An explanation of what I am talking about.

[lawcat]

I agree with much of your post. But,

 

So let's get back to that question; what do you need to know about the nature of the data you are to explain, in order to create a valid set of definitions?

 

We need only determine by evidence whether the set is distinguishable at the boundary.

 

it is not so much that a photon is "frozen in time", or "traveling 0 length" or "in superposition when we are not looking" or has constant speed when measured from any given inertial frame, as it is the specific definitions of time and space (etc) that are related to each others and to the specific definition of "a photon" that way. Just as an arbitrary example from the top of my head.

 

Agreed to a degree. But, a proton is a set with distinguishing boundary in our mind, and that set exhibits behavior as you mentioned, and as predicted when we compare what's in our mind to what is outside.

 

I can only know why it is valid to conceive things in terms of photons and all its associated definitions.

Yes.

 

An experimental verification never comes in play with this topic

and that is the problem. There is nothing to compare to. There is no developed system to check for consistency. There is nothing outside of us to compare to.

[AnssiH]

We need only determine by evidence whether the set is distinguishable at the boundary.

 

I'm afraid I don't understand what you are referring to :)

 

Agreed to a degree. But, a proton is a set with distinguishing boundary in our mind, and that set exhibits behavior as you mentioned, and as predicted when we compare what's in our mind to what is outside.

 

Oh yeah, exactly. If I understad what you are saying... You are saying that a proton, while being a lot more "tangible" object than a photon, does also exhibit wave like properties? And that's exactly the thing. Oh, I guess that's what you were calling for in your first post, wasn't it?

 

And indeed, there is much to be said about that, about how the definitions behind "massive things" are related to other definitions in our world view in specific ways.

 

That stuff can get a bit too complicated to handle intuitively in one's mind, because there are a lot of definitions entangled with each others in the play there; there are all the pre-existing definitions that led to quantum theory; i.e. those classical definitions that posed the problem called ultraviolet catastrophe, which led to Planck's solution of defining non-continuous properties, which ultimately yielded the rest of the quantum mechanical definitions. And ultimately we ended up with those QM expectations that everything around us should exhibit wave-like properties.

 

In DD's analysis, you can find the reasons how and why quantum mechanical expectations must be valid way to interpret some information. And given those definitions, as is the case with photons, so is the case with any defined object. Analytically speaking, "proton" is something we recognize as being "evidently present" due to recognizing some circumstance in some information. That recognition already entails the existence of a huge number of definitions, but given the validity of those definitions as a very effective data ordering mechanism, those wave-like properties are just an integral part of the circumstance defined as "a proton"... That is, protons are required to behave that way by their very definition.

 

Note that we did not just accidentally realize that protons have those properties. Although we could have, but it was through the work of Planck, Bohr, Heisenberg, Einsten and so on, that we came to realize that the definitions behind "protons" (and everything), actually REQUIRE that they behave that way. Under careful analysis, we came to have the expectation that they ought to behave that way if we just setup certain types of circumstances (experiments). If you wish, you could view DD's work partly as an analytical examination to those types of requirements arising from the interplay of definitions...

 

and that is the problem. There is nothing to compare to. There is no developed system to check for consistency. There is nothing outside of us to compare to.

 

Well yeah, the closest thing we have for a "developed system to check for consistency" is the field of mathematics, and certainly the validity of the logic behind the analysis does hinge on the validity of the mathematical tools used in the deductions... ...but then that's the best thing that any field operating with "logic" can do, including standard theoretical physics, and I would say that's pretty good already.

 

-Anssi

[lawcat]

I'm afraid I don't understand what you are referring to :)

 

Your question was: what do we need for a valid set of definitions. My answer was that it just needs to be (1) a vaild (2) set. A set is valid if it is distinct. But my answer went a bit farther. For a set to be distinct it has to be distinct only at the boundary but not in content. So to answer your question, what we need for a valid set of definitions, my answer was we just need a set that is distinct at the boundary.

 

Now, for a set to be distinct, there has to be another set. Otherwise neither is valid. on its own So if we say there is valid set A, than in the least, fundamentally, there has to be a set B which is not A. So there has to be a pair of sets,each valid, each distinct at the boundary, for there to exist even one valid set. Hence, there must be for example off if there is on, fundamentally. otherwise we would not know whether off is on or off. We would have no way of distinguishing it. It would not be valid.

 

Such set must be distinct at the boundary but not in content. So sets A, and B (not A), can be exactly the same in content. But they are nevertheless valid if we can distinguish them by distinct boundaries. Of course, we can designate content to mark the boundary of each set in which case each set would not be distinct, and that would invalidate sets for the purposes of the inquiry.

[AnssiH]

Your question was: what do we need for a valid set of definitions.

 

Actually, to be accurate, the question was "what do you need to know about the data you are to explain, in order to create a valid set of definitions (the definitions making up "an explanation" for that data)

 

I was very much struggling with the wording, but the point I was trying to get to was the fact that it would be oxymoronic to think about some characteristic of the actual "information to be explained", even though we often tacitly do.

 

I suppose you understand why it is oxymoronic; because whatever we'd think of is something we think in some defined terms. I.e. whatever distinct features we can think of, are already features of "an explanation to the information", not features of the information itself.

 

In that sense, we are always working with an interpretation of something, using our decisions about "what constitutes an object" (etc). While the same underlying information could be interpreted in terms of some other definitions just as well.

 

So that is what raises the question about how explanations are related to some information whose nature is completely unknown? How does the explanation even begin to form a valid set of definitions, if logically NOTHING can be known about the nature of the data at the get go.

 

And that is what gets us to those symmetry constraints, arising from the simple requirements of self-coherence.

 

(Remember that old thread "What can we know about reality?". The title of the thread was clearly an attempt to get to this same point of impossibility of knowing anything at the get-go)

 

My answer was that it just needs to be (1) a vaild (2) set. A set is valid if it is distinct. But my answer went a bit farther. For a set to be distinct it has to be distinct only at the boundary but not in content. So to answer your question, what we need for a valid set of definitions, my answer was we just need a set that is distinct at the boundary.

 

Now, for a set to be distinct, there has to be another set. Otherwise neither is valid. on its own So if we say there is valid set A, than in the least, fundamentally, there has to be a set B which is not A. So there has to be a pair of sets,each valid, each distinct at the boundary, for there to exist even one valid set. Hence, there must be for example off if there is on, fundamentally. otherwise we would not know whether off is on or off. We would have no way of distinguishing it. It would not be valid.

 

Such set must be distinct at the boundary but not in content. So sets A, and B (not A), can be exactly the same in content. But they are nevertheless valid if we can distinguish them by distinct boundaries. Of course, we can designate content to mark the boundary of each set in which case each set would not be distinct, and that would invalidate sets for the purposes of the inquiry.

 

I'm sorry but I don't understand that. I don't think I understand the terminology you are using. From what I can pick up, it does sound like a little bit different issue than what I was clarifying above...?

 

-Anssi

[AnssiH]

What makes your conclusion different from any other simple uncircumscribed existential statement, such as there exists a purple duckbill platypus?

 

That the conclusion is not an existential statement, for starters.

 

I argue that DD's "tau axis" of a four dimensional Euclidean geometry is ad hoc, untestable, nonexistent in the real world, imaginary.

 

Of course it is, just as imaginary as the [imath]\Psi[/imath]. It is part of the logical tool-set that is being used to trace the relationships between definitions. I did not read all your posts, but a quick scan made it clear to me that your objections arise from your interpretation that this work is an attempt to argue something about reality. That is a mis-interpretation. It is rather an argument about physics definitions. (among other things...)

 

This thread might be helpful for you, but I would like to make one more comment. Your posts gave me the impression that your interpretation of relativity is that it is an argument about the "actual form of reality". Do you see it as an argument that reality is literally a 4 dimensional relativistic spacetime, that is literally bent into the kinds of shapes described by general relativity? Or wouldn't it be more accurate and objective to say that relativity is a statement about the relationships between some very carefully defined entities, while careful changes to those definitions would yield different, but equally valid presentation form (capable of describing the same exact situations, but doing that with different terminology and with different "mental visualizations").

 

I think you probably agree with the latter, being that you pointed out some euclidean presentations of relativity yourself. Anyone who is using the common presentation form of relativity to yield predictions, still cannot argue that it is the one and true form that reality also conforms to. I.e. the individual definitions themselves are just as "ad hoc" as the tau-axis in DD's analysis. (i.e. they do not appear in other presentation forms)

 

If you understand what I mean by that, you should be able to appreciate the fact that this analysis is not a theory about reality. For more information, please scan back this thread a bit.

 

-Anssi

[modest]

What makes your conclusion different from any other simple uncircumscribed existential statement, such as there exists a purple duckbill platypus?

 

That the conclusion is not an existential statement, for starters

 

I assume you mean that DD's proposition is not existential. I think that is true, but some exposition is here required. In the other thread Rade said the following:

 

Logically, it makes no sense to hold DD to falsify anything---in fact---since his use of pure reason "deductive conclusion" approach is not a scientific theory there is nothing to falsify, not as the word is used by Popper.

 

Since an existential statement cannot usually be falsified it is only natural that CC made that deduction. Nonetheless, I believe Raid is mistaken in that DD's proposition cannot be falsified. As an existential statement DD's claim would be of the form:

There exists an internally consistent explanation which follows my fundamental equation

That is not the claim I've seen made. DD's claim is more akin to:

Every internally consistent explanation follows my fundamental equation

which is not existential but rather universal and therefore can be falsified. All it needs is a counterexample.

 

If an internally consistent explanation is found which does not follow DD's fundamental equation then the claim is falsified. As I recall, Erasums has pointed out Newtonian mechanics as a counterexample which falsifies the claim:

 

Re: So far from being right, it isn't even wrong!

 

Re: “Why” Relativistic Mechanics?

 

I've not yet seen a convincing rebuttal of Erasmus' point, and it seems a rational point to me—so I am of the tentative opinion that DD's fundamental claim is falsified. I should, however, qualify that by saying that I haven't kept up with all the discussion so Will's counterexample may well be refuted and I missed it. Also, I would welcome any future refutation. And, besides all that, I find the x,y,z,tau relativity metric fascinating regardless if DD's claim about his fundamental equation has been falsified or not.

 

~modest

[Doctordick]

Hi modest,

 

I was watching “The Mentalist” and it came to a commercial. Since I absolutely hate commercials, I booted my PC and discovered your post and I just had to respond.

As an existential statement DD's claim would be of the form:

There exists an internally consistent explanation which follows my fundamental equation

That is not the claim I've seen made.

You are correct, I have never actually made that specific claim. My paradigm does in fact fulfill that claim; however, I can not prove it is the only internally consistent explanation which does.

DD's claim is more akin to:

Every internally consistent explanation follows my fundamental equation

which is not existential but rather universal and therefore can be falsified. All it needs is a counterexample.

Akin to perhaps. It depends on exactly what one means by “akin”. I think my statement is considerably more accurate, “any internally consistent explanation can be interpreted in a manner which obeys my fundamental equation”. That is true because it can be mapped into my paradigm which must be a solution to that equation.

If an internally consistent explanation is found which does not follow DD's fundamental equation then the claim is falsified.

That statement is not actually very clear. I would have said, if an internally consistent explanation is found which can not be interpreted in terms of Dick's paradigm then the claim is falsified. However, if that is the case then there has to be an error in my deduction: i.e., reality has absolutely nothing to do with the question. You will never understand that statement until you make an effort to understand the deduction. I think I will post the first part, “Laying out the problem to be solved!”, Friday. Perhaps that will give you an inkling of what I am doing.

As I recall, Erasums has pointed out Newtonian mechanics as a counterexample which falsifies the claim:

 

Re: So far from being right, it isn't even wrong!

 

Re: “Why” Relativistic Mechanics?

 

I've not yet seen a convincing rebuttal of Erasmus' point, and it seems a rational point to me—so I am of the tentative opinion that DD's fundamental claim is falsified.

I think post=20522 is not the post you mean as that post was made by pgrmdave over five years ago. I think you are missing a digit.

 

Regarding the other reference Erasmus is simply making it clear that he does not understand my proof.

Here is my problem- there are mathematical proofs that classical mechanics IS a consistent system. It is axiomatic, and mathematicians have proven that the system is self-consistent. This is a deductive truth.

There are serious issues of internal consistency within Newton's system. The finite speed of light being an important one. In fact, as I remember it, Newton was the first person to show that the speed of light was finite. Now I have specifically shown that Schrödinger's equation is an approximate solution to my fundamental equation under the assumption that the velocity of objects are insignificant as compared to the speed of light and there are whole books devoted to the fact that Newton's mechanics directly follow from the validity of Schrödinger's equation. It follows that Erasmus' claim that Newtonian mechanics does not obey my equation are entirely specious.

I should, however, qualify that by saying that I haven't kept up with all the discussion so Will's counterexample may well be refuted and I missed it.

I thought I had already posted the above refutation but I might not have. Erasmus really has not been a very serious critic; he tends to jump from issue to issue without taking into account anything I say. I am afraid he is a serious convert to the religion of modern physics and not about to be reasoned with.

 

I tell you what, you carefully read the post I will post tomorrow and if you seriously think I have made an error in that presentation we can talk some more about the issues. If you understand that post, you should understand why I say, “any explanation”. My whole approach is to avoid any presumptions whatsoever as to what that flaw free explanation is.

 

Have fun -- Dick

[modest]

I think my statement is considerably more accurate, “any internally consistent explanation can be interpreted in a manner which obeys my fundamental equation”. That is true because it can be mapped into my paradigm which must be a solution to that equation.

 

Yes, I think the point being made was that classical mechanics cannot be so mapped.

 

That statement is not actually very clear. I would have said, if an internally consistent explanation is found which can not be interpreted in terms of Dick's paradigm then the claim is falsified. However, if that is the case then there has to be an error in my deduction: i.e., reality has absolutely nothing to do with the question.

 

The error in deduction, as I understand... actually, I'll just quote Will:

 

As to the major error- dick takes his symmetry constraints and moves to his "dirac-type" equation as if this is the only way to implement these symmetries. This is simply not true- there are many equations (with very different solutions) that obey the symmetry constraints that are not dirac type.

 

I think I will post the first part, “Laying out the problem to be solved!”, Friday.

 

I look forward to it.

 

I think post=20522 is not the post you mean

 

Thank you, yes, that was the thread number. I've fixed the link.

 

There are serious issues of internal consistency within Newton's system.

 

Again, quoting Will,

 

Further, you can show that classical mechanics leads to no inconsistencies-see the work of mathematicians (not physicists- mathematicians work solely in the context of the MODEL, they do not connect it to the real world in any way), specifically Lagrange,Hamilton and the work that came after. This is not an open question- mathematicians have shown classical mechanics self-consistent.

 

After Will made that statement I looked it up and it is spot on.

 

Now I have specifically shown that Schrödinger's equation is an approximate solution to my fundamental equation under the assumption that the velocity of objects are insignificant as compared to the speed of light and there are whole books devoted to the fact that Newton's mechanics directly follow from the validity of Schrödinger's equation.

 

Again, quoting Will,

 

Quantum mechanics is AXIOMATICALLY REQUIRED to reproduce classical mechanics. Doctor Dick's system does not include the necessary axioms (essentially the correspondence principle + measurement). Quantum mechanics is MORE than just an equation- reproducing Schroedinger's equation DOES NOT mean you have reproduced quantum mechanics.

 

These things seem true and I've seen no convincing rebuttal.

 

I am afraid he is a serious convert to the religion of modern physics and not about to be reasoned with.

 

The ad hominems are extremely off-putting.

 

To be honest, I'm personally far more interested in your metric than its derivation and association with valid explanations. I've finished reading the OP in your newest thread and I believe it deserves to be seriously considered by philosophers who are convinced that GR definitively informs the ontology of space and time. When I have time I plan to read and consider that model in detail.

 

~modest

[Doctordick]

The ad hominems are extremely off-putting.

I had no intention of making any “ad hominim” arguments. I have been interacting with Erasmus for a good length of time. Initially I hoped that he would be interested in what I was saying as, being a physics graduate student, he seemed to be the only person here trained in physics and I had never managed to get the attention of anyone cognizant in the details of modern physics before. However, he continually brought up cavils which, apparently in his mind, were proofs that I was a crackpot. Whenever I commented on the fact that those cavils did not apply and my reasons for that argument, he changed the subject and brought up another inapplicable cavil. At no time did he ever admit that any of my arguments were of any serious worth; he simply never responded again on the specific issue. This is exactly the kind of response religious fanatics are fond of and I just assumed he was a religious fanatic on the issue of physics.

To be honest, I'm personally far more interested in your metric than its derivation and association with valid explanations.

I am very sorry to hear that as, sans an understanding of my proof, the “metric” you refer to is a rather undefendable assertion.

When I have time I plan to read and consider that model in detail.

Without comprehending my proof, you have utterly no comprehension of the model standing behind that post. And, assigning that proof to the interest of modern philosophers is ludicrous, no modern philosopher has even the slightest comprehension of what I am talking about. (At least that is my impression!)

 

See you around -- Dick

[AnssiH]

Nonetheless, I believe Raid is mistaken in that DD's proposition cannot be falsified. As an existential statement DD's claim would be of the form:

There exists an internally consistent explanation which follows my fundamental equation

That is not the claim I've seen made. DD's claim is more akin to:

Every internally consistent explanation follows my fundamental equation

which is not existential but rather universal and therefore can be falsified. All it needs is a counterexample.

 

If an internally consistent explanation is found which does not follow DD's fundamental equation then the claim is falsified.

 

Yes, albeit it would be almost impossible to actually demonstrate and prove an error that way, because it is not necessarily at all clear how an explanation should be mapped into DD's paradigm (i.e. into the terminology that the fundamental equation works with).

 

I mean, the fundamental equation is an expression of statements that basically just say, that the expectations for a specific (recognized) circumstance cannot change arbitrarily. I think the actual statements themselves are pretty hard to take as erroneous, but it is of course always possible that there is an error in the deductions that got us to the actual expression called "fundamental equation". But to find that error, it would be far easier to look at the actual derivation.

 

But here's something to think about; quite many relationships of modern physics have already been shown to be consequential to the fundamental equation. If it turned out that their derivation was made possible by a logical error - that just so happened to be exactly proper kind of error to accidentally lead to modern physics - I would say that's quite a co-incident ;)

 

Anyway, about Erasmus' argument;

 

As I recall, Erasums has pointed out Newtonian mechanics as a counterexample which falsifies the claim:

 

Re: So far from being right, it isn't even wrong!

 

Re: “Why” Relativistic Mechanics?

 

I've not yet seen a convincing rebuttal of Erasmus' point, and it seems a rational point to me—so I am of the tentative opinion that DD's fundamental claim is falsified.

 

But classical mechanics does not obey your equation, and it is certainly self-consistent.

 

Me and DD went on to point out two subtle problems with that assertion, namely that;

 

1. Newtonian mechanics do obey the equation (approximately)

2. Newtonian mechanics are not self-consistent

 

:D

 

Hehe, it's pretty clear we were talking past each others. I think I can explain what is going on.

 

First, it is pretty obvious to me that he must be mis-interpreting something, in order to make a blunt comment that newtonian mechanics do not obey the equation, since the equation itself is just a statement about non-changing expectations for well defined situations.

 

As I already commented, it is not very clear how a specific world view / model is to be properly mapped into the terminology of the fundamental equation, but what allows DD to confidently say that Newtonian mechanics does obey the equation is that he has already derived Schrödinger's Equation, and further derivations to newtonian mechanics exist.

 

Erasmus had a problem with that argument, saying "You need extra assumptions to move from Schroedinger to classical mechanics (the correspondence principle/measurement). Your equation doesn't have these additional constraints."

 

Now I have never followed such derivations, and I do not know if one needs to make assumptions about the meaning of the information-to-be-explained to get there, but the fact that Newtonian mechanics does not violate Schrödinger's equation already mean that it does not violate the fundamental equation either (with given approximations of course).

 

Remember, the fundamental equation is not by itself a specific world view, it's validity is not to argue that reality is made of dust motes that obey probability functions akin to quantum mechanics (which is perhaps what Erasmus had in mind when he said it is in conflict with newtonian mechanics). Its validity means valid world views can be interpreted in such terms, because the structure only disallows circumstances that would be results of internal conflicts (in terms of expectations).

 

Then the second point, about whether newtonian mechanics are self-consistent. Erasmus means it is proven self-consistent as an axiomatic system, saying Self-consistency means that a given axiomatic system will deduce a consistent answer for any true/false statement derivable from those axioms.

 

Well, taken as an axiomatic system (taking only few essential definitions into account), I would pretty confidently say it obeys the fundamental equation pretty exactly, since that statement from Erasmus is perfectly analogous to the statement of the fundamental equation itself.

 

What DD and me meant of it not being self-consistent has to do with looking at it as an integral part of an actual explanation to reality. I.e. as a part of the scientific world view of its time. What I was trying to explain in that thread was that the scientific world view of the time did contain not-so-obvious conflicting statements. I.e. statements/ideas that are the source of the problems ("apparent paradoxes") that better physics theories would at a later date solve... I.e. things that would eventually lead to advances in physics (to things like relativity).

 

I think most people would find that statement odd, given the common perception of how relativity came to be, and how people view science as a matter of just measuring things around us... And perhaps it wouldn't be so important to make that comment, except that it has to do with the arguments that are used in DD's analysis to yield special relativity, about how relativity itself turns out to be a requirement of self-consistency.

 

I am moved to make one more related comment. When I was browsing Wikipedia, I saw this;

 

The energy conservation law is a consequence of the shift symmetry of time; energy conservation is implied by the empirical fact that the laws of physics do not change with time itself.

 

That had to do with Noether's theorem, and isn't it just a bit topsy turvy to say that it is "an empirical fact" that the laws of physics do not change...

 

I mean, such a feature should become pretty obvious as an epistemological requirement already, if you look at it from the perspective of DD's analysis. One of the fundamental symmetries was shift symmetry in time (time being defined as an evolution parameter related to accumulation of information), i.e. your expectations for a given situation cannot be a function of "t"; your expectations are a function of the recognized situation itself, "whenever" that situation is recognized.

 

Given some finite amount of information, of course it would be (theoretically) possible to create any sort of arbitrary ontology to explain it, and make it work with some complex rules that would just change at every "t" according to whatever was needed to "explain" the information correctly. Like a giant game of Calvinball, where anyone can declare a new rule at any time. But as a predictive world view this would be pretty useless as you would never know what the rules are for the next "t". I.e. you could not generate any expectations for the future.

 

That is to say, for a predictive world view, the defined rules have to arise from the familiarity of some recurring patterns one way or another. Recurring patterns are what will be turned into some defined "laws" that are not a function of "t".

 

I.e. whatever kind of defined ontology you come up with, it must be such that its entities obey laws that don't change over time!

 

And once you have those laws, you also have means to define something called "energy" (which is conserved in the universe, as you have come to interpret it).

 

Can you say something is "empirically proven", if you also have the epistemological requirement that your interpretation of reality must be like that anyway?

 

-Anssi

[modest]

Anyway, about Erasmus' argument;

 

But classical mechanics does not obey your equation, and it is certainly self-consistent.

 

Me and DD went on to point out two subtle problems with that assertion, namely that;

 

1. Newtonian mechanics do obey the equation (approximately)

2. Newtonian mechanics are not self-consistent

 

 

You did no such thing. Saying "classical mechanics is not self-consistent" doesn't make it so. A quick google search finds an MIT professor's course notes:

 

1 Introduction

 

Classical mechanics is internally consistent. No amount of examination of Newton’s Laws as an abstract system will lead you to quantum mechanics. The quantum world forced itself upon us when physicists tried and failed to explain the results of experiments using the tools of classical mechanics.

http://mit.edu/8.06/www/Landau.pdf

 

Or, quoting Feynman from 1964,

Classical mechanics is a mathematically consistent theory, it just doesn’t agree with experience.

 

By the lack of refutation, I'm convinced that the assertion regarding Dick's fundamental equation and internally consistent explanations is falsified.

 

What DD and me meant of it not being self-consistent has to do with looking at it as an integral part of an actual explanation to reality. I.e. as a part of the scientific world view of its time.

 

We're talking about a well-defined mathematical system and its ability to explain unknown data, not the complete worldview of a dead alchemist.

 

~modest

[AnssiH]

You did no such thing. Saying "classical mechanics is not self-consistent" doesn't make it so.

 

Hehe, hey! Did you read anything below the winky smiley? Like the part about us talking past each others... And:

 

Erasmus means it is proven self-consistent as an axiomatic system, saying "Self-consistency means that a given axiomatic system will deduce a consistent answer for any true/false statement derivable from those axioms."

 

Well, taken as an axiomatic system (taking only few essential definitions into account), I would pretty confidently say it obeys the fundamental equation pretty exactly, since that statement from Erasmus is perfectly analogous to the statement of the fundamental equation itself.

 

Erasmus specifically wanted to look at it as an axiomatic system, as do the people you quote, and yes it is self-consistent if you take it that way, and yes it does obey the fundamental equation exactly in that form (at least I have no idea why do you take it as not obeying the equation).

 

I mean, what you are referring to is essentially a study into how the different definitions of classical mechanics align with each others, it's not a study of where the definitions came from as an explanation to some unknown information.

 

Now if you are at all interested as to what DD is talking about (of classical mechanics arising as an approximaton to the equation etc), you should read from the "What DD and me meant of it not being self-consistent has to do with..."-part onwards.

 

I'm a bit puzzled I must say. You pluck out a small set of definitions from an entire explanation, then establish that that set of definitions does not contradict itself, and then argue that these definitions looking different from the fundamental equation in some way (that I don't understand) means the fundamental equation is falsified?

 

A single set of axiomatic definitions produces the same expectations for the same circumstances, every time, no?

 

And obviously an arbitrary sub-set of the definitions is not suitable for analyzing the consequences of self-coherence requirements for the entire explanation. Obviously it is the entire explanation that must be self-coherent with itself, not just parts of it. If you think it is okay to choose some sub-set, why did you choose classical mechanics? I'm sure there are much smaller sub-sets that could be shown to be self-coherent very trivially. What would it accomplish to choose just couple of definitions that are defined in terms of each others?

 

We're talking about a well-defined mathematical system and its ability to explain unknown data, not the complete worldview of a dead alchemist.

 

We were talking about explanations to unknown data with DD, but what you are talking about right now is a small set of definitions related to already defined entities.

 

Newtonian mechanics by itself does not have the ability to explain "unknown data" (if that's at all what you were implying), but rather that sort of explanation for unknown data can always be formed, where the defined entities obey newtonian mechanics (given few approximations). What I'm saying is that it is not the equations of newtonian mechanics that explain unknown data directly.

 

I'm really a bit unsure what you are thinking so excuse me if my post seems like I'm stabbing in the dark... ...because I am :D

 

-Anssi

[modest]

Hehe, hey! Did you read anything below the winky smiley?

Did I reply to something below the smiley?

 

Erasmus specifically wanted to look at it as an axiomatic system, as do the people you quote, and yes it is self-consistent if you take it that way

 

Thank you, I agree.

 

and yes it does obey the fundamental equation exactly in that form (at least I have no idea why do you take it as not obeying the equation).

 

Classical mechanics has delta function probability distributions. Delta functions can't solve the fundamental equation.

 

I'm a bit puzzled I must say. You pluck out a small set of definitions from an entire explanation, then establish that that set of definitions does not contradict itself, and then argue that these definitions looking different from the fundamental equation in some way (that I don't understand) means the fundamental equation is falsified?

 

I did not say that the fundamental equation is falsified. I said that the assertion 'every self-consistent explanation follows the fundamental equation' is falsified. There exist self-consistent explanations which cannot be solved by the equation falsifying the claim.

 

~modest

[Doctordick]

Modest, I am really disappointed by your current approach to these issues. There is a very big difference between a theory being “internally consistent with itself” and its being “internally consistent with all information it is supposed to explain”. Your quote of Feynman suggests that, in his opinion, Newton's theory fails the that second requirement entirely.

Classical mechanics is a mathematically consistent theory, it just doesn't agree with experience.

Apparently you have decided to fall back to the common philosophic tactic of depending upon obscurant characteristics of the English language to promote your arguments.

Classical mechanics has delta function probability distributions. Delta functions can't solve the fundamental equation.

False on both counts. First, no presentation of classical mechanics has any need to make use of delta function probability distributions. Anyone who knows anything about physics, knows full well that classical mechanics never considers any experiment on an accuracy level even approaching the kind of measurements made in quantum mechanics and therefore the best an exact reporter (which you clearly are not) could say is that classical mechanics presumes that all measurements are made on an anthropomorphic level (that is, with the accuracy of common human physical interactions).

 

Furthermore, if one restricts their measurements to such gross relative accuracy, every result of classical mechanics can be correctly represented by solutions of Schrödinger's equation. In fact, such representations are a common part of any presentation of quantum mechanics in general and anyone competent in physics would know that. If Schrödinger's work had not satisfied that constraint (commonly referred to as the correspondence principle), I am sure we would never even have heard of Schrödinger's work. As Feynman would say: if, on the anthropomorphic level, it did not yield classical mechanics relationships, it just wouldn't agree with experience.

 

And secondly, if you had ever taken the trouble to follow my deduction of that “fundamental equation” you would be well aware of the fact that delta function probability distributions do indeed constitute a possible solution to my equation. In fact I make use of that very fact in the deduction itself. On the other hand, the solutions are not exactly consistent with any explanations I have seen (except for extreme determinism) as they make predictions (for ones expectations) of an infinitely hard vacuum. Of course, we can't prove that solution is invalid because we don't have the capability of making measurements accurate enough to check the issue and it thus does not apply to any “real” measurements anyway. :lol: :lol: :lol: :lol:

 

(Anssi, don't worry about it, I am sure this comment will carry someone here off into the no-no land of baseless philosophical argument. I think that is what the ignore list is for!)

 

And finally, that brings up another gross misrepresentation implied by modest.

We're talking about a well-defined mathematical system and its ability to explain unknown data, not the complete worldview of a dead alchemist

I have no idea who this “dead alchemist” is; but modest appears to be implying that my assertion concerns explaining unknown data. It does not!

It is then clear, at this point, that the problem of finding [imath]\vec{\Psi}[/imath] is one of interpolation. We need to find a function which fits the known circumstances (known for specific t indices) and use that function to express the hypothetical probabilities for all circumstances outside those known circumstances. The problem confronting us becomes quite obvious here: any mathematician knows that there exists an infinite set of solutions even for the simplest of such problems. Since each and every such solution is a flaw free explanation of the known circumstances, a blind search for a solution from the given perspective is clearly a complete waste of time.

Does that sound like I am proposing a mathematical system to explain unknown data? I am looking at ALL POSSIBLE functions which yield exactly the apparent probability distribution of the known data. I develop my fundamental equation via consideration of a number of rather straight forward symmetry requirements and the result is an expression of our expectations for unknown data, not a statement of what the unknown data will be. The two are very different concepts. It appears to me that you have decided to fall back to that common philosophic tactic of depending upon obscurant characteristics of the English language together with subtle misrepresentation for the sole purpose of promoting argument. I personally can see no other rational for your presentation.

 

It is becoming quite clear to me that both you and Erasmus will descend to practically any subterfuge and/or misrepresentation necessary to discredit my work rather than make the slightest attempt to follow the derivation of my equation. It is a sad note that no one who has any decent education in mathematics has ever made an attempt to follow that deductions; I had hoped for a little more objectivity than what you have to offer. I think you both do this forum a disservice.

There exist self-consistent explanations which cannot be solved by the equation falsifying the claim.

There you go again, using "authority" as your main weapon. And my equation "solves" nothing; however, I have shown that many aspects of modern physics amount to approximate solutions to that equation, a significantly different thing. What I said was that "any totally flaw free internally consistent explanation of anything can be interpreted in a way which will satisfy my equation" and you certainly have not proved that is false.

 

Anssi, I don't think I will respond to these two any more. I have not yet put them on my ignore list but I am sorely tempted to do so. I will leave their complaints to you.

 

Have fun -- Dick

[modest]

There is a very big difference between a theory being “internally consistent with itself” and its being “internally consistent with all information it is supposed to explain”. Your quote of Feynman suggests that, in his opinion, Newton's theory fails the that second requirement entirely.

 

You are putting constraints on the information that is supposed to be explained? Earlier in this thread you said:

What I will end up proving is that the underlying ontological elements lying behind any explanation of anything are...

I assure you, classical mechanics is a perfect explanation for some easily given set of data. If you require that data set to be an actual experience of our world then that is an entirely different ball 'o wax.

 

Apparently you have decided to fall back to the common philosophic tactic of depending upon obscurant characteristics of the English language to promote your arguments.

 

:D

 

Anyone who knows anything about physics, knows full well that classical mechanics never considers any experiment on an accuracy level even approaching the kind of measurements made in quantum mechanics and therefore the best an exact reporter (which you clearly are not) could say is that classical mechanics presumes that all measurements are made on an anthropomorphic level (that is, with the accuracy of common human physical interactions).

 

Classical mechanics is clearly inaccurate at small scales in a real world experiment. But, classical mechanics itself gives no indication of that. It preserves symmetries as a perfectly consistent closed system,

 

As is well known, ad hoc approximations tend to break exact properties (e.g., symmetries, conservations laws, unitarity, etc) of a theory, while internally consistent approximations tend to preserve them, and so they are, in principle, preferable. (Classical mechanics is precisely an example of a consistent approximation, namely, to quantum mechanics.)

http://arxiv.org/PS_cache/quant-ph/pdf/0701/0701054v1.pdf

 

Perhaps you mean to say that any internally consistent explanation *that comports to the real world* follows your fundamental equation. If that is the case then I have greatly misunderstood.

 

On the other hand, the solutions are not exactly consistent with any explanations I have seen (except for extreme determinism) as they make predictions (for ones expectations) of an infinitely hard vacuum.

 

There is nothing wrong or self-inconsistent with a data set being deterministic.

 

Of course, we can't prove that solution is invalid because we don't have the capability of making measurements accurate enough to check the issue and it thus does not apply to any “real” measurements anyway.

 

Again, you're talking about real measurements. I think I have misunderstood in that I believed any self-consistent explanation that explains some unknown information would follow your fundamental equation. I was not led to believe the information had to be real world.

 

I think that is what the ignore list is for!

 

I agree. Given the unprovoked insults and general unpleasantness of your post it is difficult to imagine any sustained correspondence.

 

And finally, that brings up another gross misrepresentation implied by modest.

I have no idea who this “dead alchemist” is; but modest appears to be implying that my assertion concerns explaining unknown data.

 

The dead alchemist is Newton. The "unknown data" is Anssi's description from this thread:

 

we are indeed talking about how the relationships expressed by modern physics are not embedded into the content of the data-to-be-explained, but are a result of ordering a plethora of

unknown data

into useful and simple form, in self-coherent manner. (=obeying the symmetry arguments; "not letting the unknown/undefendable aspects of the data affect the probabilities")

 

Ironic

 

I have not yet put them on my ignore list but I am sorely tempted to do so. I will leave their complaints to you.

 

You actually can't do that, but don't worry, I'll leave you and Anssi to your mutual support.

 

~modest

[AnssiH]

Just a quick reply...

 

I'm not surprised at all that DD is frustrated about this, and I don't see this as such a complicated issue, I am not sure why it's so hard to explain this.

 

Classical mechanics has delta function probability distributions. Delta functions can't solve the fundamental equation.

 

I don't understand what that means, but I'm guessing you are talking about determinism, judging from the newer posts.

 

In that case, I need to point out again that approximations were involved in getting to Schrödinger (and I'm sure approximations are involved also in order to get from there to the classical scales)

 

The reason I said that, "as an axiomatic system classical mechanics obeys the fundamental equation exactly", is because that equation is an expression of symmetries to one's expectations, which are also quite evident in classical mechanics (the expectations for the "same circumstances" stay the same).

 

But it is not to be forgotten that the probabilities themselves are seen as related to the past information, which is of finite amount, and as such, determinism can never really be assumed to be true in universal sense. That doesn't mean that classical mechanics cannot be seen as an approximated solution to the equation, obviously.

 

This all just gets very muddy in discussions proceeding in english language, so I just need to repeat that I really think the best way to understand what the fundamental equation is - and what does it mean that self-coherence requirements alone are guaranteed to yield an explanation that follows the fundamental equation - is to look at the math. (that much should be obvious IMO, since the fundamental equation is those self-coherence requirements :)

 

I did not say that the fundamental equation is falsified. I said that the assertion 'every self-consistent explanation follows the fundamental equation' is falsified. There exist self-consistent explanations which cannot be solved by the equation falsifying the claim.

 

Not the way I understand the claim...

 

You are putting constraints on the information that is supposed to be explained?

 

No, he is pointing out what the analysis is about. That it has to do with consequences that arise when you place (inductively deduced) meaning onto information whose explicit meaning is unknown.

 

And that those consequences lead to an approximated solution generally known as "classical mechanics".

 

That issue is completely different from taking a handful of definitions that are defined in terms of each others, which is what DD's "internally consistent with itself" refers to.

 

It seems to me that perhaps you have not understood, that the "placing meaning onto information whose explicit meaning is unknown" does NOT refer to a process of observing bunch of objects and coming to a conclusion that they obey classical mechanics. (I think your comment "We're talking about a well-defined mathematical system and its ability to explain unknown data" implied that is what you had in mind)

 

Instead, it refers to a process of classifying recurring events/circumstances into a terminology where those events are considered to be the evidence for some "persistent objects". I.e. it is some recurring events that offer the "foot hold" for meaningful definitions, such as what "an object" means. This all refers to the process of coming able to interpret something unknown in that way.

 

It is very hard to tell what exactly happens when bunch of alien events are structured into a terminology of persistent defined entities, but the analysis refers to limiting illogical possibilities to that sort of "data ordering". That was why my old comment states that this has to do with "ordering a plethora of unknown data".

 

And I hope you understand why that is different from what classical mechanics is, and why I said that you are not referring to an explanation of unknown data per se (except in semantical sense, I get it), you are in fact referring to the defined behaviour of "already defined" entities.

 

And I hope with that you understand why and how...

 

I assure you, classical mechanics is a perfect explanation for some easily given set of data.

 

...that's off the mark; you are not talking about unknown data, you are talking about data that is already structured/interpreted in certain terminology.

 

And I hope you understand now that;

 

If you require that data set to be an actual experience of our world then that is an entirely different ball 'o wax.

 

...he is simply requiring that the meaning of the information is not known prior to its explanation. He is specifically requiring you to NOT start with pre-defind "things", such as an axiomatic setup giving meaning to certain objects.

 

Perhaps you mean to say that any internally consistent explanation *that comports to the real world* follows your fundamental equation. If that is the case then I have greatly misunderstood.

 

Nope, he does not mean that, apart from it being implied in the sense that an explanation to real world is an explanation of unknown information.

 

But the point of that argument is precisely that nothing about the real world itself needs to be ontologically of specific kind, because these features arise as features of the interpretation that can always be placed on the data, via picking up the meaning of the data from any recurring patterns.

 

I.e. the discussion can be seen as referring universally to any explanation of anything that is not pre-defined.

 

I think I have misunderstood in that I believed any self-consistent explanation that explains some unknown information would follow your fundamental equation.

 

It seems the misunderstanding is rather in what "unknown information" is supposed to mean.

 

The dead alchemist is Newton. The "unknown data" is Anssi's description from this thread:

...

Ironic

 

DD was referring to the fact that his analysis is not a specific explanation by itself, it is "universal explanation", i.e. referring to limiting possibilities. In that sense you could say it "concerns" explaining unknown data. I'm afraid we are sitting in the middle of the muddy waters of semantics :(

 

Oh, just one more side note that you might find interesting. There's this thread about mass, "Explain mass", and the OP is essentially asking what mass and inertia is in ontological sense.

 

That is a question that is essentially resolved via this analysis, without referring to any type of ontological anything (so perhaps not satisfactory to all).

 

When we refer to "mass", we are referring to a whole bunch of expected behaviour between defined things in various circumstances. If you can show that that behaviour arises as a feature of some definitions, that exist as a valid interpretation to ANY recurring patterns, it means that mass is - for all we know - just a handy feature of our world view. Basically "mass" is the name of an epistemological side-effect of bunch of references (defined things) to some recurring patterns. It is a possibility that arise whenever an explanation is created for ANY recurring patterns.

 

Ultimately the reason for its validity is in how the objects we see as evidently "massive" or "without mass" came to be part of our explanation of reality. That is why mass is defined in such a circular way.

 

The little question that people should ask themselves more often is, what do we know about the reality behind any apparent "persistence" to anything around us?

 

-Anssi

[Rade]

The little question that people should ask themselves more often is, what do we know about the reality behind any apparent "persistence" to anything around us?

Hi, this is a very nice little question--but--in the end not such a littler answer. To further discussion of this question, and how it may relate to DD philosophy, let me provide a logical answer to your little question--then we see how the discussion relates to DD thinking about the concepts "know" and "reality" and "things" and "behind" and "apparent persistence":

 

Little Question Answer: There are two ways to "know" about "reality" behind any apparent persistence to anyTHING (1) from inside the THING (2) from outside the THING.

 

Now, let us develop the DD philosophy along these two logical paths.