[AnssiH]

bravox, on 15 March 2012 - 02:12 PM, said:

Certainly not, but that is the difference between physics and math. In physics you can't work totally in the abstract, the entities must be capable of being interpreted, whatever that means.

Or perhaps better to say, "some information" needs to be capable of being interpreted. It is common to any mental language, that information is interpreted via categorizing it into some collection of carefully defined "entities", via some translation process. And what that translation process is in itself, is not really available for us to understand, apart from understanding it in terms of those entities; the very results of the translation process itself.

I'm sure you know that age-old problem that I'm referring to, and I would just point out that the key point to take out from that problem is that "understanding" something does not entail at all that you know what it is "in itself", it just entails you are capable of expressing expectations of it, in some arbitrary mental language. The entities defined by physics being exactly that, an arbitrary language to express expectations.

Note that the only way to check the validity of any mental language, is to check whether it generates valid predictions. But that of course does not verify whether it is the only possible mental language; it would always be possible to express the same underlying noumenaic information in terms of different entities and concepts, and still get just as valid expectations.

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Indeed, and that is exactly the problem! What does "the photon goes through both slits at the same time" mean? The mathematics behind it are solid, our interpretaion is not. That probably means our concepts of "particle" and "wave" are slightly incorrect, but what other concepts do we have? You seem to be saying, "we need no concepts", and in that case I could not agree.

I'm not exactly saying that we don't need concepts, we certainly do in our practical everyday life.

But if we want to talk about the logical foundations of the whole double-slit conundrum, there are few things to be pointed out about the concepts we use.

First, the translation process from "some noumenaic information" to "the entities of physics" (or any world view) contains a host of assumptions that cannot be really checked. Or perhaps a better way to express how I mean that is to say that, the set of defined entities/concepts of any world view contains features that are not actually features of "reality" (or the noumenaic information), they are merely features necessary for that particular representation of reality(/expectations).

I.e., the representation form commonly called "modern physics", contains various features necessary for that particular representation form, and the existence of those features also lead into the fact that, if you represent expectations in this form, your valid understanding of "double slit experiment" (or whatever it is that really happens there) contains semi-idealistic relationship between the entities (that you have defined) and observation.

Those undefendable features are not merely embedded to the definitions of those entities (such as photons), they are just as much related to all the concepts that are necessary to understand what is meant by those entities (e.g. definitions of space and time)

Second, while it is not really possible to prove any given representation form of reality to be somehow correct (over and beyond it providing valid expectations), it is possible to point out how/why those undefendable features of modern physics arise as common epistemological necessities, if only you choose to handle those necessities in particular way.

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I'm not entirely sure I understand you. Waves, of any kind, do not have a physical existence. The waves you see, for instance, in the surface of the ocean are just water going up and down. Nothing is moving sideways. But we can imagine an abstract entity moving sideways, and we can actually say a lot of stuff about this imaginary entity.

All I was saying was that, we should view the "particles" the same way as you are viewing waves. They are also an expression of some noumenaic information, and there is no actual way to check whether or not reality is actually structured in a way where there are actual particles that are actually floating in actual space. All we can do is check whether that sort of interpretation of some noumenaic information yields valid expectations. (And it sure does)

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But the double-slit experiment is real, and it makes no sense. Why do you think it doesn't matter that it makes no sense?

Because the reasons why it makes no sense can be traced to some epistemological necessities, and when a person forms understanding of that fact, they can see why it makes sense to see things this way, all the while they understand reality is not literally like that. It's kind of the same thing as viewing "negative numbers" as absurd, on the grounds that you can't have a negative number of potatoes. That's right, yet as part of a mental language to represent things in reality, negative numbers can be very useful.

There are very good purely logical reasons why quantum mechanical representation of expectations is useful, there there is absolutely no reason to view quantum mechanical entities (or any other defined entities) as literally real objects.

-Anssi

This post has been edited by AnssiH: 19 March 2012 - 12:57 AM

[bravox]

(deleted)

This post has been edited by bravox: 20 March 2012 - 12:07 PM

[Bombadil]

AnssiH, on 06 March 2012 - 02:48 AM, said:

And I think you have this right as well. I.e., it is always possible to represent the inductive expectations in terms of defining "quantum mechanical particles", by which I mean elements that behave exactly the way that world has been defined in modern quantum physics. Which implies something about modern physics.

Yes it would imply something about modern physics, it is also a statement that I don't think that you can convince me of until you have proven the necessity of the definitions used by modern physics. On the other hand I agree that the same notation as is used in modern quantum physics can be used.

It's like this, at this point I have little interest in the implications of this to modern physics because quite simply it seems to me to be too early in the derivation to have any (at least until we except the derivation of the Schroedinger equation to be assumption free and that every solution to it to be equivalent to modern physics or we decide what assumptions are being made). Now if you want to make the assumptions that it seems to me you are making, that is fine. But from where I am sitting all of your arguments of the necessity of the universe to obey modern physics are based on the fact that they have been derived from the fundamental equation.

Every one seems to be either of the opinion that there are no assumptions in any of the derivations or of the opinion that there must be assumptions. To me both groups have a point I have to wonder if ether group is right.

Unfortunately there is only one way in my mind to settle the issue and it is perhaps beyond me, at least at present, and that is to prove it one way or the other. In my mind this requires the derivation of a solution to the fundamental equation that is not consistent with modern physics or a proof that no such explanation can exist.

Don't take this to mean that I disagree with the derivation of the fundamental equation. Quite to the contrary. I have yet to see any thing that seems to be a flaw in the derivation that would limit the explanations that can be represented, the only problem I have, is that I have no reason to assume that the approximations that have been made are anything more then approximations.

Doctordick, on 03 March 2012 - 07:45 AM, said:

I am afraid the representation (that the fundamental elements which communicate the information can be numerically labeled) is fundamental to the derivation. In fact, that is all the derivation is based upon. My deductions are pure consequences of the fact that the signals (signs, symbols, gestures, etc.) are arbitrary and may be numerically labeled. Nothing else has any significance whatsoever.

I am not disagreeing with this. All that I am saying is that you have chosen the notation so that it is very much a notation that already existed. Just to give an example, we could recast the fundamental equation using Einstein notation and get rid of the summation symbols of course this would beg the question of why we would do such a thing and the only reason that I can think of is if we felt that it made it more aesthetically pleasing or if we simply wanted to abuse the notation for some reason. Of course there must be other options that haven't even been thought up yet but is anybody going to seriously say that it is a different equation if we did such a thing?

Doctordick, on 03 March 2012 - 07:45 AM, said:

My fundamental equation is written (in all its glory)





where I define those alpha and beta operators as anti-commuting operators with a magnitude of one half. These are essentially quite analogous to the operators in quantum mechanics called “spinors”. (Sorry about that, I apparently misspelled the thing in that earlier post.)

OK, that is why it didn't come up when I searched it.

Doctordick, on 10 February 2012 - 06:42 PM, said:

All functions can be divided into a sum of anti-symmetric and symmetric components. The only issue internal to my deduction is the fact that, if multiple things are real (and thus there exist multiple elements which no explanation can omit), there must exist anti-symmetric components: i.e., anti-symmetric functions must be there. So, essentially the insertion of the requirement of those “spinner” operators allows the possibility that there exist multiple “real” things. Omitting them would make solipsism the only possibility: i.e., everything would have to be hypothetical. What you should comprehend is that being entirely hypothetical does not require the absence of anti-symmetric solutions; these are entirely different issues.

OK now I am confused. What do the spinors have to do with the existence of real or hypothetical elements. From everything that you have said in the past I have come to conclude that the use of the spinors was a convenience to make three equations into one, and had no influence outside of the notation that it allowed us to use to represent explanations, but you seem to be giving them some greater meaning here.

Doctordick, on 03 March 2012 - 07:45 AM, said:

For the very simple reason that my derivation is invalid if ontological elements represented by symmetric functions are real. I am afraid you have a concept of “real” which is not well thought out. (Your definition of “real” is apparently the fact that you believe it exists.) My definition of real is quite simple: if something is “real” there can exist no explanation which omits it. Until you know “all possible explanations” you cannot possibly prove anything is real: i.e., “required by all explanations”.

Just which step is it that assumed that a real element was symmetric?

Doctordick, on 03 March 2012 - 07:45 AM, said:

Again, how do you define “real”. It seems to me that, from your perspective, belief is the only measure of that identification.

Let me see if I can clarify this slightly, from what you have said a real element is real only if it appears in every possible explanation, the problem is that we would have to know every possible explanation in order for us to call an element real. Now you have just said that an explanation exists in which every element is an anti-commuting element. The simple geometric proof.

Now suppose that we had just two explanations of the same thing that were not exactly the same explanation but they are of the same thing. How could we tell if an element has a representation in both explanations, we would have to look at the other elements in the explanation to compare them. The problem with this idea is that we have no way of telling if we are right or not, all we could do is ask how probable is it that these are the same elements. To make this worse we know that an explanation exists in which all of the element would be symmetric elements and so we know that there exists at least one explanation that has all of the elements representable and at least one that has them all as anti-symmetric elements. And then there of course must be an infinite number of explanations based on these that simply have a different number of hypothetical elements.

So indeed belief would seem to be the only measure of if an element is real or not, no matter how we define real, since we don't even have a way to determine if two explanations are explaining the same thing.

Doctordick, on 03 March 2012 - 07:45 AM, said:

Yeah, the photon is certainly a consequence of Maxwell's explanation of what are normally referred to as electromagnetic effects. Are you trying to assert that there exists no other possible explanation of those effects?

Just which effects are you referring to? Do you mean the consequences of Maxwell's equations or do you mean the context that leads to the maxwell equations?

If you mean the effects that lead to the use of the Maxwell equations then of course there are other explanations that will lead to the same effects, you have already given one in your simple geometric proof. But of course we should not forget that if we use this interpretation then the Maxwell equations must of course be wrong in this interpretation because they would give different expectations. But of course this is obvious.

But if you mean an explanation that includes all of the expectations of the Maxwell equations then the photon being one of the the expectations of the equations leads one to suspect that there is no explanation that gives the same expectations as the Maxwell equations without including photons. They are one of the expectations of the equations after all.

Doctordick, on 03 March 2012 - 07:45 AM, said:

I get the feeling that you are misinterpreting what I mean by “context”. What I mean by “required context” is the entire collection of circumstances (sans hypothetical elements) upon which your explanation is based. In actual fact, your explanation is probably based on what you think constitutes the entire collection of circumstances (which most probably includes hypothetical elements) upon which your explanation is based.

Wouldn't this be the entire past?

Doctordick, on 03 March 2012 - 07:45 AM, said:

Please let me know how you intend to define “a photon” without using any aspects of Maxwell's equations.

But isn't that exactly what you are doing when you say things like,

Doctordick, on 25 July 2009 - 11:28 AM, said:

It is interesting to note that if the second entity (the supposed massless element) is identified with the conventional concept of a free photon, its energy is given by c times its momentum.

In fact isn't your derivation of the Dirac equation based on doing just that?

Doctordick, on 03 March 2012 - 07:45 AM, said:

What you are omitting is that you are requiring the assumption that your explanation is “correct”. No flaw in that explanation will ever be found.

I'm somewhat puzzled by your use of the word flaw and correct, isn't an explanation only flawed if it is self inconsistent? And the use of the word correct implies an explanation can be wrong but this is meaningless since we have no way of knowing what it is that would make an explanation correct. it sounds like you are using these words in exactly the same way as you always say I am using these words.

What defense is there for even the approximations made in the derivation of the Schroedinger equation?

[Doctordick]

Bombadil, on 20 March 2012 - 07:53 PM, said:

... you have proven the necessity of the definitions used by modern physics.

I have not proven any such thing; it is communicating their ideas which requires using the same definitions. All you can do is work at trying to understand those definitions.

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But from where I am sitting all of your arguments of the necessity of the universe to obey modern physics are based on the fact that they have been derived from the fundamental equation.

No, none of them have been derived from my fundamental equation. Science is totally ignorant of my equation. All those relationships have been discovered to be valid via the “guess and by golly” mechanism in standard use by science. The issue in my presentation is that, under any internally consistent definitions of the ontological elements referred to by the numerical reference labels , any communication represented by a collection of circumstances must obey my fundamental equation (I have proved that).

When I deduced that equation, I had utterly no idea that it would say anything about modern physics. What I found astounding was the fact that, under exactly the specific assumptions associated with various important components of modern physics fields (and no other assumptions), the equations the scientists had discovered in those fields were approximate solutions to my fundamental equation. I think that was a rather surprising outcome.

The issue is that modern physics is supposed to assert truth about reality whereas my equation says absolutely nothing about reality! It concerns only the internal consistency of the interpretation of the communication and nothing else. It is essentially a tautological construct. "In propositional logic, there is no distinction between a tautology and a logically valid formula". All internally consistent interpretations of any data should therefore be included (even those which are wrong). Think of that as referring to alternate possible universes. It says that all explanations of all possible alternate universes must obey my equation (that is what I have proven). The fact that modern physics relations are all approximate solutions to that equation says that the rules proposed by scientists (designed to tell us about reality) tell us no more than the consequences of internal consistency: i.e., the result must also be tautological. That is a rather astounding realization; something most all scientists will deny to the death.

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... or a proof that no such explanation can exist.

That is exactly what my proof is!

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... the only problem I have, is that I have no reason to assume that the approximations that have been made are anything more then approximations.

What approximations are you talking about?

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All that I am saying is that you have chosen the notation so that it is very much a notation that already existed.

No, I have chosen a notation that is entirely general: i.e., absolutely any communication can be so represented. Now the notation for TCP-IP packets is essentially identical to mine but, as far as I know, no one except me has ever considered the consequences of requiring internal consistency on all communications via numerical packets without specifying the exact design of TCP-IP packets involved: i.e., valid for all possible internally consistent packet designs. Most people jump immediately to the idea that "all possible" means they can change the packet design at random which is not at all what I mean. My deduction is based upon the fact that the packet design is consistent but otherwise unknown.

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Just to give an example, we could recast the fundamental equation using Einstein notation ...

Oh could you now? I would like to see that! Einstein's notation requires some very major presumptive understandings. (That is why it takes a good period of time to learn what is and is not allowed in Einstein's notation.) My notation makes no constraints whatsoever on what is being expressed.

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... and get rid of the summation symbols ...

In Einstein's “notation” you get rid of the summation symbols but only by presuming when the indices are doubled, summation is implied. He has to do that; otherwise his equations get so large and complex that it is extremely difficult to write them on a single piece of paper.

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OK now I am confused. What do the spinors have to do with the existence of real or hypothetical elements.

Spinors associate with real and/or hypothetical elements due to the fact that they yield exchange consequences (two symmetric solutions can be made antisymmetric with respect to exchange via effects imposed by those spinors; they amount to alternate representations of internal correlations in that abstract space of the vector function ). The common physics parlance for that circumstance is the fact that two fermions can act in a coherent manner yielding effects commonly attributed to bosons. Super conductivity is a direct consequence of those mathematical effects.

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From everything that you have said in the past I have come to conclude that the use of the spinors was a convenience to make three equations into one, and had no influence outside of the notation that it allowed us to use to represent explanations, but you seem to be giving them some greater meaning here.

It was put in there, not as a “convenience” but rather as a necessity. And I never implied it had no further influence on possible results. I am attaching no greater meaning; rather, I am merely pointing out another subtle consequence of that required antisymmetry.

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Just which step is it that assumed that a real element was symmetric?

(I think you mean “antisymmetric”!)

There was no step which made any such “assumption”. When I added in the hypothetical tau axis, its purpose was to solve a problem created when two numerical labels were identical. That additional tau axis was required when I changed over from “a set of numbers” to “a set of positions on an x axis”. That change results in a loss of information if you don't add in that additional tau axis. (How many times that particular value of “x” appeared would be lost as a point can only represent a number once; in order to represent multiple occurrences you need a mechanism in your notation to separate them out.) The problem is that, if you extend the thing to an infinite amount of information, assuring that different tau component provides the required separation vanishes. By making the antisymmetric it guarantees the information will not be lost.

Losing information on “real” elements (defined to be elements required by all explanations) means the won't necessarily explain them and that would be a serious flaw in the representation.

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So indeed belief would seem to be the only measure of if an element is real or not, no matter how we define real, since we don't even have a way to determine if two explanations are explaining the same thing.

Again, you seem to have the shoe on the wrong foot. Whether or not something is real is of utterly no consequence here. The only thing of importance is that we not presume nothing can possibly be “real”. In order to assure that presumption is not made, we have to include the possibility of antisymmetric solutions and their existence has consequences. But being antisymmetric can not be taken as an indicator the thing is “real”. On the other hand, being symmetric implies the entity is hypothetical and that possibility is specifically demonstrated by my geometric proof. (Just consider that representation of only the antisymmetric components: i.e., all the boson activity is ignored as unnecessary.) Any collection of circumstances can still be represented.

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... if we use this interpretation then the Maxwell equations must of course be wrong in this interpretation ...

Not “wrong”, just totally inapplicable.

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They are one of the expectations of the equations after all.

No, the it is the consequences of their “activity” which constitutes our expectations. Two atoms change state in a particular way and we “presume” a photon was exchanged. The explanation must yield the change in state of the atoms. The cause of that change is a hypothetical issue. The existence of photons yields a nice explanation but that is no proof there exists no other explanation.

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Wouldn't this be the entire past?

Let us say, whatever you presume to be the past: i.e., if you omit any part of the past you believe to be true, you are presuming that omitted information plays no roll whatsoever in the explanation you are communicating: i.e., if you omit the information necessary to establish the meanings of your ontological elements one's ability to comprehend your intentions with regard to the what is being communicated is severely limited. Take a look at the problems of understanding linear A. The issue is the fact that the communications intended by those “messages” is not understood for the very simple reason that we lack sufficient context to interpret the intentions of the messages. The problem with those who think in terms of “counter examples” invariably want to present their counter examples in a form which omits exactly that context information.

My equation concerns “all possible explanations” of a given message. You omit the intended context and the possible interpretations get rather large quickly: well beyond what can be written down and “meaningless” is the interpretation most people jump to in such a case. Why don't they jump to “meaningless” symbols when it comes to linear A? Because they are quite confident there are meaningful interpretations there (why else would people make the effort to create so many tablets); the researchers just don't know what they are (because sufficient context to reduce the possibilities to something reasonable is missing).

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But isn't that exactly what you are doing when you say things like, ...

No, I have noticed an interesting solution to my equation which happens to map 1:1 into Maxwell's photon. That is quite a different issue.

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In fact isn't your derivation of the Dirac equation based on doing just that?

What you call my “derivation” of the Dirac equation is based upon noticing that some rather simple approximations yield the fact that Dirac's equation is indeed an approximation to my equation. I didn't derive Dirac's equation, Dirac did that. I merely showed it was an approximation to my equation.

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I'm somewhat puzzled by your use of the word flaw and correct, isn't an explanation only flawed if it is self inconsistent?

My definition of a “flawed” explanation is that it doesn't fit the known facts (you should understand that self inconsistency is only one of the possibilities there). My definition of a “correct” explanation is that no new facts will ever imply a flaw in that explanation. An explanation can be proved flawed but no proof exists that any explanation is correct because that requires you know everything that is possible to know.

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What defense is there for even the approximations made in the derivation of the Schroedinger equation?

Did you look at the approximation I made? The only defense for making those approximation is that they make Schrödinger's equation an approximation of my equation. If you look closely at the approximations you will understand that they are exactly the common approximation made by modern physicists when they go to apply Schrödinger's equation: i.e., they found an approximate solution to my equation without even knowing my equation existed. Don't you think that is rather astounding? They even knew what approximations they had to make!

Have fun -- Dick

[Bombadil]

Doctordick, on 22 March 2012 - 03:36 PM, said:

I have not proven any such thing; it is communicating their ideas which requires using the same definitions. All you can do is work at trying to understand those definitions.

And I never said that you did lets look at what you quoted, this time lets include more of the sentence,

Bombadil, on 20 March 2012 - 07:53 PM, said:

it is also a statement that I don't think that you can convince me of until you have proven the necessity of the definitions used by modern physics.

notice the “until you have proven the necessity” in there,

My point is that you have proven that modern physics is an approximation to the fundamental equation, but you have not proven that all approximations of the fundamental equation are equivalent to modern physics. Or that all solutions of the fundamental equation can be approximated by modern physics.

The problem that I see is that it seems that it must be possible to define an element so that it can behave in any way, if this is the case even if physics allows elements to be defined so that they can behave in any possible way, this would only increase the problem as we would have to ask why we don't use such definitions. And it would make the question of “just what do we consider modern physics to be” a question with perhaps not a obvious answer.

You and AnssiH seem to be of the opinion that what you have proven is that modern physics is nothing more then a means of generating an explanation of any possible information, I can see that you have a strong defense for this even stronger then the physicists that say that reality is really like physics says it is, in fact I would go so far as to say that you clearly have proven them wrong, reality is not like physics says it is physics is just a means of generating an explanation.

The question is, how general of an explanation is physics? And how general is the context that physics uses?

Doctordick, on 22 March 2012 - 03:36 PM, said:

No, none of them have been derived from my fundamental equation. Science is totally ignorant of my equation. All those relationships have been discovered to be valid via the “guess and by golly” mechanism in standard use by science. The issue in my presentation is that, under any internally consistent definitions of the ontological elements referred to by the numerical reference labels , any communication represented by a collection of circumstances must obey my fundamental equation (I have proved that).

OK I may have phrased that in a bad way. I should have said something like, you seem to be suggesting that the universe must obey modern physics because you have shown that you can approximate the fundamental equation with the same equations as modern physics uses.

Further more I am not disagreeing with you having proven that any circumstances must obey your fundamental equation, but have you proven that this is still the case with the Schroedinger equation or the Dirac equation? If not is there some branch of physics that is using an equation that is the same as the fundamental equation, my impression is that there is not.

Doctordick, on 22 March 2012 - 03:36 PM, said:

When I deduced that equation, I had utterly no idea that it would say anything about modern physics. What I found astounding was the fact that, under exactly the specific assumptions associated with various important components of modern physics fields (and no other assumptions), the equations the scientists had discovered in those fields were approximate solutions to my fundamental equation. I think that was a rather surprising outcome.

Yes I suppose that it must have been quite surprising and probably somewhat exciting. I suspect part of the issue here is that in hind sight it seems to me to be a statement that at least the first part of which must be true, the second part is perhaps more interesting though. As it implies that modern physics is true by the definitions that they use, which should not be to surprising but can be looked at as somewhat of an achievement to have happened by the “guess and by golly” approach, as you are calling it.

I think that it is worth remembering that any possible consistent means of explaining any thing can be derived from the fundamental equation if we just know the right context and are precise enough with our use of it.

Doctordick, on 22 March 2012 - 03:36 PM, said:

The issue is that modern physics is supposed to assert truth about reality whereas my equation says absolutely nothing about reality! It concerns only the internal consistency of the interpretation of the communication and nothing else. It is essentially a tautological construct. "In propositional logic, there is no distinction between a tautology and a logically valid formula". All internally consistent interpretations of any data should therefore be included (even those which are wrong). Think of that as referring to alternate possible universes. It says that all explanations of all possible alternate universes must obey my equation (that is what I have proven). The fact that modern physics relations are all approximate solutions to that equation says that the rules proposed by scientists (designed to tell us about reality) tell us no more than the consequences of internal consistency: i.e., the result must also be tautological. That is a rather astounding realization; something most all scientists will deny to the death.

I think that I would agree with this except perhaps I would have to change the ending I would not say that “ rules proposed by scientists tell us no more than the consequences of internal consistency” I would say that they tell us no more then the consequences of a particular internal consistency.

The only problem that I have is something like this, we know that we can't solve the fundamental equation in any type of general setting but suppose that we made approximations so that we could, how would we know if our result was even a unique result and that we couldn't make the same approximation in different ways and get a different result. Or that we could still look at the approximate result as an approximation to any possible solution to the original equation.

Can there be other universes that look nothing like ours or are the odds against such a thing existing so much so that they all must look the same in the end.

Doctordick, on 22 March 2012 - 03:36 PM, said:

What approximations are you talking about?

That only one element is of consideration and that the rest of the universe can be looked at as being known, that the equation can be used as an equality (that is we are looking at non-relativistic elements). These both seem like simple ideas and are needed for what you have done, but I have to wonder how similar solutions would look if we forgot these and made approximations that made both of these circumstances from very difficult to defend, to clearly wrong.

Or the context that you made in showing the approximation of Dirac's equation.

Doctordick, on 22 March 2012 - 03:36 PM, said:

Oh could you now? I would like to see that! Einstein's notation requires some very major presumptive understandings. (That is why it takes a good period of time to learn what is and is not allowed in Einstein's notation.) My notation makes no constraints whatsoever on what is being expressed.

Maybe I don't understand what the purpose here is but I am under the impression that Einstein notation is simply the use of the convention of summation over upper and lower script to remove the need for summation. In which case wouldn't it only be a question of choosing the scripts in such a way as to remove the need for the summations?

Doctordick, on 22 March 2012 - 03:36 PM, said:

It was put in there, not as a “convenience” but rather as a necessity. And I never implied it had no further influence on possible results. I am attaching no greater meaning; rather, I am merely pointing out another subtle consequence of that required antisymmetry.

What necessity, as far as I can tell you used them only to turn multiple equations that seem to represent very different but necessary constraints into one equation representing all of the constraints, in your words.

Doctordick, on 19 December 2010 - 09:33 AM, said:

These three mathematical constraints can be cast into a single mathematical constraining relationship via a rather simple mathematical trick. If one defines the following mathematical operators (both the definition of “[a,b]” and the specific alpha and beta operators):

So what is the necessity of the spinner operators?

My reasoning for understanding that they had no further influence on possible solutions is that you seem to have never given any reason that they are necessary and only ever demonstrated that you could derive your constraints form the fundamental equation by using them, so unless you have a reason to include them it would only make sense to use them if they have no influence beyond the notation that is being used.

So why did you use them in the first place and not just work with the original constraints?

Doctordick, on 22 March 2012 - 03:36 PM, said:

Did you look at the approximation I made? The only defense for making those approximation is that they make Schrödinger's equation an approximation of my equation. If you look closely at the approximations you will understand that they are exactly the common approximation made by modern physicists when they go to apply Schrödinger's equation: i.e., they found an approximate solution to my equation without even knowing my equation existed. Don't you think that is rather astounding? They even knew what approximations they had to make!

What amazes me is not so much that they where found as an approximation to your equation as we know that this must be true by definition if they where consistent, what amazes me is that by applying the same approximations to your equation you were able to derive these equations. This implies a great deal of consistency even in their derivations.

There is however a related issue that seems like it is obvious but I can't come up with a reason to believe it, and that is one of uniqueness of the result of applying the approximations to the fundamental equation. Is there any reason to believe that the result of applying those approximations will give a unique result. It seems that the obvious answer to this is that the result of applying these approximations must be unique but why should it be beyond just making it an elegant result. Is the idea that we don't see any other ways of applying these approximations really sufficient to say that the result is unique?

[AnssiH]

Bombadil, on 13 April 2012 - 09:00 PM, said:

My point is that you have proven that modern physics is an approximation to the fundamental equation, but you have not proven that all approximations of the fundamental equation are equivalent to modern physics. Or that all solutions of the fundamental equation can be approximated by modern physics.

The problem that I see is that it seems that it must be possible to define an element so that it can behave in any way, if this is the case even if physics allows elements to be defined so that they can behave in any possible way, this would only increase the problem as we would have to ask why we don't use such definitions. And it would make the question of “just what do we consider modern physics to be” a question with perhaps not a obvious answer.

...

Can there be other universes that look nothing like ours or are the odds against such a thing existing so much so that they all must look the same in the end.

You can find answers to those questions if you manage to look at this from the exactly proper perspective. Think about it this way;

Regardless of what some universe is like, your explanation about it (i.e. "what it looks like to you") is entirely dependent on an ability to represent valid expectations. That is, regardless of the actual structure of reality, all that your worldview can recognize - and ultimately label as some defined elements with some sort of expected behaviour - is something that can be in some sense recognized from some "information" as recurring "patterns" of some sort (with some valid probabilities).

The generality of the fundamental equation springs exclusively from generalities when representing expectations regarding recurring patterns. Not from generalities embedded to any kinds of hypothetical "structures of reality".

Note that, as long as we are using the terminology of modern physics to think about physics experiments or theorize about various things, we are very much locked in to arriving into certain kinds of conclusions, just because those conclusions are consistent with the language we are using. Those connections are purely logical but so complex that they are very far from obvious. Theoretical physics is about trying to recognize those connections, and it often takes years and years of intense thinking from the brightest minds to realize certain connections are there, simply because the language being used makes them very unapparent. Nevertheless, the existence of those connections is what prevents us from defining arbitrarily behaving entities, in the framework of modern physics.

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The question is, how general of an explanation is physics? And how general is the context that physics uses?

It's general to the point that you can consider the approximations between FE and modern physics to be general. You can view those approximations simply as things required for practical purpose. An entirely general multi-body equation over the entire collection of information is just not practical (/possible) way to generate expectations.

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Further more I am not disagreeing with you having proven that any circumstances must obey your fundamental equation, but have you proven that this is still the case with the Schroedinger equation or the Dirac equation?

Their validity requires that noumenaic reality is interpreted via using the necessary approximations. I would say that, for instance, defining elements in ways that they have a minimal feedback to the rest of the universe, is very crucial step. Without it, things could look very different. But such a solution would also be incredibly impractical.

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If not is there some branch of physics that is using an equation that is the same as the fundamental equation, my impression is that there is not.

Nope, because it cannot be solved without approximations.

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What amazes me is not so much that they where found as an approximation to your equation as we know that this must be true by definition if they where consistent, what amazes me is that by applying the same approximations to your equation you were able to derive these equations. This implies a great deal of consistency even in their derivations.

It just means that the most general solutions known by modern physics (especially QM) was close enough to the entirely general expression (i.e. FE) for it to become possible to see the route (i.e. the small collection of approximations) from one to another.

If at present the most general solution known to mankind would be newtonian physics, I doub't anyone could find the route from FE the Newtonian physics, and even if they could, the route would contain approximations whose epistemological role would not be clear at all, and thus the meaning of that route might not be clear either.

-Anssi

[Doctordick]

Bombadil, on 13 April 2012 - 09:00 PM, said:

notice the “until you have proven the necessity” in there,

“Necessity” is not ever the issue here. Using their definitions is essential to communication of their thoughts and never necessary to the thoughts themselves. That aspect is always contained in the complete collection of information necessary to learn their language: i.e., the fact that their assertions in entirety can be expressed via a collection of circumstances representable by is sufficient.

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My point is that you have proven that modern physics is an approximation to the fundamental equation, but you have not proven that all approximations of the fundamental equation are equivalent to modern physics. Or that all solutions of the fundamental equation can be approximated by modern physics.

Of course not! The possibility exists that modern physics could be wrong. And, in fact, I have pointed out a number of issues within modern physics are clearly wrong. Their definition of time, the idea that there exist five different forces unrelated to one another and the idea that the “Higgs” particle is necessary to have “mass”. In particular, the conflict between quantum mechanics and Einstein's GR is a clear instance of error.

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The problem that I see is that it seems that it must be possible to define an element so that it can behave in any way, if this is the case even if physics allows elements to be defined so that they can behave in any possible way, this would only increase the problem as we would have to ask why we don't use such definitions.

No language uses elements for which the users have no use.

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And it would make the question of “just what do we consider modern physics to be” a question with perhaps not a obvious answer.

Well, as far as I can see it, “modern physics” is a belief system apparently consistent with “scientific experimentation” (at least it is so long as one does not look too closely). My presentation is designed to yield experimental results no matter what information is being represented. The probability of any circumstance, , must be expressible by the magnitude of where is a solution to my fundamental equation. No constraints whatsoever have been placed on what is being represented.

What I have done is quite analogous to the Dewey Decimal system for categorizing library books: it is designed to allow all possibilities to be represented. Modern physics is supposed to be a science attempting to find the rules of the universe, quite a different matter. They presume there are discoverable rules. My approach makes only two constraints: that the explanation must be internally consistent and that it must give non-zero probability to the information which is known.

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You and AnssiH seem to be of the opinion that what you have proven is that modern physics is nothing more then a means of generating an explanation of any possible information, I can see that you have a strong defense for this even stronger then the physicists that say that reality is really like physics says it is, in fact I would go so far as to say that you clearly have proven them wrong, reality is not like physics says it is physics is just a means of generating an explanation.

It is the scientists who assert that scientific work is a means of generating explanations. Essentially they are defining things and then discovering that their experiments are consistent with their definitions: i.e., they never take the trouble to examine the consequences of their definitions. That is what I have done by examining the result of requiring “universal” internal consistency.

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The question is, how general of an explanation is physics? And how general is the context that physics uses?

Physics explanations are almost always valid only in very specific cases (cases defined by context which is usually ignored, as they have no idea as to how to bring that context to bear on the problem being examined). I suspect my technique is the only way to bring every piece of context to bear on every problem. It is, in fact, very analogous to quantum mechanics as quantum mechanics, in a very real sense, actually concerns itself with the impact of context: i.e., they specifically express the presumptions they are making (at least for the most part).

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OK I may have phrased that in a bad way. I should have said something like, you seem to be suggesting that the universe must obey modern physics because you have shown that you can approximate the fundamental equation with the same equations as modern physics uses.

Well, any solution to the fundamental equation must essentially obey quantum mechanics as the relationships required by quantum mechanics are quite similar to those required by my equation. Oh, approximations must be made; but of what character are those approximations? They all amount to presuming that some portion of the context can be ignored and recognizing exactly what is being ignored. If we can't ignore any part of the context, we have to solve the whole problem in one fell swoop. And that simply will never be accomplished as it requires you to be all knowing. And, by the way, that explanation is well known: it is the “what is” is “what is” explanation.

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... but can be looked at as somewhat of an achievement to have happened by the “guess and by golly” approach, as you are calling it.

Yeah, a million years of “by guess and by golly” have managed to achieve usable results without every considering the logical consequences of their definitions. I'm impressed.

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I think that it is worth remembering that any possible consistent means of explaining any thing can be derived from the fundamental equation if we just know the right context and are precise enough with our use of it.

Yeah, and exactly what do you mean by “any possible means”. Can't you comprehend that part of the problem to be solved is what other people mean by the sounds and gestures they use. I have shown you a representation which presents the “known information” as a changing collection of points in an abstract four dimensional space. “Any possible means” is an assertion referring to those hypothetical elements added into the problem so as to allow the creation of an explanation.

I have shown that “mass” and “time” are required abstract concepts (required in order to create an explanation). The implied internal factors include a number of specific forces which are easily identified with forces used in common parlance. Actual contact, electric charge, magnetic fields, gravitational, nuclear, nuclear weak and even Pauli exclusion. Chemistry is an inherent consequence there. The issue arises as to what the underlying nature of “any possible means” is. Clearly it is going to require much of what we find common in our world: objects collected together by large macroscopic object (to keep entities together long enough to study the problem), molecular structures capable of creating macroscopic collections of elements able to use chemistry to achieve control necessary to create thinking entities, etc., etc., etc., ... So it is going to look one hell of a lot just like the world we find ourselves in!

In fact, you can not prove that your neighbor's concept of the universe bears any resemblance to yours. In learning his language, you have come up with a way identifying what he means by his words, gestures and signs (your context as you see it) in terms of your personal concept of the universe. Does the fact that the information you have received can be so interpreted prove that the underlying experiences are what you think they are? That they are is a presumption (perhaps a useful presumption but that doesn't mean you can prove it is true).

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... how would we know if our result was even a unique result and that we couldn't make the same approximation in different ways and get a different result.

It is clear that you can not know! It is a presumption you make when you decide you understand what your neighbor is saying.

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Or that we could still look at the approximate result as an approximation to any possible solution to the original equation.

It isn't “any possible solution” that we are interested in. We are interested in a solution which yields our personal experiences as having a non-zero probability.

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Can there be other universes that look nothing like ours or are the odds against such a thing existing so much so that they all must look the same in the end.

Try proving to me that your concept of the universe looks anything like mine while still allowing all possible meanings to the words, gestures and signs we use in communicating.

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Or the context that you made in showing the approximation of Dirac's equation.

Look, if the solution is not consistent with the massive amounts of information (the context) I need to explain, it's invalid from the get go! That is, those approximations are required: they are approximations made by the scientific community and making those approximations allow their solutions (checked by hundreds of thousands of experiments: i.e., known information) to be approximate solutions to my equation.

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Maybe I don't understand what the purpose here is but I am under the impression that Einstein notation is simply the use of the convention of summation over upper and lower script to remove the need for summation.

If he removed the need for summation, why in the devil did he need the convention “of summation over upper and lower script”. The summations are still there just in a much shorter notation.

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What necessity, as far as I can tell you used them only to turn multiple equations that seem to represent very different but necessary constraints into one equation representing all of the constraints, in your words.

With several equations, you need to find all possible solutions to all the equations and then find the solution set which solves both. That is a far more difficult task than solving one equation. Essentially I showed that a transformation existed which inevitably solved both equations (so long as one is operating in what is essentially a center of momentum frame of reference). The problem you propose to solve is more easily solved by solving my equation first and then transforming the solution to a frame of reference where the total momentum does not vanish. But what purpose do you propose for being able to generate that particular solution? It is no more than a restatement of the "center of momentum" solution.

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So what is the necessity of the spinner operators?

They allowed me to present a single equation to be solved!

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My reasoning for understanding that they had no further influence on possible solutions is that you seem to have never given any reason that they are necessary and only ever demonstrated that you could derive your constraints form the fundamental equation by using them, so unless you have a reason to include them it would only make sense to use them if they have no influence beyond the notation that is being used.

Anyone familiar with solving partial differential equations would be well aware of the problems introduced by trying to find simultaneous solutions to different equations.

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This implies a great deal of consistency even in their derivations.

Well, considering the experiments standing behind those results, one should expect them to be rather self consistent. In the same vein, I express no surprise that the common world view of the universe is quite consistent with their day to day experiences. Evolution has had millions of years to weed out erroneous perceptions of reality.

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Is the idea that we don't see any other ways of applying these approximations really sufficient to say that the result is unique?

I suspect the problem here is your concept of “unique”. If I make the approximations I make (essentially ignoring specific context) I get exactly the same equation. That is a “unique” result traceable to those specific approximations.

Have fun -- Dick