic as quickly as possible. I don't see any logical problems with the differential constraints at all.

I don't have that feeling at all.

 

Have fun -- Dick

[AnssiH]

Hi again. I was surprised to find your response to last nights post this morning. That was quick.

 

Yeah, because I really had no time to try and think over the math issues properly, so I decided I might as well whip up a quick reply. Such is the case this time as well.

 

Amazingly, I think I understand exactly what you are saying about Bell experiments, and definitely I think the notion of "local realism" is kind of mixed up thing in people's heads. And yeah, I do know for a fact that it is in fact logically possible to find a valid solution to that whole Bell inequality conundrum from deeper understanding of relativity (or its logical roots).

 

I don't understand your fundamental equation yet well enough to see what implications it makes exactly, but I must say it is pretty amazing if it does offer an explanation to Bell inequality through epistemological concerns... In that case I can certainly understand what you mean by Bell experiments offering a confirmation of your paradigm, even though with the common interpretation of relativity it would seem like exactly the opposite is true (Once again we see that one paradigm cannot be investigate from within another...)

 

I mean that is pretty solid evidence right there, but that part is also something that needs to be presented very carefully and with absolute clarity or people tune out automatically as they think it is being implied that relativity is flat out false. The good thing is that I'm certain that a lot of people would find that explanation to Bell experiments once again quite satisfying as long as they really understood what is being said. A lot of people actually do understand that it is kind of a slippery thing to try and hold an ontological view where Bell experiments and relativity exist at the same time... ...without ending up to dualism at least.

 

Sparking any interest anyone...? (with much better math skills than mine :D)

 

I guess one could say yours is an explanation that actually unifies relativity and quantum mechanics in the sense that it becomes understood why both can describe the same universe, would you say?

 

Well, I think next on my list is to try and go through post #203 then. I'll have a lot of questions about that one once I get there :I

 

But before that just trying to clarify the issue to Buffy;

 

So, Dick, I have to admit that your last response to me still did not get across the reasons why you think that the fundamental equation *must* obey shift symmetry, precisely because it can be arbitrary and obey any number of perfectly valid, "pure" mathematical rules.

 

The issue is "why is the probability function shift symmetrical (shift in the assignment of labels)".

 

I believe the communication problem here is that your assumption as to the exact meaning of the labels is slightly askew, and perhaps the "electron vs. Volkswagen" example is too silly to be picked up properly :) Maybe a better example is to ask about the difference between "electron" and "positron", or "water" and "ice". The point being that whatever patterns you find from the raw data, they will tell you what you are seeing. Call that context or properties or behaviour or what you will, the fact is that the entities you perceive, you perceive because you have a definition as to "what sort of pattern is entity X" (in the raw data), and that allows you to recognize that element.

 

The labels to so-called "ontological elements" are there so we have a meaningful way to discuss and track their behaviour through the differential constraints, and the assertion that the probability function must be shift symmetrical to the assigned labels is essentially an assertion that your expectations about the future of that data lie in the patterns of the data, not in whatever labels you put onto the elements constituting those patterns (perhaps it helps to see the labeling as a procedure that is done just for the purpose of this very analysis)

 

To be more accurate, what I say above is just one way to see the situation, and I hope I had a better grasp of the constraints and their implications by now so that I could make better comments (I'm certain there are many ways to conceive these logical constraints and their implications), but I can say this, when someone is presenting ideas about such a slippery subject as epistemology & ontology, certain level of ambiguity will always be preventing communication.

 

There has been many issues that have been too ambiguous for me to pick up and there has been cracks in my knowledge (still are), but they tend to bridge themselves later on as it becomes clear why something has been presented the way it has been.

 

What I'm saying is, don't fear the cracks on the earth too much, just walk over them and see if they disappear along the way :)

 

Well that gets us to Qfwfq;

 

I tend to agree, there must be some choices along the way, at the very least when Dick says "an approximation of" implies the matter of which approximation.

I haven't been able to follow the details of the math, since Dick revised the shift symmetry I didn't even quite catch exactly how these are consequential to what. Did you get that straight Anssi? I'm at a loss to see exactly which choices are hidden along the way.

 

The revision to shift symmetry was, as far as I can tell, more of a revision to the presentation of the issue (the presentation had an invalid argument as to why the K is to be held constant).

 

What is important is that the [imath]\vec{\Psi}[/imath] can be any sort of function at all, since we are merely interested in its logical constraints under the premise that has been put forth (the x,tau,t-table etc).

 

My math skills are not up to par to immediately understand why Doctordick does not want K to be function of the indices (but I'm sure your are if you put time to it), apart from understanding that there's some algebraic advance to it, i.e. it makes things simpler.

 

As far as I can tell, in this differential analysis it is quite valid to keep K constant as long as it does not limit [imath]\vec{\Psi}[/imath].

 

About what choices led to "newtonian-like" tracking of the elements, I really cannot tell at this time. One should carefully examine the logical arguments leading to the 4 differential constraints (that's mostly philosophy, but I don't see any immediate objections there), and one should carefully examine the deduction of the fundamental equation from the 4 constraints (my math skills are not up to par to spot any hidden choices there).

 

Overall it sounds like you expect with high probability to find hidden assumptions somewhere, probably because you don't expect symmetry & self-coherence arguments to be enough to deduce all that. Again I am out of depth with math to give you any answers, but I can tell you it should not be too surprising if this analysis is all valid, because this topic has as much to do with how any objects are identified as it has to do with how they behave (in our conception of them anyway).

 

I think you have a fairly good grasp about ontological and epistemological issues, so just keep firmly in mind that this analysis tells us absolutely nothing about what reality is like, it just tells us - potentially - how initially meaningless data gets to be tracked in self-coherent way with help of various symmetries... ...and how it gets assigned with meaning along the way.

 

I'll be here to help with the (ambiguous) communication parts as best I can :) (And trying to learn math)

 

-Anssi

[Doctordick]

Hi Annsi, I hope you will understand. A lot of thought has gone into this post as my perspective is quite askew to the view of a modern physicist. I have also decided to start a new thread as the “What can we know of Reality” thread has become quite lengthly.

 

I think you understand far more than you let on. Some of the issues you bring up I found very intriguing many years ago and I would seriously like to discuss them; however, I think I have to proceed a little further in my development before we can really walk that path. You brought up relativity and I think that issue should probably be discussed next. It should be clear to you that at least some aspects of relativity are somehow embedded in my fundamental equation since, in order to , I had to presume the total energy of the event of interest was approximately equal to [imath]mc^2[/imath] where m was the rest mass. This approximation clearly says that, in my paradigm, Schroedinger's equation is a non-relativistic approximation. Look at it this way, if aspects of relativity were not embedded in my equation, why would such an approximation be necessary.

 

As I said, I am starting another thread where we can discuss my view of relativity. We can continue to use this thread to discuss any difficulties you have in understanding the derivation of my fundamental equation.

 

Have fun – Dick

[AnssiH]

As I said, I am starting another thread where we can discuss my view of relativity. We can continue to use this thread to discuss any difficulties you have in understanding the derivation of my fundamental equation.

 

Okay. Last weekend I had some time to look at that post #203, but actually ended up going way back to the physics forums posts while trying to get a clearer picture of everything. Some things that I did not quite understand back then properly seemed to make more sense this time around... At any rate as I have time I'm re-running through these things and once I end up to parts I feel I really don't have a hang of (like #203 :D), I'll be replying to this thread then...

 

-Anssi

[Rade]

?? This is the end of the thread ?? -- a shame, since after all this time we have no answer to the OP question from Doctordick...What can we know of reality". What we get is a very detailed mathematical derivation of a "fundamental equation" that deals with "explanation itself", but no hint how to link this equation to answer the OP question that Doctordick began many moons ago.

 

But then, is it really of any interest to discuss what "we" can know about reality, since it is not possible for a "we" to know anything, only the "I" can know, and the only thing that any "I" can know is that "it exists".

[AnssiH]

?? This is the end of the thread ??

 

No it's not :D

Don't worry about it... all in good time.

 

-- a shame, since after all this time we have no answer to the OP question from Doctordick...What can we know of reality". What we get is a very detailed mathematical derivation of a "fundamental equation" that deals with "explanation itself", but no hint how to link this equation to answer the OP question that Doctordick began many moons ago.

 

If you are still expecting some specific ontological description in the end of this, don't hold your breath just yet :beer:

 

-Anssi

[Doctordick]

Hi Anssi, as per usual, you seem to comprehend exactly where this all is heading. Thank you. You have mentioned post #203 several times and I thought I would take a look at it to see what the difficulties might be. That post is nothing more than a response to Bombadil regarding his inability to see what the actual form of “f” has to be. It is entirely directed to a statement I made in post #194.

The function f must be a linear weighted sum of alpha and beta operators plus one single term which does not contain such an operator. That single term arises from the final integral of the time derivative of [imath]vec{Psi}_2[/imath] on the right side of the original representation of the result of integration:

[math]\int \vec{\Psi}_2^\dagger\cdot\frac{\partial}{\partial t}\vec{\Psi}_2dV_2.[/math]

 

(I put that expression outside the quote so it would be easy to see it.) It isn't really necessary to see exactly what the f looks like to understand the derivation of Schroedinger's equation; all that is necessary is that you realize that it has to be a sum of terms multiplied by alpha and beta operators (plus that one term arising from the time differentiation). It is the fact that cross terms vanish (when an operator consisting of weighted alpha and beta operators is squared) which is important here. That fact makes the final result a simple collection of functions multiplying those operators squared (each of which are exactly 1/2).

 

Rereading post #203, I can see where it can be confusing as I don't make it very clear as to exactly which “curly brackets” I am referring to. In particular,

... Furthermore the last term of the declared result is clearly the first term of what is enclosed in the last curly bracket ...

this term isn't even inside the curly brackets (I had already factored it out) :doh: . I am doing nothing except examining the original result of integration (picking out two specific terms in my concluded result) and then defining f to be everything else. It is actually quite simple algebra together with the fact that simple integration over the context expectations (the sum of all possibilities) has to be unity. If you want to go over post 203 in detail, I will answer any questions you want but understanding post #194 is much more important. :shrug:

(By the way, I just made some small corrections to that post which I think could have been confusing. Removed two open parentheses which had no business being there and changed e for energy to E and p for momentum to P) Sorry about being sloppy and inconsistent.

?? This is the end of the thread ?? -- a shame, since after all this time we have no answer to the OP question from Doctordick...What can we know of reality". What we get is a very detailed mathematical derivation of a "fundamental equation" that deals with "explanation itself", but no hint how to link this equation to answer the OP question that Doctordick began many moons ago.

The fact that the fundamental elements upon which your personal explanation of reality is built must approximately obey Schroedinger's equation (and thus Newtonian mechanics) has nothing to do with the world view you possess? Or is it rather that you do not believe the fundamental elements of your world view are not representable via numerical references? If it is the second case, I hold that your world-view is not flaw-free: i.e., you have not thought the issue out.

But then, is it really of any interest to discuss what "we" can know about reality, since it is not possible for a "we" to know anything, only the "I" can know, and the only thing that any "I" can know is that "it exists".

Please tell me what you mean when you say you “know” something. When I say I know something I mean that I possess some coherent view of it that makes sense: that is to say, I possess expectations with regard to aspects of the things I know. No, this thread is not yet finished.

If you are still expecting some specific ontological description in the end of this, don't hold your breath just yet :)

As always, you have the essence in mind. :)

 

Have fun -- Dick

[AnssiH]

Hi Anssi, as per usual, you seem to comprehend exactly where this all is heading. Thank you.

 

Yeah I think I have a pretty good idea what this is about :)

 

You have mentioned post #203 several times and I thought I would take a look at it to see what the difficulties might be. That post is nothing more than a response to Bombadil regarding his inability to see what the actual form of “f” has to be. It is entirely directed to a statement I made in post #194.

 

Yes, actually last week, whenever I've had some time at my hands, I've just walked through the thread again (all the way from PF), since now I have little bit better overall idea about what you are trying to say, or where things are headed. This time I know from the start that you are heading to those "momentum" and "interaction" terms (i.e. that the elements are going to be seen like "moving dust motes")... I did not have that much time this week though, and I am still unsure how that momentum term works exactly, but I think I understand the interaction term...

 

It essentially has to do with the fact that information would always be lost if multiple "dust motes" were allowed to enter the same location, and since that constraint prevents it, it essentially means some sort of interaction or transformation must occur between the dust motes instead of them entering the same location... ...and that is where the "invalid ontological elements" also come to play, I think you've mentioned a few times something to the effect that they can be used to produce your expectations, and it was not clear to me how you meant that before. (albeit I have an idea how that works in common terms in our worldview, but it is still slightly different matter when we talk about that differential equation, obviously)

 

At any rate, it seems to be helpful to go through things at this point, and I'll have questions from #194 I'm sure once I really get to it. I won't comment more at this time...

 

-Anssi

[Doctordick]

Hi Anssi, sorry I have been so slow to respond. Every time I look at the two threads I have open at Hypography I just get terribly disappointed. No one seems to understand what I mean when I say they are bringing too much baggage to the discussion. I was particularly disappointed with Qfwfq. I was hoping for a little more thought from him but he has made it quite clear that he doesn't read what I say; he just scans it and interprets it in terms of what he thinks I am saying (that is, in terms of his presumed valid world-view). The details of what I say are invariably overlooked by everyone. You are the only one who seems to have some comprehension of my thrust and, even you, seem drawn off into an interpretation which will allow you to ignore the details.

 

I have built an analytical tautology which yields very surprising results and no one wants to accept the internal validity of that construct itself. They won't even look at it seriously. I will try to put down the essential details in the order they should be comprehended.

 

The issue is epistemological constructs and the need to avoid flaws in those structures. (How can one refer to themselves as scientific if they have no interest in the possible flaws in their views.)

 

All epistemological constructs are based upon a set of beliefs thought to be true (represented by a collection of events). The set is finite as we cannot possess an infinite set of ideas. What name you give to these beliefs (or events) is immaterial as the names are mere reference labels and the meaning of the labels are not embedded in the labels themselves but must be interpreted from the whole. Thus it should be clear that one can use numerical labels for these references (computers use numerical labels for everything; even this very message you are reading).

 

If one has a flaw-free epistemological construct, then that construct can be used to generate expectations applicable to the future. Any expectations can be seen as probabilities of specific collections of referenced events. Thus any universe of any kind may be seen as a mathematical function [imath]\vec{\Psi}[/imath](a set of numerical labels) where the probability is given by the squared magnitude of that function. If anyone disagrees with that fact, let me know why you feel that way!

 

Simple symmetry considerations demand that [imath]\vec{\Psi}[/imath] obeys the following equation.

[math]\left\{\sum_i \vec{\alpha}_i \cdot \nabla_i + \sum_{i neq j}\beta_{ij}\delta(x_i -x_j)\delta(\tau_i - \tau_j) \right\}\vec{\psi} = K\frac{\partial}{\partial t}\vec{\psi} = iKm\vec{\psi}[/math]

 

under the simple constraints that [imath]\sum \vec{\alpha_i} \vec{\Psi}=\sum \beta_{ij}\vec{\Psi}=0[/imath]. If anyone disagrees with that fact, let me know why you feel that way!

 

That's a tautology! It is true by definition! If anyone disagrees with that fact, let me know why you feel that way!

 

The first astounding thing which falls out of that tautology is the fact that, if I use the words “momentum”, “energy” and “mass” to be references to specific terms in that equation, Schroedinger's equation (and thus Newtonian mechanics) simply falls out as an approximation to that equation(post #194). Not only does it fall out as a necessary consequence of that equation but it falls out without any “free parameters” of any kind.

[math]m=\frac{q\hbar}{c}[/math] , [math]c=\frac{1}{K\sqrt{2}}[/math] and [math]V(x)= -\frac{\hbar c}{2q}G(x)[/math]

 

If one examines the replacement above carefully, they will discover that c arises because of the fact that the x and tau axes are defined differently (i.e., in common physics, distance in the coordinate system is defined twice); mass and momentum are also essentially the same thing defined twice and energy is no more than the magnitude of the total momentum. Finally, it is not difficult to show that the value of K is essentially immaterial to the dynamics of any solution (that proof involves defining a clock which I would be willing to do if I could obtain agreement on the above tautology).

 

I seen no reason to proceed further without agreement that my fundamental equation is a valid starting point for any discussion.

 

Have fun -- Dick

[Doctordick]

Hi Anssi, I started to answer your note concerning momentum and your examination of post #194 when I realized that there was an issue there which is apparently clear to no one. I decided to bring it up again here on the main thread (in the hopes that it will dawn on someone what post #194 is all about).

 

If I have asked once, how one tells the difference between an electron and a Volkswagen, I have asked it a dozen times. Somehow no one seems to grasp the import of that question. I have given an explicit answer several times, “the difference is expressed by the context”, but the answer seems to fall on entirely on deaf ears. If you examine any scientific analysis of anything, you will find that all modern scientists make the assumption that the context is understood. In fact that is a blanket assumption made by everyone in the analysis of anything.

 

Think of it this way. If it is the context which provides the information which delineates the difference between an electron and a Volkswagen then, if your explanation allows for that context to change (and allows identified entities to continue to exist into the future), it is entirely possible for an event that was originally identified to be an electron to be later identified as a Volkswagen. Now no rational explanation includes the possibility of an electron transforming into a Volkswagen; such a thing would be seen as ridiculous by everyone. But what they don't realize is that their position in actuality asserts that context can not change; or rather that change in context can be universally ignored. That is clearly something which can not be proved and is an assumption, a very significant assumption of every theory ever put forth.

 

You should note that my fundamental equation,

[math]\left\{\sum_i \vec{\alpha}_i \cdot \vec{\nabla}_i + \sum_{i \neq j}\beta_{ij}\delta(x_i -x_j)\delta(\tau_i - \tau_j) \right\}\vec{\Psi} = K\frac{\partial}{\partial t}\vec{\Psi},[/math]

 

is explicitly what is normally referred to as a many body equation. If you examine the collection of mathematical relationships used by the physics community, you will find that they are almost universally one or two body equations. When you see a many body equation, that equation will be built out of concepts defended via two body interactions. If you ask the physicists why they do this they will inform you that it is because many body problems can not be solved directly. The actual fact is that the relationships used to deduce these relationships simply ignore context: i.e., if they didn't ignore context, they couldn't solve any problems.

 

The central problem here is that the symmetry properties I used to deduce my equation are not valid in the presence of context. Those symmetries are only valid when there exists no information outside the information embedded in that equation: i.e., the equation is only valid in a context free environment. But we all know that a general many body equation cannot be directly solved so the whole issue seems to be rather moot; at least on the surface anyway.

 

The advantage I have is the fact that [imath]\vec{\Psi}[/imath] is an expression of your expectations (as deduced from your explanation of reality) and not at all a statement of reality (as Buffy has pointed out many times). As such, the context is a figment of your imagination (part and parcel of your explanation) and not bound by the nature of reality itself. That is to say, the context is the presumed solution of that equation for the events not under examination. All the equation requires is that the elements of that context, the elements your explanation is ignoring, must obey that equation. The point being that your explanation is in fact ignoring the impact of a great number of important elements: i.e., ignoring context is a fact and not an assumption. This is the single most important difference between my attack and the standard scientific approach.

 

The first half of post #194 has to do with the process of eliminating the context to be ignored from the equation while maintaining the fact that the context obeys the equation. The removal is accomplished by stating that the portion of [imath]\vec{\Psi}[/imath] relating to the element of interest is known (that is, your expectations for that part of the context is a known thing). The first context I remove is that part expressing the explicitly invalid elements. I do that because it points out that it is the Dirac delta function which inherently provides the connection between the behavior of the elements in general. I then remove all the elements except the one explicitly being examined. That is because I know that I cannot actually solve the equation until I reduce it to a two body equation (the two "bodies" of interest are, the element under examination and the impact of the context which can not be ignored: i.e., what I have called the interaction term).

 

I hope that clears things up a bit.

 

Have fun -- Dick

[AnssiH]

Hi, yeah, sorry to all for being so silent here lately, just been quite busy :eek:

 

The details of what I say are invariably overlooked by everyone. You are the only one who seems to have some comprehension of my thrust and, even you, seem drawn off into an interpretation which will allow you to ignore the details.

 

Yeah, that may be true, but to my defense I am at least actively trying to understand what are the important details :( I'm not deliberately looking for ways to ignore important details when I'm trying to interpret the differential equation in different ways.

 

And regarding that dust mote interpretation, so am I reading the situation correctly that even though the presentation started with "unordered" presents, the differential constraints will not actually allow any (self-coherent) worldview to look like bunch of randomized presents once all is said and done? And that is because it is the patterns that the so-called "ontological elements" form that allow for a definition of any normally perceived "entity", and their behaviour must be shift symmetrical, at least in so far that no undefendable assumptions are allowed in one's worldview... Well I don't feel I have a very good grasp of all that yet, so if the above did not make any sense just tell me so :I

 

If I have asked once, how one tells the difference between an electron and a Volkswagen, I have asked it a dozen times. Somehow no one seems to grasp the import of that question. I have given an explicit answer several times, “the difference is expressed by the context”, but the answer seems to fall on entirely on deaf ears.

 

I think I understand what you are getting at with that question. Would you say it is okay to also express this by saying that in the x,tau,t-presentation, an electron and a Volkswaken are things that are found from the patterns of the "ontological elements" (once the pattern of "electron" or "Volkswagen" are defined)?

 

The central problem here is that the symmetry properties I used to deduce my equation are not valid in the presence of context. Those symmetries are only valid when there exists no information outside the information embedded in that equation: i.e., the equation is only valid in a context free environment.

 

I am actually not sure what you are saying here :I

 

Perhaps it will make perfect sense as soon as I'm done with #194; I'll get to that one properly tomorrow as it's getting late...

 

-Anssi

[Bombadil]

Of the fundamental equation I’m going to have to agree that there is nothing that can be wrong with it now as for what it tells us I think that you and anssih are getting a lot more out of it then I am. Firstly as you have said more then once it tells us nothing about reality I have to agree there is nothing about reality that it can tell us. Now you have also said that it does tell us something about our expectations and while I can see that it must, anything that it tells about those expectations seems to me to be only understood under a certain interpretation and I have seen vary little that tells me anything about such an interpretation. Now what I have seen seems to tell me something about what a mathematical explanation of anything must satisfy.

 

Essentially, what I am saying is that, by showing Schroedinger's equation is an approximation to my equation, all of the physics derivable from Schroedinger's equation is derivable (as an approximation) from my equation. Since all of Newtonian mechanics is derivable from Schroedinger's equation, so is all of Newtonian mechanics. Another way of looking at this is to realize that the semi validity of Newtonian mechanics tells us absolutely nothing about reality; it is no more than a consequence of requiring our explanation of reality to be internally self consistent. This itself is a profound philosophical statement.

Have fun -- Dick

 

This statement seems to me that it is quite a statement although I cant see how we can say this because you have set some constraints on the equation and you have yet to show how these constraints have limited the equation. Now if you can show that these constraints have not limited the solution I think that I will have to agree with such a statement but I don’t think that you have gone into any details on their effect.

 

What it seems to me that you have shown is that by ignoring the effect of the context on the form of the solution the Schroedinger equation becomes the simplest solution to derive. Perhaps this would make Newtonian mechanics the simplest way to understand something with a consistent explanation.

 

Now you have on several occasions suggested that you have derived all or at least most of physics from the fundamental equation this seemed at first like quite a statement. But without some means of understanding what you have derived this means vary little to me. For instance suppose you had derived the Schroedinger equation without knowing anything about it, you should understand that I know vary little about it and I have no idea of the actual mathematical working of it in any setting but what you have put it in, in fact had you not said what it was that you had derived I would not have recognized it.

 

The first half of post #194 has to do with the process of eliminating the context to be ignored from the equation while maintaining the fact that the context obeys the equation. The removal is accomplished by stating that the portion of vec{Psi} relating to the element of interest is known (that is, your expectations for that part of the context is a known thing). The first context I remove is that part expressing the explicitly invalid elements. I do that because it points out that it is the Dirac delta function which inherently provides the connection between the behavior of the elements in general. I then remove all the elements except the one explicitly being examined. That is because I know that I cannot actually solve the equation until I reduce it to a two body equation (the two "bodies" of interest are, the element under examination and the impact of the context which can not be ignored: i.e., what I have called the interaction term).

Have fun -- Dick

 

Then the term [imath]\vec{\Psi}_r[/imath] that appears in the equation after you have limited it to a one body equation (actually a two body equation) is nothing more then the effect that the context has on the object of interest?

 

Then is the first constraint that you added equivalent to the context having no effect on the form of [imath]\vec{\Psi}[/imath] and the seconded constraint being equivalent to the context being unchanged by changes in t, if so what does this make the third constraint equivalent to?

 

Also at one point you seem to suggest that without the first two constraints that it still turns into the Schroedinger equation but that it is a slightly more complex version of it am I correct in understanding it this way?

 

I would like to know more about what you are presenting but I defiantly get the impression that either I’m misunderstanding something or that I’m not being vary clear about how I understand something. If you have some idea what it is that I’m missing I would like to know what it is so I can try and clear it up.

[AnssiH]

Having divided the arguments into two sets, a competent understanding of probability should lead to acceptance of the following relationship: the probability of #1 and #2 (i.e., the expectation that these two specific sets occur together) is given by the product of two specific probabilities: [imath]P_1[/imath](#1), the probability of set number one, times [imath]P_2[/imath](#2 given #1), the probability of set number two given set number one exists. The existence of set #1 in the second probability is necessary as the probability of set #2 can very much depend upon that existence.

 

I am not sure what you mean when you say "probability of set number two given set number one exists". I guess it's not the same as just including both sets to the arguments of [imath]P_2[/imath]. Does it mean that the probability of set #2 cannot be known until we know if set #1 actually became true?

 

If so then I think I understand what you mean by "the probability of set #2 can depend upon the existence of set #1".

 

=== QUOTE #194 ===

It should be clear that, under these definitions (representing the argument [imath](x,\tau)_i[/imath] as [imath]\vec{x}_i[/imath]),

 

[math]\vec{\Psi}(\vec{x}_1,\vec{x}_2,\cdots, t)=\vec{\Psi}_1(\vec{x}_1,\vec{x}_2,\cdots,\vec{x}_n, t)\vec{\Psi}_2(\vec{x}_1,\vec{x}_2,\cdots, t).[/math]

======

 

There doesn't seem to be any mention about "the probability of set #2 depending on the existence of set #1" in that equation, or does that expression actually mean that both sets are included as arguments to both Psis?

 

=== QUOTE #194 ===

Substituting this result into our fundamental equation, what we obtain can be written

 

[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]

======

 

I pretty much have to take that on faith at this time... :I

 

=== QUOTE #194 ===

Under this picture, set #2 is certainly context as since they are invalid ontological elements, they can be anything so long as they are consistent with the explanation: i.e., the only requirement here is that they need to obey the fundamental equation. Thus it is that I will take the position that, if we know a flaw-free explanation, we know the method of obtaining our expectations for set #2: i.e., we know [imath]\vec{\Psi}_2[/imath].

======

 

That seems perfectly valid...

 

=== QUOTE #194 ===

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]

======

 

...and now I'm lost :I

 

=== QUOTE #194 ===

Notice that [imath]\int \vec{\Psi}_2^\dagger \cdot\vec{\Psi}_2dV_2 [/imath] equals unity by definition of normalization.

======

 

Um... Does that essentially mean that the integral of "all the possibilities" is 1? I'm just reading alien language here...

 

=== QUOTE #194 ===

Furthermore, since the tau axis was introduced for the sole purpose of assuring that two identical indices associated with valid ontological elements existing in the same [imath](x,\tau)_t[/imath] would not be represented by the same point, we came to the conclusion that [imath]\vec{\Psi}_1[/imath] must be asymmetric with regard to exchange of arguments.

======

 

We did? Oh, but then it was [imath]\vec{\Psi}_2[/imath] that could be symmetric to exchange of arguments (i.e. the invalid elements)? Looks like I will need to refresh my memory regarding that issue... For now I take it on faith.

 

=== QUOTE #194 ===

If that is indeed the case (as it must be) then the second term in the above equation will vanish identically as [imath]\vec{x}_i[/imath] can never equal [imath]\vec{x}_j[/imath] for any i and j both chosen from set #1.

======

 

Yup, seems valid

 

=== QUOTE #194 ===

If the actual function [imath]\vec{\Psi}_2[/imath] were known (i.e., a way of obtaining our expectations for set #2 is known), the above integrals could be explicitly done and we would obtain an equation of the form:

 

[math] \left\{\sum_{i=1}^n \vec{\alpha}_i \cdot \vec{\nabla}_i +f(\vec{x}_1,\vec{x}_2, \cdots,\vec{x}_n,t)\right\}\vec{\Psi}_1 = K\frac{\partial}{\partial t}\vec{\Psi}_1. [/math]

 

The function f must be a linear weighted sum of alpha and beta operators plus one single term which does not contain such an operator. That single term arises from the final integral of the time derivative of [imath]\vec{\Psi}_2[/imath] on the right side of the original representation of the result of integration:

 

[math]\int \vec{\Psi}_2^\dagger\cdot\frac{\partial}{\partial t}\vec{\Psi}_2dV_2.[/math]

======

 

And here I got lost again.

 

On a related note, I still do not have a very clear picture of the time derivative on the fundamental equation;

[math]K\frac{\partial}{\partial t}\vec{\Psi}[/math]

 

Since [imath]\vec{\Psi}[/imath] was shift symmetrical, I suppose that means the derivative is 0? But then I don't understand it (zero) being multiplied by K... Here's what you said about it;

 

=== QUOTE #220 ===

In the absence of the “interaction” term, the fundamental equation is exactly

 

[math]\sum_i \vec{\alpha}_i \cdot \vec{\nabla}_i \vec{\Psi} = K\frac{\partial}{\partial t}\vec{\Psi}.[/math]

 

which is eminently separable. The right hand side has the simple solution [imath]\vec{\Psi}= e^{\frac{t}{K}}[/imath]: i.e., Energy is conserved and is proportional to K (K being defined by your definition of time).

======

 

I don't understand where that solution comes from and over all I am kind of struggling to understand that time derivative....

 

The next part of #194 essentially performs the same procedure again to reduce the differential into a single body equation, so I think I need to figure out the above first and then I should understand that next step too. Looking at the rest of the post, I think I have plenty on my plate on this first step already. Sorry I am so slow; most of the math looks quite alien to me :/ I am willing to take parts of this deduction on faith if you think it's better for the first pass.

 

-Anssi

[Doctordick]

Hi Anssi, my wife and I have been down to the Gulf coast for the weekend and we just got back: i.e., I have not been checking the internet. I will answer your post in detail as soon as I make a few comments on the two previous posts (your earlier post and the one made by Bombadil).

Yeah, that may be true, but to my defense I am at least actively trying to understand what are the important details :) I'm not deliberately looking for ways to ignore important details when I'm trying to interpret the differential equation in different ways.

This is what I am talking about when I complain about people bringing too much baggage to the discussion. Until we have a specific solution to the fundamental equation, we have no justification for any interpretation of the equation itself. The equation is no more than a statement of a requirement demanded by self consistency; the implications of that constraint are so complex (in their entirety) that those consequences are essentially beyond comprehension.

 

In deducing Schroedinger's equation (and thus Newtonian mechanics by default) I have shown that it makes no difference what you are talking about, whatever it is, it can be seen as approximately obeying Newtonian mechanics: i.e., it is either something that is not changing, something that is changing in a consistent way or there is something changing the way in which it changes which we call “a force” (there is no other possibility). Physicists get upset when I express Newtonian mechanics in that way but it's true nonetheless. In many senses, that is exactly the nature of “the dust mote interpretation”. The dust mote is one element in a context (the context being the other dust motes) which essentially doesn't change (at least with respect to our expectations). The dust mote of interest changes in a consistent manner (it “moves” in a straight line in our coordinate representation) unless something changes that motion (it bounces off another dust mote). The net result of the interactions with the contextual dust motes (remember, we created these contextual dust motes to make our explanation work) is that “force” which explains the changes. It is no more than a tautological construct which provides an explanation of what we see.

 

By the way, if you knew differential equations well, you would know that the dust mote interpretation is a valid general solution to my fundamental equation so long as the circumstance is examined on a sufficiently fine scale: i.e., the distance (in that Cartesian coordinate system) between interactions is enough to ignore the interactions most of the time. Since the interaction is a Dirac delta function, one can always look at a finer scale. No matter how fine a scale we examine, the range of the interactions (the Dirac delta function) is still zero! :lol:

And regarding that dust mote interpretation, so am I reading the situation correctly that even though the presentation started with "unordered" presents, the differential constraints will not actually allow any (self-coherent) worldview to look like bunch of randomized presents once all is said and done?

That is not true. What is true is that no one's mind is capable of handling the complexities inherent in a full collection of randomized presents. That is why I keep bringing up the issue of “data compression”: the consequence of ignoring everything except a single temporal string of events. If you do that (ignore everything except a single temporal string of events defined by that ignored context) then those things you are examining must follow some quite simple rules.

And that is because it is the patterns that the so-called "ontological elements" form that allow for a definition of any normally perceived "entity", ...

Instead of “any normally perceived 'entity'”, can we instead say “anything we can explain”?

and their behavior must be shift symmetrical, at least in so far that no undefendable assumptions are allowed in one's worldview...

It is not “their behavior” which is bound by shift symmetry but rather the entire universe which is so bound. It is the consequences of that shift symmetry which yield the fact that, when you divide the universe into two parts (the element you are interested in and the context: i.e., the rest of the universe) you get some rather simple relationships. Simple universal relationships which appear in your world-view as “principals”.

I am actually not sure what you are saying here :I

Perhaps I have made it a little clearer in this post.

... anything that it tells about those expectations seems to me to be only understood under a certain interpretation and I have seen vary little that tells me anything about such an interpretation.

I have essentially stated that one's world-view is built from a mixture of things: things which are true representations of reality and things which are figments of your imagination; now, if you are going to suggest that your world-view is built only from things you know are true, I will assert that you are both closed minded and deluded. What I have said is that, no matter what the “true facts” are, there exists a collection of “figments” which will make my equation valid (for both the “true facts” and the “figments”).

 

I have further proved that under such an interpretation (the interpretation which makes my equation valid) individual elements of that explanation approximately obey Newtonian mechanics. So exactly what do you see as the difference between your world-view and the interpretation I have pointed out? As I see it, your world-view (for the most part) consists of elements which obey Newtonian mechanics plus things you cannot explain. My world view, on the other hand consists of elements which I can explain plus things I cannot yet explain. The only difference between my world view and your world view is that you have not closed the door to the possibility that relationships which do not obey my equation might explain some of those things you can not yet explain. As I see it, as far as the things you can explain with consistent logic, your subconscious has made exactly the “certain interpretation” I have been referring to. Certainly there exists no information available to me that you have not made exactly that interpretation; scientific research has backed up my position to the hilt. It is only with regard to things not yet explained that you could defend the idea that your “interpretation” is different than the one which makes that equation valid.

Now what I have seen seems to tell me something about what a mathematical explanation of anything must satisfy.

Why can't you change that sentence to, “now what I have seen seems to tell me something about what a logical explanation of anything must satisfy”? Is not mathematics the essence of logic?

Now if you can show that these constraints have not limited the solution I think that I will have to agree with such a statement but I don’t think that you have gone into any details on their effect.

These constraints have certainly limited the solutions to a very distinct set; however, I have proved that there exists no set of “true facts” which cannot be reproduced as a solution to my equation. The problem is that the proof is somewhat abstract and that bothers a lot of people; they want the consequences (which are, as I said, essentially beyond comprehension) to be clearly comprehended.

What it seems to me that you have shown is that by ignoring the effect of the context on the form of the solution the Schroedinger equation becomes the simplest solution to derive. Perhaps this would make Newtonian mechanics the simplest way to understand something with a consistent explanation.

What you seem to miss is that it is the general presumption of science that context can be ignored. That is exactly what is happening when they give a name to an entity; the name presumes the context defining the thing is well understood and does not change.

For instance suppose you had derived the Schroedinger equation without knowing anything about it ...

That certainly could have happened. What I have done could have been done before Schroedinger was born. In that case, I would have had to find the solutions and their implications for myself; not and easy task; however, I was lucky, many people had already worked out many of those solutions and their implications. I said, “one would not have recognized it” because, in the normal graduate course work, all one ever sees is the simple V(x) interaction.

Then the term [imath]vec{Psi}_r[/imath] that appears in the equation after you have limited it to a one body equation (actually a two body equation) is nothing more then the effect that the context has on the object of interest?

Yes, except for the fact that you have omitted the elimination of [imath]\vec{\Psi}_r[/imath] via summation over all possibilities for that context (multiplication by [imath]\vec{\Psi}_r^\dagger[/imath] and integration over all arguments except the x of interest). The “two bodies” here are, the one under examination and your expectations for that entity called, "the rest of the universe" (at least the components you are not going to ignore).

Then is the first constraint that you added equivalent to the context having no effect on the form of [imath]vec{Psi}[/imath] and the seconded constraint being equivalent to the context being unchanged by changes in t, if so what does this make the third constraint equivalent to?

In order to avoid the problem with LaTex in quotes, I will use Anssi's approach to quoting

That brings us down to the final constraint,

[imath]K\sqrt{2}\frac{\partial}{\partial t}\vec{\Phi}\approx -iq\vec{\Phi}[/imath]. If we multiply this relationship through by [imath] i\hbar[/imath] and divide by [imath]K\sqrt{2}[/imath] the definitions given for m and c above imply the constraint can be written

[math]i\hbar\frac{\partial}{\partial t}\vec{\Phi}\approx q\hbar c \vec{\Phi}= \left( \frac{q\hbar}{c}\right) c^2\vec{\Phi} = mc^2\vec{\Phi}.[/math]

 

The term [imath]mc^2[/imath] should be familiar to everyone and the left hand side, [imath]i\hbar\frac{\partial}{\partial t}[/imath], should be recognized as the energy operator from the standard Schroedinger representation of quantum mechanics. Putting these two facts together, it is clear that the redefinition of [imath]\vec{\Phi}[/imath] to [imath]\vec{\phi}[/imath] in the above deduction was completely analogous to adjusting the zero energy point to non-relativistic energies. This step is certainly necessary as Schroedinger's equation is well known to be a non-relativistic approximation: i.e., Schroedinger's equation is known to be false if this approximation is not valid.

===End Quote===

 

It should be clear to you that the last constraint was that the problem was not a "relativistic" problem. If it is "relativistic" Schroedinger's equation is well known to be "WRONG!".

 

Also at one point you seem to suggest that without the first two constraints that it still turns into the Schroedinger equation but that it is a slightly more complex version of it am I correct in understanding it this way?

Yes!

If you have some idea what it is that I’m missing I would like to know what it is so I can try and clear it up.

I would say that all you are missing is an understanding of advanced calculus and physics. Just as an aside, I would never have dreamed this thing up if I had been ignorant of modern physics. In many respects, what I have done is just bring a broad array of well known facts against one another; usually these facts are kept well away from one another. Physicists are notorious for their desire to get that context out of the picture so they can get down to something they can mentally handle; it has been a very successful approach. My approach has been scoffed at for centuries as not being worthy of examination.

 

So now we can get down to Anssi's questions. As that will be a rather extensive post, I will post it as a separate issue.

 

Have fun -- Dick

[AnssiH]

Hi Anssi, my wife and I have been down to the Gulf coast for the weekend and we just got back: i.e., I have not been checking the internet.

 

Cool, hope you had great time

I've been wanting to reply to this mail since yesterday but been little bit busy, so this will be short... I think

 

This is what I am talking about when I complain about people bringing too much baggage to the discussion. Until we have a specific solution to the fundamental equation, we have no justification for any interpretation of the equation itself. The equation is no more than a statement of a requirement demanded by self consistency; the implications of that constraint are so complex (in their entirety) that those consequences are essentially beyond comprehension.

 

Yeah, I think I know what you are saying. I was not implying that I'm trying to figure out any ontological interpretation from the constraints, if that's at all what you are worried about :lol: I'm just talking about anything that allows me to understand the differential constraints in some sense (as in those dust motes).

 

On the same note, I don't expect to find any specific ontological truth from any of this, or from any given experiment (or experience) we could ever have... That's the part that I understand quite clearly :hyper:

 

That is not true. What is true is that no one's mind is capable of handling the complexities inherent in a full collection of randomized presents. That is why I keep bringing up the issue of “data compression”: the consequence of ignoring everything except a single temporal string of events. If you do that (ignore everything except a single temporal string of events defined by that ignored context) then those things you are examining must follow some quite simple rules.

 

Oh I see. Okay, and I guess if I manage to understand the mathematical deductions of #194, I should understand something about why this is so...?

 

Instead of “any normally perceived 'entity'”, can we instead say “anything we can explain”?

 

Indeed.

 

It is not “their behavior” which is bound by shift symmetry but rather the entire universe which is so bound.

 

And here "entire universe" refers to all the data that one happens to hold about the universe...? I.e. all of one's "past"

 

It is the consequences of that shift symmetry which yield the fact that, when you divide the universe into two parts (the element you are interested in and the context: i.e., the rest of the universe) you get some rather simple relationships. Simple universal relationships which appear in your world-view as “principals”.

 

Okay, yeah definitely I need to understand the math better to be able to see how this unfolds...

 

-Anssi