What can we know of reality?

[Doctordick]

Sorry about the delay in my responce to Bombadil. In his post, he brings up an issue first breached by Qfwfq last October.

Originally Posted by Qfwfq

However, I'm not so sure K needs to be constant (x-independent), it seems to me that a real-valued K(x) wouldn't break the symmetry as would have an x-independent modulus anyway (indeed, I get the second derivative of P being zero too).

I came to the conclusion that this issue needs to be settled once and for all. In an attempt to get an understanding of the difficulty everyone seems to have comprehending what I am doing, I went back through the entire thread looking at what I said in the past an how people reacted to it. As a consequence, I came to the conclusion that everyone is missing one very significant point. My work was not at all ever concerned with creating explanations of anything. The opening issue (using numerical labels to refer to the underlying ontological elements on which the explanations are based together with the idea of expressing our expectations as a probability of seeing some specific set) allowed me to express a one to one correspondence between any explanation and a mathematical function. The known past IS a tabular representation of specific points on that function: i.e., the ”what is”, is “what is” tabular explanation.

I expressed that function as the norm of a vector in an abstract space for the simple reason that absolutely any mathematical function can be so represented: i.e., can represent any possible transformation from one set of numbers to another. So the solution (the explanation) lies in a specific function . I am not concerned with that problem at all. My only interest is with the constraints imposed upon that solution by the fact that the definitions of those reference labels used to express that solution are defined by the solution: i.e., there exists no information outside the things those reference labels refer to. So what I am presenting is an additional set of constraints imposed on the solution not by reality but simply by the symmetries brought on by the freedom of that labeling system. By expressing the explanation as a mathematical function, I am able to write down the explicit constraints flowing out of the symmetries required by the freedom in that labeling system.

This post is very much directed to Qfwfq, Buffy and Erasmus00 as they seem to have dropped out of the discussion. I do not know if they have simply lost interest in the thread or have decided that I can not be argued with. Neither possibility appeals to me as I very much respect their reasoning powers and would like to have their respect as a rational person.

As I said, I was moved to write this when Bombadil brought up the issue originally complained about by Qfwfq. That was my assertion that K in my fundamental equation is a constant. Essentially Bombadil is once again asking exactly that very same question.

Let's go back to the idea that shift symmetry requires which I presume you will all accept (except perhaps for Buffy who has never responded to my last post to her; I would really like to know what your reaction was to that argument). Having defined P to be the squared norm of an abstract vector function we need to express this constraint on that function. I don't think you had any problem with the idea that would satisfy that constraint. The problem arose when I proposed replacing that expression with (the first i is a tag on x whereas the second i is the imaginary number ). I wanted K to be limited to a constant. You, on the other hand, wanted to open the issue up to more complex functionality and I baulked. Perhaps you can comprehend my complaint if you can understand the following argument.

Try looking at my position from this perspective: I chose the form of because it placed utterly no limitation on the method of obtaining P. Within that set of “all methods” of obtaining P the expression

yields exactly the same expectations as . You held that the solutions would be opened up by adding in the possibility that K could be a function of the . What you seem to have failed to appreciate was the fact that my move had not added any solutions to the mix. When P is calculated as the norm of an abstract n dimensional vector, the possibility of a plane in that space representing a mere shift in direction of that vector with respect to rotation in that plane always exists. All I did was abstract that plane out of that vector representation and express its consequences in an explicit manner. Why did I do that? First, because it was very easy to represent such a possibility in my paradigm, second, the representation yielded a very convenient fundamental equation and third, the existence of such a phase shift in no way altered the effective probabilities was created to express.

You wanted to add more complex functions. My question is, why? What purpose would such an addition fulfill? We have already included “all possibilities” in the very structure of . I did what I did for my convenience, not because it had to be done. Just as an aside, “ probably reflects the real world somehow” and it could certainly be embedded in an abstract space used to represent . If that could be abstracted out as some kind of complex 248-dimensional rotation yielding no change in expectations expressed by then it might very well yield an additional valuable alteration to my equation. If I were fifty years younger, I think I would find examination of such a project interesting but, for the moment, it is not in my plans.

But the issue here is, “keep it simple!” Erasmus00, you were apparently very disturbed by constraining my examination to a first order linear differential equation.

Originally Posted by Erasmus00

However, if one can rigorously show that NO linear equation can provide those probabilities (i.e. show that there exist non-linear equations that cannot map to linear equations), does that imply your equation is wrong?

You also need to comprehend the fact that any procedure for generating your expectations can be seen as a way of getting from the description of the case of interest to your expectations and that can be seen as the definition of . All I have done is written down an equation on required by the simple fact that the “language?” used to express your description is a totally undefined structure. This is no more than a very simple additional constraint required by a logical analysis of the source of that language. As such, it must display some very interesting symmetries some of which are represented by my fundamental equation. You should be sufficiently familiar with first order linear differential equation to understand that the equation puts no real constraints on the form of (that form is set by the boundary conditions: what we know), it merely tells us how those solutions must change in order to be consistent with the symmetries. It is little more than an additional logical constraint on rational expectations such that new information will not change the structure of your solution. Scientists do that all the time, this is no more than an analytical expression of the idea.

Finally, to Buffy, I would really like to hear your current position on what I have been saying. If you have decided that I am a nut not worth reading, I would like to know about that also and I will take no offense.

So, at this point, I think I am ready to respond to Bombadi.

Originally Posted by Bombadil

Then the function f has the form

f = K left{int vec{Psi}_2^dagger cdot frac{partial}{partial t}vec{Psi}_2 dV_2 right}vec{Psi}_1 + sum_{i neq j #1}beta_{ij}delta(vec{x}_i -vec{x}_j)delta(vec{tau }_i -vec{tau }_j)Psi}_1

I'm having some problems getting the latex to work right for this equation if you don't understand what it's suppose to say I'll have to try to get it to work right.

After close examination of your latex, I found two apparent errors: first I believe the # sign requires a back slash as it apparently has some meaning to the latex software. Secondly, you need a “\vec{“ opening on the last Psi. (Not to mention the need for a “math” and “/math” tag to run the latex software. If those changes are made, what results is

which is not a correct representation of f. I do not know if that is simply a problem with your latex or with your understanding. Please examine the equation immediately preceding my assertion that f would be a weighted sum over alpha and beta operators plus one term without such an operator and you should be able to work a representation of that sum out. If you cannot, let me know and I will write it out in detail. There is really no need to work it out in detail as the only fact of interest at this point is that every term (except one) has either a single alpha or a beta operator multiplying it. After we do the integrals, we have to have a weighted sum of those operators plus one term lacking such an operator.

Originally Posted by Bombadil

Then we know that the t dependence of under the constraint that you are suggesting is because you are saying that the probability does not depend on the t (or time) axis and when the norm of the function containing that term is taken it becomes equal to 1. Now is the term just any constant term or function or does it matter what it is?

Remember, one of the original constraints was which has a trivial solution where has no dependence upon t at all. I wouldn't say the norm is one since the norm is dependent upon the other arguments. What is important here is that shift symmetry in t requires a conserved quantity “”. Exactly the same argument goes through for . If the probability distribution of the “rest of the universe” is not a function of time, then one has essentially exactly the same consequence as previously engendered by shift symmetry which, once again leads us to a conserved quantity related to that differential. In this case, I represented the conserved quantity by “”. Likewise the same arguments go through for the invalid elements represented by . I get the definite impression that you understand this; I just wrote it out again to make sure. If you have no arguments with what I just said, we won't need to worry about it.

Originally Posted by Bombadil

Also this is nothing more then a approximation so that when we have finished solving for this may in fact not be the case and the right side may have a more complex form.

Absolutely correct; but we are not going to worry about it because I have already said we are only going after an approximation. My purpose has nothing to do with finding solutions but rather with expanding the vocabulary which can be used with my paradigm.

Originally Posted by Bombadil

I’m not quite sure how you did this, ...

That cross term should certainly be there; however, when I set up my first approximation, I essentially said this term has a negligible influence on the result.

Originally Posted by Doctordick

The first of these three is that the data point of interest, , is insignificant to the rest of the universe: i.e., is, for practical purposes, not much effected by any change in the actual form of : i.e., feed back from the rest of the universe due to changes in can be neglected.

What you are looking at is the partial of with respect to . Now that partial is essentially a measure of the change in the form of G as a function of changes in : i.e., it is essentially a kind of feed back effect which I approximate as negligible so I can drop the term. The whole purpose of this particular exercise is to establish a definition of momentum (together with mass and energy). Having done that, the term which we have omitted is quite clearly is analogous to inserting momentum dependence in the potential used in the Schroedinger equation but I could not have said such a thing without defining “momentum”.

Originally Posted by Doctordick

The serious question then is, what happens to my derivation when those constraints are relaxed. If one examines that derivation carefully, one will discover that the only result of these constraints was to remove the time dependent term from the linear weighted sum expressed by g(x). If this term is left in, g(x) will be complicated in three ways: first, the general representation must allow for time dependence; second, the representation must allow for terms proportional to and, finally, the resultant V(x) will be a linear sum of the alpha and beta operators.

As I said, momentum dependent potentials are not seen except in quite advanced applications of Schroedinger's equation. Just take my word for it as the only issue here is that any solution of Schroedinger's equation is an approximate solution to my fundamental equation.

Originally Posted by Bombadil

I can only conclude that on the first line the -+ term is suppose to be just + and on the second line the g(x) is suppose to be a upper case G(x) both of which seem to be just minor errors in the latex.

You are absolutely correct. I erased the q and forgot the sign. When I rewrote the relationship divided by 2q, I went back to lower case. I carried the same error down to the definition of the potential. I apologize for being so sloppy and I will edit the post to fix these errors.

There is an additional comment which can be made here. Notice that mass is essentially momentum in the tau direction (that fictional axis I inserted in order to avoid loss of information in the representation). The Heisenberg uncertainty principal, that the uncertainty in x times the uncertainty in momentum in the x direction is given by (which comes from wave analysis: Schroedinger's equation is a “wave equation” by the way), informs us that the uncertainty in m can be dammed near zero. So the world view in this paradigm is of a four dimensional Euclidean universe where everything of interest is momentum quantized in the tau direction. That very issue removes tau from observation (it is projected out by the uncertainty in tau). This brings to mind the fact that almost all experiments done by scientists are performed in laboratories constructed of “mass quantized entities” and analyzed with instruments which are also made of “mass quantized entities”. Just pointing out that my paradigm isn't really all that implausible.

There is another interesting observation to be made here. In this paradigm, negative mass is simply momentum in the negative direction in tau. (Note that, if q in my derivation is taken to be negative, we just make p=-q and divide by 2p (essentially removing the other factor from the pair on the right). The point being that we will again obtain : i.e., we do not obtain a negative mass. Essentially Energy is the magnitude of the four dimensional momentum. In my paradigm, it is no more possible to convert mass directly to energy than it is to convert momentum directly to energy; both transitions are severely constrained by kinematics and there is no need to alibi away the failure of massive objects to spontaneously decay into energy. (Just some interesting observations!)

Originally Posted by Bombadil

Would this also be equivalent to saying that the function also has no time dependence?

Not really as, in the Schroedinger representation a phase term is still there (the energy would be zero otherwise). Furthermore, we have not removed the entire contribution of K (i.e., ) there is still an energy term associated with and that energy would need to be represented by a phase term.

Originally Posted by Bombadil

It looks to me like the Schroedinger equation is still a partial differential equation and so it still is not even a solution, even if we have a solution to the Schroedinger equation it only give us the function so will we have to reverse the substitutions that you did to obtain the corresponding function .

The actual solution is very dependent upon the context as are the solutions to Schroedinger's equation. If we know that context (we know our expectations for the rest of the universe) our expectations for the elemental reference “x” is fundamentally given by Schroedinger's equation; there is very little to reverse here so long as we are satisfied with the approximations that need to be used (mainly that the energy is very close to ). Note that m here is what is ordinarily called rest mass (since mass is essentially momentum in the tau direction, the energy is not unless the momentum perpendicular to tau (what physicists ordinarily call momentum) is a negligible component: i.e., this is a non-relativistic situation. In fact, for a free element (free meaning the context implies v(x) is neglectable) the actual energy associated with the index x (i.e., without that energy level shift made to achieve Schroedinger's equation) would be given by ; another rather familiar relativistic expression.

Originally Posted by Bombadil

Now is it an approximate solution in that any solution to it won’t satisfy the fundamental equation or that it will only give rise to a particular family of solutions to the fundamental equation?

It is exactly the correct solution to my equation if the approximations I have put forth are negligible to our interests; remember we are generating our expectations, we are not predicting the future.

Originally Posted by Bombadil

Just how did you come to these definitions?

They are exactly the representation used in the Schroedinger's equation by hypothesis (physicists defined momentum, mass and energy long before Shroedinger's equation existed). I defined them the way I did (notice that, prior to this, my paradigm did not contain any definitions beyond x, tau, and t) because I have the freedom to define any mathematical relationships I wish, so long as I make it clear as to what I mean by the term.

Originally Posted by Bombadil

It also seems that we could have by a slightly different set of substitutions and integrations have arrived at the same equation for the invalid elements. The residue resides in the integrals used to develop G(x). Once the identity with energy is obtained, it becomes clear that it is possible for the solution to exchange energy

That is not difficult to do at all and it has to be true from the constraint that, whatever the rules of behavior are, the valid and invalid elements must obey exactly the same rules: i.e., the equation cannot provide a mechanism for differentiating between valid and invalid ontological elements.

Originally Posted by Bombadil

This seems to lead me to the question can this be generalized to an N dimensional Schroedinger equation although I have no idea how the Schoedinger equation is used let alone what we would use such a generalization for?

I will simply let that slide until we get further down the road as the only real issue I intended to bring forth here is that Schroedinger's equation is an approximation to my fundamental equation and use this fact to provide support for my definitions of momentum, mass and energy as reasonably in line with conventional meanings of these terms.

As I said, there are whole books which show how Newtonian mechanics can be deduced from Schroedinger's equation. This suggests a very profound notion: that is the fact that any internally consistent explanation of anything will be ruled by Newtonian physics so long as the necessary approximation are valid. It is likewise, very reasonable that we would all have essentially the same background mental image of reality: it is the only internally self consistent background image possible.

Have fun -- Dick

[Bombadil]

Originally Posted by Doctordick

Try looking at my position from this perspective: I chose the form of vec{Psi} because it placed utterly no limitation on the method of obtaining P. Within that set of “all methods” of obtaining P the expression

e^{-iK(x_1+x_2+cdots+x_n)}vec{Psi}

yields exactly the same expectations as vec{Psi}. You held that the solutions would be opened up by adding in the possibility that K could be a function of the (x_1,x_2,cdots,x_n). What you seem to have failed to appreciate was the fact that my move had not added any solutions to the mix. When P is calculated as the norm of an abstract n dimensional vector, the possibility of a plane in that space representing a mere shift in direction of that vector with respect to rotation in that plane always exists. All I did was abstract that plane out of that vector representation and express its consequences in an explicit manner. Why did I do that? First, because it was very easy to represent such a possibility in my paradigm, second, the representation yielded a very convenient fundamental equation and third, the existence of such a phase shift in no way altered the effective probabilities vec{Psi} was created to express.

From the start of the idea of adding the element I don’t think that the complaint has been with if it will change the probability of P but that the term would change the partial derivatives to x and tau and modify the value of . What at least I had missed is that the value of has no real significance only the constraints on and as a result the resulting constraints on P are what is of interest. After some closer examination of the constraints it is clear that by modifying the K in to a function rather then a constant can add no additional element that can have any effect on how P behaves (it also can’t remove any element from P).

I’m putting this on not because I’ve still got a problem with what you did but because I think I have some idea of how we can say K is a constant and perhaps putting it on this way might help some people understand just what you did and why you did it this way, as well as giving you some more ideas as to what some of the problems other people have had with what you have done.

Originally Posted by Doctordick

After close examination of your latex, I found two apparent errors: first I believe the # sign requires a back slash as it apparently has some meaning to the latex software. Secondly, you need a “vec{“ opening on the last Psi. (Not to mention the need for a “math” and “/math” tag to run the latex software. If those changes are made, what results is

f = K left{ int vec{Psi}_2^dagger cdot frac{partial}{partial t}vec{Psi}_2 dV_2right}vec{Psi}_1 + sum_{i neq j #1}beta_{ij}delta(vec{x}_i -vec{x}_j)delta(vec{tau}_i -vec{tau}_j)vec{Psi}_1

which is not a correct representation of f. I do not know if that is simply a problem with your latex or with your understanding. Please examine the equation immediately preceding my assertion that f would be a weighted sum over alpha and beta operators plus one term without such an operator and you should be able to work a representation of that sum out. If you cannot, let me know and I will write it out in detail. There is really no need to work it out in detail as the only fact of interest at this point is that every term (except one) has either a single alpha or a beta operator multiplying it. After we do the integrals, we have to have a weighted sum of those operators plus one term lacking such an operator.

I had copied the code from a couple of different places and I must have missed the /vec and didn’t realize that a / was needed to be used with the # symbol as for the math tags every time I put them on it just displayed a syntax error.

After closer examination I have came up with



as the form f should take. This still doesn’t seem quite right to me for one thing it seems the beta elements should all vanish also the first term has a 1/n term due to it being inside of the sum in your equation from 1 to n (I can only conclude that this is all elements in set #1) so it could be removed by moving it to the outside of the sigma. This is what I’m coming up with for the function f that should be substituted in the equation



which is the reason for leaving out the term at the end of the equation.

Originally Posted by Doctordick

There is an additional comment which can be made here. Notice that mass is essentially momentum in the tau direction (that fictional axis I inserted in order to avoid loss of information in the representation). The Heisenberg uncertainty principal, that the uncertainty in x times the uncertainty in momentum in the x direction is given by frac{hbar}{2} (which comes from wave analysis: Schroedinger's equation is a “wave equation” by the way), informs us that the uncertainty in m can be dammed near zero. So the world view in this paradigm is of a four dimensional Euclidean universe where everything of interest is momentum quantized in the tau direction. That very issue removes tau from observation (it is projected out by the uncertainty in tau). This brings to mind the fact that almost all experiments done by scientists are performed in laboratories constructed of “mass quantized entities” and analyzed with instruments which are also made of “mass quantized entities”. Just pointing out that my paradigm isn't really all that implausible.

I suspect that an explanation of how the term comes about is for the time being unimportant and unnecessary but I’m not sure just what the term is, the way that you are using it, it seems that it is just a constant but does it have a certain value or should it be considered just any constant?

Now will the Heisenberg uncertainty principal only be valid with the Schroedinger equation? That is, the uncertainty in x times the uncertainty in momentum in the x direction is only given by as long as we are using the Schroedinger equation as a solution. If so, is there a generalized form of it that can be used with the fundamental equation?

Also, the Schroedinger equation is a wave equation and it will satisfy the fundamental equation with the constraints you have put on it so, are all possible solutions to the fundamental equation without those constraints also going to be a wave equation?

Originally Posted by Doctordick

The actual solution is very dependent upon the context as are the solutions to Schroedinger's equation. If we know that context (we know our expectations for the rest of the universe) our expectations for the elemental reference “x” is fundamentally given by Schroedinger's equation; there is very little to reverse here so long as we are satisfied with the approximations that need to be used (mainly that the energy is very close to mc^2). Note that m here is what is ordinarily called rest mass (since mass is essentially momentum in the tau direction, the energy is not mc^2 unless the momentum perpendicular to tau (what physicists ordinarily call momentum) is a negligible component: i.e., this is a non-relativistic situation. In fact, for a free element (free meaning the context implies v(x) is neglectable) the actual energy associated with the index x (i.e., without that energy level shift made to achieve Schroedinger's equation) would be given by E=csqrt{P_x^2+P_y^2+P_z^2+m^2c^2}; another rather familiar relativistic expression.

Then will all the solutions to the fundamental equation also be dependent on the context (it seems that it must be)?

The term looks somewhat familiar, maybe the energy term for total energy although this may not be the case (I’m not sure what the P terms are I think that they are partial derivatives) although I’m not very familiar with relativity so this is likely why I’m not sure what it is, also I’m not sure of just how you got it.

[Doctordick]

Hi Bombadil, sorry about being so slow in my response. For a number of reasons, I wasn't exactly sure how I should respond. Since I have had a number of household projects underway and not a lot of time to think about my response, I have been sort of waiting for Anssi to get free enough to continue our conversation. Meanwhile, I have come up with a little free time and I had promised that, if you couldn't come up with the correct form of f, I would show you the correct procedure. I have laid it out below.

is not even close to the correct representation of f as you have not included all the integrations required. I have a suspicion that your understanding of algebra is not up to the task of following my work. See if you can follow the following. You need to start from the expression

Then take a look at expression following the sentence, “If the actual function 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:”

The first expression was written in the form of three elements enclosed by curly brackets so that you would see it as such a collection. The first curly bracket contains

which contains no arguments at all from set #2. It follows that, so far as that term is concerned, left multiplcation by and integrating over all arguments from set #2 has yielded exactly one (the sum total of all possibilities has a probability of one by definition). Secondly, since is asymmetric with regard to exchange of any arguments, the Dirac delta function shown there must exactly vanish. Thus that first curly bracket comes down to

This is exactly the first term of the declared result of the above integration. Furthermore the last term of the declared result is clearly the first term of what is enclosed in the last curly bracket (where, once more, the integration over set #2 is exactly one), specifically.

It follows trivially that f must be the collection of remaining terms (what is enclosed in the middle curly brackets plus that other time derivative in the third curly bracket; namely,

or, rearranging terms,

Simple observation discloses that, if is known, the integrals can be done and the only arguments left in the expression are from set #1 (all other arguments have been integrated out) and that f is a weighted sum of alpha and beta operators (weighted by the various integrals) plus one term without such an operator.

The rest of your post seems to indicate a rather common misunderstanding of my intentions here. Reading your post reminds me of an old joke. The joke involves three characters: an engineer, a physicist and a mathematician. The question is, what is their behavior while walking down a hall at the university and noticing a waste basket full of paper which is on fire in a class room. The engineer gets a bucket of water and pours it into the waste basket; thus putting the fire out. The physicist examines the fire, measuring the height, temperature and color of the flames. He checks how the fire lights up the room, influences the temperature of the room and feels at various distances away from it. When he cannot think of anything else to examine, he gets a bucket of water and pours it into the basket putting the fire out. The mathematician immediately reduces the fire to a problem he has already solved and forgets about it, continuing to walk on down the hall.

Of course the central issue of the joke is the fact that a professional engineer has little if any interest in why things are the way they are but only concerns himself with the quickest and best way to achieve the result he desires. The physicist wants to believe he understands the thing. Without understanding, what purpose does his knowledge serve? Finally, as Buffy has said, mathematics has absolutely nothing to do with reality.

What I am putting forth here are arguments concerning the fundamental underpinnings of science itself. Common science always makes the assumption that their current expectations for the future are substantially correct and examines their past (what they know or think they know) for events which contradict those expectations. Experimentalists don't really concern themselves with explaining these contradictions; they only search them out. It is supposedly the theorist who is charged with discovering an explanation which will remove the contradictions. If you look at the historical record, you will discover that very few people have been able to conceive of theories which yielded decent explanations and they have all usually been hailed as geniuses.

The thing is that most people who try to come up with such solutions are seen as nuts. There is an old adage, “there is a fine line between genius and insanity”. That is a direct consequence of what I call the “by guess and by golly” approach to solving the problem. Good guesses are hard to come by and, even today, there are still quite a large number of problems with those wonderful guesses which those recognized geniuses have put forward. Professional physicists do not like to talk about such things because doubt of their beliefs is damaging to their authority; however, serious discussion of almost all such questions exists. Essentially these problems can be divided into two very specific sets: those where the physics theories seem to give the wrong answers and those which revolve around the assumptions upon which the theories rest.

If you read back over my general presentation, you should perceive that I have no concern at all with “wrong answers”. I have specifically stated that I am only concerned with rules which the “flaw-free” explanations must obey: i.e., if they are flaw-free, they cannot give any “wrong answers” with regard to any known information. Everyone seems to jump to the conclusion that I am putting forth a theory here whereas It should be clear to all of them that my attack is not designed to produce any theories of any kind; I am only concerned with the problem of expressing the logical constraints imposed by self consistency itself.

Absolutely the first issue which arises if one thinks about such things is the problem of induction. Look around on this very forum and you will find a large number of posts concerning the fact that induction can never be substantiated as logically sound. What I have asked is, “exactly what can one say, without bringing induction to the table”. The answer is quite simple and I think I have demonstrated the logic of that answer: any explanation of anything can be seen as a mathematical function which must obey the equation

Now that is a nice deduction but relatively worthless without two very important factors. First, one needs to be able to solve the equation and second, the solutions must have some significance: i.e., one needs to establish that “concept-reality” connection which Buffy is so worried about. In order to make such a connection, one must relate solutions of that equation to actual facts of reality (and come up with a good reason for that relation). You simply cannot do that without knowing some solutions and anyone familiar with modern mathematics knows full well that finding a general solution to such an equation is essentially impossible. That expression is a partial differential equation constraining what amounts to, when all invalid ontological elements are included, an infinite number of variables. A general solution to such a differential equation is simply beyond the capability of modern mathematics.

There are a lot of differential equations in modern physics where general solutions can not be found. For example, Schroedinger's equation for the universe:

can not be solved for even if we happened to know the exact proper form of . In fact, we can't find a closed form general solution for the case n=3. As a matter of fact, the theorem of “conservation of momentum” is the critical factor in allowing us to find a general solution to a two body problem. Without conservation of momentum, the only problem for which a general solution can be found, given the exact nature of that potential V, is the solution for one body. The rest of the “solutions” are obtained by a technique commonly referred to as “perturbation theory”. Some will point out that group theory can give exact results for many body circumstances; however, these are not bone fide “general” solutions but rather apply only to constrained cases.

What I am getting at is the fact that the life blood of physics (and the source of their apparent ability to explain almost all underlying phenomena) is approximation. I have a Ph.D. in theoretical physics and, in my experience, theoreticians have complete faith in the correctness of their underlying theories. Their real concerns is, “given those theories, how do we calculate answers”. Notice that Richard Feynman got a Nobel prize for coming up with a notation for keeping track of terms of a perturbation series. I don't mean this as an insult as he was one of the most brilliant theoretical physicists of his day. I bring it up only to point out just how important finding solutions is. To my knowledge, no modern physicists are thinking about “new” theories; they are all thinking in terms of perturbation on current theories. That is exactly what “dark matter” and “dark energy” is all about: they are no more than justification for specific perturbations on current theories.

What I am getting at is the fact that I do not have any intentions of teaching physics and/or mathematics here. I will explain the exact logic behind any individual step in my deductions as that is a relatively short process; however, explaining physics and/or mathematics in general is a lifetime process. There are many physicists out there who have excellent comprehension of things like the Schroedinger Equation, Heisenberg uncertainty and how the factor comes to be an important quantity.

Back in my first year of graduate school, I read “Mr Tompkins in Wonderland “ by George Gamow. It was written to explain the important physical constants by imagining alternate worlds where these constants are supposed to have very different values from those they have in our world. It is an excellent discourse on these various constants; however, Gamow has made some serious errors. In particular, his discourse on “Mr. Tompkins goes to Quantum Land” where has a very large value is clearly just plain wrong (Mr. Tompkins goes on a tiger hunt and it talks about his problems which arise from Heisenberg uncertainty). At the time, I tried to work out what the world would really look like if were large and I failed miserably. I could not find any starting point where some measurement would be totally and absolutely independent of . That number so pervades physics that I eventually came to the conclusion that it was circularly defined. I talked to my advisor about it and he told me that my problem was that I didn't understand physics; there was absolutely no way it was circularly defined. If it were, physicists would be well aware of the fact.

In my derivation of Schroedinger's equation it is most certainly circularly defined as, in that derivation, it is a simple constant which is multiplied through my fundamental equation (its actual value is of utterly no consequence at all). If you use the standard value for in that representation then the result is exactly the standard Schroedinger equation.

Logically, let's look at it and see what happens if one uses a different value. Suppose one uses ten times the standard value. From my definitions of m, c and V (presuming we have an established solution of my fundamental equation) m and V will be exactly ten times as large and c will have the same value as before. This yields exactly 10 times as large. The resultant Schroedinger equation is exactly the same as before except that each term has been multiplied by ten. The ten is no more than a scale factor on energy; the physical problem being solved is identical. What I am getting at is the simple fact that modern physics is based on separate variables independently defined (through induction) which are actually related through my fundamental equation: i.e., these physical constants are a consequence of multiple effective definition (they are essentially circularly or overly defined).

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

[AnssiH]

Originally Posted by Doctordick

Hi Bombadil, sorry about being so slow in my response. For a number of reasons, I wasn't exactly sure how I should respond. Since I have had a number of household projects underway and not a lot of time to think about my response, I have been sort of waiting for Anssi to get free enough to continue our conversation.

And it shouldn't take long now. Technically, the next week is still supposed to be busy for me (another extension for our schedules), but it seems like I'm starting to have some more free time on my hands already; actually have had some time to get back to the posts where I left.

I've read all the posts and I have to say that everything you are saying makes a lot of sense to me, but I definitely need to get myself up to speed with all the math.

One finding that is somewhat surprising to me is - what you've mentioned couple of times - that it seems newtonian mechanics is a "consequence of requiring our explanation of reality to be internally self consistent". It seems like a logical finding but I need to understand the math better to see it for myself.

Why it's surprising is I would have just assumed that an important factor at coming up with a "newtonian worldview" is also our ability to define (/identify) ontological elements freely; i.e. that a very specific type of classification AND self-consistency yields newtonian behaviour to those defined elements (and that just happens to be among the simplest views prediction-wise... in some sense that I did not understand yet).

What I'm asking is, isn't it possible to be self-consistent with more complicated worldview's as well? I.e. that it is not self-consistency alone that yields newtonian mechanics?

I have to look at the math more to see these things in detail for myself though...

Back in action soon,
-Anssi

[Qfwfq]

Originally Posted by AnssiH

I.e. that it is not self-consistency alone that yields newtonian mechanics?

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.

[Doctordick]

Hi Anssi, it is sure nice to hear from you. Hope everything turned out well.

Originally Posted by AnssiH

I've read all the posts and I have to say that everything you are saying makes a lot of sense to me, but I definitely need to get myself up to speed with all the math.

Just point out the first mathematical step which you don't follow and I will do my best to give you the details, doing the best I can to leave nothing to presumption.

Originally Posted by AnssiH

... I would have just assumed that an important factor at coming up with a "newtonian worldview" is also our ability to define (/identify) ontological elements freely; i.e. that a very specific type of classification AND self-consistency yields newtonian behaviour to those defined elements (and that just happens to be among the simplest views prediction-wise... in some sense that I did not understand yet).

The question has to be, exactly what is it, that we have to work with. I have used many terms for “whatever that might be”: “knowable data”, “ontological elements”, “noumena”... It really makes no difference what actual tag you place on the “????”; the only important issue to remember is that, sans an epistemological construct (“explanation”, “world view”, “understanding”, ... whatever), no matter what it is, it is totally undefined. The moment you lose sight of that fact, you have lost sight of the problem confronting you. A really significant issue resides exactly on this point: undefined means undefined: we do not know “what they are” or anything about “what they are” . When I complain about people bringing baggage to the discussion, I am talking about people bringing meaning to those reference tags, “knowable data”, “ontological elements”, “noumena”....etc..

Let me add another tag to that collection; a tag I have avoided, because of the tendency of people to bring meaning with tags, but a very nice tag none the less (if you can remember not to bring meaning with the tag). Suppose we give these unknown things the name “events”. It turns out that, after understanding my paradigm, this name corresponds quite well with what physicists commonly refer to as “events”. Thus the fundamental dichotomy upon which all explanations are built comes down to “real” events and “presumed” or “imagined” events (events which are required by the explanation).

Originally Posted by AnssiH

What I'm asking is, isn't it possible to be self-consistent with more complicated worldview's as well? I.e. that it is not self-consistency alone that yields newtonian mechanics?

What you are missing is the fact that you (I would say “your brain” except for the fact that that concept itself brings in massive quantities of supposedly well defined “baggage”) have/has absolutely nothing to work with except a collection of totally undefined events.

Suppose you have a “more complicated world-view. For me to understand that world-view, you would have to explain it to me and exactly how do I come to understand your explanation? Your explanation arrives via “events” which I need to comprehend usually by means of a language which uses reference tags to which I have already attached meaning: i.e., my problem (understanding your explanation) is, in total (including understanding that language and my own experiences on which that understanding is based), exactly the same as the problem of understanding any ”totally undefined collection of events”.

Once an epistemological construct (“explanation”, “world view”, “understanding”, ... whatever) has been built, the builder can express the past (what he knows, or thinks he knows) in the form of a ”what is”, is “what is” table via numeric reference tags. Likewise, his expectation can be represented by the probability he places on any future entry to that table. If that probability is to be represented by the squared magnitude of (which can clearly represent absolutely any procedure possible) then must obey my fundamental equation. It follows, as the night the day, that the numerical reference tags of those undefined “events” must approximately obey Newtonian mechanics. Absolutely no other assumptions need be made.

Originally Posted by 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.

In my derivation of Schroedinger's equation (and thus of Newtonian mechanics) I had to make an approximation that (essentially the energy associated with the momentum in the tau direction) had to be approximately E (the total energy of the system): i.e., the approximation that the energy associated with the standard three dimensional momentum had to be a negligible component of the total energy. In simple words, that means it is a non-relativistic solution which is entirely consistent with the normal interpretation of Schroedinger's equation which is well known to be invalid representation of a relativistic situation. That in no way implies my fundamental equation is an approximation; my fundamental equation is a derived relationship which is required to be obeyed by any flaw-free explanation (quite a different matter).

Originally Posted by Qfwfq

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.

I am at a loss to understand what you are unable to follow. I wish you would make it clear to me. As far as I am concerned, there are no “hidden choices” in my deduction. Every choice is spelled out in detail and seems rather obvious to me. Sorry if it doesn't seem obvious to you. I would try to help if I knew what was bothering you.

Have fun -- Dick

[AnssiH]

Originally Posted by Qfwfq

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?

No, I've been away for a while and I'll basically continue from post #171 soon... :P I suspect that's not far from where you left so it would be good if you have time to follow the thread too, and possibly help me out with some math etc..

Originally Posted by Doctordick

It follows, as the night the day, that the numerical reference tags of those undefined “events” must approximately obey Newtonian mechanics. Absolutely no other assumptions need be made.

I think my comment may have been misunderstood a bit (I'm not that lost with the topic ... hmm, and I think I have also misinterpreted your comment at the end of #203

I mean, I don't find it too odd that self-consistency alone can allow us to build newtonian worldview. While it's astonishing finding, the reason I don't find it that incredibly odd is simply because we are free to define reality into just such an elements that allows us to say they obey newtonian mechanics... )

But I first interpreted your comment as "self-consistency forces us to a newtonian worldview", which I see is not exactly what you said... (when I made that interpretation, it stroke me as a bit odd since surely it must always be possible to build a plethora of self-consistent worldviews that look nothing like newtonian mechanics... albeit most of them must be incredibly complex :P)

I still have a minute here so let me just say...

Originally Posted by Doctordick

The central issue there is that . The complex conjugate of is found by changing the sign of the imaginary parts (those parts multiplied by i). Thus it is that the resultant probabilities are not affected by these terms

...Okay, I think I understand that.

In Schroedinger's expression of quantum mechanics, momentum of an object represented by a given wave function is defined to be given by some constants times or rather, the expectation of the momentum is given by integrated over all x. In quantum mechanics, this relationship is essentially established by postulated axiom. If that definition is taken as a true expression of the classical idea of momentum, then the many body equation

is no more than a statement that the sum of the momentum of all the bodies involved is zero (and that would be in the “rest position of the center of mass” of the system).

Okay I see... Heh, it's funny since that's how the rest position would be defined itself

Anyway, should I familiarize myself with the Schroedinger's expression of quantum mechanics more? I don't understand it very well.

I'll continue from here, hopefully soon...

-Anssi

[Bombadil]

I suspect part of the problem is I don’t in fact know how much to try and understand now and how much of it is better left for a later time and so I may be trying to understand some things that would be better left for a later time.

As for your post I think that it is in fact quite interesting on several points and in fact answered some things that I was beginning to wonder about as well as giving me some new things to think about although there are not many questions about it that seem worth asking at this point.

Of the form of the function f this seems relatively straight forward and I have no problems with what you have done I suspect that part of the problem I had with trying to solve for f is that there are some things that you have in it that I don’t understand (partly this is I think due to never having seen some of the things that you are using before). At this point I still have some questions about it but I think that it is probably best just to leave this part where it is until you are ready to begin showing just what the effects of it are.

Originally Posted by Doctordick

What I am getting at is the fact that I do not have any intentions of teaching physics and/or mathematics here. I will explain the exact logic behind any individual step in my deductions as that is a relatively short process; however, explaining physics and/or mathematics in general is a lifetime process. There are many physicists out there who have excellent comprehension of things like the Schroedinger Equation, Heisenberg uncertainty and how the factor hbar comes to be an important quantity.

Trying to have you do either of these here is not what my intention was but rather my questions stepped outside of what you are presenting and into theory due to some of the things that you are mentioning seem to be based off of ideas from quantum mechanics and I was just wondering where they came from without realizing that it was in fact outside of what you are presenting.

I am wondering at this point would it be reasonable to say that whenever we make an approximation to the fundamental equation or when we are working with an equation that approximates the fundamental equation that we are in fact working with a theory and that there is in fact no deductive method of obtaining the equation so it is only an inductive solution to the problem?

Originally Posted by AnssiH

But I first interpreted your comment as "self-consistency forces us to a newtonian worldview", which I see is not exactly what you said... (when I made that interpretation, it stroke me as a bit odd since surely it must always be possible to build a plethora of self-consistent worldviews that look nothing like newtonian mechanics... albeit most of them must be incredibly complex :P)

I suspect that what anssih has in mind is, aren’t there a lot of different approximations that you could have made instead of the ones that you did and won’t some of them lead to equations that won’t have Newtonian mechanics as a good approximation?

[Doctordick]

Originally Posted by AnssiH

I mean, I don't find it too odd that self-consistency alone can allow us to build newtonian worldview. While it's astonishing finding, the reason I don't find it that incredibly odd is simply because we are free to define reality into just such an elements that allows us to say they obey newtonian mechanics... )

There is a lot of truth to that statement. Notice that the first things we identify are things that do not change; things that are the same all the time: “statics” so to speak and we expect them to continue to “stay the same”. The second thing is things that change in a simple way and we expect them to continue to change in that same way. Our model of reality is only one step away fro Newtonian mechanics. All we need is a reason to explain why things do not continue in the same way as they did. Our explanation is, “something happened” and we give the name “a force” to that which “happened”.

Originally Posted by AnssiH

Anyway, should I familiarize myself with the Schroedinger's expression of quantum mechanics more? I don't understand it very well.

Not unless you want to understand physics. As I said to Bombadil, I am not much concerned with either physics or mathematics. Mathematics has a plethora of internally consistent constructs and one could easily spend a lifetime trying to learn them all. Physics is also a very complex field and I really doubt anyone could actually master every aspect of physics. That is why the field is chock full of specialists.

When I was young, I wanted to understand the world I found myself in and that is why I went into physics. Physicists seemed to be actually interested in explaining why things were the way they were. Until I got into graduate school, I really thought they understood the fundamental issues of their field. I never had any interest in “doing physics”. That is one reason I essentially dropped out of the field almost the day I got my Ph.D. By that time I had realized that they had taught me all they had to say about the foundations of the field. All that really interested me was understanding why it all worked the way it did and they simply couldn't answer that question. I think I have actually discovered the answer. Anyway, it is certainly not necessary to understand physics in order to understand why it works. Besides that. there are plenty of people out there who can do the required mathematics given the starting point. It is that starting point which concerns me and I suspect it is that starting point which interests you also.

That starting point is in fact my fundamental equation. What is most important is that you understand exactly why that equation is valid under all possible circumstances. Showing that the rest of physics follows from that fact is actually quite trivial and one need little more than a cursory comprehension of integration and algebra to show that fact. My real problem is that no one takes the trouble to look. There are lots of people who could follow the logic if they really cared to. The problem is that their real interest is in showing that I couldn't possibly be correct. Their income depends upon the fact that they “know the truth”. Just as religionists income depends on people believing they “know the truth” or, for that matter, astrologist's income depends upon the world believing they could have a real handle on the truth. It's all the same the world over. Knowledge is Power and people guard that power with their life.

Suggesting that the authorities are wrong is always the “wrong” thing to do if you want recognition. The authorities won't recognize you and their minions will fight you tooth and nail.

Have fun -- Dick

[HydrogenBond]

Suggesting that the authorities are wrong is always the “wrong” thing to do if you want recognition. The authorities won't recognize you and their minions will fight you tooth and nail.

One of the conceptual problems I have with the aspects of theoretical physics, which address the foundations of reality, is the observation that there are many alternatives for reality. We have quantum, wave, strings, etc. If you look at this logically, reality should only be one way and not suffer from a multiple personality disorder. In other words, reality should be one thing and not ten things that all appear valid in their own way. Since all can be supported with math, this multiple personality disorder universe approach is considered valid science.

If we stand outside the debate, and look at this logically, if any one of these theories is correct, then that would imply the others are illusions. It would also imply that math can be used to make illusions appear real. Another way to look at it is, each theory is part of the truth of reality, but none of the theories is the whole truth, or else there would be no need for many. This implies math can also be used to support partial truth so it can appear to be the entire truth to some people. It is not easy to fight such an irrational state of affairs, when physics can't even see there is a problem. It is self policing. The math and theories get quite complicated, exempting common sense from adding to the discussion. In my opinion, the divergence problem needs a convention where they iron it out and reduce reality to one. But none of the theories are solid enough to be the core.

One way to integrate would be to create the requirement that the divergence needs to interface with the preponderance of the data and not just pet data. The preponderance data is connected to an adjacent area of science that is integrated. This is chemistry. In other words, if we stack all the physics reality data and all the chemistry reality data, the one with the biggest pile should be closer to reality. If we hook up with the little pile there can be problems leading to divergence. Ironically, the big pile of physical-chemical data is not built upon divergence, even though there is far more data. This area of science is integrated. Physical chemistry is one place where both physics and chemistry agree and integrate with the big pile of data. After that the divergence begins to get worse and worse because it is no longer attached to the big pile, but to a little pile that is self serving. If we combine this with math allowing half truth to look like full truth.....

The entire affect, may have begun due to creating synthetic matter, not found in nature, and using this as the basis for defining reality. If you think of it logically, where in nature are particles accelerated and then collided? It is not BB, since they were not colliding but expanding, so only the pre-collision data is valid for early BB. This data does not show the same level of diversity but looks more like the chemical data with motion.

Maybe we can get this material within a collapsing star for a brief fraction of its life, yet this 1% is called 100% . This is detached from the big pile, but can be supported with math, so it appears to be real. While the divergence is due to others sensing this is not quite right. But because each can be supported with math, the multiple personality disorder universe is considered a valid form of science. This topic is about what we can know of reality. I would conclude it is not based on a multiple personality disorder, even if this condition can be supported with math. This condition needs therapy which can be done by requiring it interface the big data pile.